VJTI PROJECT REPORT ON RPC

A Final Year Project Report on

REACTIVE POWER COMPENSATION IN RENEWABLES

Submitted by
NAME ID
Prajwal Patil 161030042
Nayan Dhakre 161030059
Urjita Chaudhari 161031020
Tanu Sonwane 161031038
Renuka Dhait 171031980

A Project report submitted as a partial fulfillment of requirements for the degree of

BACHELOR OF TECHNOLOGY
IN
ELECTRICAL ENGINEERING
2016 – 2020.

Under the guidance of

Prof. H. B. Chaudhari

VJTI
Matunga, Mumbai.

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Index
Chapter 1
REACTIVE POWER
1.1 Power ….. 4
1.2 Power triangle ….. 4
1.3 Reactive Power ….. 6
1.4 Why reactive power is necessary ? ….. 7
1.5 Power Factor ….. 8

Chapter 2
REACTIVE POWER IN AC AND DC
2.1 Reactive power in AC ….. 12
2.2 Reactive power flow in AC ….. 14
2.3 Reactive power in DC ….. 14

Chapter 3
REACTIVE POWER IN RES
3.1 Introduction ….. 16
3.2 Reactive Power and Power Grid Performance ….. 17
3.3 Reactive Power Compliance Requirements for Res ….. 23
3.4 Reactive Power Capability of Wind Generators ….. 25
3.5 Reactive Power Capability of Solar-PV Generators ….. 27
3.6 Reactive Power Capability of Other Res ….. 30
3.7 Reactive Power Support Devices ….. 30
3.8 Control Strategies Developed For Reactive Power Management in Res ….. 35

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3.9 Reactive Power Coordination & Optimization Strategies ….. 39

Chapter 4
CONVERTERS
4.1 Dc Dc converters ….. 43
4.2 voltage derivations ….. 53

Chapter 5
REACTIVE POWER COMPENSATION IN RENEWABLES
5.1 A Simulation Model for Reactive Power Compensation ….. 56
5.2 Photovoltaic reactive power compensation scheme ….. 63

5.3Reactive Power Compensation in a Wind Farm ….. 74

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Chapter 1 Reactive Power

1.1 Power
 Power is defined as the rate of doing work.
 Electric power is the rate, per unit time, at which electrical energy is transferred by an
electric circuit. The SI unit of power is the watt, one joule per second.
 In other words, the electric power is defined as the rate of the transferred of energy.

1.2 Power triangle

Where:
P is the I2R or Real power measured in watts, W.
Q is the I2X or Reactive power measured in volt-amperes reactive, VAr.
S is the I2Z or Apparent power measured in volt-amperes, VA.
Φ is the phase angle in degrees. The larger the phase angle, the greater the reactive power
Cos(Φ) = P/S = W/VA = power factor, p.f.
Sin(Φ) = Q/S = VAr/VA
Tan(Φ) = Q/P = VAr/W
The power factor is calculated as the ratio of the real power to the apparent power because
of this ratio equals cos(Φ).
Real power (P), also known as true or active power, performs the “real work” within an
electrical circuit. Real power, defines the power consumed by the resistive part of a circuit.
Then real power, (P) in an AC circuit is the same as power, P in a DC circuit. So just like
DC circuits, it is always calculated as I2R, where R is the total resistive component of the
circuit.

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As resistances do not produce any phasor difference (phase shift) between voltage and
current waveforms, all the useful power is delivered directly to the resistance and converted
to heat, light and work. Then the power consumed by a resistance is real power which is
fundamentally the circuit’s average power.
To find the corresponding value of the real power the rms voltage and current values are
multiplied by the cosine of the phase angle, Φ as shown.

Real Power P = I2R = VIcos(Φ) W

But as there is no phase difference between the voltage and the current in a resistive circuit,
the phase shift between the two waveforms will be zero.
Reactive power (Q), (wattless power) is the power consumed in an AC circuit that does
not perform any useful work but has a big effect on the phase shift between the voltage and
current waveforms. Reactive power is linked to the reactance produced by inductors and
capacitors and counteracts the effects of real power. Reactive power does not exist in DC
circuits.
Unlike real power (P) which does all the work, reactive power (Q) takes power away from
a circuit due to the creation and reduction of both inductive magnetic fields and capacitive
electrostatic fields, thereby making it harder for the true power to supply power directly to
a circuit or load.
The power stored by an inductor in its magnetic field tries to control the current, while the
power stored by a capacitors electrostatic field tries to control the voltage. The result is that
capacitors “generate” reactive power and inductors “consume” reactive power. This means
that they both consume and return power to the source so none of the real power is
consumed.
To find reactive power, the rms voltage and current values are multiplied by the sine of the
phase angle, Φ as shown.
Reactive Power Q = I2X = VIsin(Φ) VAr

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Apparent Power
We have seen above that real power is dissipated by resistance and that reactive power is
supplied to a reactance. As a result of this the current and voltage waveforms are not in-
phase due to the difference between circuit’s resistive and reactive components.
There is a mathematical relationship between the real power (P), and the reactive power
(Q), called the complex power. The product of the rms voltage applied to an AC circuit and
the rms current flowing into that circuit is called the “volt-ampere product” (VA) given the
symbol S and whose magnitude is known generally as apparent power.
This complex Power is not equal to the algebraic sum of the real and reactive powers added
together, but is instead the vector sum of P and Q given in volt-amps (VA). The rms value
of the volt-ampere product is known more commonly as the apparent power as,
“apparently” this is the total power consumed by a circuit even though the real power that
does the work is a lot less.
As apparent power is made up of two parts, the resistive power which is the in-phase power
or real power in watts and the reactive power which is the out-of-phase power in volt-
amperes, we can show the vector addition of these two power components in the form of a
power triangle. A power triangle has four parts: P, Q, S and θ.
The three elements which make up power in an AC circuit can be represented graphically
by the three sides of a right-angled triangle, in much the same way as the previous
impedance triangle. The horizontal (adjacent) side represents the circuits real power (P),
the vertical (opposite) side represents the circuit’s reactive power (Q) and the hypotenuse
represents the resulting apparent power (S).

1.3 Reactive Power

The reactive power moves between the source and load of the circuit. This power is not
doing any useful works on the load. The reactive power is stored in the circuit, and it is
discharged by the induction motor, transformer or by solenoids. Q represents the reactive
power, and it is measured in VAR.
Q = I2X = VIsin(Φ) VAr

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The Beer Analogy

The mug capacity represents apparent power (kVA). The beer itself represents active
power (kW). The foam represents reactive power (kVAR). Power factor is the ratio
between the active power (kW) and the apparent power (kVA). Using the beer analogy, we
obtain the power factor by dividing the beer by the mug capacity, and it’s clear, you’re
getting less beer than you’re paying for with all that foam taking up space. Even if foam is
occupied the space, but we enjoy the foam more than the beer. So the foam is not feeding
our stomach but it fulfills our enjoyment.

1.4 Why reactive power is necessary?

Voltage control in an electrical power system is important for proper operation for
electrical power equipment to prevent damage such as overheating of generators and
motors, to reduce transmission losses and to maintain the ability of the system to withstand
and prevent voltage collapse. In general terms, decreasing reactive power, causing voltage
to fall; while increasing it, causing voltage to rise. A voltage collapse occurs when the
system try to serve much more load than the voltage can support.
When reactive power supply lower voltage, as voltage drops current must increase to
maintain power supplied, causing system to consume more reactive power and the voltage
drops further . If the current increase too much, transmission lines go off line, overloading
other lines and potentially causing cascading failures.

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If the voltage drops too low, some generators will disconnect automatically to protect
themselves. Voltage collapse occurs when an increase in load or less generation or
transmission facilities causes dropping voltage, which causes a further reduction in reactive
power from capacitor and line charging, and still there further voltage reductions. If voltage
reduction continues, these will cause additional elements to trip, leading further reduction
in voltage and loss of the load. The result in these entire progressive and uncontrollable
declines in voltage is that the system unable to provide the reactive power required
supplying the reactive power demands.
Motor loads and other loads require reactive power to convert the flow of electrons into
useful work. When there is not enough reactive power, the voltage sags down and it is not
possible to push the power demanded by loads through the lines.
Reactive power (VARS) is required to maintain the voltage to deliver active power (watts)
through transmission lines.

1.5 Power factor

In electrical engineering, the power factor of an AC electrical power system is defined as
the ratio of the real power absorbed by the load to the apparent power flowing in the
circuit, and is a dimensionless number in the closed interval of −1 to 1 (A power factor of
less than one indicates the voltage and current are not in phase, reducing the average
product of the two. Due to energy stored in the load and returned to the source, or due to a
non-linear load (that distorts the wave shape of the current drawn from the source); the
apparent power may be greater than the real power. A negative power factor occurs when
the load generates power, which then flows back towards the source.
In an electric power system, ‘a load with a low power factor draws more current than
a load with a high power factor for the same amount of useful power transferred’.
The higher currents increase the energy lost in the distribution system, and require
larger wires and other equipment. Because of the costs of larger equipment and
wasted energy, electrical utilities will usually charge a higher cost to industrial or
commercial customers where there is a low power factor.
Power-factor correction increases the power factor of a load, improving efficiency for the
distribution system to which it is attached.
Linear loads with low power factor (such as induction motors) can be corrected with a
passive network of capacitors or inductors.

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Non-linear loads (such as rectifiers) distort the current drawn from the system. In such
cases, active or passive power factor correction may be used to counteract the distortion
and raise the power factor.
Real power is the instantaneous product of voltage and current and represents the capacity
of the electricity for performing work. Apparent power is the product of RMS current and
voltage. The devices for correction of the power factor may be at a central substation,
spread out over a distribution system, or built into power-consuming equipment.
1.5.1 Unity power factor
Unity power factor exists in an AC circuit when the angle between the voltage and the
current is zero. That usually occurs when there is no capacitive or inductive reactance in
the load or when the reactance has been neutralized.

1.5.2 Lagging and Leading power factors

There is also a difference between a lagging and leading power factor. The terms refer to
whether the phase of the current is lagging or leading the phase of the voltage.
A lagging power factor signifies that the load is inductive, as the load will
“consume” reactive power, and therefore the reactive component Q is positive as
reactive power travels through the circuit and is “consumed” by the inductive load.
A leading power factor signifies that the load is capacitive, as the load “supplies”
reactive power, and therefore the reactive component Q is negative as reactive power
is being supplied to the circuit.

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If θ is the phase angle between the current and voltage, then the power factor is equal to
the cosine of the angle:
│P│═│S│cos θ
Since the units are consistent, the power factor is by definition a dimensionless number
between −1 and 1.
When power factor is equal to 0, the energy flow is entirely reactive and stored
energy in the load returns to the source on each cycle. When the power factor is 1, all
the energy supplied by the source is consumed by the load. Power factors are usually
stated as "leading" or "lagging" to show the sign of the phase angle. Capacitive loads
are leading (current leads voltage), and inductive loads are lagging (current lags
voltage).
If a purely resistive load is connected to a power supply, current and voltage will change
polarity in step, the power factor will be 1, and the electrical energy flows in a single
direction across the network in each cycle.
Inductive loads such as induction motors (any type of wound coil) consume reactive power
with current waveform lagging the voltage.
Capacitive loads such as capacitor banks or buried cable generate reactive power with
current phase leading the voltage.
Both types of loads will absorb energy during part of the AC cycle, which is stored in the
device's magnetic or electric field, only to return this energy back to the source during the
rest of the cycle.

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1.5.3 How inductive and capacitive values affect reactive power ?

Capacitors and inductors (which are sometimes called reactors) are passive devices that
generate or absorb reactive power. They accomplish this without significant real-power
losses or operating expense. The output of capacitors and inductors is proportional to the
square of the voltage.
Inductors are discrete devices designed to absorb a specific amount of reactive
power at a specific voltage. They can be switched on or off but offer no variable
control. Capacitor banks are composed of individual capacitor cans. The cans are
connected in series and parallel to obtain the desired capacitor-bank voltage and
capacity rating. Like inductors, capacitor banks are discrete devices but they are
often configured with several steps to provide a limited amount of variable control
which makes it a disadvantage compared to synchronous motor.
The inductor absorbs more when voltages are highest and the device is needed most. The
relationship is unfortunate for the more common case where capacitors are employed to
support voltages. In the extreme case, voltages fall, and capacitors contribute less, resulting
in a further degradation in voltage and even less support from the capacitors; ultimately,
voltage collapses and outages occur.
Inductive-reactive power is conventionally positive (absorbed by an inductive load), while
capacitive-reactive power is negative (supplied by a capacitive load).
The current flowing through capacitors is leading the voltage by 90°. The corresponding
current vector is then in opposition to the current vector of inductive loads. This is why
capacitors are commonly used in the electrical systems, in order to compensate the reactive
power absorbed by inductive loads such as motors.
As reactive-inductive loads and line reactance are responsible for voltage drops, reactive-
capacitive currents have the reverse effect on voltage levels and produce voltage-rises in
power systems.

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Chapter 2 Reactive Power in AC and DC

2.1 Reactive power in AC

Reactive power can best be described as the quantity of “unused” power that is developed
by reactive components in an AC circuit or system. Reactive power is used by most types
of electrical equipment that uses a magnetic field, such as motors, generators and
transformers. It is also required to supply the reactive losses on overhead power
transmission lines.
2.1.1 Reactive power in Transformer
The reactive power drawn by power transformer could be as high as 5% of the transformer
rating when supplying full load current. ‘Power factor at the primary of the transformer is
usually lower than what is measured at the secondary’, due to this reactive power
requirement of transformer. If the metering is done at medium voltage then the additional
reactive power consumed by the transformer will also be measured.
In cases like these it is important to know how much reactive power is drawn by the
transformer so that it can be subtracted from the load reactive power demand. This is
usually the case when the electric utility meter is at the primary and the transformer
is owned by the electric utility as well. It makes no sense to bill for the reactive
power consumed by the utility owned transformer since they could have very well
put the metering on the LV side and customer will not have to pay for it if that’s the
case. When the customer owns the transformer then the reactive power drawn by the
power transformer will be metered by the utility.
The power produced by turbines is active power (which is the real mechanical power). The
real power produced by these mechanical machines cannot be transmitted for long distance,
so here comes the conversion of energy from one form to another( The mechanical Energy
into electrical energy).
The conversion of energy principle works in many applications, this reduces loss and cost
of the equipment required. Since this mechanical energy has to be carried for the long
distance, the reactive power comes into the play, they are the carriers of the real power
produced by the mechanical machines. The usable power is not destroyed but converted
into other form whereas these reactive powers are not usable but acts as the vehicle to
transmit the usable power.
The generators produce high current and low voltage real power, this power is then
converted into high voltage and low current(This involves change of energy through

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reactive element in the transformers). This high voltage low current from the transformer
has mirrored or carrying the usable power produced by the generator via turbine. Thus
power rating of transformer remains constant(Law of conservation of Energy). There are
no extra power is being produced but changed into different form. This is the reason
turbines are rated with real power kW and Transformers are rated with reactive power
kVA.
2.1.2 Reactive power in Induction motor
Motor loads and other loads require reactive power to convert the flow of electrons into
useful work. When there is not enough reactive power, the voltage sags down and it is not
possible to push the power demanded by loads through the lines.
Because the rotor field always lags behind the stator field, the induction machine always
consumes reactive power, regardless of whether it is operating as a generator or a motor. A
source of excitation current for magnetizing flux (reactive power) for the stator is still
required, to induce rotor current.
Reactive power is unused power that is pushed forth and back. It causes an unwanted
current on the transmission line. Consequently, reactive power causes losses on AC
transmission lines. By the way, there is reactive power when the angle between voltage and
current is pi/2.
2.1.3 Reactive power in Synchronous motor
Reactive power from a capacitor bank decreases when grid voltage decreases, while a
synchronous condenser can increase reactive current as voltage decreases. However,
synchronous machines have higher energy losses than static capacitor banks. Synchronous
motor is a constant speed motor. It is a doubly excited machine and it is not self-started.
Load connected to the shaft of the motor is mechanical type and always oppose the
rotational inertia of the shaft. This kind of load lags the load current behind the terminal
voltage and acts as lagging electrical load. Huge mechanical load connected to the shaft
draws huge current in it via stator from the supply side causes decrease in back EMF
induced in the rotor terminal .The field fluxes are kept constant and this huge current in the
rotor causes reduce in field fluxes but as synchronous motor is constant speed motor and
the rotor is dragged by the rotational magnetic poles in the air gap created by three phase
supply.
So during huge load placed on the shaft it intends to reduce the speed of the shaft and it
makes a contrast against the RMF and rotor rotation thus slightly reduce the speed of the
shaft and a slight oscillation takes place over the shaft to overcome this situation the rotor
tries to catch up the synchronous speed thus suddenly reaches to the super synchronous

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speed for a while. This situation is called hunting and back to the synchronous speed again.
This huge load makes the power factor low and decreases the stability as well as reduces
the efficiency of the motor, this situation is called under excited state . To overcome this
situation field supply is increased and compensate the density of fluxes in the air gap and
improves the power factor of the motor , the angle between the load current and output
voltage is made closed to zero or trying to make them in phase which improves the stability
of the system as well as efficiency of that motor.
2.2 Reactive power flow in AC
In any circuit, the current and voltage drop takes place according to Kirchhoff’s law (KVL
& KCL), when looking to power flow it also behave in the same manner. Reactive power
flows from higher bus voltage magnitude to lower bus voltage magnitude. Delay in the
voltage frequency between the starting and ending points of a wire produces power flow.
2.3 Reactive power in DC
In case of DC system, we do not convert any kind of power so need of reactive power. In
case of DC, active power itself provides both electric and magnetic field.
2.3.1 Why reactive power is not there in DC ?
In a direct current (DC) circuit, the power is of constant intensity and can only flow in one
direction. Current and voltage in alternating current (AC) circuits, on the other hand,
fluctuate rapidly and power appears to flow in all directions. The phase angle is important
both at a single location and between two points. The speed of fluctuations is referred to as
the frequency and the delay between two “frequencies” is their phase angle.
An important consideration in AC circuits is the delay between voltage and current
fluctuations at any single point. Delay in the voltage frequency between the starting and
ending points of a wire produces power flow. When current and voltage at a single point
are perfectly in phase with each other, thus having the exact same timing, all of the power
resulting from the flow is real power. As the delay between current and voltage increases,
so does the amount of reactive power. Reactive power is present whenever current either
“lags” or “leads” voltage.

2.3.2 How can we generate reactive power in DC circuit ?

PV is a DC power source. In this case, there is no reactive power associated with PV
itself. When a PV is connected to a load via a dc/dc converter, the voltage and current of
the PV can be varied by the converter, such that active power can be control. The ideal case

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will be to extract the maximum active power from the case, and such control will be known
as MPPT. A dc/dc converter cannot inject or absorb any reactive power.
Reactive power is a concept unique in AC power system. When an inverter is used,
the reactive power can be injected into the grid by varying the magnitude and angle of the
inverter voltage. If voltage-oriented control (VOC) method is used to control the inverter,
reactive power can be controlled by controlling the q-axis current.
In order to perform MPPT and Q injection at the same time, an inverter must be
used. Two common structures will be possible: single stage power conversion or two stage
power conversion:
1. In single stage power conversion, the PV is connected directly to the inverter
without any dc/dc converter (hence termed single stage). In the case if VOC is
used for the inverter control, q-axis current will be controlled to vary the
active power, hence to achieve MPPT. At the same time, q-axis current will be
used to control the reactive power injection. Take note that in this structure,
the dc-link of the inverter is connected directly to the PV terminals, and will
fluctuate with the PV voltage.
2. In a two stage system, PV panel is connected first to a dc/dc converter, then to
an inverter. The dc/dc converter will perform the MPPT task to extract
maximum active power from the PV. The inverter on the other hand still
controls the active and reactive power. However, in this case, the inverter is
not doing the MPPT, but merely injecting active power to the grid (by
controlling d-axis current) to maintain a fixed dc-link voltage (dc-link voltage
control). At the same time, q-axis current is controlled to vary the reactive
power. In this structure, the dc-link voltage of the inverter is maintained at a
constant value all the time.

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Chapter 3 Reactive Power in Renewable Energy Sources

3.1 Introduction
Due to the global drive towards renewable and sustainable energy systems, power
electronic converter (PEC) interfaced renewable energy generators (REGs), such as wind
generators and solar-PV systems have widely been adopted in power networks around the
world. The Kyoto Protocol was one of the major catalysts for the global drive towards
renewable energy generation. In addition, due to the technical advances in the electronic
materials, manufacturing cost of REGs have significantly reduced during the past decade
while encouraging wide-scale adoption of PEC interfaced REGs in power networks.
In 2016, REGs were accounted for the two thirds of the new generation added to power
networks, and approximately 165 GW of renewable power generation capacity was added
to power networks around the world. Among renewable energy sources, the solar-PV
capacity was growing by 50%, while exceeding the total installed capacity beyond 74 GW,
which is higher than the net annual growth in coal power generation. Figure 3.1 illustrates
the electricity capacity additions by fuel type for 2016.

Fig 3.1 Electricity capacity additions by fuel type for 2016

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At the early stage of renewable energy integration, REGs could be either connected or
disconnected from the power grid without significant impact on grid stability, due to their
low penetration level. However, with the increased renewable power generation, it is no
longer possible to connect or disconnect REGs at operators’ discretion, since it would
adversely affect the power system stability and reliability. Therefore, requirements for grid
integration of REGs are now being strictly stipulated in grid codes.
Reactive power compensation and voltage stability have become major concerns for
utility grid operators with significant renewable power penetration. Consequently, reactive
power requirements are now becoming mandatory for REGs (e.g. wind farms). Major
blackouts were also caused due to voltage instability as a consequence of insufficient
reactive power reserve in power networks.
With the large-scale integration of renewable energy sources to the power grid,
reactive power reserve would decrease as they displace the conventional synchronous
generators, and hence power grids are becoming more vulnerable for instability.
Moreover, because of the intermittent and variable nature of some renewable energy
sources (e.g. variable solar irradiation and wind speed), power system likely to become
unstable during system contingencies. In transient fault conditions, without proper reactive
power support mechanisms, the low inertial wind turbines, and the inertia- less solar-PV
systems are unable to provide sufficient voltage support to the grid. Furthermore, due to
long distance between the load centres and large-scale REGs (e.g. MW- scale wind farms)
transmission corridors likely to become unstable during system contingencies due to lack
of reactive power support to stabilize the voltage.
Therefore, it is imperative to review reactive power management strategies reported
in the literature for power grids with high renewable power penetration.

3.2 Reactive power and power grid performance

Reactive power plays an important role in power grid, particularly power grid voltage
management and stability. This explains the active and reactive power relationships with
network voltage, and also delineates influence of reactive power on network stability.

3.2.1 Reactive power v/s grid voltage

To find the relationship of active and reactive power with the grid voltage, let’s assume a
Thevenin’s equivalent circuit of a node-k power system (see Figure 3.2). The apparent

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𝑉𝐾 ∠𝛿𝐾 −𝐸𝑇𝐻 ∠0
power can be calculated from the relationship, S=𝑉𝐾 𝐼𝐾 ∗, where 𝐼𝐾 = and real
𝑍𝑇𝐻 ∠0
and reactive power can be derived as:
𝑉𝐾 𝑉𝐾 𝑉𝐾 𝑉𝑇𝐻
S=𝑉𝐾 𝐼𝐾 ∗ = ( ) ∠𝜃 − ( ) ∠(𝜃 + 𝛿𝐾 )(1)
𝑍𝑇𝐻 𝑍𝑇𝐻

Real Power:
𝑉𝐾 𝑉𝐾 𝑉𝐾 𝑉𝑇𝐻
𝑃𝐾 = ( ) cos(𝜃 ) − ( ) ∠𝑐𝑜𝑠(𝜃 + 𝛿𝐾 ) (2𝑎)
𝑍𝑇𝐻 𝑍𝑇𝐻
Reactive Power:
𝑉𝐾 𝑉𝐾 𝑉𝐾 𝑉𝑇𝐻
𝑄𝐾 = ( ) ∠ sin(𝜃 ) − ( ) ∠𝑠𝑖𝑛 (𝜃 + 𝛿𝐾 ) (2𝑏)
𝑍𝑇𝐻 𝑍𝑇𝐻

Now, for small excursions from the nominal voltage, ∂Vk, change in real and reactive
power can be found as:
𝜕𝑃𝐾 2𝑉𝐾 𝐸𝑇𝐻
=( ) cos(𝜃 ) − ( ) cos(𝜃 + 𝛿𝐾 ) (3𝑎)
𝜕𝑉𝐾 𝑍𝑇𝐻 𝑍𝑇𝐻
𝜕𝑄𝐾 2𝑉𝐾 𝐸𝑇𝐻
=( ) sin(𝜃 ) − ( ) sin(𝜃 + 𝛿𝐾 ) (3𝑏)
𝜕𝑉𝐾 𝑍𝑇𝐻 𝑍𝑇𝐻

For small change in phase angle 𝛿𝐾 , active and reactive power relationships would be:
𝜕𝑃𝐾 𝑉𝐾 𝐸𝑇𝐻
=( ) sin(𝜃 + 𝛿𝐾 ) (4𝑎)
𝜕𝑉𝐾 𝑍𝑇𝐻
𝜕𝑄𝐾 𝑉𝐾 𝐸𝑇𝐻
=( ) cos(𝜃 + 𝛿𝐾 ) (4𝑏)
𝜕𝑉𝐾 𝑍𝑇𝐻

In transmission systems, the reactance 𝑋𝑇 is much greater than 𝑅 𝑇 projecting 𝜃 close to

90°.That is cos(𝜃 ) ≈ 0, sin(𝜃) ≈ 1, cos(𝜃 + 𝛿𝐾 ) − sin(𝛿𝑘 ) 𝑎𝑛𝑑 sin(𝜃 +
𝛿𝐾 ) ≈ 𝑐𝑜𝑠(𝛿𝑘 ) , and for small changes of nominal voltage,
𝑉𝐾 ≈ 𝐸𝑇𝐻 , cos(𝛿𝐾 ) ≈ 1, and 𝑠𝑖𝑛(𝛿𝑘 ) ≈ 𝛿𝑘 ≈ 0.

Based on these approximations:

𝜕𝑃𝐾 𝜕𝑃𝑘 𝑉𝑘 𝐸𝑇ℎ
≈ 0; and ≈( ) (5𝑎)
𝜕𝑉𝐾 𝜕𝛿𝑘 𝑍𝑇ℎ

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𝜕𝑄𝐾 2𝑉𝐾 𝐸𝑇𝐻 𝐸𝑇𝐻 𝜕𝑄𝑘

=( )−( )≈( ); and ≈ 0 (5b)
𝜕𝑉𝐾 𝑍𝑇𝐻 𝑍𝑇𝐻 𝑍𝑇𝐻 𝜕𝛿𝑘

Equation (5a) indicates a strong relationship between real power, Pk and phase angle δk, and
equation (5b) shows a strong coupling between reactive power, Qk and voltage, Vk. The X/R ratio
of the transmission system is always high due to high reactance (X), and hence, reactive power
injection is necessary to boost the voltage at the end of the line. However, in distribution
systems, the X/R ratio is usually low, approximately closer to 1 for overhead lines, and therefore,
reactive power injection does not necessarily boost the voltage, and hence active power injection
becomes more feasible for voltage management.

Fig 3.2 Thevenin equivalent circuit of a node-k power system

3.2.2 MV-LV Distribution Feeder Voltage Management

Due to large-scale integration of REGs in power distribution networks, steady -state
voltage management has become a major planning and operation issue in modern power
net- works. REGs (e.g. wind generators and solar-PV systems) rated less than 50 MW are
connected to the MV network, while the REGs rated less than 10 kW (mostly solar-PV
systems) are connected to the LV distribution feeders. As the distribution feeder voltage
might increase beyond the maxi- mum stipulated limit in certain time periods of the day,
conventional voltage regulation approaches are infeasible for regulating distribution feeder
voltage with high renewable penetration. In conventional distribution feeders (i.e. without
REGs), the voltage decreases from the LV side of the distribution transformer towards the
end of the feeder. Consider the distribution feeder shown in Figure 3.3, where a load (P +
jQ) is attached at the receiving end, and the sending end voltage can be approximated as:

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𝑃−𝑗𝑄
Vs = Vr + I (R+j X); whereI = 𝑉𝑟∗
𝑅𝑃 + 𝑋𝑄 𝑋𝑃 − 𝑃𝑄
= [ 𝑉𝑟 + ]+𝑗[ ] (6)
𝑉𝑟 𝑉𝑟
For distribution networks, the phase-angle deviation is very small due to low reactance, and
therefore the imaginary part of the equation (6) can be neglected and sending-end voltage
can be approximated as:
𝑅𝑃 + 𝑋𝑄
𝑉𝑠 = 𝑉𝑟 +
𝑉𝑟
𝑅𝑃 + 𝑋𝑄
𝑉𝑠 − 𝑉𝑟 =
𝑉𝑟
𝑅𝑃 + 𝑋𝑄
∆𝑉 =
𝑉𝑟
Therefore, it is evident from equation above that voltage drop, ∆V, of the distribution
feeder depends on the power factor of the connected load and the impedance of the
distribution feeder. Contrarily, by injecting reactive power in the opposite direction to the
active power, voltage drop could be mitigated. The active power losses in the line can be
determined as:

𝑃 2 + 𝑄2
Active Power Losses = I R = [
2
]𝑅 (8)
𝑉𝑟 2

According to equation (8) both active and reactive power of the load contribute to active
power losses. By improving the lagging power factor of the load, the voltage drop will
decrease, contrarily by improving the leading power factor of the load, the voltage drop
will increase. However, irrespective of the load operating as either lagging or leading
power factor, system losses decrease with the improved load power factor, and hence,
reactive power-flow in the distribution feeder must be minimized to reduce the line losses.
Reactive power management and voltage regulation for MV-LV distribution feeders with
REGs have been extensively researched. However, with increasing REG integration into
distribution feeders, the MV-LV feeder voltage management is still a vibrant field of
research.

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3.2.3 Reactive power influence on voltage and transient stability

Power grid stability is defined as,” the ability of the power grid to regain equilibrium after
occurrence of disturbances or faults in the power system”.
Power grid stability issues can be classified into three types:
1) Rotor-angle stability,
2) Voltage stability, and
3) Frequency stability.
Rotor-angle stability can be further subdivided into transient stability, and small-signal
stability. Transient stability is defined as “the ability of the power system to remain in
synchronism after severe transient disturbances or faults, and electromechanical
oscillations should be damped within a reasonable time- frame”. Therefore, transient
stability mainly deals with the rotor-angle stability of synchronous generators in the
network.
Voltage stability is defined as “the ability of power grid to restore the nominal voltage
levels in all network nodes after any disturbance or transient condition”.
During fault conditions or disturbances, both active and reactive power interacts very
closely, and their relationship becomes very complex. When REGs are integrated to the
power grid, significant portion of the synchronous generation is displaced without
adequately compensating for the reactive power provided by the synchronous generators.
Consequently, voltage control capability of the power grid reduces significantly. If
adequate reactive power is not provided during the post-fault period, then the grid enters
into an unstable state, and subsequently grid voltage will collapse leading to a blackout.
The sequence for voltage instability is reactive power only. If the injected reactive power
couldn’t able to increase the voltage magnitude, then the system is considered to be voltage
unstable. Aforementioned, voltage instability leading towards voltage collapse, which is a
sequence of unstable voltage conditions leading to low-voltage profile in a large portion of
the power network. Ultimately, voltage instability would lead to transient instability, since
it would create electro- mechanical power imbalance at the synchronous generator.
Therefore, adequate dynamic reactive power reserve must be maintained in order to
improve both voltage and transient stability of the power network.

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3.2.4 Grid stability improvement by reactive power

Several measures can be taken to improve static and dynamic reactive power reserves in
the power grid. Usually it is achieved by deploying reactive power support devices, such
as on-load tap changing (OLTC) transformers, excitation control, switchable and non-
switchable shunt capacitors or reactors, synchronous condensers, and flexible AC trans-
mission system (FACTS) devices (e.g. static synchronous compensators (STATCOMs)).
Some wind generators based on asynchronous machines cannot contribute to the voltage
regulation as they absorb reactive power during steady-state operation. However, variable-
speed wind generators (VSWGs) with PEC interface, such as the doubly- fed induction
generator (DFIG) can provide reactive power. Unfortunately, rotor converter rating of the
DFIG is limited to only steady-state requirements to keep this technology within a
reasonable cost margin. Therefore, the reactive power capability of the DFIG is not
adequate as the primary safeguard during transient conditions. Similar limitations could be
experienced with the full-converter wind generators (FCWGs). Hence, FACTS devices are
used in wind farms to improve voltage stability using their dynamic reactive power
capability.
Excitation controllers also play an important role in reactive power compensation in power
systems. Yet this type of controllers lack accuracy as they are designed considering static
load model. Although VSWG technologies, such as DFIGs are more widely used due to
their superior control capabilities, they have very limited dynamic reactive power reserve
in comparison to the synchronous generators. Nevertheless, PEC interfaced STATCOM
devices could be used to improve the dynamic reactive power capability of wind farms to
comply with grid-codes.

3.3 Reactive power requirements for REGs

With the increasing renewable power penetration levels in power networks, the grid
operators (e.g. transmission system operators (TSOs) and distribution system operators
(DSOs)) have started to stipulate strict grid-codes for REGs on fault ride-through (FRT),
reactive power management and voltage control. Above mentioned, reactive power
strongly influence on network steady-state voltage, and voltage recovery during system
contingencies, hence grid-codes specify both steady- state and dynamic reactive power
capabilities for REGs. The grid-code specifications for FRT and voltage control are also
closely related with the static and dynamic reactive power requirements for REGs.
Therefore, reactive power grid-code requirements set for the wind generators and PEC
interfaced generators (e.g. solar PV) are discussed in following subsections.

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3.3.1 Reactive power requirements for wind generators

Almost all the grid codes specify steady-state reactive power requirements for wind
generators. However, these requirements vary w.r.t. point of common coupling (PCC),
voltage level at the connection point, specification of the actual capability of the system,
and whether the reactive power requirement is expressed in terms of the power factor, or
fraction of the rated power output etc.
In Danish grid code, for generators rated greater than 25 MW must have a reactive power
capability of +/-0.3 p.u. For active power range between 0.2 to 0.8 p.u. and that has been
progressively decreased from +/-0.3 p.u. to +/-0.2 p.u. when the active power level
increases from 0.8 p.u. to 1 p.u.
This indicates a reduced reactive power requirement at high active power levels, which is a
reasonable reactive power specification in terms of the cost and technical limits of wind
generators. A similar reactive power specification is stipulated in other grid codes for wind
generators. These reactive power requirements are usually expressed as P-Q diagrams (i.e.
available active power versus available reactive power).
National Electricity Rules (NER) require wind generators to have reactive power control
capability of +/-0.93 power factor at full output at the point of connection (POC),
throughout the full operating range of active power, and +/-10% of nominal voltage.
However, the minimum access standard specifies no or zero reactive power capability for
either reactive power supply or absorption
3.3.2 Reactive power requirements for PEC Interfaced Energy Systems
The grid operators are yet to implement strict grid code specifications for different types of
PEC interfaced energy systems (wind generation is excluded here), such as small- scale
solar-PV systems, fuel cells, battery energy storage systems etc. According to AS/NZS
4777.2:2015 standard for four possible voltage ranges, namely V1, V2, V3, and V4 having
default voltage values of 207, 220, 244, and 255 V respectively, should have 30% leading
power factor capability for V1, 30% lagging power factor capability for V4, and no
regulation (i.e. 0%) is required for V2 and V3.
In German grid-code, the generating plant should able to provide reactive power at the
POC with 0.95 lagging power factor to 0.95 leading power factor. The reactive power
generation can either be fixed or adjustable over different values of active power. For low
voltage (LV) generation unit, such as solar-PV, the operation range can be divided into
three levels:
SPV < 3.68 kVA: the system should operate in between cos φ = 0.95 (under-excited/
lagging power factor) to cos φ = 0.95 (over-excited/leading power factor)

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3.68 kVA < SPV < 13.8 kVA: the system should accept any set point in between cos φ =
0.95 (under-excited/ lagging power factor) to cos φ = 0.95 (over-excited/leading power
factor)
SPV > 13.8 kVA: the system should accept any set point in between cos φ = 0.90 (under-
excited/ lagging power factor) to cos φ = 0.90 (overexcited/ leading power factor).
Contrary to the German grid-code, the French grid-code distinctly mentions that the low
voltage solar-PV systems should not absorb any reactive power at its entire operating
range.
3.3.3 Dynamic reactive power requirement for FRT
Aforementioned, small and medium-scale REGs (rated less than 50 MW) are connected to
distribution networks (i.e. LV or MV), which is not typically designed to transfer power
into the transmission grid. Therefore, voltage will increase during periods of high active
power production from REGs. This eventually increases the need for dynamic reactive
power support and fault ride-through (FRT) capability, due to weak dynamic voltage
regulation capability of distribution networks. In some grid codes, the FRT requirements
are specified as low voltage ride-through (LVRT) and high voltage ride-through (HVRT)
for smooth operation of the power grid during symmetrical or asymmetrical fault
conditions.
When a grid fault occurs, voltage decreases significantly around the fault node, and
subsequently voltage depression propagates across a wide-area of the network until the
fault is cleared. During the fault, asynchronous wind generators demand more reactive
power while worsening the voltage levels across the net- work. If the wind penetration
level is high, and it is not supported by adequate dynamic reactive power reserve, then
wind generators will start to disconnect from the grid due to decrease of their terminal
voltage below the LVRT voltage specification, while leading to a catastrophic voltage
stability issue in the power network.
A similar kind of issue could happen for solar-PV systems under fault conditions.
Therefore, dynamic reactive power specifications are given in grid codes to improve LVRT
capability of REGs. Voltage swell could occur when a large amount of load disconnects
from the grid within a very short time-span or during significantly intermittent active
power production from REGs (e.g. solar-PV systems or wind generators). Inefficient
switching of capacitor banks or reactive power sources can also lead to voltage swell. To
solve this issue, REGs are usually switched off during voltage swells. However, with
increased penetration of renewable power generation in power networks, by switching off
large amount of wind generators or solar-PV systems would lead to frequency stability
issues. Therefore, nowadays in most grid codes, the HV Requirements are specified for

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REGs. To meet these HVRT requirements, REGs should essentially have reactive power
absorb capability.
3.4 Reactive power capability of wind generators
Wind generators are typically categorized into four (4) types:
1)Type-1: Fixed-speed wind generator (FSWG) (based on SCIG),
2) Type-2: Limited variable-speed wind generator (based on wound rotor induction
generator (WRIG)),
3) Type-3: Doubly-fed induction generator (based on WRIG), and
4)Type-4: Full-converter wind generator (FCWG).
The FCWGs can be further subdivided depending on the generator type (e.g. permanent
magnet synchronous generator (PMSG) and electrically excited synchronous generator).
Fig 3.3 shows typical wind generator configurations. It must be noted that both the SCIG
and the WRIG machines are also known as the asynchronous generator (AG).
The first and most simple configuration is the FSWG, which directly connects the SCIG to
the grid, and a gear box is used in the drive-train to maintain the constant rotational speed.
This type of wind generators produces real power when the shaft rotational speed is greater
than the electrical frequency of the grid (i.e. when producing a negative slip), however
these generators consume reactive power. For a given wind speed, the operating speed of
the turbine varies linearly with the torque. The mechanical inertia of the drive-train limits
the rate-of-change-of electrical power output under varying wind conditions. This
configuration is depicted in Figure 3.3. There is no active or reactive power control
scheme, except the pitch angle control (PAC) scheme maintains the maximum power point
(MPP) and curtails the wind power extraction at high wind speeds. To avoid high transient
starting current, a soft-start device (e.g. back-to- back thyristor) is used in FSWGs.
The Type-3 wind generators are commonly known as the doubly-fed induction generators
(DFIGs), and the configuration of the DFIG is illustrated in Figure 3(iii).

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Fig 3.3 Typical wind generator configurations: I) Fixed-speed wind generator (FSWG); ii)
Limited variable-speed wind generator; iii) Doubly-fed induction generator (DFIG); iv)
PEC interfaced fully-fed AG based FCWG; v) Electrically excited synchronous generator
based FCWG; and vi) Permanent Magnet synchronous generator (PMSG) based FCWG.

In this type of wind generators, the stator circuit is connected to the grid directly, and the
rotor is connected via a back-to-back PEC interface, by making it a doubly-fed machine.
Because of the superior active and reactive power controllability of the DFIG, this wind
generator type is heavily being used in the wind power industry, and hence substantial
research has been conducted on DFIGs during last 15 years to improve their performance.
The Type-4 wind generators (also known as the FCWG) use a fully-rated PEC interface to
connect with the grid, and three different configurations are show in Figure 3.3(iv)-(vi).
The Figure 3.3(iv) shows a FCWG based on the AG, and the WRIG is mostly used as the
AG. The FCWG configurations based on synchronous generators can either be excited
electrically via slip rings as shown in Figure 3.3(v), or they can be self-excited permanent
magnet synchronous generators (PMSGs) as shown in Figure 3.3(vi).

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3.5 Reactive power capability of solar-pv generators

Having no rotating magnetic field or coil arrangements, the solar-PV systems supply power
through an inverter. Solar PV panel itself does not have any reactive power support as it
produces electricity using photovoltaic effect. However, the inverter used for DC/AC
conversion can provide significant amount of reactive power support during normal
operating conditions or even in fault conditions. The solar-PV inverter also provides other
ancillary services, such as, MPPT control, LVRT etc. Although, reactive power support is
not yet mandatory for solar-PV systems in most grid codes, as the penetration level
increases more controllability over active and reactive power will become a necessity. A
typical single- phase grid connected solar-PV system is illustrated in Figure3.4. There are
several reactive power compensation techniques implemented by the researchers for solar-
PV systems. Traditionally, this is done by employing a control scheme in the inverter
control circuit.

Fig 3.4 A typical single-phase grid connected solar-PV system

3.5.1 Various controllers used in solar-PV inverters
Implementing a control scheme by means of a controller at the solar-PV inverter for active
and reactive power control is one of the simplest ways for reactive power compensation.
The control schemes are usually implemented either using digital signal processors (DSPs),
field programmable gate arrays (FPGAs), or microcontrollers. FPGAs are renowned for
their low power consumption and ability to achieve high level of parallelism.
Hossain et al. proposed a reactive power compensation methodology for grid tied
solar- PV system using FPGAs. They have implemented the control strategy based
on digital sinusoidal pulse-width modulation (DSPWM) and the phase-shift between
inverter and grid voltages. With this control technique the injected reactive power
can be dynamically modified and controlled. A similar kind of implementation using

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FPGA can be found. DSPs can also be employed to design reactive power controller
and maximum power point tracking (MPPT) unit for solar-PV systems.
Libo et al. proposed a modified incremental conductance MPPT controller and a
reactive cur- rent controller using a DSP. In simplified reactive power control
schemes are proposed using a microcontroller, where current-mode asynchronous
sigma-delta modulation (CASDM) is employed to improve the dynamic response.
Besides these, a large number of researchers have employed different techniques and
controllers in the inverter control circuit to implement reactive power support
schemes.
3.5.2 Using cascaded multilevel converters
Because of the modular structure, scalability, and enhanced energy harvesting capability,
cascaded multilevel converters are gaining popularity in solar-PV system applications.
Liu et al. proposed cascaded multilevel converters to enhance reactive power support
for solar-PV systems. They have developed a reactive power compensation
algorithm suitable for different types of cascaded solar- PV systems. In this proposed
strategy, they have first con- verted the output voltages from each solar-PV module
in d- q reference frame. Then, they obtained the active power of each module from
MPPT control. Consequently, the output voltage from each converter module is also
analysed, and active and reactive power is distributed in each converter module
accordingly. A block diagram of a typical cascaded multilevel converter based solar-
PV system is shown in fig 3.5

Fig 3.5 A typical cascaded multilevel converter based solar-PV system.

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3.5.3. Using ESS

Coordinated use of ESS and solar-PV inverters are also being proposed as a solution for the
voltage and reactive power control of the distribution network. Droop-based ESS is used
and analysed along with solar-PV inverters to mitigate the voltage rise issue and reactive
power support by Kabir et al. They have found that if the R/X ratio of the line is 4.5 to 5,
then reactive power compensation alone is not sufficient for voltage regulation. Therefore,
urban areas where the R/X ratio is close to unity, the solar-PV inverters are sufficient to
provide reactive power support. However, in rural areas where the R/X ratio is much
higher, the ESS should be added along with the solar-PV inverters for better reactive power
support and voltage control. The authors have also investigated both constant and variable
droop based reactive power control schemes for the ESS, and found that constant droop-
based scheme requires a large battery, whereas, variable- droop based scheme requires a
smaller battery.
3.5.4 Using high frequency link converter
Because of the low cost, high power density, and capability to provide isolation between
the solar-PV panels and the grid, high frequency link converters are being used in grid-tied
solar-PV systems. This type of converters also has the bidirectional power flow capability
from the grid to the DC source, which enable it to provide reactive power support and
voltage regulation.
Robles et al. implemented reactive power compensation scheme in a grid tied solar-
PV system using a high frequency link converter. Using the push- pull topology they
have investigated the performance of the proposed system and validated the results
through simulation studies.
3.5.5 Using transformer less solar-pv inverters
Among transformer less solar-PV inverters do not have reactive power compensation
capability because of the absence of freewheeling path in the negative power region.
However, modulation techniques are proposed by the researchers to provide bidirectional
freewheeling current path. In space-vector based PWM modulation strategy is proposed,
which is operated in two stages;1)Inverter modulation, and 2) Reactive power modulation.
They also designed a proportion-integration-resonance (PIR) current controller to subdue
zero-crossing current distortion. This is similar to the sinusoidal PWM with the exception
that it requires additional duty-cycle generators for each switch. The proposed PWM
scheme is illustrated in Figure 3.6

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Fig 3.6 The PWM technique used to implement reactive power support capability
3.6 Reactive power capability of other REGs
Other than solar PV, and wind generators, the renewable generators, such as hydro, wave
energy, tidal power, bio fuel, or fuel-cells can also be connected to the grid by means of
PECs or synchronous generators. Separate reactive power compensation strategy is not
required for renewable generators, which uses synchronous machines to produce power.
Besides, the renewable generators which are connected to the grid through a PEC, can use
reactive power compensation techniques used in solar-PV converters.
3.7 Reactive power support devices
Besides the internal reactive power control schemes implemented in REGs (i.e. machine or
converter level), there are several reactive power control devices which can be connected at
the PCC or some other place for reactive power support and voltage stability of the power
grid. Usually, FACTS devices, such as STATCOM, SVC, DVR etc. as well as
conventional devices, such as OLTC transformers, and capacitor banks are used for
reactive power compensation. However, FACTS devices provide better controllability and
flexibility compared to conventional reactive power compensation devices. Reactive power
support devices used in the power grid are illustrated in Figure 3.7. Both the conventional
and contemporary reactive power control devices are discussed with elaboration on their
current research progress in following subsections.

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Fig 3.7 Reactive power support devices used in the power grid

3.7.1. OLTC transformers

OLTC transformers are used to regulate system voltage by changing the turn’s ratio of the
transformer under loaded condition. However, the mechanically switched OLTCs are not
fast enough to provide reactive power support for dynamic loads connected to power
system.
Combination of OLTCs with other reactive power control devices is usually used to
provide efficient voltage control. For instance, in a similar combined approach using the
OLTC along with the SVC is proposed for reactive power compensation. A coordinated
control of the OLTC transformer and local wind turbine controllers is implemented, the
OLTC is modelled as a finite machine and coordinated controller is designed for both the
DFIG controller and the OLTC transformer.
3.7.2. Capacitor banks
Parallel switched capacitor banks are usually installed at the PCC of the REGs, to enhance
the reactive power support (mainly in Type-1 and Type-2 wind turbines). They behave as
reactive power sources during transient conditions. However, there are some major
advantages and disadvantages of using capacitor banks as a source of reactive power.
Among the advantages, the power quality enhancement by power factor improvement, and
thus reduction in thermal losses and increase in system capacity are the main.

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However, there are some disadvantages, such as capacitor switching creates strong
transients propagating throughout the network. It also creates high-frequency harmonics.
The inductive lines and capacitor banks form RLC circuits which may create resonance
issues. Because of these issues additional harmonic filters are required, which leads to
additional cost and system complexity; the capacitive reactive power is proportional to the
square of the terminal voltage, hence capacitor banks are not a very good dynamic reactive
power source.
3.7.3 ESS
ESS improves the reliability, and dynamic stability of the power system by enhancing the
power quality and transmission capacity of the grid. There are various types of energy
storage systems, such as battery energy storage systems, super-capacitors or ultra-
capacitors, flywheel energy storage systems, pumped hydro energy storage systems,
compressed- air energy storage, and electrochemical energy storage, such as fuel cells etc.
Battery energy storage is the most widely used ESS, and usually used for active and
reactive power support for REGs in distribution networks. Currently, ultra-capacitor/ super-
capacitor are also becoming very popular for active and reactive power support. For
example, in ultra-capacitor is added into the DC- link of the converter of wind or solar-PV
systems for better reactive power support capability.
3.7.4 STATCOM
Gyugyi first proposed the concept of STATCOM in 1976. A STATCOM is a
FACTS device usually consisted of a VSC, a controller, and a step-up transformer or
coupling reactor as shown in Figure 3.8.

Fig 3.8 Schematic diagram of a STATCOM

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It is typically used at the PCC of a wind farm or solar-PV generator for reactive power
compensation and voltage control. By turning on/off the VSC switches (e.g. IGBTs) of the
STATCOM, the output voltage of the VSC is regulated, and hence the output current can
be controlled.
It is evident, either capacitive or inductive current can be achieved by regulating the VSC
output voltage, Vo. For the values of Vo larger than Vpcc, the STATCOM will operate in
the capacitive mode, whereas for the values of Vo smaller than Vpcc it will operate in
inductive mode. The active and reactive current characteristics of a STATCOM are
illustrated in Figure 3.9. The STATCOM is capable of providing strong dynamic reactive
power support in comparison to capacitor banks and other conventional devices.

Fig 3.9 Active and reactive current characteristic curves of a STATCOM

3.7.5 SVC
SVC is a parallel connected static var absorber or generator which can be controlled to
stabilize the grid voltage. SVC can be used to provide dynamic reactive power to the grid.
SVC contains a voltage measurement circuit, and a voltage regulator, and their output is
fed into a thyristor control circuit. A schematic diagram of a typical SVC, employed with a
thyristor-controlled reactor (TCR), a thyristor switched capacitor (TSC), a harmonic filter,
a mechanically switched capacitor and a mechanically switched reactor, is shown in Figure
3.10.

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The active and reactive current characteristic curves are shown in Figure 3.11 SVCs are
used with REGs in distribution networks for reactive power compensation and voltage
stability improvement.

Fig 3.10 Schematic diagram of a typical SVC.

Fig 3.11 Active and reactive current characteristic curves of an SVC.

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3.7.6 DVR
The DVR is a FACTS device which contains a VSC having an energy storage system
(ESS) connected to the DC-link. It is connected to the power network in series with a
transformer and coupling filters as shown in Figure 3.12

Fig 3.12 Schematic diagram of a DVR

DVR is capable of either generating or absorbing real and reactive power independently. It
is used along with REGs for voltage control and LVRT improvement.

3.8 Control strategies developed for reactive power management in REGs

For reactive power management in REGs, various control strategies, such as sliding mode
control (SMC), model predictive control (MPC), droop control, current mode control
(CMC), synchrophasor based control, and soft computing-based control strategies are used.
Figure 3.13 illustrates these control techniques. In the following subsections application of
these control strategies for reactive power control are discussed.

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Fig 3.13 Various control techniques used for reactive power management in REG
integrated power grid.

3.8.1. Sliding Mode Control

Sliding mode control (SMC) was first introduced in 1962 based on B. Hamel’s idea of
nonlinear compensators. Now, it is the most widely used nonlinear control strategy for
reactive power compensation in REGs. In SMC, usually three steps are defined to design
the control scheme:
1)A sliding surface is identified; 2) The existence of such a surface is tested, and 3)
Stability analysis is done inside that defined surface. There are some variants of SMC
applied in literature for reactive power support in REGs.
Yang et al. proposed perturbation and observe (P&O) based SMC for maximum
active power extraction and reactive power control in DFIG based wind generators.
A fuzzy SMC is used by Wang et al.for reactive power compensators, such as SVCs.
In a fuzzy SMC is also implemented for transient stability improvement and reactive
power compensation of the system.
Discrete SMC was adopted by Pande et al. for real and reactive power control, and
used discrete representation for system dynamics. Second or higher order SMC is
deployed for reactive power compensation in a DFIG. Besides these, SMC is also

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adopted by researchers extensively for active and reactive power support for
converter based REGs.
3.8.2 Model Predictive Control
As the name suggests, the model predictive control (MPC) uses a model explicitly to
predict the output of the process in future time instants, and then the objective function is
minimized by calculating a control sequence. However, finding an appropriate model of the
process is the most daunting task in this type of control scheme.
Yaramasu et al. proposed an MPC algorithm using the discrete time model of an
inverter for a wind energy conversion system. An MPC controller is proposed for
modular multilevel converters.
3.8.3. Droop Control
Among linear control strategies, droop control is the most commonly used control
technique for reactive power compensation in REGs. As the output of REGs is variable and
intermittent in nature, the controller has to respond accordingly to compensate this
variation in active power.
3.8.4 Current Mode Control
Current mode control uses sensed inductor-current ramp in the PWM modulator and has a
two-loop structure compared to its counterpart, voltage mode control, which has a single
loop structure.
This control scheme is incorporated mostly in converters of REGs for active and reactive
power control. For instance, peak current mode control is used for a solar-PV converter.
Both voltage mode control and current mode control were deployed and compared for a
dual active bridge converter.
3.8.5 Synchrophasors Based Control
In synchrophasor based control, phasor measurement units (PMUs) perform digital signal
processing to estimate phasor components from measured analog waveforms, which is then
used in control algorithms for various control purposes. Jiang et al. proposed an auxiliary
coordinated control, and multiple-input and multiple-output (MIMO) model-predictive
control (MPC) using synchrophasor measurement data for a distribution system with high
penetration of renewable generation.

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3.8.6 Soft Computing Methods

Soft computing methods are the emerging group of problem-solving methods, which strive
to imitate the intelligence found in nature. Actually, these methods exploit tolerance for
imprecision, uncertainty, and partial truth to achieve tractability, low cost, and robustness.
Among the notable soft computing methods, fuzzy logic, neural networks, genetic
algorithm, particle swarm optimization, and wavelet theory are more widely being used in
control applications. The use of various soft computing methods for reactive power control
is discussed in the following subsections.
3.8.6.1 Fuzzy logic
Fuzzy logic controllers are being used extensively in recent control applications because of
their robustness, ability to handle imprecise inputs, non-linearity and their ability to work
without an accurate mathematical model.
A fuzzy logic controller was developed for a fixed-speed wind energy conversion
system by Krichen et al. for active and reactive power control. Medjber et al.
proposed a fuzzy logic controller to control active and reactive power of a DFIG. A
fuzzy logic supervisor is deployed to control a flywheel energy storage system of a
DFIG based wind energy conversion system.
Fuzzy logic is also used to tune the parameters of a unified power-flow controller (UPFC)
for reactive power compensation of a stand-alone wind-diesel-tidal hybrid system.
Rezaei and Esmaeili employed a decentralized voltage control method based on
fuzzy logic, and optimized it by gradient descent algorithm (GDA) to control
reactive power of distributed solar-PV and wind-based power system. Besides these,
fuzzy logic controllers are also used for reactive power control of REGs.
3.8.6.2 Artificial Neural network
The biologically inspired computational model, artificial neural network (ANN), consists
of elements (called neurons) processing and identifying connections between the elements
along with their coefficients. These element connections make neuronal structure, and
training and recall algorithms attached to them.
Bansal et al. tuned the parameters of an SVC controller using ANN for an
autonomous wind-diesel hybrid power system. An ANN based thyristor-controlled
series compensator (TCSC) controller is developed for reactive power compensation
in wind-diesel-PV hybrid system. ANN is also used to tune the PI gains of a
STATCOM controller of an autonomous wind-diesel hybrid system.

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Saxena and Kumar used ANN to control reactive power of a STATCOM in a

decentralized hybrid power system. A similar kind of work with ANN based
STATCOM controller is proposed by Mauboy et al. for power system stability
enhancement.
3.8.6.3 Genetic Algorithm
Genetic Algorithms (GA) are evolved from biological concepts, and are being used in
various control applications.
Vrionis et al. tuned the GSC and the RSC controller of a DFIG for reactive power
compensation and LVRT operation using GA. In GA is employed to optimize
reactive power in wind generators. For solar-PV systems, a multi objective GA is
used for volt-var control.
3.8.6.4 Particle-Swarm Optimization
Kennedy and Eberhartfirst proposed the particle swarm optimization (PSO) algorithm in
1995. It is a population based stochastic search, and this optimization technique can avoid
local optimum like other evolutionary algorithms (EAs), such as GA.
Sayadi et al. performed the optimal scheduling of an OLTC transformer, and shunt
capacitors of a solar-PV system for reactive power control using PSO method.
Similar kind of research studies using adaptive PSO have been conducted for
reactive power management in offshore wind farms.

3.9 Reactive Power Coordination & Optimization Strategies

Reactive power compensation for REGs can be implementedat three different levels:
a) At the machine level, i.e. inside the REGs, such as in GSC of the DFIG,
b) At the PCC level,i.e. connecting FACTS devices or energy storage systems (ESSs) at the
PCC and controlling them using various control methods, and
c) At the overall distribution network level, i.e. connecting the reactive power
compensation devices away from the PCC or at the load connecting point and controlling
& optimizing them efficiently.
Reactive power can also be controlled centrally in the distribution network, or can be
managed at local generation and load. The objective of reactive power optimization in an
AC power system is to determine the best values for control variables (e.g. generator
voltages, transformer tap positions, and reactive power compensator’s output) within given

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constraints (e.g. active and reactive power flow limits, and voltage deviation range). This
problem can be divided into two distinct parts; 1) the optimal placement of reactive power
compensators, 2) the optimal operation of the existing reactive power compensators, as
shown in Figure 3.14.

Fig 3.14 The reactive power optimization types.

The reactive power optimization of distribution networks with REGs is usually performed
with the well-known optimal power flow (OPF) method. Its combines an objective function
with the power flow equations to form an optimization problem. Usually, the system losses
decrease with the increase in reactive power capability up to a certain point, and after that
minimum point further increase in reactive power will increase the system losses.
Therefore, an optimization problem is solved to find that optimal point at which the system
losses become minimum.
3.9.1 Using linear programming
Linear programming methods are reliable techniques to obtain solution for optimization
problems characterized by linear constraints and linear objects. They are usually robust
techniques applicable to electric power systems, but some- times they provide with
incorrect evaluation of the system losses and get trapped in a local optimal solution.

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Guggilam et al. constructed a quadratic constrained quadratic program by leveraging

on linear approximation of the power flow problem to develop an OPF problem with
solar-PV systems in distribution networks. However, alarge amount of literature can
be found on reactive power management using linear programming method.
3.9.2 Using nonlinear programming
As constraints of the reactive power planning are nonlinear, the nonlinear programming
would be the most practical method for solving the optimization problem. Sequential
quadratic programming, extended Lagrangian method, generalized gradient method, and
interior-point method are mostly used non-linear programming methods in electric power
systems.
Meegahapola et al. solved OPF and voltage constrained OPF problems for a DFIG
based wind power system using the Newton Lagrangian method. According to their
study the wind farms should dispatch optimal reactive power to improve active
power losses.
Chen et al. used nonlinear programming to find an optimal size of the centralized
capacitor banks, and to control them for reactive power management in distribution
networks.
3.9.3 Using Mixed-integer nonlinear programming
Mixed-integer nonlinear programming methods are used to solve optimization problems
containing nonlinear functions in the objective function. They combine the difficulty of
optimizing discrete variable sets with nonlinear functions, which means that they include
both nonlinear programming and mixed-integer linear programming as subproblems.
Kulmala et al. used mixed-integer nonlinear programming to optimize distribution
network voltage control. They assumed all the optimization variables to be
continuous, and solved the problem using MATLAB optimization toolbox.
Genetic algorithm was used in to solve the mixed- integer nonlinear programming problem
to optimize the re- active power requirements. Branch flow model based relaxed OPF is
used to formulate a mixed-integer second order conic programming problem for active and
reactive power optimization.
Tiwari et al. first formulated the reactive power optimization problem as a mixed
integer dynamic optimization, which is then converted into mixed integer nonlinear
problem by means of simultaneous discretization.

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In reactive power elements, such as capacitor banks, voltage regulators, and under-load tap
changing (ULTC) transformers are considered as control variables, and reactive power
optimization is achieved through mixed- integer nonlinear programming.
Nick et al. presented a control technique for optimal sizing and placement of the ESS
for reactive power control in distribution networks using Benders decomposition
method. They have also considered the stochastic nature of the renewable energy
sources and the load demand.
3.9.4 Using nonlinear dynamic optimization
In nonlinear dynamic optimization, linear optimization is first achieved, and then linear
optimization values are used as initial guesses for nonlinear optimization. A dynamic
optimization approach called control vector parameterization (CVP) is used to find the
optimal location and amount of reactive power support required for a distribution network.
The CVP approach was also upgraded by trajectory sensitivity analysis, singular value
decomposition, and linear optimization programming. Liu et al. proposed a constrained
dynamic optimization model using quadratic objective function for reactive power and
voltage control problem in a distribution network. Their work has explicitly taken into
account the time-varying projection operation of constrained dynamic optimization.

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CHAPTER 4 CONVERTERS

4.1 DC-DC converters

A DC-to-DC converter is an electronic circuit or electromechanical device that converts a
source of direct current (DC) from one voltage level to another. It is a type of electric
power converter. Power levels range from very low (small batteries) to very high (high-
voltage power transmission).
The basic DC-DC converter will take the current and pass it through a "switching element".
This turns the signal into a square wave, which is actually AC. The wave then passes
through another filter, which turns it back into a DC signal of the appropriate voltage
necessary.
A DC to DC converter takes the voltage from a DC source and converts the voltage of
supply into another DC voltage level. They are used to increase or decrease the voltage
level. This is commonly used automobiles, portable chargers and portable DVD players.
Some devices need a certain amount of voltage to run the device. Too much of power can
destroy the device or less power may not be able to run the device. The converter takes the
power from the battery and cuts down the voltage level, similarly a converter step-up the
voltage level. For example, it might be necessary to step down the power of a large battery
of 24V to 12V to run a radio. The converter takes the power from the battery and cuts
down the voltage level, similarly a converter step-up the voltage level. For example, it
might be necessary to step down the power of a large battery of 24V to 12V to run a radio.

4.1.1 Different type of DC-DC converters

4.1.1.1 Buck converter

A buck converter is a DC-to-DC power converter which steps down voltage
from its input to its output. It is a class of switched-mode power supply
typically containing at least two semiconductors and at least one energy storage
element, a capacitor, inductor, or the two in combination.
The buck converter is so named because the inductor always “bucks” or acts
against the input voltage. The output voltage of an ideal buck converter is equal
to the product of the switching duty cycle and the supply voltage. When the
switch is opened the supply current to the inductor is suddenly interrupted.

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Fig4.1 Buck converter

Fig4.2 Waveform of buck converter

Working of a Buck Converter
The working of a buck converter can be broken down into a few steps.
STEP – 1:
The switch turns on and lets current flow to the output capacitor, charging it up. Since the
voltage across the capacitor cannot rise instantly, and since the inductor limits the charging
current, the voltage across the cap during the switching cycle is not the full voltage of the
power source.

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Fig 4.3 Circuit with closed key

STEP – 2:
The switch now turns off. Since the current in an inductor cannot change suddenly, the
inductor creates a voltage across it. This voltage is allowed to charge the capacitor and
power the load through the diode when the switch is turned off, maintaining current output
current throughout the switching cycle.

Fig4.4 Circuit with key open

These two steps keep repeating many thousands of times a second, resulting in continuous
output.

4.1.1.2 Boost converter

A boost converter is a DC-to-DC power converter that steps up voltage from its
input to its output. It is a class of switched-mode power supply containing at least
two semiconductors and at least one energy storage element: a capacitor, inductor, or
the two in combination.

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Fig 4.5 Boost Converter

Fig 4.6 Waveform of boost converter

Working

It’s time to take a really deep breath, we’re about to plunge into the depths of power
electronics. To understand the working of a boost converter, it is mandatory that you know
how inductors, MOSFETs, diodes and capacitors work. With that knowledge, we can go
through the working of the boost converter step by step.

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STEP – 1
Here, nothing happens. The output capacitor is charged to the input voltage minus one
diode drop.

Fig 4.7 Circuit with key open

STEP – 2
Now, it’s time to turn the switch on. Our signal source goes high, turning on the MOSFET.
All the current is diverted through to the MOSFET through the inductor. Note that the
output capacitor stays charged since it can’t discharge through the now back-biased diode.
The power source isn’t immediately short circuited, of course, since the inductor makes the
current ramp up relatively slowly. Also, a magnetic field builds up around the inductor.
Note the polarity of the voltage applied across the inductor.

Fig 4.8 Circuit with key closed

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STEP – 3
The MOSFET is turned off and the current to the inductor is stopped abruptly.
The very nature of an inductor is to maintain smooth current flow; it doesn’t like sudden
changes in current. So it does not like the sudden turning off of the current. It responds to
this by generating a large voltage with the opposite polarity of the voltage originally
supplied to it using the energy stored in the magnetic field to maintain that current flow.
If we forget the rest of the circuit elements and notice only the polarity symbols, we notice
that the inductor now acts like a voltage source in series with the supply voltage. This
means that the anode of the diode is now at a higher voltage than the cathode (remember,
the cap was already charged to supply voltage in the beginning) and is forward biased.
The output capacitor is now charged to a higher voltage than before, which means that we
have successfully stepped up a low DC voltage to a higher one!

Fig 4.9 Circuit showing direction of current

These steps happen many thousands of times (depending on the frequency of the oscillator)
to maintain the output voltage under load.

4.1.1.3 Buck boost converter

The buck–boost converter is a type of DC-to-DC converter that has an output voltage
magnitude that is either greater than or less than the input voltage magnitude. It is
equivalent to a fly back converter using a single inductor instead of a transformer. Two
different topologies are called buck–boost converter. Both of them can produce a range of
output voltages, ranging from much larger (in absolute magnitude) than the input voltage,
down to almost zero.
The output voltage is of the opposite polarity than the input. This is a switched-mode
power supply with a similar circuit topology to the boost converter and the buck converter.
The output voltage is adjustable based on the duty cycle of the switching transistor. One
possible drawback of this converter is that the switch does not have a terminal at ground;
this complicates the driving circuitry. However, this drawback is of no consequence if the
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power supply is isolated from the load circuit (if, for example, the supply is a battery)
because the supply and diode polarity can simply be reversed. When they can be reversed,
the switch can be on either the ground side or the supply side.

A buck (step-down) converter combined with a boost (step-up) converter

The output voltage is typically of the same polarity of the input, and can be lower or
higher than the input. Such a non-inverting buck-boost converter may use a single inductor
which is used for both the buck inductor mode and the boost inductor mode, using switches
instead of diodes, sometimes called a "four-switch buck-boost converter", it may use
multiple inductors but only a single switch as in the SEPIC and Ćuk topologies.

Fig 4.10 Buck Boost converter

Fig 4.11 Waveform of Buck Boost converter

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The buck boost converter is a DC to DC converter. The output voltage of the DC to DC

converter is less than or greater than the input voltage. The output voltage of the magnitude
depends on the duty cycle. These converters are also known as the step up and step down
transformers and these names are coming from the analogous step up and step down
transformer. The input voltages are step-up/down to some level of more than or less than
the input voltage. By using the low conversion energy, the input power is equal to the
output power. The following expression shows the low of a conversion.
Input power (Pin) = Output power (Pout)

For the step up mode, the input voltage is less than the output voltage (Vin < Vout). It
shows that the output current is less than the input current. Hence the buck booster is a step
up mode.

Vin < Vout and Iin > Iout

In the step down mode the input voltage is greater than the output voltage (Vin > Vout). It
follows that the output current is greater the input current. Hence the buck boost converter
is a step down mode.

Vin > Vout and Iin < Iout

The working operation of the DC to DC converter is the inductor in the input

resistance has the unexpected variation in the input current. If the switch is ON
then the inductor feed the energy from the input and it stores the energy of
magnetic energy. If the switch is closed it discharges the energy. The output
circuit of the capacitor is assumed as high sufficient than the time constant of
an RC circuit is high on the output stage. The huge time constant is compared
with the switching period and make sure that the steady state is a constant
output voltage Vo(t) = Vo(constant) and present at the load terminal.
There are two different types of working principles in the buck boost converter.

 Buck converter.
 Boost converter.

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Buck Converter Working

The following diagram shows the working operation of the buck converter. In the buck
converter first transistor is turned ON and second transistor is switched OFF due to high
square wave frequency. If the gate terminal of the first transistor is more than the current
pass through the magnetic field, charging C, and it supplies the load. The D1 is the
Schottky diode and it is turned OFF due to the positive voltage to the cathode.

Fig4.12 Buck Converter Working

The inductor L is the initial source of current. If the first transistor is OFF by using the
control unit then the current flow in the buck operation. The magnetic field of the inductor
is collapsed and the back e.m.f is generated collapsing field turn around the polarity of the
voltage across the inductor. The current flows in the diode D2, the load and the D1 diode
will be turned ON.

The discharge of the inductor L decreases with the help of the current. During the first
transistor is in one state the charge of the accumulator in the capacitor. The current flows
through the load and during the off period keeping Vout reasonably. Hence it keeps the
minimum ripple amplitude and Vout closes to the value of Vs

Boost Converter Working

In this converter the first transistor is switched ON continually and for the second transistor
the square wave of high frequency is applied to the gate terminal. The second transistor is
in conducting when the on state and the input current flow from the inductor L through the
second transistor. The negative terminal charging up the magnetic field around the
inductor. The D2 diode cannot conduct because the anode is on the potential ground by
highly conducting the second transistor.

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Fig4.13 Boost Converter Working

By charging the capacitor C the load is applied to the entire circuit in the ON State and it
can construct earlier oscillator cycles. During the ON period the capacitor C can discharge
regularly and the amount of high ripple frequency on the output voltage. The approximate
potential difference is given by the equation below.

VS + VL
During the OFF period of second transistor the inductor L is charged and the capacitor C is
discharged. The inductor L can produce the back e.m.f and the values are depending up on
the rate of change of current of the second transistor switch. The amount of inductance the
coil can occupy. Hence the back e.m.f can produce any different voltage through a wide
range and determined by the design of the circuit. Hence the polarity of voltage across the
inductor L has reversed now.

The input voltage gives the output voltage and at least equal to or higher than the input
voltage. The diode D2 is in forward biased and the current applied to the load current and it
recharges the capacitors to VS + VL and it is ready for the second transistor.

Modes of Buck Boost Converters

There are two different types of modes in the buck boost converter. The following are the
two different types of buck boost converters.

 Continuous conduction mode.

 Discontinuous conduction mode.

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Continuous Conduction Mode

In the continuous conduction mode the current from end to end of inductor never goes to
zero. Hence the inductor partially discharges earlier than the switching cycle.

Discontinuous Conduction Mode

In this mode the current through the inductor goes to zero. Hence the inductor will totally
discharge at the end of switching cycles.

Applications of Buck boost converter

 It is used in the self regulating power supplies.

 It has consumer electronics.
 It is used in the Battery power systems.
 Adaptive control applications.
 Power amplifier applications.

Advantages of Buck Boost Converter

 It gives higher output voltage.
 Low operating duct cycle.
 Low voltage on MOSFETs

4.2 Voltage derivation

4.2.1 Buck convertor

For the buck converter,
(𝑉𝑠 − 𝑉0)𝐷𝑇 = −𝑉0(1 − 𝐷 )𝑇
Hence, the dc voltage transfer function, defined as the ratio of the output voltage to the
input voltage, is
𝑉0
𝑀𝑣 = =𝐷
𝑉𝑠
The average output voltage is given by,

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𝑇1
1 𝑇1
𝑉𝑜𝑎𝑣𝑔 = ∫ 𝑉𝑜𝑢𝑡 𝑑𝑡 = 𝑉𝑖𝑛 = 𝑓𝑇1𝑉𝑖𝑛 = 𝐷𝑉𝑖𝑛
𝑇 𝑇
0
The average load current is given by,

𝑉𝑜𝑎𝑣𝑔 𝐷𝑉𝑖𝑛
𝐼𝑜𝑎𝑣𝑔 = =
𝑅 𝑅
Where,
T is the chopping period
D is the duty cycle
F is the chopping frequency
The rms value of the output voltage is given by,

𝐷𝑇 1/2
1
𝑉𝑜𝑟𝑚𝑠 = ( ∫ 𝑉 2 𝑜𝑢𝑡 𝑑𝑡) = √𝐷𝑉𝑖𝑛
𝑇
0

In case the converter is assumed to be lossless, the input power to the converter will be
equal to the output power. Hence, the input power (P) is given by in,
𝐷𝑇 𝐷𝑇
1 1 𝑉𝑜𝑢𝑡 2 𝑉𝑖𝑛2
𝑃𝑖𝑛 = ∫ 𝑉𝑜𝑢𝑡𝐼𝑜𝑢𝑡 𝑑𝑡 = ∫ 𝑑𝑡 = 𝐷
𝑇 𝑇 𝑅 𝑅
0 0
The effective resistance seen by the source is,
𝑉𝑖𝑛 𝑅
𝑅𝑒𝑓𝑓 = =
𝐼𝑜𝑎𝑣𝑔 𝐷

The duty cycle can be varied from 0 to 1 by varying T1, T or f. Thus, the output voltage
Voavg can be varied from 0 to Vin by controlling D and eventually the power flow can be
controlled.

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4.2.2 Boost convertor

Using Faraday’s law for the boost inductor
𝑉𝑠𝐷𝑇 = (𝑉0 − 𝑉𝑠)(1 − 𝐷)𝑇
from which the dc voltage transfer function turns out to be
𝑉0 1
𝑀𝑣 = =
𝑉𝑠 1−𝐷
The peak to peak ripple current in the inductor is given by,

𝑉𝑠
∆𝐼 = 𝑇1
𝐿

The average output voltage is,

∆𝐼 𝑇1 1
𝑉𝑜 = 𝑉𝑠 + 𝐿 = 𝑉𝑠 (1 + ) = 𝑉𝑠
𝑇2 𝑇2 1−𝐷

From above equation the following observations can be made:

1. The voltage across the load can be stepped up by varying the duty ratio D
2. The minimum output voltage is vs and is obtained when D =0.
3. The converter cannot be switched on continuously such that D=1. For values
of D tending to unity, the output becomes very sensitive to changes in D.

4.2.3 Buck-Boost converter

The condition of a zero volt-second product for the inductor in steady state yields

𝑉𝑠𝐷𝑇 = −𝑉0(1 − 𝐷 )𝑇

Hence, the dc voltage transfer function of the buck-boost converter is

𝑉0 𝐷
𝑀𝑣 = = −
𝑉𝑠 1−𝐷

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Chapter 5 REACTIVE POWER COMPENSATION IN

RENEWABLES

5.1 A Simulation Model for Reactive Power Compensation

In the modern power system the reactive power compensation is one of the main issues, thus we
need to work on the efficient methods by which VAR compensation can be done easily and we
can optimize the modern power system. VAR control technique can provides appropriate
placement of compensation devices by which a desirable voltage profile can be achieved and at
the same time minimizing the power losses in the system. The hybrid systems can be used for
dual compensation of reactive power and DC magnetic bias in distribution systems, and it
results in desired real power in the system.
Voltage control in an electrical power system is important for proper operation for electrical
power equipment to prevent damage such as overheating of generators and motors, to reduce
transmission losses and to maintain the ability of the system to withstand and prevent voltage
collapse. In general terms, decreasing reactive power causing voltage to fall while increasing it
causing voltage to rise. A voltage collapse occurs when the system try to serve much more load
than the voltage can support. When reactive power supply lower voltage, as voltage drops
current must increase to maintain power supplied, causing system to consume more reactive
power and the voltage drops further . If the current increases too much, transmission lines go
off line, overloading other lines and potentially causing cascading failures. If the voltage drops
too low, some generators will disconnect automatically to protect themselves. Voltage collapse
occurs when an increase in load or less generation or transmission facilities causes dropping
voltage, which causes a further reduction in reactive power from capacitor and line charging,
and still there further voltage reductions. If voltage reduction continues, these will cause
additional elements to trip, leading further reduction in voltage and loss of the load. The result
in these entire progressive and uncontrollable declines in voltage is that the system unable to
provide the reactive power required supplying the reactive power demands. Reactive power
compensation is a very important issue in the operation of electric distribution systems. The
load requires reactive power for magnetizing purposes. Reactive power required by the load
depending on the nature of the load, which is mainly decided by the magnetic circuit
configuration. Reactive power requirement change continuously with the load and voltage
level. Voltage control in a distribution system mainly related to the control of VAR. Reactive
power control in addition to control of reactive power in the distribution system may have such

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advantages as reduction of real power losses and improvement of power factor in the system.
Reactive power compensation (VAR) and voltage control in power systems can be easily
achieved by connecting reactive power compensation devices such as shunt capacitors, series
capacitors, static compensators, tap changing transformers, and automatic voltage regulators
and even now with the new FACTS tools like STATCOMS, UPFC and other FACTS devices.
Reactive power supply and voltage control can be provided by transmission facilities, and
generation facilities. In competitive electricity markets, Independent System Operators (ISOs)
operate the grid, but do not own transmission facilities and generation. Therefore, reactive
power must be procured. The cost of installing transmission facilities is normally recovered as
part of the cost of basic transmission services. Reactive power support voltages, which must be
controlled for reliable power system operation.

5.1.1 Reactive Power Control in Distribution Systems

One of the most fundamental and important problems in electric distribution systems is
reactive power/voltage control. High voltage difference between voltages in different buses in
distribution system is the sole indicator of reactive power imbalance in the system. The main
problem is that the voltage drop occurs when reactive power flows through the inductive
reactance of power lines and when the system is constrained to supply the normal requirements
of reactive power. Voltage problem is compounded when reactive power demand increases and
is shipped over the already heavily loaded lines.
Reactive power control has been looked at as an important issue in distribution systems
for many reasons.
First, the need for most efficient operation of power systems has increased with the price
of fuel. For a given distribution of power, the losses in the system can be reduced by
minimizing the flow of reactive power.
Second, the extension of the power network especially in the distribution level has been
curtailed in general by high interest rates, and in particular cases by right-of-way. In many
cases power transmitted through older networks has been increased, requiring the application of
reactive power control measures to restore stability margins.
Third, voltage is considered as one of the most important parameters of the quality of
power supply. Its deviation from the normal value may be harmful and expensive. Reactive
power control is an essential tool in maintaining the quality of supply.
An extensive amount of research has appeared dealing with reactive power control in
power systems. In general, most of this research falls within the following subgroups of the
/voltage control problems. The reactive power planning and operation is an optimization

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problem of nonlinear, non-smooth, and non-continuous function. It is one of the most complex
problems of power systems because it is requires the simultaneous minimization of real power
losses to reduce the operating cost and improve the voltage profile, and the cost of additional
reactive power sources. Capacitors are widely installed on Distribution systems for reactive
power compensation to improve the voltage profile and to reduce power and energy losses in
the system. The extent of these benefits depends upon how the capacitors are placed in the
network and how effective the control schemes designed for them are. The general capacitor
placement problem consists of determining the optimal number location, types, and sizes of
new and existing capacitors and their control schemes, such that objective function (savings
associated with the capacitor placement minus the cost of capacitors )is maximized while the
load and operation constraints (voltage magnitude, current flow rating, etc)at different load
levels are satisfied.

5.1.2 Reactive Power Compensation Principles

In a linear circuit, the reactive power is defined as the ac component of the instantaneous
power, with a frequency equal to 100/120 Hz in a 50- or 60-Hz system. The reactive power
generated by the ac power source is stored in a capacitor or a reactor during a quarter of a
cycle, and in the next quarter cycle is sent back to the power source.
In other words, the reactive power oscillates between the ac source and the capacitor or reactor,
and also between them, at a frequency equals to two times the rated value (50 or 60 Hz). For
this reason it can be compensated using VAR generators, avoiding its circulation between the
load (inductive or capacitive) and the source, and therefore improving voltage stability of the
power system.
Reactive power compensation can be implemented with VAR generators connected in parallel or
in series. The principles of both shunt and series reactive power compensation alternatives are
described below:

Shunt Compensation
Fig. 5.1 shows the principles and theoretical effects of shunt reactive power compensation in a
basic ac system, which comprises a source ( ), a power line, and a typical inductive load. Fig.
1(a) shows the system without compensation and its associated phasor diagram. In the phasor
diagram, the phase angle of the current has been related to the load side, which means that the
active current is in phase with the load voltage ( ).
Since the load is assumed inductive, it requires reactive power for proper operation and hence,

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the source must supply it, increasing the current from the generator and through power lines. If
reactive power is supplied near the load, the line current can be reduced or minimized,
reducing power losses and improving voltage regulation at the load terminals. This can be
done in three ways: 1) with a capacitor; 2) with a voltage source; or 3) with a current source. In
Fig. 5.1(b), a current-source device is being used to compensate the reactive component of the
load current. As a result, the system voltage regulation is improved and the reactive current
component from the source is reduced or almost eliminate.

Fig.5.1 Principles of shunt compensation in a radial ac system.

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If the load needs leading compensation, then an inductor would be required. Also, a current
source or a voltage source can be used for inductive shunt compensation. The main advantage
of using voltage- or current-source generators (instead of inductors or capacitors) is that the
reactive power generated is independent of the voltage at the point of connection.

Series Compensation
VAR compensation can also be of the series type. Typical series compensation systems use
capacitors to decrease the equivalent reactance of a power line at rated frequency. The
connection of a series capacitor generates reactive power that, in a self- regulated manner,
balances a fraction of the line’s transfer reactance. The result is improved functionality of the
power transmission system through:
Increased angular stability of the power corridor;
Improved voltage stability of the corridor;
Optimized power sharing between parallel circuits.

Like shunt compensation, series compensation may also be implemented with current- or
voltage-source devices, as shown in Fig. 5.2. Fig. 5.2(a) shows the same power system of Fig.
5.1(a), also with the reference angle in , and Fig. 5.2(b) shows the results obtained with the
series compensation through a voltage source, which has been adjusted again to have unity
power factor operation at . However, the compensation strategy is different when compared
with shunt compensation. In this case, voltage VCOMP has been added between the line and
the load to change the angle of , which is now the voltage at the load side. With the
appropriate magnitude adjustment of VCOMP, unity power factor can again be reached at .
As can be seen from the phasor diagram of Fig. 5.2(b), VCOMP generates a voltage with
opposite direction to the voltage drop in the line inductance because it lags current Ip.

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As was already mentioned, series compensation with capacitors is the most common strategy.
Series capacitors are installed in series with a transmission line as shown in Fig. 5.3, which
means that all the equipment must be installed on a platform that is fully insulated for the
system voltage (both the terminals are at the line voltage). On this platform, the main capacitor
is located together with overvoltage protection circuits. The overvoltage protection is a key
design factor as the capacitor bank has to withstand the throughput fault current, even at a
severe nearby fault. The primary overvoltage protection typically involves nonlinear metal–
oxide varistors, a spark gap, and a fast bypass switch. Secondary protection is achieved with
ground mounted electronics acting on signals from optical current transducers in the high-
voltage circuit.
Independent of the source type or system configuration, different requirements have to be
taken into consideration for a successful operation of generators. Some of these requirements
are simplicity, controllability, dynamics, cost, reliability, and harmonic distortion. The
following sections describe different solutions used for generation with their associated
principles of operation and compensation characteristics.

5.1.3 Simulation Model and Results

Simulation is done for reactive power compensation. A hybrid system modeling is done by
combining the chopper circuit to realize the dual compensation of reactive power and DC
magnetic bias, we use the Simulink to run the simulation, its models and results are as
follows:

Fig.5.3.Simulation Model

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Fig. 5.4.Phase voltage, current and power without compensation of reactive power

Fig. 5.5.Phase voltage, current and power with reactive power compensation

The results shows that, when we use the compensation device, it can balance the voltage and
current to normal levels, as we know that there is reactive power due to capacitive and
inductive elements in the grid which can make the current and voltage phase difference, due to
which the real power in the system reduces from the ideal level, but after we introduce the
compensation device, the current and voltage waveforms have same phase, and due to this
compensation effect, power in the system achieves to the desired value with stable voltage.

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5.2 Photovoltaic reactive power compensation scheme

The international trend to limit the use of conventional energy sources
based on fossil fuels due to environmental concerns has led to the increased
utilization of Renewable Energy Sources (RES). However, the increasing RES
integration can influence the operation and stability of the power system. When
a solar PV system is exporting power to the grid, it can cause a voltage rise at
the consumer premises, which is highly undesirable as it can damage
consumer’s appliances and sensitive equipment, cause the disconnection of
some loads due to over voltage protection and can reduce the lifetime of
appliances. Sensitive equipment may include, adjustable speed drives,
microprocessors, industrial processes, electric motors, fluorescent lights, etc.
Consequently, RES systems must be equipped with auxiliary functions, such as
Fault Ride through (FRT) and reactive power compensation, in order to support
the power system in the event of faults and prevent voltage rise. Nowadays,
almost all distribution network operators impose regulations in order to utilize
the presence of RES systems for the benefit of the power system.
The generated PV power is injected into the grid through the Grid Side
Converter (GSC). The amplitude of the grid voltage can be highly affected by
the power generation of PVs. Under high penetration of PVs and during sunny
conditions, residential PV systems can cause a reverse power flow in the low-
voltage feeders and thus, the distribution network’s voltage can be critically
increased. Further, the standard practice of Distribution System Operators
(DSO), especially in passive distribution grids, is to set the grid voltage of the
secondary distribution transformer considerably above the nominal voltage in
order to ensure that the voltage at the end of the line consumer will not be lower
than the minimum limit. Under such circumstances, it is not uncommon to
observe violation of the 10% upper voltage limit, especially under high
penetration of residential PV installations. Therefore, under high PV power
generation, inductive reactive power compensation is required by the PVs for
decreasing the voltage within the regulation limits. The Electricity Authority
has recently adopted a reactive power compensation based on the generated PV
output power as shown in Fig. 5.6. The adopted compensation scheme is fixed
for the entire PV systems transformer. The effectiveness of such a fixed reactive
support scheme on the voltage regulation across the feeder may be limited since
the voltage drop is directly related to the distance from the transformer.

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cosφ

0.2 0.4 1.0 P

Inductive (Reactive
Power Absorption)

Fig. 5.6: Reactive power compensation curve, where power factor

is defined according to generated active power

To investigate the effectiveness of different reactive power compensation

schemes on the voltage regulation across the distribution grid, an accurate
modeling of both the distribution grid and the PV systems is needed. Thus, an
accurate model is developed for the purposes here, in order to allow the
investigation of the distribution grid operation under steady state and fast
transient events. In the Distribution Network (DN) under investigation, several
prosumers have been considered consisting of loads and PV systems. Each PV
installation has been modelled based on an accurate discrete time EMT model
that considers the PV panels, the GSC and its controller. The Q-compensation
scheme has been integrated within the GSC controller, analyzing in this way the
effect of compensation on the operation of the DN.

The work takes into consideration several RES systems connected to a grid
model that is dynamically investigated through simulation work. The existing
EAC grid regulation for PV systems is analyzed and its weaknesses arising by
the fixed reactive power compensation scheme adopted are identified.
Consequently, this paper proposes a modified compensation scheme based on
the distance of prosumers from the distribution network low-voltage
transformer. The results show a positive impact on the compensation
capabilities of RES and the operation of the power system.
5.2.1 Distribution network and PV system model
The impact of reactive power compensation on the operation of a
distribution network can be evaluated by implementing a dynamic power grid
model along with several RES within the same simulation framework. For this
investigation a realistic low-voltage distribution grid has been modeled
consisting of 50 prosumers, as shown in Fig. 5.7. All the prosumers consist of a
5 kVA PV installation (interconnected through a GSC) and a balanced 2000 W/
500 load. The line parameters are set according to the overhead lines typically

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used by the Electricity Authority and realistic lengths have been considered
between the prosumers and secondary transformer in order to design this test
system for the distribution grid. The lines used are 4x100 mm2 aluminum lines
from pole to pole and 2x22 mm2 or 4x22 mm2 from pole to each prosumer. The
MV/LV transformer steps down the voltage to distribution level to which all the
prosumers are connected. The GSC of the PV systems is a power electronics-
based converter capable of delivering the desired active and/or reactive power if
properly controlled. An LCL filter is employed after the GSC to enable the
injection of high quality currents. The control of GSC is designed in a
synchronous reference frame, where an error signal is provided to a Proportional
Integral (PI) controller along with the feed forward and cross-coupling terms.
The GSC control system mainly consists of an active/reactive power controller,
a current controller, and a synchronization scheme. The active/reactive power
controller generates the d and q-axis references for the current controller based
on desired active and reactive power. The reactive power reference Qref is
obtained from the desired compensation pattern, from which, the q-axis
reference current is generated by the PQ controller. The current controller
performs the function of tracking the references with zero steady state error.
The synchronization scheme, usually a Phase-Locked Loop (PLL), is the key
element in the control process since it extracts the necessary phase, frequency
and amplitude information from the grid voltage. The extracted information is
required for SRF transformations and implementation of current controller’s
feed forward terms. This synchronization is achieved using an advanced PLL
algorithm that can work under any abnormal grid condition and the current
controller that enables the injection of high quality current according to. The
design parameters for the power system, renewable energy system and tuning
parameters for the current controller and PLL are listed in Table I.

5.

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5.2.2 Existing Reactive Power Compensation

When residential PV systems deliver maximum power to the grid (under

sunny conditions), the network voltage at some points may exceed the
upper voltage limit due to reverse power flow. This may have a cascading
effect to neighboring consumers and to the grid as already discussed in
the introduction. The presence of a power electronic based GSC for the
grid interconnection of the PV systems, offers the possibility to diversify
its role by requesting to deliver active and/or reactive power as per the
requirements. The accurate control of the GSC allows the injection of the
desired reactive power in addition to the active power for the necessary
compensation of over or under voltage case scenarios. In most of the
cases, especially during the day time, PV systems inject a large amount of
active power and thus the voltage is increased. However, during night
time, when the PV systems switch off, the voltage at the PCC returns
back to the grid voltage supplied by the system. It is worth mentioning
that the maximum deviation in voltage mainly appears at the end of the
line buses due to the cascading effect that each PV system has on the bus
it is connected to. As the injected PV power increases, the voltage at each
bus will increase and each subsequent bus will experience the voltage of
the previous bus.

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The test case of Fig. 5.8, shows the deviation of the voltage at all buses of the LV
distribution grid when the PV power is increased from 0 to 5 kW. All the buses
contain 2000 W/250 balanced loads (similar for all the investigations, except for
the one in Fig. 4). The deviation in voltage for the end of the line bus (i.e.,
V100%) is higher compared to the buses near the transformer (i.e. V20%).
Consequently, for the bus at the end of the line, if the system voltage is already at
a higher value, this change in voltage can cause the bus to violate the upper
voltage limit. For example, if the voltage at the distribution transformer is set at
245 V, the increase in voltage at the furthest bus (100% of distance) for 5000 W
PV power injection, will be 12.22 V. The upper voltage limit (253 V) will
therefore be violated. Furthermore, a test case has been carried out to analyze the
operation of the distribution network for various photovoltaic power outputs and
loading conditions. The operating and loading conditions for this investigation are
listed in Table II and the results are shown in Fig. 4. For cases with high PV
power and small loads, there is an increase in the voltage, especially at buses
which are located further away (i.e., V80% and V100%). Thus, there is a need for
regulations on inductive compensation utilizing the technology of the RES
systems.

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Considering the problem of voltage rise, the Electricity Authority has recently
imposed a grid code based on which, after a specific converter percentage power
output, the reactive power compensation scheme is applied (the converters are
preconfigured for this scheme). If the power generated by the PV converter (𝑃)
exceeds 40% of its rated power output, a certain amount of reactive power must
be absorbed by the converter in order to limit the increase in voltage and
compensate the effect of reverse power flow. The grid code provided by EAC is
shown in Fig.5.6 and PV system installers are required to preconfigure the GSCs
accordingly. Examining the characteristic power output curve shown in Fig. 5.6,
the reactive power compensation is controlled by changing the power factor
depending on the real power output of the GSC. For example, up to 40% of the
rated converter output power (𝑃𝑟𝑎𝑡), the power factor is equal to 1 meaning that
all the power generated by PV is injected as active power. When the generated
power exceeds 40% of the GSC’s capability, the power factor varies linearly
according to Fig. 5.6.

The current grid code applies a fixed amount of Q- compensation for all the PV
systems connected to the distribution network depending on the GSC’s rated
power output and the available PV generated power, irrespective of the distance
from the substation. The change in prosumer bus voltage as per the EAC
compensation is shown in Fig. 5.10. It can be seen that the further away a
prosumer is from the distribution transformer, the greater the increase in voltage.
Under the current EAC regulation, the voltage for prosumers far away from the
transformer is compensated the least when compared to prosumers nearer the
transformer. For example, examining the voltages at prosumer buses 80%l and
100%l, the EAC compensation is not designed so as to regulate the rise in
voltage accordingly.
The Q-compensation scheme of EAC seems to show a significant
improvement on the voltage variation, however, there is an opportunity
for even further improvement. As depicted by the results of Fig. 5.9 and
Fig. 5.10, the prosumers located furthest away, require more reactive
power compensation compared to the ones which are closer to the
substation transformer. Furthermore, for buses nearer the substation
transformer and for which the same compensation scheme is applied, the
result is an unnecessary loss of injected active power. Consequently,
providing a fixed amount of reactive power compensation for all
prosumers may not be the ideal solution. The grid voltage at the LV
transformer of the distribution network is around 1.08-1.09 pu, however,
the upper voltage limit is 1.1 pu. As a result, prosumer buses far away
from the LV substation transformer will almost certainly violate the
voltage limit during reverse power flow. Consequently, more
compensation should be provided for these buses. A modified
compensation scheme providing compensation based on the bus distance

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from the distribution network LV substation transformer. The modified

pattern is obtained by introducing shift forward and shift reverse
compensation patterns; these patterns are applied to the prosumers based
on their location. The resulting compensation pattern shows a positive
impact on the distribution network.

5.2.3 Possible Modifications

In this section, the proposed modified reactive power compensation
schemes are discussed. The PV systems have sufficient capacity to generate
power up to their rated values and this comes up with the problem of voltage
rise at the connection point. Although the pre-defined and uniform reactive
power compensation scheme according to the current EAC regulations
decreases the rise in voltage, it can be improved as already discussed.
Consequently, two modified patterns based on distance are proposed referred,
to as Shift Forward Compensation (SFC) and Shift Reverse Compensation
(SRC).

A. Shift Forward Compensation (SFC)

Shift Forward Compensation reduces the amount of reactive power
compensation and is suitable for buses that lie at a distance (d) less than 50%
of the distribution feeder length (l) from the distribution network LV
substation transformer.
In this compensation pattern, the threshold point from which the
compensation starts is shifted forward to 0.6 and the power factor requirement
at rated power is increased to 0.95 inductive. As mentioned earlier, the buses
which are near the substation require less compensation. This scheme takes
this into consideration as can be realized by the proposed scheme. Thus,
unnecessary compensation is avoided and the prosumer is not “penalized”
with the respective loss of active power and energy (kWh).
It is worth mentioning that the same pattern holds for any rated power of
residential rooftop systems.
The proposed SFC is applied to the distribution network and the results are
presented in Fig. 7. The SFC is suitable for the buses close to the distribution
network LV transformer, but as we move towards the end of the line
(V100%), the reactive power compensation seems to be insufficient.
Consequently, this compensation can be used for buses located less than 50%
of feeder length from the distribution substation transformer.

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B. Shift Reverse Compensation (SRC)

Shift Reverse Compensation is suitable for prosumers located far away
from the distribution transformer. In this case, the amount of reactive power
that prosumers need to generate is comparatively greater. In addition, the
compensation is applied beginning from an even lower rated converter power
output as compared to the existing EAC grid code (30% instead of 40%), as
shown in Fig. 8. The SFC compensation is suitable for the prosumers that lie
at a distance greater than 50% of the total length of the feeder from the
distribution substation transformer. The threshold point from which the
compensation is applied is shifted backwards to 0.3, whereas the slope of the
reactive compensation curve is set to maintain a power factor of 0.85 lagging
when delivering active power equal to 100% of the rated value.

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The effect of SRC compensation is shown in Fig. 9 and is more suitable for
far away buses. Based on the above discussion, a combined version of SRC
and SFC is applied to the distribution network model. The converters on buses
located at a distance within 50% of the line distance (d<0.5l) from the
distribution substation transformer are preconfigured with the SFC scheme
and the converters on buses located at a distance more than 50% away from
the LV substation transformer (d>0.5l) are preconfigured with the SRC
scheme. The results for this Distance Dependent Reactive Power
Compensation (DDRPC) scheme are shown in Fig. 10. DDRPC appears to be
more efficient, as it offers the desired compensation as a function of distance.
For example, if the voltage at the distribution transformer is 251 V, the
increase in voltage at the furthest bus (V100%) with a 5000 W PV system and
2000 W/ 500 load is 1.9 V (0.82% of the nominal). However, with the

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existing reactive power compensation, the voltage rise is 6.3 V (2.74% of the
nominal), violating in this case the 10% upper limit. The results clearly reflect
the DN voltage improvement.
Based on the discussion above, the complete set of Q compensation for DDRPC
is given by

5.2.4 Model Analysis (Solar PV model for output reactive power

calculation)

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Fig 5.11 Reactive power measurement

Fig 5.12 PV Model

Voltage deviation resulting from the power generation of distributed

Renewable Energy Sources (RES) can be a serious problem especially as the
penetration of RES is increased in the distribution grids. For example,
residential photovoltaic (PV) systems can raise the voltage of the low voltage
distribution feeder due to reverse power flow. Especially at the peak PV power
production, the network voltage might even deviate from the upper voltage
limit as defined by the grid regulations, causing cascading problems to
neighbouring consumers and to the grid.
This model performs a simulation-based investigation regarding the
effectiveness of the existing regulations of the Electricity Authority. The
investigation is enabled by applying the Q-compensation scheme on several
PVs installed in a typical low voltage distribution feeder.

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5.3 Reactive Power Compensation in a Wind Farm

Presently, renewable energies and especially wind energy are gaining a special
relevance in the electrical market worldwide. This is due to the more and more
urgent need to find alternative energies that supplant those derived from fossil
fuels. Within this present framework of renewable energy development, it is
worthy of mention the rapid advancement of wind energy and its notable
penetration into the electrical systems of different countries, both in Europe and
worldwide. This current rate of growth motivates the wind farms to not limit
themselves to producing energy, but also to provide stability to the network
within its capabilities, making then possible to increase the power percentage
relative to the total power of the system. So, actual objective is to adapt the
installations that produce wind energy in such a way that they give a maximum
amount of support in any given moment to the electrical network.
From the above, the necessity to continue increasing and developing
wind energy as a clean source of electrical energy production can be appreciate.
Therefore, new problems related to the management and operation of energy
transfer and distribution, and to the efficient distribution of renewable energy in
the grids, are actually arising. These problems bring with them the need for the
various wind farms to not limit themselves to produce energy, but also to
provide stability to the network within its capabilities, of such a form that it will
be possible to increase the percentage of power installments relative to the total
power of the system. To achieve this goal, different regulations are being put
into effect in this area, in the same way that other regulations have been put into
effect with the aim of increasing the development of wind energy.

5.3.1 Current Legislation

Presently, there are many regulations that govern the different aspects
concerning power quality. This standard focuses exclusively on the voltage
quality and includes a series of definitions and limit-values for the different
disturbances that can take place in an electric network. Following set of
complementary standards that help to clear up different aspects of wave quality
and the measurement thereof are:

IEC 61000-4-30: Defines the different methods of measurement for the various
established parameters.
IEC 61000-4-7: Establishes the measuring procedures of the harmonics and
interharmonics.
IEC 61000-4-15: Determines the functional specifications and the design of
the flicker measurer (flicker meter).

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Also, there is a regulation relative to the wave quality in the systems of wind
generation:
IEC 614000-21: Defines the form of measure and evaluation of the delivery
quality of the wind turbines connected to the network.
Now, in the light of the importance of the production of wind energy and its
integration into power networks with a percentage of electricity production
from wind power of 5%, a more global contribution to the network is required,
not only in terms of production but also in terms of help or support to the
networks of transportation and distribution. Within the various possibilities of
providing support to the network, there are two that are fundamental:

1)Compensation of the Reactive Power: Earlier, wind farms were only

required to maintain a unity power factor to reach a 4% bonus, however, now
the maximum bonus has been established at 8%, but according to the
following chart (Table II)

POWER FACTOR BONUS (%)

Peak Normal Valley

TYPE
<0,95 -4 -4 8
0,95>= cos Phi <0,96 -3 0 6
INDUCTIVE 0,96>= cos Phi <0,97 -2 0 4
0,97>= cos Phi <0,98 -1 0 2
0,98>= cos Phi <1 0 2 0
1 0 4 0
0,98>= cos Phi <1 0 2 0
0,97>= cos Phi <0,98 2 0 -1
CAPACITIVE 0,96>= cos Phi <0,97 4 0 -2
0,95>= cos Phi <0,96 6 0 -3
<0,95 8 -4 -4

Table II Bonus by power factor

2) Maintenance of the connection during tension gaps: 5% bonus for those

installations which are capable of maintaining continuity of supply during
tension gaps. The current curve established by REE with which the different
installations must comply, as a minimum requisite, to guarantee the constant
supply of energy in case of a tension gap, can be seen in Fig. 5.12.

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Fig.5.12 Voltage – Acceptable Time at the Connection Point Curve

5.3.2 Support of the wind energy installations to the electrical

network
One of the main objectives in the installations that produce wind energy is to
adapt them in such a way that they give the maximum support to the
electrical network at any given moment.
Currently, there are different technologies that try to reach this objective
according to the characteristics and specific needs of each farm:

1) Automatic Capacitor Banks.

2) SVC (Static Compensator) – TCR/TCSCl
3) STATCOM
4) Wind Turbine with Power Electronic Converter (DFIG)

The research presented in this article is focused on incorporating automatic

capacitor banks into wind farms, even though this methodology can also be
applied to the other technologies mentioned by simply amplifying the
algorithms according to the specific characteristics of the option elected.
Likewise, though the data used in this study come from a concrete wind farm,
there is no limitation concerning the characteristics and behaviors of any other
installation that could be studied. Following this premise, a detailed analysis of
the specific needs of a wind farm has been carried out, as well as a search for
the optimum performance for the compensation of reactive power during peak
time.

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5.3.3 Study of the Needs and Description of the Farm

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All of the measurements were taken over the course of several months between
2004-2005 with the aim of understanding the farm’s different aspects of
seasonal functioning due to wind variations. Amongst the studies, the
description of the farm using the PQ curve is included. From this curve we can
understand the real necessities of reactive power that a wind farm presents
constantly according to the amount of generated power.
As it is possible to see in Fig. 5.12, the necessities of reactive power have been
analyzed with the purpose of being able to obtain, at any given time, the
required values according to the RD 436/2004.
An approximation of the PQ curve using a third-degree polynomial is made in
order to be able to work efficiently with the data collected from the wind farm
(Fig.3). In this way, the implementation of the optimization algorithm that has
been developed is easier and faster.

Q=3. 𝑒 −11.𝑃3 +3. 𝑒 −06.𝑃2 +0.0091.P-1364.7 (1)

On the other hand, it is absolutely necessary to know not only the necessities of
reactive energy but also the relative frequency of the active power that is
generated (Fig.4), as well as of the reactive energy necessary for the
compensation (Fig.5). These data will serve as the base that will allow us to
better optimize the capacitor banks according to the real function of this specific
wind farm.

5.3.4 Studies
With the aim of reaching the maximum degree of adjustment with the present
legislation, RD 436/2004, the fundamental variables that have to be
considered to optimize the value of the capacitor banks are the pay-off period
of the installation and the benefits in 5 years. (Fig.7 and Fig.8).

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Where,
· Cap Bank Price = Capacitor bank price in €.
· Annual Prod = Annual production of the wind farm in kW/h.
· ART = Average Reference Tariff in €/kW/h.
· fi = relative frequency of production from fixed active power
· Bonusi = Bonus achieved from the fixed active power
An algorithm has been developed in Matlab with a Father-Son structure, In
order to carry out this study, as shown below.

Using this algorithm, the problem of regulating the capacitor banks is

independent of the problem of calculating the optimum value for the smallest
capacitor unit. This is done in such a way that using diverse functions, which
are aimed at the regulation of the steps of the capacitor banks, the same
structure is maintained regardless of the configuration of the bank of
capacitors. And on the basis of this common structure for the diverse
configurations, the problem of the optimum value can be tacked according to
the capacitor bank price and the Average Reference Tariff (ART). This
structure also allows us to best study the influence of the variations of these
two parameters: the capacitor bank price and ART.

A. Influence of the capacitor bank’s configuration

The regulation of reactive power by means of capacitor banks is carried out

using groups or steps. So, the optimum value of the diverse steps that compose
the capacitor banks is according to its configuration. The scenarios studied

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were the following ones:

Configuration 1-1-1
Configuration 1-2-4
Configuration 1-2-2
Configuration 1-2-2-4
Configuration 1-1-2-2

Fig. 7 shows the pay-off period of the capacitor banks according to their
configuration and the value of the principal step, or group. From the figure one
infers, by default as well as by excess, that the configurations 1-1-1 and 1-2-2-4
respectively display a behavior different from that of the other configurations.
In the case of type 1-1-1 the pay-off periods remain low except in the case of
very small values in the principal group. This is basically due to the reduced
benefits obtained from such a limited capacitor bank. Also, it is possible to be
observed in Fig. 5 that the capacitor bank’s frequency of use is reduced when
presenting values between 500 and 1500 K.
On the other hand, the type 1-2-2-4 shows some pay-off periods longer than
those of the other configurations due the cost increase of the actual capacitor
bank

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B. Influence of the ART’s variation

The decrease of the ART involves a direct loss of profits, and even losses
for very low values. As far as the optimum of the capacitor banks is concerned,
it can be seen that for small values of the ART, the difference between the
optimum value and other close values are not important. And a displacement of
the optimum point toward lower values in the steps of the capacitor banks can
also be produced.

C. Influence of the citation of the price of the capacitor banks

The optimum point of the capacitor banks is influenced by the price of this
capacitor banks directly.

5.3.5 Study Analysis

From the study carried out on the influence of the capacitor bank type on the
optimum mode of operation From the remaining configurations we can see that
1-1-1 and the 1-1-2-2 demonstrate a greater work period outside of the
performance range established by RD436/2004, such that they will not be able
to compensate for the installation up to the established values with a capacitive
power factor of 0.95 in these periods.
The growing development of wind farms on a global scale brings with it the
necessity to move ahead in the field of wave quality introduced into the
electric network. This is so important that no longer are wind farms
considered as mere passive elements, but their possibilities as elements
helping the systems of transport and distribution are also taken in mind when
they provide energy to these systems.

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