Research on Reactive Power Optimization Control
Strategy of Distribution Network with Photovoltaic
Generation
1st Xuke Cheng
Electric Power Research Institute of 2nd Xiaowei Chen 3rd Yuchen Fan
State Grid Liaoning Electric Shenyang Institute of Engineering Measurement Center of Liaoning
Power Supply Co. Ltd., Shenyang, China Electric Power Co., Ltd.,
Shenyang, China E-mail:646620727@qq.com Shenyang,China
E-mail: 664081466@qq.com E-mail:253759626@qq.com
4th Yitao Liu 5th Shenghui Li 6th Qingsong Zhao
Electric Power Research Institute of Electric Power Research Institute of Electric Power Research Institute of
State Grid Liaoning Electric State Grid Liaoning Electric State Grid Liaoning Electric
Power Supply Co. Ltd., Power Supply Co. Ltd., Power Supply Co. Ltd.,
Shenyang, China Shenyang, China Shenyang, China
mail:2470915816@qq.com mail:1048292747@qq.com E-mail:1106996125@qq.com
Abstract ü What the thesis studies is the active and reactive distribution network of multi-photovoltaic power generation
decoupling control method of photovoltaic grid-connected system is studied firstly 2 .According to the mathematical
inverter, and then the reactive power of grid-connected inverter model of grid-connected inverter under the rotation
is optimized by genetic algorithm with the objective of reference frame, independent regulation of active and
minimizing network loss, So as to realize reactive power reactive power is realized by decoupling the output voltage of
optimization control of the photovoltaic power generation
system.An algorithm based on genetic algorithm for reactive
grid-connected inverter in D and Q axis components. The
power optimization of photovoltaic power generation and reactive power optimization control model of photovoltaic
distribution network is proposed.A mathematical model for power generation system based on genetic algorithm is
reactive power optimization of distribution network has been established.Considering the constraints of minimum network
established. The mathematical model includes those of loss and node voltage, the reactive power of grid-connected
photovoltaic power generation system Considering the limits of inverter is optimized to realize reactive power optimization
not only minimum network loss but also node voltage, what is control of photovoltaic power generation system.
used to optimize the reactive power of photovoltaic power
generation is genetic algorithm. The example simulation results
II. CONTROL STRATEGY OF VOLTAGE SOURCE
indicate the designed optimization algorithm is effective and
correct in reducing power loss and improving voltage quality. GRID-CONNECTED INVERTER
Key words ü Photovoltaic power generation, Reactive power The mathematical model of the three-phase voltage source
optimization,Grid-connected inverter, Genetic algorithm grid-connected inverter is a general mathematical description
of the voltage source inverter based on the topology of the
I. INTRODUCTION1 three-phase voltage source grid-connected inverter and the
P hotovoltaic power generation has the characteristics of basic circuit law,Kirchhoff's law of voltage and current, in the
dispersion and random variation. The connection of a three-phase static coordinate system.The design of the control
large number of photovoltaic power sources will have effect system generally adopts double loop control, i.e. voltage
on the secure and steady working of the electrical distribution outer loop and current inner loop, in order to establish dq
system. Due to the influence of photovoltaic power model of three-phase voltage PWM inverter. The function of
generation in different degrees, traditional power distribution the voltage outer loop is mainly to control the DC side voltage
system analysis methods, such as power flow calculation, of the inverter, while the function of the current inner loop is
state estimation, reliability evaluation, fault analysis, power mainly to control the current according to the current
supply recovery, etc., need to be improved and improved. In command output by the voltage outer loop. We usually
this paper, the reactive power optimization problem of choose that the Q axis coincides with the grid electromotive
force vector E in order to realize independent control of
reactive components, so that the Q axis represents the
This paper is funded by the project: Analysis of The Operation Impact reference volume of reactive components and the D axis
of Distribution Network with Distributed Power Sources. (SGLNPJ00FZ
JS1900380).
978-1-7281-4094-0/19/$31.00 ©2019 IEEE 4026
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represents the reference volume of active components. on both AC and DC sides of the rectifier. The reactive current
*
given id can be directly used as the reactive power given
input of the system, or the reactive power given q * can be
*
adopted and transferred to the reactive current given id
1
through coefficient transformation eq .
Synchronous PI current control has obvious advantages: it
can realize decoupling control of active/reactive current and
independent adjustment of active/reactive power by adopting
Fig. 1 Principle block diagram of Synchronous PI current control.
control under synchronous coordinate system; Using PI
The current inner loop realizes sinusoidal current control at regulator can realize no static difference regulation.Moreover,
the network side.Three-phase symmetrical AC power grid using PI regulator can get quite good dynamic and static
voltage and AC current are converted into DC in the characteristics and can make switching frequency fixed, etc.
synchronous rotating coordinate system because the
synchronous rotating coordinate system control structure is III. REACTIVE POWER OPTIMIZATION OF DISTRIBUTION
adopted. Therefore the current inner loop can realize no static NETWORK WITH PHOTOVOLTAIC POWER SUPPLY
difference adjustment by using PI regulator (The principle Reactive power optimization of photovoltaic power
block diagram of synchronous PI current control is shown in generation and distribution network is to ensure that the node
fig. 1). By realizing independent control of reactive power voltage is within the specified range. The reactive power
components, the space vector and Q axis direction of power control scheme is adopted to reduce the active power loss of
grid electromotive force are the system by controlling the reactive power emitted by
°eq Em photovoltaic power supply. Three parts are included in its
® (1) mathematical model: objective function, power flow equation
°̄ed 0 equality constraint and inequality constraint. From the above
Where Em is the peak electromotive force of the power analysis, it can be seen that the output reactive power of grid
connected inverter can be adjusted by changing the setting
grid.
q* of reactive power. Generally , photovoltaic power
In dq coordinate system the mathematical model of the
generation systems have certain reactive power regulation
three-phase voltage source inverter is as follows:
capability. The reactive power compensation capability of
diq
L Em Z Lid Riq vdc sq (2) each distributed power source can be utilized to improve the
dt operation performance of the distribution network. Therefore,
did the reactive power of the distribution network of distributed
L Z Liq Rid vdc sd (3) power sources can be optimized by optimizing the given
dt
The active power and reactive power of the system are as reactive power of each distributed power source.
follows The objective function of reactive power optimization in
this paper is to minimize the network loss of multi-distributed
3
°° p 2 eqiq
power distribution network. Assuming a certain reactive
power capacity is owned by the inverter. The basic principle
® (4)
of the reactive power optimization algorithm for distribution
°q 3 e i network with DG is: When a series of constraints are met, the
°̄ 2
q d
genetic algorithm can be used to optimize the reactive power
The active current component is represented by the Q axis q* of each distributed power source, and the reactive power
while the reactive current component is represented by the D compensation control of each inverter can be realized by
axis. This makes the design of the controller difficult because using the control algorithm described in section 1.
it can be seen from the mathematical model that the D axis
and the Q axis are coupled to each other. Using feedforward
decoupling control strategy, the active and reactive currents, A. Objective Function
i.e. the active and reactive components on the three-phase The minimum network loss is selected as the objective
network side, can be independently adjusted.The dq axis of function:
the current generates the midpoint voltage vd ,vq of the n
three-phase bridge arm through respective PI regulators and min F Ploss ¦
i 1, jh
Gij (U i 2 U j 2 2U i 2U j 2 cos Tij ) (5)
feedforward decoupling control methods. The voltage is
converted to two-phase static coordinate system, and the Ploss is the network loss. U i , U j is the voltage
switches of rectifier bridge are driven by the output pulse amplitude of nodes i , j ; Gij , Bij , T ij are the conductance,
after SVPWM modulation. susceptance and voltage phase angle differences between
The Q axis represents the active current component, nodes i , j respectively; H represents all node sets directly
*
therefore the PI regulator outputs iq active current as the connected to node i .
current inner loop to control the transmission of active energy
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B. Equality Constraint of Power Flow Equation exceeding the limit; VVi is the voltage over-limit deviation
The objective function constraints are divided into power value of the load node i ; When Vi d Vi min ,
flow equation constraints and operation limit constraints to VVi Vi min Vi ; When Vi min d Vi d Vi max , VVi 0 ;
ensure the safe operation and power quality of the system When Vi t Vi max , VVi Vi Vi max .
The constrained conditions for active power and reactive According to the objective function and constraint
power balance of each node are as below: conditions determined above, the specific optimization model
is transformed into a general mathematical model as follows:
Pi U i ¦ U j (Gi j cos Ti j Bi j sin T i j ) (6)
jH min f (u, x ) ½
°
Qi Ui ¦ Uj (Gi j cos T i j Bi j sin Ti j )
h(u, x) 0 ¾ (11)
(7)
jH g (u , x) t 0 °¿
Where Pi and Qi are active and reactive power injected
Reactive power optimization of DG system is a
by node i ; U i , U j is the voltage amplitude of nodes i , j ;
multivariable and nonlinear complex optimization problem,
Gij , Bij , T ij are the conductance, susceptance and voltage so genetic algorithm can be used in this paper to obtain better
phase angle differences between nodes i , j respectively; H optimization results. Genetic algorithm is adopted to solve the
represents all node sets directly connected to node i . reactive power optimization problem. The steps are as
C. Inequality Constraints follows: Firstly, a group of initial power flow solutions are
randomly generated, then they are coded, and they are
Variables in reactive power optimization are divided into
recombined through operations such as selection, crossover
control variables and state variables. Reactive power belongs
and mutation, and finally the solutions tend to be optimal.
to the control variable category, and node voltage belongs to
For the "select" operation, the method of roulette is
the state variable category. The main output of photovoltaic
adopted in this paper. The probability of each individual
power to power system is active power.High reactive power
being selected is
demand will bring threat to grid connected inverter. From an
economic point of view, the capacity of reactive power f ( xi )
F ( xi ) N
should be limited. (12)
The conditions to be met by the control variables are as ¦ f (x )
i 1
i
follows:
f xi is the fitness of the xi , the higher the fitness
Qgi min d Qgi d Qgi max (i 1, 2,...n) (8) volume, the bigger the possibility of being selected.
Qgi max , Qgi min is the upper and lower limits of reactive The "crossover" operation is to calculate the two
power compensation capacity, and n is the number of individuals in the population according to the linear formula
photovoltaic power supplies connected. shown.
State variables need to meet: c1 p1
a p 2 * (1 a ) (13)
Ui min d Ui d Ui max (i 1, 2,...m, i z s ) (9) c2 p1* (1 a ) p 2 * a (14)
U i max , U i min is the upper and lower limits of node voltage p1, p 2 are the original two individuals in the population,
amplitude, m is the number of load nodes, and s is the a are random variables from 0 to 1, c1, c 2 are the newly
balance node. generated two individuals.
An extended objective function with load node voltage The "mutation" operation is to randomly designate the loci
crossing as penalty function. The control variable constraints of their mutation points to individuals in the population, and
of reactive power optimization will be satisfied by setting the change the values of these loci with preset mutation
search boundary of control variables. State scalar constraints probability, thus realizing individual mutation.
can usually be treated by penalty function method. The new In this paper, penalty function method is used to deal with
objective function is formed because constraints are the constraint problem in order to ensure that the node voltage
introduced into the original objective function, which is the does not exceed the limit p (x ) is considered as a penalty
basic idea of penalty function method. Therefore, a series of function. Minimization is specified as follows:
unconstrained optimization problems form the original
constrained optimization problems.The specific method is p ( x ) 0, x is feasible.
® (15)
that the constraint of boundary inequality is added to the ¯ p ( x ) 0, other
original objective function in the form of penalty term, thus Maximization is specified as follows:
forming a new objective function. By applying the idea of
penalty function, the above objective function of reactive p( x) 0, x is feasible.
® (16)
power optimization can be converted into:
2
¯ p( x) ! 0, other
n
VVi After the objective function is added to the penalty function,
min F Ploss O ¦
i 1,i z s Vi max Vi min
(10) it is:
min F Ploss p ( x) (17)
Where: O is the penalty factor for the load node voltage
If U i U i max d 0 and U i U i min t 0 are satisfied, The
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penalty item is assigned to p ( x) 0 , if not, it is assigned to 2 1 1.11 1.051 1.064
p ( x) 10 .
3 0.94 1.04 1.039 1.051
IV. CASE STUDY 4 0.94 1.04 1.033 1.041
IEEE 30-node
5 1 1.11 1.051 1.034
The IEEE 30-node example network structure is shown in
fig. 2. The IEEE 30-node system includes 6 generators 6 0.94 1.04 1.035 1.037
(nodes 1, 2, 5, 8, 11, 13, of which 1 node is a balancing node
7 0.95 1.05 1.034 1.029
and nodes 2, 5, 8, 11, 13 are PV nodes), 4 transformers
(branches 9-6, 6-10, 12-4, 28-27, with variation ratios of 8 1 1.10 1.050 1.043
1.05,0.975,1.025,1.025, respectively) and 2 reactive
compensation points (nodes 10 and 24), Constraints of 9 0.95 1.05 1.044 1.050
control variables and state variables are shown in table 1. the 10 0.95 1.05 1.021 1.048
data are in the form of normalized values. the reference power
is assigned to 100MVA and the reference voltage is assigned 11 1 1.10 1.050 1.022
to 10KV. 12 0.95 1.05 1.034 1.049
7 8
1 2 5 13 1 1.10 1.050 1.062
13
3
4 6
28 14 0.95 1.05 1.018 1.036
29 15 0.95 1.05 1.012 1.032
12 27
14 11 9
16 0.95 1.05 1.021 1.042
15 10 17 0.95 1.05 1.016 1.041
16 17
30
18 18 0.95 1.05 1.003 1.026
19 20
22
21 19 0.95 1.05 1.001 1.025
25 26
23
24
20 0.95 1.05 1.005 1.030
Fig.2 IEEE30 .
21 0.95 1.05 1.007 1.035
TABLE 1
CONTROL AND STATE VARIABLE CONSTRAINS. 22 0.95 1.05 1.007 1.035
Reactive power
23 0.95 1.05 0.999 1.023
Generator compensation
terminal capacity Load node voltage
24 0.95 1.05 0.989 1.019
voltage
Q10 Q24
25 0.95 1.05 0.984 1.004
Upper
limit 1.1 0..5 0.1 1.05 26 0.95 1.05 0.966 0.986
value
27 0.95 1.05 0.990 1.003
Lower
limit 1 0 0 0.95 28 0.95 1.05 1.036 1.037
value
29 0.95 1.05 0.970 0.983
The parameter values of the genetic algorithm adopted in 30 0.95 1.05 0.958 0.971
this example are: the crossover probability is 0.8, the
mutation probability is 0.001, the population size of each The reactive power optimization time was 842.15s, and the
generation is 20 individuals, the number of iterations is 100. network loss decreased from 7.698MW to 6.96MW, a
Binary code has 8 bits.Node voltage data before and after decrease of 9.59%. The variation of objective function value
optimization are shown in Table 2. is shown in fig. 3. In this paper, reactive power optimization
algorithm for distribution network with multiple photovoltaic
TABLE 2 power generation systems is studied.The simulation results
THE NODE VOLTAGE COMPARISON OF BEFORE AND show that the algorithm is feasible, which can reduce the
AFTER OPTIMIZATION power loss and improve the voltage quality. The output
Optimiza capacity of reactive compensation is shown in Table 3.
Node Lower Upper Initial
tion TABLE 3
number limit value limit value state
results REACTIVE POWER OUTPUT
Reactive Lower limit Upper limit Optimizati
Initial state
1 1 1.11 1.051 1.081 power value value on results
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Networks Based on a Quantum Krill Herd Algorithm.Electric Power
Q10 0 0.5 0 0.2514 Components and Systems.2019
[4] Jinyuan Liu, Xuefeng Wu, Jin Pand and Ce Xiu 2017 Study on
Q24 0 0.1 0 0.0657 technology of electronic power engineering cost based on data
mining.2017 IEEE Conference on Energy Internet and Energy System
Integration (EI2),2017
[5] Li Yun Zhi, Quan Yuan, Yang Zhao, and Qian Hui Gang.2015 A
Novel Reactive Power Compensation Approach Based on Particle
Swarm Optimization.Applied Mechanics and Materials.2015
Fig.3 Change of the objective function.
V. CONCLUSION
The thesis researchs the work on reactive power
optimization model and algorithm for distribution network
with multi-distribution power generation. It is determined
that the minimum network loss is taken as the objective
function, the power flow equation constraint is taken as the
equality constraint, and the reactive power output of
photovoltaic power generation is taken as the control variable.
Penalty functions are constructed to solve the results, while
genetic algorithms are used for optimization.The feasibility of
the genetic algorithm with strong convergence and rapidity is
verified through the simulation results of several
examples.Moreover, the genetic algorithm plays a great role
in decreasing network power loss and enhancing voltage
quality.
REFERENCES
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Active Distribution Network Based on Bifurcation Theory,Applied
Mechanics and Materials,2015,24 (7):31-36.
[3] Yuancheng Li, Rongyan Yang and Xiaoyu Zhao 2019,Integrated
Reactive Power Optimization Method for Active Distribution
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