Sliding Mode Control for a Transformerless Single-

Phase Grid-Connected Photovoltaic System

Khalid Chigane* Mohammed Ouassaid
Department of electrical engineering Department of electrical engineering
Mohammadia school of engineers Mohammadia school of engineers
Mohammed V University Mohammed V University
Rabat, Morocco Rabat, Morocco
Khalidchigane@research.emi.ac.ma ouassaid@emi.ac.ma

Abstract— In this paper, a nonlinear control of the active and main drawback of this strategy lies in its sensitivity to change
reactive power for a photovoltaic system is presented. A in system parameters [3]. The CHC is one of the simplest
transformless voltage source inverter is used to ensure the control techniques as it is easy to design and realize. However,
connection into the electrical network. The design of the in spite of its fast dynamic response and simplicity, the
controller is based on the Sliding mode approach to establish the
switching frequency is inconsistent [4].
inverter control laws. An analysis based on Lyapunov stability
approach is developed to guarantee the global asymptotic In addition to the above-mentioned control strategies, some
stability of the system. So as to verify the effectiveness of the new approaches based on backstepping control [6,7], droop
proposed controller, the obtained results are compared with control scheme [8], artificial neural networks [9], fuzzy logic
those of the conventional linear controllers under changing in
solar irradiance. The results show that the proposed control is
[10], digital repetitive control [11] and predictive control
efficient and gives good performance in terms of unity power [12,13] are presented in the literature. All these techniques of
factor and references tracking. Moreover, the power quality control are characterized by their complex design and
injected into the grid is enhanced by decreasing the total implementation, need more computational development and
harmonic distortion, even under low irradiance. require a good knowledge of the system parameters in order to
decrease the harmonic noises and enhance the dynamic
Keywords— Sliding mode control; Grid connected inverter; response [4].
Total harmonic distortion; Active and reactive power control.
Since a long time, Sliding Mode Control (SMC) has
I. INTRODUCTION attracted much attention in photovoltaic energy conversion
systems. Actually, SMC is an appropriate control for nonlinear
The increased penetration of photovoltaic energy into systems due to its simple implementation, strong robustness,
modern power systems requires to active participation in the disturbance rejection, fast responses and low sensitivity to
electric grid operation by an appropriate control strategy. The plant parameter variations which eliminate the necessity of
connection of the PV array into the grid is mainly made by a exact modeling [14-17].
voltage source converter (VSC), and it may include a
transformer, intermediate DC–DC converter, or even both. It The rest of this paper is organized as follows. The
has been reported that transformerless inverters are higher mathematical model of the PV cell and the nonlinear system is
efficiency and have smaller size and weight, in comparison presented in Section 2. Then, Section 3 deals with a nonlinear
with their counterparts with galvanic separation [1]. Sliding mode approach using the Lyapunov stability.
Illustrative simulation results of the proposed control in
Several current control techniques have been implemented comparison with those of the conventional PI control for
and discussed for photovoltaic systems integration into the different solar radiations are given in section 4. Finally, some
grid. The Proportional Resonant (PR) control, Proportional concluding remarks are mentioned in section 5.
Integral (PI) controller, dead-beat control (DBC) and Current
Hysteresis Control (CHC) are the significant ones [2,3,4]. The
II. MATHEMATICAL MODEL OF GRID CONNECTED VOLTAGE
PR controller, which has gained a large popularity in the last
decade, inserts a high gain at the electrical network frequency, SOURCE INVERTER AND PV CELL
allowing the elimination of the steady-state error [5]. The
disadvantage of this controller is its bad transient response and A. Modeling of the photovoltaic cell
vulnerability to instability in the case of the system parameter
variation. Despite its simplicity, the PI controller is sensitive Fig. 1 shows the electrical equivalent-circuit of a solar cell. It
to parameter disturbances and does not ensure good is composed of a light generated current source, a single diode
performances when the operating point varies [2]. In the case representing p-n junction cell, a shunt resistance Rp and a series
of DBC, a high dynamic response can be achieved, but the resistance Rs describing an internal resistance of cell to the

     
 


current flow [18]. The solar cell terminal current can be (Boost and Inverter) and the electrical grid filter is presented in
expressed as follows Fig. 2.
The system can be described in the stationary reference frame
Icell I ph  Id  I p (1) α-β according to Fig. 2 by the following equation [19]:

where: ªVeD º d ª I sD º ª I sD º ªVsD º

Iph is the current generated by the incident light, « » L « » R« »« » (4)
Id is the current through the diode, ¬VeE ¼ dt ¬ I sE ¼ ¬ I sE ¼ ¬VsE ¼
Ip is the current through the parallel resistor Rp.
where (Isα, Isβ), (Veα, Veβ) are the outputs current and voltage of
The characteristic equation for the current and voltage of a PV the inverter respectively and (Vsα, Vsβ) is the supply voltage
array is described by the following equation: components in the stationary reference frame α-β. L is the
inductance and R is the parasitic resistance of inductance.
ª q V  Rs I cell º
q(V  Rs I cell ) Representing (4) in the rotating reference frame using d-q
I cell N p I ph  N p I rs «e nkTN s  1»  N p (2)
« » Ns Rp transformation at the supply frequency gives:
¬ ¼
where:
T is the reference cell operating temperature, ­ dI sd 1
°° dt LZ I sq  RI sd  Ved  Vsd
V is the cell output voltage (V), L
Irs is the cell reverse saturation current, ® (5)
q is the electron charge (1.60217646 × 10• 19 C), ° dI sq 1
 LZ I sd  RI sq  Veq  Vsq
°̄ dt L
n is the diode ideality constant,
k is the Boltzmann constant (1.3806503 × 10• 23 J/K),
Np and Ns are the number of parallel and series cells where Z 2S f ( f =50 Hz is the grid frequency). For a single
respectively. phase grid connected system, the active and reactive powers
Rp and Rs are the shunt and series resistors of the cell, outputs, seen from the grid side, can be expressed as:
respectively.
The generated photocurrent Iph is related to the solar ­ Vs max I s max
irradiation by the following equation: ° Pg ˜ cos(M )
° 2 2
® (6)
°Q V I
G  s max ˜ s max sin(M )
I ph I sc  ki T  Ta (3) °̄ g 2 2
1000
where:
Isc: cell short circuit current at reference temperature and Here Ismax and Vsmax are the maximum output current of inverter
irradiation, and supply voltage respectively and φ is the phase difference
ki: Short-circuit current temperature coefficient . between the output current Is and the grid voltage Vs.
Ta: Cell reference temperature, Moreover, the initial angle of the phase 1 is set to 0 and the
G: Solar irradiation in W/m², initial angle of the d-q reference frame is set to π/2, this leads
the Vsq component to be zero. In this reference frame, (6) will
Rs become:
Icell

Iph Id Ip ­ 1
°° Pg 2
Vsd I sd
® (7)
D Rp V °Q 1
 Vsd I sq
°̄ g 2

Hence, the reactive and active power can be controlled by the

quadrature and direct components current respectively. It is
Figure 1. Simplified equivalent circuit of a photovoltaic cell. worth to notice that the DC-bus voltage has been controlled
using a conventional PI controller to eliminate the
B. Modeling of the grid connected VSI
instantaneous error.
The comprehensive photovoltaic energy conversion system
composed of the photovoltaic generator, the PWM converters
 PV Boost Inverter dS
panel S = 0 and 0 Ÿ u (t ) ueq (t )
dt
Lb L R Hence the derivative of the sliding surfaces (9) using (5) is
S1 S3 given as
CPV Sb Cdc Vdc Ve Grid
­ dS d (t ) § dI *sd ·
° kd ¨  a2 I sq  a3 I sd  a1 (Ved  Vsd ) ¸
°° dt ¨ dt ¸
S4 S2 © ¹
® (11)
° dS q (t ) § dI sq
* ·
Sb S1,2,3,4 ° dt kq ¨  a2 I sd  a3 I sq  a1Veq ¸
¨ dt ¸
PWM PWM ¯° © ¹
Duty cycle Veαβ
IPV αβ
MPPT dq
VPV
Vedq
where a1=1/L , a2=ω , et a3=R/L. To ensure the Lyapunov
I*sd Isdq
dq dS
Vdc
- PI αβ
Isαβ stability criteria i.e. ˜ S 0 , the nonlinear control inputs
+ Sliding mode dt
Vdc_ref Control Vsαβ
I*sq dq
αβ
Ved_eq and Veq_eq are defined as
Vsdq
­ dS d (t ) 1 § dI *sd ·
° 0 Ÿ Ved _ eq ¨¨  a2 I sq  a3 I sd  a1Vsd ¸
Figure 2. Block diagram of the proposed control method of the VSI.
°° dt a1 © dt ¸
¹
® (12)
1 § dI sq ·
*
III. NONLINEAR CONTROL OF VOLTAGE SOURCE INVERTER ° dS q (t )
° dt 0 Ÿ Veq _ eq ¨  a2 I sd  a3 I sq ¸
USING SLIDING MODE APPROACH a1 ¨ dt ¸
¯° © ¹

The nonlinear switching inputs Ved_n and Veq_n can be chosen as

In order to control the active and reactive power using follows
Sliding mode control, the desired value I*sd of Isd is generated
by the PI controller of the DC-bus voltage, and I*sq the ­ 1
°Ved _ n D d a sgn esd
reference value of Isq is forced to be equal zero so as to obtain ° 1
a unity power factor. We define the tracking error signals ® (13)
°V 1
involving the desired variables I*sd and I*sq respectively: D q sgn esq
°̄ eq _ n a1

­
°esd I *sd  I sd where d and q are a positive constants and the sign function
® *
(8) is defined to reduce the chattering noise as [20]:
°̄esq I sq  I sq
S (t )
The sliding surfaces are chosen as follow sgn( S (t )) (14)
S (t )  H
­° Sd (t ) kd esd (t ) where ε is a positive constant.
® (9)
°̄ Sq (t) kq esq (t ) Then, the control voltage laws for the active and reactive
power tracking is expressed as
where kd and kq are a positive constants.
In order to satisfy the sliding mode existence laws, the ­ 1 § dI *sd ·
control inputs are chosen to have the structure: °Ved _ref ¨¨  a2 I sq  a3 I sd  a1Vsd  D d sgn(esd ) ¸
°° a1 © dt ¸
¹
u(t ) ueq (t )  un (t ) (10) ® (15)
1 § dI sq ·
*
°
°Veq _ ref ¨  a2 I sd  a3 I sq  D q sgn(esq ) ¸
where un(t) is a nonlinear switching input, which drives the °¯ a1 ¨ dt ¸
© ¹
state to the sliding surface and maintains the state on the
sliding surface in the presence of the parameter variations and
disturbances and ueq(t) is an equivalent control-input that Theorem 1. The asymptotic convergence of the active and
determines the system’s behavior on the sliding surface reactive powers to their reference trajectories Pg and Qg=0,
[14,20]. Considering the invariance condition, the equivalent respectively is guaranteed when the dynamic sliding mode
control-input is given by the following condition control laws (15) are applied to the voltage source inverter.
Proof: By replacing (15) in (11), the derivative of the Sliding Fig. 6 demonstrates that the THD of the injected current is less
surfaces can be derived as follows: sensitive to the solar irradiance change while the PI controller
displays a large increase of THD when solar irradiance
­ dSd (t ) ­ dSd (t ) decreases. Table 1 reports the third and the fifth harmonics. It
°° dt kd D d sgn esd °° Sd (t ) dt 0 can be seen that they have not an order of increasing or
® Ÿ® (16) decreasing.
° dSq (t ) kqD q sgn esq ° S (t ) dSq (t ) 0
°¯ dt ¯°
q
dt

Consequently, it is evident that the reaching condition of

sliding mode is guaranteed.

IV. SIMULATION RESULTS

In order, to assess the performances of the proposed

controller, a comparative simulation study between the
conventional control using PI controllers and the Sliding mode
controller has been performed using MATLAB/Simulink
software under temperature of 25°C and variation of solar
irradiance. .

A. Performance of the proposed control method

The control parameters of the Sliding mode control are d = 200 V/div
1.5 and q=5 and a switching frequency of 10 kHz was used in 10,3 A/div
the simulations for the both methods of control.
Fig. 3.a shows that the current injected into the grid has the
sinusoidal waveform and it is in phase agreement with the
supply voltage. Moreover, it can be noticed that the power
factor of proposed controller, is unitary. Also, the root mean
square values of current and voltage with Sliding mode control
present a good performance and fast response as shown in Fig.
3.b.
As can be seen in the Fig. 4, the frequency is less disturbed (a)
around 50 Hz in the proposed control than the conventional
control method. Furthermore, the reactive power is equal to its
reference, which is set to 0 VAr even under the solar irradiation
variation, while the linear controller shows instability.
In Fig. 5, it can be observed that the active power in the
Sliding mode method tracks very well the reference and has a
better dynamic response compared with the conventional PI
control strategy.

B. Impact of the solar irradiance on the THD

Table 1 shows the third and the fifth harmonics of the

current injected into the electrical grid computed by the
discrete Fourier transform for the two control methods. The
THD of the current for the two strategies of control is depicted (b)
in Fig. 4 and Fig. 6.
Figure 3. Waveforms of the current and voltage injected into the grid:
Fig. 4 shows that the output current obtained using the linear (a) Sliding mode control (b) RMS values of Sliding mode control
(index s) and Conventional control (index c)
controller contains a lot of harmonics compared to the current
generated using the proposed controller. For this latest, the
spectrum of harmonics is dominated by the third and the fifth,
especially for 1000W/m² of solar irradiance.
 100 W/m² 100 W/m²

1000 W/m² 1000 W/m²

(a) (b)

Figure 4. Voltage source inverter performances: (a) Sliding mode control method. (b) Conventional method PI control

Figure 5. Active power injected Figure 6. THD of the current injected into the electrical grid
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