Simplified Active Power and Reactive Power Control with MPPT for Three-Phase Grid-Connected Photovoltaic Inverters Thong-In Suyata and Sakorn Po-Ngam Power Electronics and Motor Drives Laboratory (PEMD LAB) Department of Electrical engineering, Faculty of Engineering King’s Mongkut University of Technology Thonburi , Thailand E-mail:
[email protected] and
[email protected] Abstract—This paper presents the simplified active power and reactive power control with the maximum power point tracking (MPPT) for three-phase grid-connected photovoltaic (PV) inverters. With the proposed control strategy, the perturbation and observation method is used for the simple MPPT algorithm and the current command on the rotating reference frame is regulated by the feedback and feedforward controller. In order to guarantee the all maximum power is transferred to the grid, the d-axis current or active power command is calculated from the PV power. Moreover, the design guidelines of phase-locked loop (PLL) and current controller are also presented. Validity of the proposed grid-connected inverters is confirmed by simulation. Keywords- grid-connected photovoltaic inverters; maximum power point tracking; power and reactive power control.
I.
INTRODUCTION
Because of its quietness and cleanness, the photovoltaic (PV) power generation system has become the most promising renewable energy source for residential applications [1]. Since the best way to utilize the PV power is to inject it into the ac mains without using energy storage facilities, the gridconnected PV inverter is always necessary for the PV power system [2]. Moreover, the PV inverter is a potential candidate to provide reactive power for the utility grid to improve its power quality. As a result, the PV inverter with the reactive power supply has a very important role in the PV power system nowadays [3]. In the PV power conditioning system, the maximum power point tracking (MPPT) control technique is required to extract the maximum possible power from the PV array in order to achieve maximum operating efficiency, the current regulator is needed to control the active and reactive power. In addition, the phase-locked loop (PLL) is also needed to receive the grid voltage and current information, such as the frequency, phase angle and amplitude, for controlling overall system. Moreover, all of the maximum power from PV array should be transfered to the grid. This paper presents the q-axis and d-axis current command from demanded reactive power and maximum power PV
978-1-4799-2993-1/14/$31.00 ©2014 IEEE
array, respectively. These currents are regulated via feedback and feedforward controller. For simple MPPT algorithm [4], the perturbation and observation method is used. In order to receive grid voltage and current information, the space vector phase-locked loop is also introduced. Moreover, design guidelines of PLL and current controller are psesented. Furthermore, an analysis, design-concept and simulation are detailed. Finally simulation results verify feasibility of the proposed control schemes. PHOTOVOLTAIC POWER CONDITIONING SYSTEM
II.
Fig. 1 shows circuit configuration of the three-phase gridconnected PV inverters. The inverter is composed of a PV array, dc/dc boost converter, dc-link, dc/ac inverter and current filter. The boost converter is operated with the MPPT function. The active and reactive powers are transferred to the grid by the three-phase inverter. Boost Converter
I pv
Lb V pv
+ −
C pv Sb
3Phase Inverter
Db Cb
S1 +
−
u
S2
S3
v
Vdc
w
S4
S5
igu igv igw
L
vgu vgv vgw
n
S6
Figure 1. Circuit configuration of the three-phase gridconnected PV inverters. The parameters of three-phase 380V/50Hz PV power conditioning system are composed of the boost converter and three-phase inverter switching frequency
f s = 20kHz , C pv = Cb = 100μ F , Lb = 0.1mH and L=10mH . A. MPPT Algoritym In this subsection, the MPPT algorithm based-on the perturbation and observation [4] is described. These method measures the PV power to judge the momentary operating region. According to the region, the duty cycle (D) of boost converter is increased or decreased such that the system
operates close to the maximum power point. Because the method only compares the PV power, implementation is simple. Fig. 2 shows the MPPT algorithm, where Ppv (k ) is
reference frame, the vq equal to zero when the rotating reference frame is synchronized with the grid voltage then P and Q can be obtained by (6).
the present PV power, whereas Ppv ( k − 1) is previous value. Ppv
MPP Ppv ( k ) < Ppv ( k − 1)
Ppv (k ) > Ppv (k − 1)
Increase D
Decrease D
D
Figure 2. The MPPT algorithm. B. Active and Reactive Power Control The proposed active and reactive power control are introduced in this subsection. In Fig. 4, 3/2 and 2/3 are the transformation matrix between there phase and space vector quantity as shown in (1) and (2), respectively. Where f is the voltage or current. ⎡ fα ⎤ ⎢ ⎥= ⎣ fβ ⎦
⎡f ⎤ −1 / 2 ⎤ ⎢ u ⎥ 2 ⎡1 − 1 / 2 ⎢ ⎥ fv 3 ⎣0 3 / 2 − 3 / 2 ⎦ ⎢ ⎥ ⎢⎣ f w ⎥⎦
(1)
⎡ fu ⎤ ⎢f ⎥= ⎢ v⎥ ⎢⎣ f w ⎥⎦
0 ⎤ ⎡ 1 ⎥ ⎡ fα ⎤ 2⎢ 3/ 2⎥⎢ ⎥ ⎢ −1 / 2 3⎢ ⎥ ⎣ fβ ⎦ ⎣ −1 / 2 − 3 / 2 ⎦
(2)
Fig. 3 shows the stationary and rotating reference frame, (3)-(4) show the axis-transform and inverse axis-transform matrix, respectively. Where “ → ” denotes the space vector quantity, subscript d,q are components on the rotating reference frame and α , β are components on the stationary reference frame. The ω (= dθ / dt ) is the angular frequency of grid voltage. β
ω = dθ dt
d q
Rotating reference frame fd
G f
fβ
θ
fq
α
fα Stationary reference frame
Figure 3. Two reference frames used in proposed control. ⎡ f d ⎤ ⎡ cosθ ⎢ ⎥= ⎢ ⎣ f q ⎦ ⎣ − sin θ ⎡ fα ⎤ ⎡ cosθ ⎢ f ⎥= ⎢ ⎣ β ⎦ ⎣ sin θ
sin θ ⎤ ⎡ fα ⎤ ⎢ ⎥ cos θ ⎥⎦ ⎣ f β ⎦ − sin θ ⎤ ⎡ f d ⎤ ⎢ ⎥ cosθ ⎥⎦ ⎣ f q ⎦
(3) (4)
In the stationary reference frame, the active power (P) and reactive power (Q) are calculated by (5). In the rotating
P = vα iα + vβ iβ , Q = vα iβ − vβ iα
(5)
P = vd id + vq iq = vd id , Q = vd iq
(6)
In order to guarantee the all maximum power is transferred to the grid, the d-axis current or active power command ( id∗ ) is proposed as shown in (7). To control the reactive power, from (6), the q-axis current or reactive power command ( iq∗ ) is obtained in (8). id∗ = P* / vd = Ppv / vd ⇒ Pmax / vd (7)
iq∗ = Q∗ / vd
(8)
In Fig. 4, the state equation on stationary reference frame and rotating reference frame are shown in (9) and (10), respectively. Where “*” denotes the commanded value and “^” denotes the estimated value from the PLL. G G G di v − vg (9) = dt L d ⎡id ⎤ ⎡ 0 − ω ⎤ ⎡id ⎤ ⎡1/ L 0 ⎤ ⎡vd − vgd ⎤ ⎥ (10) ⎢ ⎥=⎢ ⎥⎢ ⎥+⎢ ⎥⎢ dt ⎣iq ⎦ ⎣ω 1 ⎦ ⎣iq ⎦ ⎣ 0 1/ L ⎦ ⎢⎣vq − vgq ⎥⎦ In the steady state condition, equation (10) becomes (11), therefore, the voltage commands are presented and shown in (12). Where vd′ and vq′ are the voltage from the current controller on d-axis and q-axis, respectively. The proposed control schemes are shown in Fig. 4. vd = vgd − ω Liq , vq = vgq + ω Lid ∗ d
v =
vd′ N
feedback term
∗ q
+ vgd − ωˆ Liq , v =
feedforward term
vq′ N
feedback term
+
(11) ˆ Li ω Nd
(12)
feedforward term
C. Design of Space vector PLL In the utility system, PLL control is needed to synchronize inverter output voltage to the inter-connected utility, therefore, the space vector PLL is introduced in this subsection. The phase voltages of the grid are detected and transformed to space vector quantity. On the rotating reference frame, the vq equal to zero when the rotating reference frame is synchronized with the grid voltage. Therefore, the vq is regulated to zero by the PI controller. Fig. 5 shows the block diagram of space vector PLL. In order to design the PI controller, the small-signal of the vq is analyzed. When vq is controlled by the PLL, a relation of vq is shown in (13). vq = −vα sin θˆ + vβ cos θˆ = − 3 / 2vm sin(θˆ − θ ) = − 3 / 2vm sin(Δθ ) (13)
Around the equilibrium operating conditions, the Δθ is very small, therefore, the sin(Δθ ) is about Δθ . The small-signal block diagram of space vector PLL as shown in Fig. 6.
Vpv +
C pv
−
and 2.51, respectively. Fig. 7 shows the phase margin ( = 76D ) at ω0 = 62.8 rad / s of the control as designed.
Pmax = Ppv = V pv I pv
P∗ Q∗
1 / vgd 1 / vgd
i +
iq* + −
vgd
Controller
vd′ + +vd* vq′ + − v* q
* d
−
Vdc
Duty Cycle ( D)
MPPT
d, q
vβ* 2 / 3
G v G i
θˆ
ωˆ L α, β
iq
d, q
PLL
vgd
i( u ,v ,w )
3/ 2
iβ
G vg
v g ( u ,v , w )
3/ 2
vg β
Figure 4. The proposed control schemes.
v =0 −
+
+
θˆ
vgα
d,q
vgd = vm 3 / 2
θˆ
1 s
ωˆ
+
vgq
Grid
ω
PI Controller
α, β
v g ( u ,v , w )
3/ 2
vg β
Figure 5. The block diagram of space vector PLL. PI Controller
vq∗ = 0 −
+ +
vm 3 / 2
+
ω
+
Δθ
θ
−
Figure 6.The small-signal block diagram of space vector PLL. From Fig. 6, the cross-over frequency ( ω0 ) of the looptransfer function should be reduced the twice frequency of the grid voltage. At the ω0 , the loop- transfer function could be expressed in (10). k ⎛ G ( s ) H ( s) s= jω = ⎜ k p + i 0 s ⎝
-135
-180
⎞ ⎛ vm 3 / 2 ⎞ =1 ⎟⎟ ⎟ ⎜⎜ s ⎠⎝ ⎠ s= jω
0
10
(10)
0
For the adequate phase margin, the corner frequency ( ωcn = ki / k p ) of PI controller should be less than ω0 .In this paper, ω0 is selected equal to 10% of the twice frequency and
1
2
10
3
10
Frequency (rad/sec)
Figure 7. Phase margin of the PLL control as designed. D. Design of Current Controller To control the commanded active and reactive power, the current control is discussed in this subsection. From the commanded voltage as previously presented in (12), the d-axis current loop as shown in Fig. 8. It should be noted that the loop-transfer function is similar to the PLL control, therefore, the PI controller as designed in the same manner. To require the rise-time ( tr ) about 2.2 ms, from tr ≈ 2.2 / ω0 , the crossover frequency ( ω0 ) is calculated equal to 1000 rad/s. and the corner frequency is selected equal to 25% of cross-over frequency. Then the k p and ki are 9.701 and 2405, respectively. The PI gain of q-axis current controller is used in the same value. Fig. 9 shows the phase margin ( = 76D ) at ω0 = 1000 rad / s of the control as designed. III.
θˆ
1 s
ωˆ
0
10
PLL : Phase − Locked Loop
∗ q
20
-40 -90
L
iα
vgα
θˆ ωˆ
40
-20
Current Controller
id
Bode Diagram Gm = -Inf dB (at 0 rad/sec) , Pm = 76 deg (at 62.8 rad/sec) 60
+
v(*u ,v , w) 3φ VSI
*
vα
α, β
+
−
Magnitude (dB)
PV Array
ωcn is selected equal to 25% of ω0 . From these design, ω0 = 62.8 rad / s and ωcn = 15.7 rad / s , the k p and ki are 0.16
Boost Converter
Phase (deg)
I pv
SIMULATION RESULTS
To verify the feasibility of proposed control schemes, the simulation is presented in this section. The PSIM software is used for this simulation. In the standard solar intensity ( 1000W / m 2 ) and at the maximum power (4080W), the PV module voltage and current are 583V and 7A, respectively. The simulation results are shown in Fig. 10 - 11. Test 1: Key waveforms of the proposed PV inverter with constant active power, the solar intensity (S) is set to 1000W / m 2 , but various reactive powers is shown in Fig. 10. Fig. 10 shows key waveforms of the reactive power command ( Q* ) and inject or absorb reactive power ( Q ), uphase grid voltage and current and three-phase grid current. In the beginning, the Q* is set to 0 var. At time interval t1 , the Q* is abruptly changed from 0 to 2000 var. Thus, the amplitude and the phase angle of igu rise due to the increment of reactive power command. Likewise, at time interval t3 , the Q is suddenly absorbed the 2000 var from the grid. At time interval t2 and t4 , the proposed PV grid-connected inverter
Var
operates at the unity power factor with 4080W injected active power to the grid. It can be found that the proposed control schemes can smoothly control the PV inverter’s reactive output power without causing seriously active power drop. Test 2: Key waveforms of the proposed PV inverter under different active power or solar intensity (S) and at constant zero reactive power operation is shown in Fig. 11. Fig. 11 shows the maximum PV power, PV power and output active power, u-phase grid voltage and current and three phase grid current. In the beginning, the S is set to 500 W / m 2 or 2020 W active power command. At time interval
Q∗
Q>0
absorb Q
t1
iu
V, A
t2
t3
t4
Unity PF .
Lagging PF .
Unity PF .
vgu /31.1
Leading PF .
iu iv iw
A
Q
