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An advanced control strategy of PV system for low-voltage ride-through capability enhancement
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 109 (2014) 24–35 www.elsevier.com/locate/solener
An advanced control strategy of PV system for low-voltage ride-through capability enhancement Fang Yang, Lihui Yang ⇑, Xikui Ma The State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China Received 29 November 2013; received in revised form 10 August 2014; accepted 11 August 2014 Available online 1 September 2014 Communicated by: Associate Editor Arturo Morales-Acevedo
Abstract This paper presents a novel control strategy of the two-stage three-phase photovoltaic (PV) system to improve the low-voltage ridethrough (LVRT) capability according to the grid connection requirement. With the help of the new strategy, the PV array can generate active power as much as possible according to the depth of the grid voltage dip and the power rating of the grid inverter to keep power balance between the two sides of the inverter by operating in different modes. It is worthy of special mention that the proposed strategy can ensure the reactive power support when a low voltage fault occurs at the point of common coupling (PCC) without additional device. Besides, the new control method introduces a feed forward compensation reflecting the instantaneous current injecting into the DC-link from the PV array to smooth the DC-link voltage fluctuations during the grid fault. The effectiveness of the proposed control strategy has been demonstrated through various simulation scenarios. Compared with the conventional protection, the proposed control strategy can not only enhance the LVRT capability of the PV system, but also provide grid support through the active and reactive power control. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Low-voltage ride-through; Photovoltaic system; Reactive power; Grid inverter
1. Introduction With the increase of grid-connected photovoltaic (PV) generation systems, it is expected that their dynamic behavior is of a notable impact on the security and reliability of the power system during voltage dips (Carrasco et al., 2013). On this basis, many grid connection codes require that the PV system should stay connected to the grid during voltage dips, and this ability is termed as the lowvoltage ride-through capability. Among the different grid codes of LVRT, the most widely adopted one is the E.ON code which is proposed by Germany (Tian et al., 2012a; Wu et al., 2012; Yang and Blaabjerg, 2013). Fig. 1(a) shows the LVRT ⇑ Corresponding author. Tel.: +86 29 82668630x201.
E-mail address: [email protected] (L. Yang). http://dx.doi.org/10.1016/j.solener.2014.08.018 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
requirement of the distributed generation (DG) system, where the DG system should keep connected to the grid when it operates in the area above the curve. The DG system should stay connected to the grid for 150 ms when the terminal voltage drops to 0V and 625 ms when the terminal voltage drops to 30% of the normal value. At the same time, the DG system should inject the appropriate reactive current to support the grid voltage recovery according to Fig. 1(b). In order to achieve the E.ON requirement mentioned above, there are two major issues should be addressed (Alepuz et al., 2009; Marinopoulos et al., 2011). The first one is the over-current that can occur in the grid-connected inverter as well as the DC-link over-voltage. And the other one is the reactive current control, which is beneficial to grid voltage recovery but is always overlooked in some existing solutions.
F. Yang et al. / Solar Energy 109 (2014) 24–35
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Ug/Ugn Fig. 1. The E.ON code for low-voltage ride-through (LVRT). (a) The LVRT requirement and (b) the reactive current requirement during the grid voltage fault.
Among the existing LVRT control methods, the chopper circuit with a resistor across the DC bus (Erlich et al., 2007; Tian et al., 2012b,c; Yang et al., 2010) is the mostly used one. During the faults, the resistor will exhaust the extra power generated by the PV array to keep the power balance between the DC and AC side of the grid inverter. Consequently, the over-voltage on the DC-link and the over-current occurred in the AC-side of the grid inverter are limited to fulfill the LVRT requirement. However, this strategy does not pay attention to the reactive current support, which is necessary in the E.ON code. Moreover, with extra hardware, the chopper circuit will not only increase the costs but also decrease the system reliability. Up to now, some new methods have been proposed for reducing the amplitude of the output current of the grid inverter as well as the DC-link over-voltage during the faults. Based on the single-phase PQ theory and the PR control scheme, a power control method is proposed for the single-stage single-phase photovoltaic system (Yang et al., 2013; Yang and Blaabjerg, 2013). The effectiveness of this method has been validated by simulations and experiments, but the performance in more serious grid fault situations has not been discussed. By switching to Non-MPPT operation mode, the two-stage single-phase PV system can realize the LVRT but without reactive power support (Wu et al., 2012). For grid stabilization of the grid-connected PV system, a control strategy is put forward to realize both the active and reactive power control, but the DC-link over-voltage is neglected (Bae et al., 2013). The current limitation is adopted to help protecting the hardware from the damage of over-current but the power balance is still an urgently need to be addressed issue (Benz et al., 2010). The references (Azevedo et al., 2009;
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Islam et al., 2011; Reisi et al., 2012; Tian et al., 2012a; Zhang et al., 2011) just pay attention to improving the quality of the output waveform of the PV system in low voltage duration, but ignore the reactive power support requirement by some grid codes. Moreover, the zero voltage ride-through (ZVRT) which is the most stringent status is not discussed in all the references mentioned above. This paper presents an advanced control strategy for both the DC/DC converter and the grid-connected inverter to improve the LVRT capacity of the two-stage threephase PV system, without using additional hardware. The main idea is to decrease the output power of the PV array through controlling the DC/DC converter according to the depth of the voltage dip so that the power in the PV generation system could keep balance during the grid voltage dip, and the over-voltage and over-current can be restrained. Simultaneously, the grid inverter delivers the specified reactive current to the grid according to the E.ON. In order to smooth the fluctuations of the DC-link voltage, a compensation term reflecting the instantaneous current injecting into the DC-link from the PV array is applied in the DC-link voltage controller. Compared with the conventional methods, the proposed method can not only effectively reduce the over-current and over-voltage in the PV system during the grid voltage dip, but also provide the reactive power support to the grid. Simulation studies are presented to validate the effectiveness of the proposed control strategy. 2. Modeling of the two-stage three-phase PV system As shown in Fig. 2, a two-stage three-phase PV system contains the PV array, the boost circuit, the grid inverter and the control system. The control system is composed of two control levels including the boost circuit control and the grid inverter control. The boost stage controls the output power of the PV array and boosts the voltage of the PV array to an appropriate level so that the grid inverter could work regularly. The grid inverter stage controls the DC-link voltage and delivers the necessary current to the grid through the multiple-loop control of voltage and current (Letting et al., 2012). A detailed dynamic model of the PV system will be introduced below. 2.1. Mathematical models of PV The model of a PV cell is depicted in Fig. 3. The series resistor Rs and the parallel resistor Rsh can be omitted in an ideal calculation and the characteristic of the photovoltaic cell (Tsai et al., 2008; Tsai, 2010) is expressed as qU PV I PV ¼ I sc I D0 e AKT 1 ð1Þ where Isc is the current produced by photons, and relates to the irradiance and the temperature of the cell. ID0 is the diode saturation current. And the output current of the PV cell IPV is a function of the PV cell voltage UPV. For
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practical application, the PV characteristic is usually converted to an explicit formula with the precondition of accuracy insurance. h i U PV I PV ¼ I sc 1 C 1 ðeC2 U oc 1Þ ð2Þ U m h i1 where C 1 ¼ 1 II msc eC2 U oc , C 2 ¼ UUocm 1 ln 1 II msc .
2.2. Mathematical model of grid inverter
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According to the mathematical model of the PV cell above, the PV characteristic curve variation with environmental impact can be obtained as shown in Fig. 4. No matter what the neighborhood, only one maximum power point (MPP) the PV cell has. By using the maximum power point tracking (MPPT) strategy, which is carried out by the boost circuit, the PV module can operate at its maximum power point as the temperature and the irradiance vary.
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The equations of the grid inverter can be given in a d-q frame rotating at the line frequency. 8 > L diLd þ RiLd xLiLq ¼ d d U dc ugd > < dt di ð3Þ L dtLq þ RiLq þ xLiLd ¼ d q U dc ugq > > : C dU dc ¼ U dc 3 d i þ d i dt
R
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0 PPV fault normal U dc Dip U dc * * - iLd iLd ud detection U dc ++ PI PI normal * dq/ PWM fault normal iLq =0 * iLq u q abc Inverter * * i fault Lq Iq / P + PI Calculation D P* Boost Non-MPPT U PV
I PV
MPPT U PV
I PV
Fig. 6. Proposed control scheme of the PV system during grid voltage dips.
where iL = iLd + jiLq is the output current vector of the grid inverter; d = dd + jdq is the grid inverter duty cycle vector; ug = ugd + jugq is the grid voltage vector; and Udc is the DC -link voltage. 2.3. PV module control strategy To track the PV array optimum operating point, a number of tracking techniques have been proposed (Enrique
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et al., 2010; Esram and Chapman, 2007; Xiao et al., 2011). Among all of the common MPPT techniques, the hill climbing method (Liu et al., 2008) has been widely used on account of its simplicity and feasibility. As shown in Fig. 4, both the voltage and the power change in the same direction when the PV module operates on the left of the MPP, and in the opposite direction when on the right of the MPP. Consequently, when operating on the left of the peak point, the subsequent voltage perturbation rises to reach the MPP if there is an increase in power, and vice versa. Such a process is repeated periodically until the optimal point is achieved. This algorithm is termed P&Q method. Similarly, the hill climbing method achieves the MPP through the duty cycle change instead of the voltage change. It is not hard to see that the system oscillates around the MPP. However, the oscillation can be ignored when the precision request is low. 2.4. Grid inverter control strategy In normal operation, the control scheme of the grid inverter is illustrated in Fig. 5. The control system adopts the double loop PWM control mode which is composed of an outer voltage loop and an inner current (active current and reactive current) loop, where the typical proportional-integral (PI) controllers are used for the regulation of the DC-link voltage and the grid current (Wu and Tao, 2009). The outter loop is used to stabilize or regulate the DC-link voltage. It should be noted that the output of the voltage loop is used as the active current reference. The grid inverter usually operates at unity power factor status so the reactive current reference is set zero. Both the active power and the reactive power are adjusted through the current control loop. In order to decouple the active current and the reactive current, the feed-forward decoupling structure is applied.
Table 1 Main parameters in simulation. Parameters of the PV panel
Maximum power Maximum power voltage Maximum power current Open circuit voltage Short circuit current Serial number Parallel number
P = 245 W Um = 29.49 V Im = 8.31 A Uoc = 37.72 V Isc = 9.01 A Ns = 20 Np = 102
Parameters of the converters
Grid voltage amplitude DC-link voltage Grid frequency LR filter of the grid inverter DC-link capacitor Switching frequency of grid inverter Inductor of the boost converter Switching frequency of boost converter PI parameters of the active current loop PI parameters of the reactive current loop PI parameters of the voltage loop
Ug = 380 V Udc = 750 V x = 2p * 50 rad/s L = 0.51 mH, R = 0.66 mX Cdc = 0.03 F f = 2 kHz LB = 2mH fB = 2 kHz Kid = 0.8, sid = 0.005 Kiq = 6, siq = 0.008 Kiv = 2.3, siv = 0.01
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Fig. 7. Simulated responses of PV system when the voltage drops to zero. (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current (d) active power.
3. Proposed low voltage ride through strategy 3.1. Overview of the proposed control method When a low voltage fault occurs, the incoming power from the PV array and the power flowing into the grid are imbalanced which will lead to transient excessive voltage at DC-side and over-current at AC-side. In order to protect the power electronic devices from the damage of over-voltage and over-current, the LVRT strategy is introduced to ensure that the PV system can keep connected to the fault grid by decreasing both the over-voltage and over-current. The control scheme of the proposed LVRT strategy during grid voltage dips is shown in Fig. 6. It contains the grid
fault detection, the power calculation, the output power controller for the PV array and the grid inverter controller. The PV system operates in MPPT mode under the normal situation. Once the grid voltage sag is detected, the PV array will switch to Non-MPPT operation mode and generate the appropriate active power according to the voltage sag depth to keep the power balance of the system. In addition, the grid inverter will provide the required reactive current to help the voltage recovery. In order to smooth the fluctuations of the DC-link voltage, a feed forward compensation term is applied in the DC-link voltage control (Xie et al., 2013; Yang et al., 2012). The parameters of all the PI controllers are tuned according to the typical II-type system by using the engineering design method in
F. Yang et al. / Solar Energy 109 (2014) 24–35
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Fig. 8. Simulated responses of PV system when the voltage drops 70%. (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current (d) active power.
order to ensure better anti-disturbance performance (Li et al., 2011; Wang et al., 2006; Wang and Li, 2006). The major difference from other methods is that the proposed control strategy can provide active and reactive power according to the depth of the grid voltage dip to improve the energy captured from the PV array and help the grid voltage recovery during the fault conditions, and significantly reduce the oscillations in the DC-link voltage and the grid inverter current at AC-side.
the voltage sag detection is necessary for LVRT control (Silvestre et al., 2013). In this paper, the root mean square (RMS) method, which computes the RMS value of the grid voltage using Eq. (4) without additional transformation, is adopted to detect the grid fault, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U g ¼ U 2gd þ U 2gq ð4Þ where Ugd is the d component of grid voltage while Ugq is the q component.
3.2. Gird fault detection 3.3. Reactive power calculation and control It is obvious that the system should convert from normal operation status to grid fault operation status as soon as the voltage dip is detected. Therefore, a fast method of
As the control reference, the specified reactive current calculation is the key to meet the LVRT requirement dur-
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Fig. 9. Simulated responses of PV system when the voltage drops 30%. (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current (d) active power.
ing the grid voltage dip as shown in Fig. 1(b). According to Fig. 1(b), depending on the magnitude of voltage sags, the ratio of the required reactive current to the nominal current can be expressed piecewise, corresponding to the line A, B and C, respectively. 8 0 U g > 0:9U gn > < Ug I qratio ¼ 2 2 U gn 0:9U gn P U g > 0:5U gn ð5Þ > : 1 U g 6 0:5U gn where Ug and Ugn are the amplitude values of the present grid voltage and the normal grid voltage, respectively (Wu et al., 2012; Yang and Blaabjerg, 2013). Hence, the reference value of the reactive current during the voltage dip is given as
I q ¼ I rated I qratio
ð6Þ
where Irated is the rated value of the grid inverter current. In normal operation, the reactive power reference of the grid inverter is kept zero in order to achieve unity power factor. However, during the grid fault, the grid inverter should deliver the required reactive power to help the grid voltage recovery according to the LVRT requirement. So when the voltage sag is detected, the reference value of the reactive current will be set according to Eqs. (5) and (6). 3.4. Active power calculation and control When a low-voltage fault occurs, the incoming power from the PV array and the power flowing into the grid
F. Yang et al. / Solar Energy 109 (2014) 24–35
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Fig. 10. Simulation results for (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current and (d) active power with 100% voltage dip (NonSTC).
are imbalanced instantaneously, resulting in the transient over-current and over-voltage in the PV system. Therefore the key point of suppressing the over-current and overvoltage in the PV system is to reduce the imbalanced energy flowing through the system. Besides, it would be best to generate as much active power as possible during voltage dips in order to increase the energy captured from the PV array. Considering the voltage sag depth, the maximum allowed active current delivered to the grid through the grid inverter during faults is I p ¼ I rated
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 I 2qratio
ð7Þ
Iqratio can be calculated by Eq. (5). So the maximum allowed active power flowing through the grid inverter during faults can be obtained 3 P ¼ U gI p 2
ð8Þ
During the grid voltage fault, the boost circuit controller switches from the MPPT mode to the Non-MPPT mode. In the Non-MPPT mode, the MPPT algorithm is replaced by the PI controller to track the reference value of the active power P* which is calculated by Eqs. 5, 7 and 8. Therefore, the active power injected into the grid inverter will be controlled according to the ability of the active power delivery of the grid inverter during faults and the imbalanced energy flowing through the PV system can be reduced. When the grid voltage drops less than 50% of its normal value, that means the amplitude of the grid voltage is more than 50% of its normal value, the PV system will continue the active power production during faults, which can increase the energy captured from the PV array. It is worth to point out that when the grid voltage dips, the DC side input current may not be equal to the output current, leading to the fluctuation of the DC-link voltage. In order to smooth the fluctuation, the item Ppv/Udc, reflecting the instantaneous current injecting into the DClink from the PV array, is used as the compensation, where
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Fig. 11. Simulation results for (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current and (d) active power with 30% voltage dip (NonSTC).
Ppv is the instantaneous power injecting into the DC-link from the PV array and Udc is the voltage across the DClink capacitor. 4. Analysis of low voltage ride though strategies The complete PV system model as shown in Fig. 2 has been established and simulated in Matlab/Simulink. The components of the simulation model are built with standard electrical component blocks from the SimPowerSystems block in Matlab/Simulink library. The simulations are conducted on a 500 kW grid-connected PV system and the specific parameters of the studied system are listed in Table 1. For comparisons, two different control strategies of LVRT, the proposed method (named strategy A) and the conventional strategy using DC-link chopper circuit (named strategy B), are investigated not only for standard test condition (STC, the irradiation S is 1000 W/m2, the temperature T is 25 °C), but also for Non-STC (S = 800 W/m2, T = 15 °C).
4.1. ZVRT and LVRT in STC This section shows the performances of the PV system in STC. Three typical symmetrical three-phase short-circuit fault scenarios, which lead to the point of common coupling (PCC) voltage dropping to 0 for 150 ms, 30% and 70% for 625 ms, are investigated. Considering the worst situation, the PCC voltage drops to 0 at 1.5 s and lasts for 150 ms. The transient responses of the PV system with strategy A and B are shown in Fig. 7. Fig. 7 shows that these two control strategies can reduce the value of transient current and the DC-link voltage, and realize ZVRT. Obviously, with the proposed control strategy A, the PV system has better LVRT behaviors of the grid inverter current, DC-link voltage, reactive power and active power than the cases with the conventional strategy B. In Fig. 7(a) and (b), the over-current and the over-voltage with the control strategy A are significantly suppressed than the cases with the strategy B. Referring to Fig. 1(b), when the voltage drops to zero, the PV system is required
F. Yang et al. / Solar Energy 109 (2014) 24–35
to provide 100% reactive current into the grid. Hence, the PV system generates 1050A reactive current with the proposed method, as shown in Fig. 7(c), and the active power is zero in this situation as shown in Fig. 7(d). The situation in Fig. 8 shows a grid fault with 70% voltage drop and 625 ms duration. In Fig. 8(a) and (b), with the strategy A, the PV system has lower over-current and lower over-voltage than with the strategy B at the stage of voltage sag. The active and reactive power with the proposed and the conventional control strategy are shown in Fig. 8(c) and (d), respectively. According to the LVRT requirement as shown in Fig. 1(b), the converter should inject 100% reactive current into the grid when the voltage value is less than 50% of its normal value. Compared with the conventional control, the proposed control is able to provide corresponding reactive current, which is helpful for the voltage recovery. Due to 100% reactive current is needed with the proposed strategy, the active current is zero, resulting in zero active power. When the voltage drops 30% of its normal value, the simulation results are shown in Fig. 9. Fig. 9(a) and (b) show that with the proposed control strategy, the fluctuations of the inverter current and the DC-link voltage are significantly reduced than with the conventional strategy. It can be found in Fig. 9(c) that the proposed method can support the specified reactive current required in the E.ON code while the conventional method provides zero. Fig. 9(d) shows that the proposed strategy delivers less active power than the conventional method during the fault. The reason is that with the proposed method the PV system supplies the grid with the reactive current as required in the E.ON code. This will reduce the ability of the active power flowing through the inverter to the grid. Even so, the PV system can supply active power to the grid as much as possible within its limit.
33
provide the reactive current required in the grid code to help grid voltage recovery, meanwhile, supply the corresponding active power in Non-STC. From the simulation in this subsection, it can be found that the proposed LVRT control strategy is still effective when the actual environment, such as irradiation and temperature, varies. 5. Conclusion On the basis of the grid security requirement, the research focuses on the low-voltage ride-through control strategy of the two-stage three-phase photovoltaic system. The control strategy enables zero-voltage ride-through and could improve the low voltage ride through capability of the PV system. During the faults, the grid inverter can deliver the regulated reactive current and the active current as large as possible within its ability of power delivery to the grid. Furthermore, the new strategy also introduces the feed forward compensation to the DC-voltage controller so as to maintain a stable DC-link voltage in low voltage events. The simulation results show that the proposed control strategy could effectively protect the PV system from both over-voltage and over-current when low-voltage even zero-voltage dip occurs. Compared with the conventional protection, the new method performs a better transient behavior and can fulfill stringent grid code requirements during various low voltage events without additional device. Acknowledgement This work was supported by National Natural Science Foundation of China (No. 51207122).
4.2. ZVRT and LVRT in Non-STC Appendix A Taking into consideration that the PV array operating point varies with environmental influences, such as the irradiation and the temperature, the comparison of the two different control strategies of LVRT in Non-STC (S = 800 W/m2, T = 15 °C) is provided. Two scenarios have been adopted to verify the effectiveness of the proposed method: grid voltage drops 100% and 30% if fault lasts for 150 ms and 625 ms, respectively. When the voltage drops to zero at 1.5 s and lasts for 150 ms, the simulation results are shown in Fig. 10. It can be found that when the PV system operates in NonSTC, the proposed control strategy can also improve the ZVRT behavior and provide 100% reactive current to the grid. The situation in Fig. 11 displays a grid fault with 30% voltage drop and 625 ms duration. Fig. 11 shows that when operating in Non-STC, the PV system with the proposed control strategy still has better LVRT behavior than with the conventional strategy. The proposed control is able to
The parameters of all the PI controllers are tuned according to the typical II-type system by using the engineering design method in order to ensure better antidisturbance performance. Take the derivation process of the parameters of the PI compensators in the active current loop as an example. Considering the delay of signal sampling in the current loop (PWM switching period) and the small inertia characteristics of the PWM control, Ts presents the switching period and 0.5 Ts stands for the small inertia characteristics of PWM. Merging the small time constant Ts and 0.5 Ts and ignoring the resistance in the AC side of the grid inverter, the simplified structure is as shown in Fig. A.1. Kid and sid are the proportional gain and the integral constant of the PI controller, respectively. KPWM is the equivalent gain of PWM. From Fig. A.2, the open-loop transfer function of the current loop can be described as
34
F. Yang et al. / Solar Energy 109 (2014) 24–35 * iLd +
id
K id
s 1
id
s
K PWM
1
1.5Ts s +1
Ls
compensators have been revised based on the calculated value in order to realize better control.
iLd
-
References
Fig. A.1. Simplified structure of the active current loop.
U dc + *
Kv
v
s 1
0.75
1
s
(Tv 3Ts ) s +1
sC
v
U dc
Fig. A.2. Simplified structure of the voltage loop.
W oi ðsÞ ¼
K id K PWM sid s þ 1 sid L s2 ð1:5T s s þ 1Þ
ðA:1Þ
It can be seen that the inner current loop is a typical II-type system. In order to improve the current response speed as far as possible, the wide bandwidth hi is needed. In engineering, hi = sid/1.5Ts = 10. Thus, sid = 15Ts. According to the parameters tuning relationship of typical II-type system, we have K id K PWM hi þ 1 ¼ sid L 2s2id
ðA:2Þ
Therefore, the integral constant of the PI parameters can be computed by K id ¼
ðhi þ 1ÞL 2sid K PWM
ðA:3Þ
The same as the current loop, ignoring the disturbance of load current iL, the simplified structure of the voltage loop is as shown in Fig. A.2. Kv and sv are the proportional gain and the integral constant of the voltage PI controller, respectively. Ts is the switching period and Tv is the voltage sampling small inertia time constant. According to Fig. A.2, the open-loop transfer function of the voltage can be achieved. W ov ðsÞ ¼
0:75K v ðsv s þ 1Þ Csv s2 ððT v þ 3T s Þs þ 1Þ
Therefore, the bandwidth of the voltage loop is sv hv ¼ T v þ 3T s
ðA:4Þ
ðA:5Þ
Based on the parameters tuning relationship of typical II-type system, we have 0:75K v hv þ 1 ¼ 2 2 Csv 2hv ðT v þ 3T s Þ
ðA:6Þ
In engineering, hv is always set to 5. If Tv = Ts, the parameters of the voltage PI compensators can be obtained on the basis of Eqs. (A.5) and (A.6). Due to the approximation and simplification introduced in the design process, the actual parameters used in PI
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F. Yang et al. / Solar Energy 109 (2014) 24–35 nent. In: 2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 25–28 June 2012, Aalborg, Denmark, pp. 403–409. Tian, H., Gao, F., Ma, C., 2012c. Novel low voltage ride through strategy of single-stage grid-tied photovoltaic inverter with supercapacitor coupled. In: 2012 IEEE 7th International Power Electronics and Motion Control Conference (ECCE 2012), 2–5 June 2012, Harbin, China, pp. 1188–1192. Tsai, H.-L., 2010. Insolation-oriented model of photovoltaic module using Matlab/Simulink. Sol. Energy 84 (7), 1318–1326. Tsai, H.-L., Tu, C.-S., Su, Y.-J., 2008. Development of generalized photovoltaic model using MATLAB/SIMULINK. In: World Congress on Engineering and Computer Science (WCECS 2008), 22–24 Oct. 2008, San Francisco, CA, USA, pp. 846–851. Wang, Y.B., Li, J.W., 2006. A novel high-performance single-phase PFC approach based on one-cycle control. In: 32nd Annual Conference on IEEE Industrial Electronics, 6–10 Nov. 2006, Paris, France, pp. 1763– 1768. Wang, Y.B., Li, J.W., Yu, J., 2006. Comprehensive analysis and design for one-cycle controlled DC side APF. In: IEEE International Conference on Industrial Technology, 15–17 Dec. 2006, Mumbai, India, pp. 750– 755. Wu, H.B., Tao, X.F., 2009. Three phase photovoltaic grid-connected generation technology with MPPT function and voltage control. In: 2009 International Conference on Power Electronics and Drive Systems (PEDS 2009), Taipei, Taiwan, 2–5 Jan. 2009, pp. 1295–1300. Wu, Y.-S., Chang, C.-H., Chen, Y.-M., Cheng, C.-S., Liu, C.-W., Chang, Y.-R., 2012. The current control of PV inverter for low voltage ride through. In: 15th International Power Electronics and Motion Control
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Conference, EPE-PEMC 2012 ECCE Europe, 4–6 Sept. 2012, Novi Sad, Serbia, LS1d.4-1-LS1d.4-6. Xiao, W.D., Elnosh, A., Khadkikar, V., Zeineldin, H., 2011. Overview of maximum power point tracking technologies for photovoltaic power systems. In: 37th Annual Conference of the IEEE Industrial Electronics Society, 7–10 Nov. 2011, Melbourne, Australia, pp. 3900–3905. Xie, D.L., Xu, Z., Yang, L.H., Ostergaard, J., Xue, Y.X., Wong, K.P., 2013. A comprehensive LVRT control strategy for DFIG wind turbines with enhanced reactive power support. IEEE Trans. Power Syst. 28 (3), 3302–3310. Yang, Y.H., Blaabjerg, F., 2013. Low-voltage ride-through capability of a single-stage single-phase photovoltaic system connected to the lowvoltage grid. Int. J. Photoenergy. http://dx.doi.org/10.1155/2013/ 257487. Yang, J., Fletcher, J.E., O’Reilly, J., 2010. A series dynamic resistor based converter protection scheme for doubly-fed induction generator during various fault conditions. IEEE Trans. Energy Convers. 25 (2), 422– 432. Yang, L.H., Xu, Z., Ostergaard, J., Dong, Z.Y., Wong, K.P., 2012. Advanced control strategy of DFIG wind turbines for power system fault ride through. IEEE Trans. Power Syst. 27 (2), 1318–1326. Yang, Y.H., Blaabjerg, F., Zou, Z.X., 2013. Benchmarking of grid fault modes in single-phase grid-connected photovoltaic systems. IEEE Trans. Indust. Appl. 49 (5), 2167–2176. Zhang, Y.J., Ma, L., Zheng, T.Q., 2011. Application of feedback linearization strategy in voltage fault ride-through for photovoltaic inverters. In: 37th Annual Conference of the IEEE Industrial Electronics Society, 7–10 Nov. 2011, Melbourne, Australia, pp. 4666–4671.
ScienceDirect Solar Energy 109 (2014) 24–35 www.elsevier.com/locate/solener
An advanced control strategy of PV system for low-voltage ride-through capability enhancement Fang Yang, Lihui Yang ⇑, Xikui Ma The State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China Received 29 November 2013; received in revised form 10 August 2014; accepted 11 August 2014 Available online 1 September 2014 Communicated by: Associate Editor Arturo Morales-Acevedo
Abstract This paper presents a novel control strategy of the two-stage three-phase photovoltaic (PV) system to improve the low-voltage ridethrough (LVRT) capability according to the grid connection requirement. With the help of the new strategy, the PV array can generate active power as much as possible according to the depth of the grid voltage dip and the power rating of the grid inverter to keep power balance between the two sides of the inverter by operating in different modes. It is worthy of special mention that the proposed strategy can ensure the reactive power support when a low voltage fault occurs at the point of common coupling (PCC) without additional device. Besides, the new control method introduces a feed forward compensation reflecting the instantaneous current injecting into the DC-link from the PV array to smooth the DC-link voltage fluctuations during the grid fault. The effectiveness of the proposed control strategy has been demonstrated through various simulation scenarios. Compared with the conventional protection, the proposed control strategy can not only enhance the LVRT capability of the PV system, but also provide grid support through the active and reactive power control. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Low-voltage ride-through; Photovoltaic system; Reactive power; Grid inverter
1. Introduction With the increase of grid-connected photovoltaic (PV) generation systems, it is expected that their dynamic behavior is of a notable impact on the security and reliability of the power system during voltage dips (Carrasco et al., 2013). On this basis, many grid connection codes require that the PV system should stay connected to the grid during voltage dips, and this ability is termed as the lowvoltage ride-through capability. Among the different grid codes of LVRT, the most widely adopted one is the E.ON code which is proposed by Germany (Tian et al., 2012a; Wu et al., 2012; Yang and Blaabjerg, 2013). Fig. 1(a) shows the LVRT ⇑ Corresponding author. Tel.: +86 29 82668630x201.
E-mail address: [email protected] (L. Yang). http://dx.doi.org/10.1016/j.solener.2014.08.018 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
requirement of the distributed generation (DG) system, where the DG system should keep connected to the grid when it operates in the area above the curve. The DG system should stay connected to the grid for 150 ms when the terminal voltage drops to 0V and 625 ms when the terminal voltage drops to 30% of the normal value. At the same time, the DG system should inject the appropriate reactive current to support the grid voltage recovery according to Fig. 1(b). In order to achieve the E.ON requirement mentioned above, there are two major issues should be addressed (Alepuz et al., 2009; Marinopoulos et al., 2011). The first one is the over-current that can occur in the grid-connected inverter as well as the DC-link over-voltage. And the other one is the reactive current control, which is beneficial to grid voltage recovery but is always overlooked in some existing solutions.
F. Yang et al. / Solar Energy 109 (2014) 24–35
Ug/Ugn
(a)
1 0.9 0.7
0.45 0.3 0.2
0
(b)
0.625
1.5 t (s)
3
Line C Lin eB
50%
Line A
Iq/Irated
100%
0.15
20%
0 10% 20% 30% 40% 50% 60% 70% 80% 90%
1
Ug/Ugn Fig. 1. The E.ON code for low-voltage ride-through (LVRT). (a) The LVRT requirement and (b) the reactive current requirement during the grid voltage fault.
Among the existing LVRT control methods, the chopper circuit with a resistor across the DC bus (Erlich et al., 2007; Tian et al., 2012b,c; Yang et al., 2010) is the mostly used one. During the faults, the resistor will exhaust the extra power generated by the PV array to keep the power balance between the DC and AC side of the grid inverter. Consequently, the over-voltage on the DC-link and the over-current occurred in the AC-side of the grid inverter are limited to fulfill the LVRT requirement. However, this strategy does not pay attention to the reactive current support, which is necessary in the E.ON code. Moreover, with extra hardware, the chopper circuit will not only increase the costs but also decrease the system reliability. Up to now, some new methods have been proposed for reducing the amplitude of the output current of the grid inverter as well as the DC-link over-voltage during the faults. Based on the single-phase PQ theory and the PR control scheme, a power control method is proposed for the single-stage single-phase photovoltaic system (Yang et al., 2013; Yang and Blaabjerg, 2013). The effectiveness of this method has been validated by simulations and experiments, but the performance in more serious grid fault situations has not been discussed. By switching to Non-MPPT operation mode, the two-stage single-phase PV system can realize the LVRT but without reactive power support (Wu et al., 2012). For grid stabilization of the grid-connected PV system, a control strategy is put forward to realize both the active and reactive power control, but the DC-link over-voltage is neglected (Bae et al., 2013). The current limitation is adopted to help protecting the hardware from the damage of over-current but the power balance is still an urgently need to be addressed issue (Benz et al., 2010). The references (Azevedo et al., 2009;
25
Islam et al., 2011; Reisi et al., 2012; Tian et al., 2012a; Zhang et al., 2011) just pay attention to improving the quality of the output waveform of the PV system in low voltage duration, but ignore the reactive power support requirement by some grid codes. Moreover, the zero voltage ride-through (ZVRT) which is the most stringent status is not discussed in all the references mentioned above. This paper presents an advanced control strategy for both the DC/DC converter and the grid-connected inverter to improve the LVRT capacity of the two-stage threephase PV system, without using additional hardware. The main idea is to decrease the output power of the PV array through controlling the DC/DC converter according to the depth of the voltage dip so that the power in the PV generation system could keep balance during the grid voltage dip, and the over-voltage and over-current can be restrained. Simultaneously, the grid inverter delivers the specified reactive current to the grid according to the E.ON. In order to smooth the fluctuations of the DC-link voltage, a compensation term reflecting the instantaneous current injecting into the DC-link from the PV array is applied in the DC-link voltage controller. Compared with the conventional methods, the proposed method can not only effectively reduce the over-current and over-voltage in the PV system during the grid voltage dip, but also provide the reactive power support to the grid. Simulation studies are presented to validate the effectiveness of the proposed control strategy. 2. Modeling of the two-stage three-phase PV system As shown in Fig. 2, a two-stage three-phase PV system contains the PV array, the boost circuit, the grid inverter and the control system. The control system is composed of two control levels including the boost circuit control and the grid inverter control. The boost stage controls the output power of the PV array and boosts the voltage of the PV array to an appropriate level so that the grid inverter could work regularly. The grid inverter stage controls the DC-link voltage and delivers the necessary current to the grid through the multiple-loop control of voltage and current (Letting et al., 2012). A detailed dynamic model of the PV system will be introduced below. 2.1. Mathematical models of PV The model of a PV cell is depicted in Fig. 3. The series resistor Rs and the parallel resistor Rsh can be omitted in an ideal calculation and the characteristic of the photovoltaic cell (Tsai et al., 2008; Tsai, 2010) is expressed as qU PV I PV ¼ I sc I D0 e AKT 1 ð1Þ where Isc is the current produced by photons, and relates to the irradiance and the temperature of the cell. ID0 is the diode saturation current. And the output current of the PV cell IPV is a function of the PV cell voltage UPV. For
26
F. Yang et al. / Solar Energy 109 (2014) 24–35
S a1
L
S b1
S c1
La
ia
+ CPV
U dc
PV
Sa4
I PV
Boost Circuit Control
Rc
S c4 N
S b4
PWM
D
Rb
Lc
ic
-
U PV
Lb
ib
C
Ra
Grid ug
Current Control
iLq - i* =0 + Lq * iLd
-+ iLd
Voltage Control
U dc
U dc* -+
Fig. 2. Schematic diagram of the PV system.
IPV Ivd Isc
Rs Rsh
+
PV curve
(a)
S=1000 W/m2,T=25 oC 90
UPV
2
o
2
o
S=800 W/m ,T=25 C S=600 W/m ,T=25 C
80 70
PPV (W)
Fig. 3. Equivalent circuit of a PV cell.
100
60 50 40 30
practical application, the PV characteristic is usually converted to an explicit formula with the precondition of accuracy insurance. h i U PV I PV ¼ I sc 1 C 1 ðeC2 U oc 1Þ ð2Þ U m h i1 where C 1 ¼ 1 II msc eC2 U oc , C 2 ¼ UUocm 1 ln 1 II msc .
2.2. Mathematical model of grid inverter
10 0
0
5
10
15
20
25
20
25
UPV (V) PV curve
(b)
100
S=1000 W/m2,T=5 oC
90
S=1000 W/m2,T=15 oC
80
S=1000 W/m2,T=25 oC
70
PPV (W)
According to the mathematical model of the PV cell above, the PV characteristic curve variation with environmental impact can be obtained as shown in Fig. 4. No matter what the neighborhood, only one maximum power point (MPP) the PV cell has. By using the maximum power point tracking (MPPT) strategy, which is carried out by the boost circuit, the PV module can operate at its maximum power point as the temperature and the irradiance vary.
20
60 50 40 30 20
The equations of the grid inverter can be given in a d-q frame rotating at the line frequency. 8 > L diLd þ RiLd xLiLq ¼ d d U dc ugd > < dt di ð3Þ L dtLq þ RiLq þ xLiLd ¼ d q U dc ugq > > : C dU dc ¼ U dc 3 d i þ d i dt
R
2
d Ld
q Lq
10 0
0
5
10
15
UPV (V) Fig. 4. Characteristics curves of a PV cell in different situation when (a) the irradiance S varies and (b) the temperature T varies.
F. Yang et al. / Solar Energy 109 (2014) 24–35
+
Udc
i PI
u gd
* Ld
++ PI
+ -
Udc *
i Ld
L
i Lq
L
+ -
PI
i Lq =0 *
ud
-
+
+
uq
+ u gq
Fig. 5. Control scheme of the grid inverter in normal operations.
0 PPV fault normal U dc Dip U dc * * - iLd iLd ud detection U dc ++ PI PI normal * dq/ PWM fault normal iLq =0 * iLq u q abc Inverter * * i fault Lq Iq / P + PI Calculation D P* Boost Non-MPPT U PV
I PV
MPPT U PV
I PV
Fig. 6. Proposed control scheme of the PV system during grid voltage dips.
where iL = iLd + jiLq is the output current vector of the grid inverter; d = dd + jdq is the grid inverter duty cycle vector; ug = ugd + jugq is the grid voltage vector; and Udc is the DC -link voltage. 2.3. PV module control strategy To track the PV array optimum operating point, a number of tracking techniques have been proposed (Enrique
27
et al., 2010; Esram and Chapman, 2007; Xiao et al., 2011). Among all of the common MPPT techniques, the hill climbing method (Liu et al., 2008) has been widely used on account of its simplicity and feasibility. As shown in Fig. 4, both the voltage and the power change in the same direction when the PV module operates on the left of the MPP, and in the opposite direction when on the right of the MPP. Consequently, when operating on the left of the peak point, the subsequent voltage perturbation rises to reach the MPP if there is an increase in power, and vice versa. Such a process is repeated periodically until the optimal point is achieved. This algorithm is termed P&Q method. Similarly, the hill climbing method achieves the MPP through the duty cycle change instead of the voltage change. It is not hard to see that the system oscillates around the MPP. However, the oscillation can be ignored when the precision request is low. 2.4. Grid inverter control strategy In normal operation, the control scheme of the grid inverter is illustrated in Fig. 5. The control system adopts the double loop PWM control mode which is composed of an outer voltage loop and an inner current (active current and reactive current) loop, where the typical proportional-integral (PI) controllers are used for the regulation of the DC-link voltage and the grid current (Wu and Tao, 2009). The outter loop is used to stabilize or regulate the DC-link voltage. It should be noted that the output of the voltage loop is used as the active current reference. The grid inverter usually operates at unity power factor status so the reactive current reference is set zero. Both the active power and the reactive power are adjusted through the current control loop. In order to decouple the active current and the reactive current, the feed-forward decoupling structure is applied.
Table 1 Main parameters in simulation. Parameters of the PV panel
Maximum power Maximum power voltage Maximum power current Open circuit voltage Short circuit current Serial number Parallel number
P = 245 W Um = 29.49 V Im = 8.31 A Uoc = 37.72 V Isc = 9.01 A Ns = 20 Np = 102
Parameters of the converters
Grid voltage amplitude DC-link voltage Grid frequency LR filter of the grid inverter DC-link capacitor Switching frequency of grid inverter Inductor of the boost converter Switching frequency of boost converter PI parameters of the active current loop PI parameters of the reactive current loop PI parameters of the voltage loop
Ug = 380 V Udc = 750 V x = 2p * 50 rad/s L = 0.51 mH, R = 0.66 mX Cdc = 0.03 F f = 2 kHz LB = 2mH fB = 2 kHz Kid = 0.8, sid = 0.005 Kiq = 6, siq = 0.008 Kiv = 2.3, siv = 0.01
28
F. Yang et al. / Solar Energy 109 (2014) 24–35
Ia
(a)
Iq
2400
Strategy A Strategy B
2200
(c)
Stategy A Stategy B
1200
Strategy B
Stategy A
2000
1000
1800
800
1600
600
Iq (A)
Ia (A)
1400
1400 1200
400 200
1000
0
800 −200
Stategy B
600 −400
Strategy A
400 −600 1.4
1.6
1.8
2
2.2
2.4
1.4
2.6
1.6
1.8
t (s) Udc
(b)
2
2.2
2.4
2.6
t (s) P
5
900
Strategy A Strategy B
Strategy B
(d)
8
x 10
Strategy A Strategy B
7
850
6
800
Strategy B
5
P (W)
700
U
dc
(V)
750 4 3
Strategy A
650 2 Strategy A
600
1
550 500
0
1.4
1.6
1.8
2
2.2
2.4
2.6
t (s)
−1
1.4
1.6
1.8
2
2.2
2.4
2.6
t (s)
Fig. 7. Simulated responses of PV system when the voltage drops to zero. (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current (d) active power.
3. Proposed low voltage ride through strategy 3.1. Overview of the proposed control method When a low voltage fault occurs, the incoming power from the PV array and the power flowing into the grid are imbalanced which will lead to transient excessive voltage at DC-side and over-current at AC-side. In order to protect the power electronic devices from the damage of over-voltage and over-current, the LVRT strategy is introduced to ensure that the PV system can keep connected to the fault grid by decreasing both the over-voltage and over-current. The control scheme of the proposed LVRT strategy during grid voltage dips is shown in Fig. 6. It contains the grid
fault detection, the power calculation, the output power controller for the PV array and the grid inverter controller. The PV system operates in MPPT mode under the normal situation. Once the grid voltage sag is detected, the PV array will switch to Non-MPPT operation mode and generate the appropriate active power according to the voltage sag depth to keep the power balance of the system. In addition, the grid inverter will provide the required reactive current to help the voltage recovery. In order to smooth the fluctuations of the DC-link voltage, a feed forward compensation term is applied in the DC-link voltage control (Xie et al., 2013; Yang et al., 2012). The parameters of all the PI controllers are tuned according to the typical II-type system by using the engineering design method in
F. Yang et al. / Solar Energy 109 (2014) 24–35
Iq
Ia
(a)
Strategy A Strategy B
2200 2000
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1600
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800
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400 200
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800 Strategy A
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t (s) U
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dc
(b)
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t (s)
x 10
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P (W)
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dc
(V)
800
2 700
Strategy A
0 650 Strategy A
−2 600
0.5
1
1.5
t (s)
0.5
1
1.5
t (s)
Fig. 8. Simulated responses of PV system when the voltage drops 70%. (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current (d) active power.
order to ensure better anti-disturbance performance (Li et al., 2011; Wang et al., 2006; Wang and Li, 2006). The major difference from other methods is that the proposed control strategy can provide active and reactive power according to the depth of the grid voltage dip to improve the energy captured from the PV array and help the grid voltage recovery during the fault conditions, and significantly reduce the oscillations in the DC-link voltage and the grid inverter current at AC-side.
the voltage sag detection is necessary for LVRT control (Silvestre et al., 2013). In this paper, the root mean square (RMS) method, which computes the RMS value of the grid voltage using Eq. (4) without additional transformation, is adopted to detect the grid fault, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U g ¼ U 2gd þ U 2gq ð4Þ where Ugd is the d component of grid voltage while Ugq is the q component.
3.2. Gird fault detection 3.3. Reactive power calculation and control It is obvious that the system should convert from normal operation status to grid fault operation status as soon as the voltage dip is detected. Therefore, a fast method of
As the control reference, the specified reactive current calculation is the key to meet the LVRT requirement dur-
30
F. Yang et al. / Solar Energy 109 (2014) 24–35 Ia
(a) 1500
Iq
(c) Strategy A Strategy B
1400 Strategy B
1300
Strategy A
1200
500
Iq (A)
Ia (A)
Strategy A Strategy B
1000
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0 Strategy A
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800 700
0.5
1
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1.5
0.5
U 780
Strategy A Strategy B 770
1.5
P
5
dc
(b)
1 t (s)
t (s)
(d)
x 10 6
Strategy A Strategy B
5.5
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5
760
Strategy B
U
P (W)
750
dc
(V)
4.5
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740
4
T:\scanning\Elsevier\Journal\SE\4047\
3.5 3
730
2.5
720
Strategy A
2 710
0.5
1
1.5
0.5
1
1.5
t (s)
t (s)
Fig. 9. Simulated responses of PV system when the voltage drops 30%. (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current (d) active power.
ing the grid voltage dip as shown in Fig. 1(b). According to Fig. 1(b), depending on the magnitude of voltage sags, the ratio of the required reactive current to the nominal current can be expressed piecewise, corresponding to the line A, B and C, respectively. 8 0 U g > 0:9U gn > < Ug I qratio ¼ 2 2 U gn 0:9U gn P U g > 0:5U gn ð5Þ > : 1 U g 6 0:5U gn where Ug and Ugn are the amplitude values of the present grid voltage and the normal grid voltage, respectively (Wu et al., 2012; Yang and Blaabjerg, 2013). Hence, the reference value of the reactive current during the voltage dip is given as
I q ¼ I rated I qratio
ð6Þ
where Irated is the rated value of the grid inverter current. In normal operation, the reactive power reference of the grid inverter is kept zero in order to achieve unity power factor. However, during the grid fault, the grid inverter should deliver the required reactive power to help the grid voltage recovery according to the LVRT requirement. So when the voltage sag is detected, the reference value of the reactive current will be set according to Eqs. (5) and (6). 3.4. Active power calculation and control When a low-voltage fault occurs, the incoming power from the PV array and the power flowing into the grid
F. Yang et al. / Solar Energy 109 (2014) 24–35
31 Iq
I
a
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x 10
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dc
U (V)
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3 Strategy A
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1
600
0 550 500
−1 1.4
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1.8
2
2.2
2.4
t(s)
−2
1.4
1.6
1.8
2
2.2
2.4
t(s)
Fig. 10. Simulation results for (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current and (d) active power with 100% voltage dip (NonSTC).
are imbalanced instantaneously, resulting in the transient over-current and over-voltage in the PV system. Therefore the key point of suppressing the over-current and overvoltage in the PV system is to reduce the imbalanced energy flowing through the system. Besides, it would be best to generate as much active power as possible during voltage dips in order to increase the energy captured from the PV array. Considering the voltage sag depth, the maximum allowed active current delivered to the grid through the grid inverter during faults is I p ¼ I rated
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 I 2qratio
ð7Þ
Iqratio can be calculated by Eq. (5). So the maximum allowed active power flowing through the grid inverter during faults can be obtained 3 P ¼ U gI p 2
ð8Þ
During the grid voltage fault, the boost circuit controller switches from the MPPT mode to the Non-MPPT mode. In the Non-MPPT mode, the MPPT algorithm is replaced by the PI controller to track the reference value of the active power P* which is calculated by Eqs. 5, 7 and 8. Therefore, the active power injected into the grid inverter will be controlled according to the ability of the active power delivery of the grid inverter during faults and the imbalanced energy flowing through the PV system can be reduced. When the grid voltage drops less than 50% of its normal value, that means the amplitude of the grid voltage is more than 50% of its normal value, the PV system will continue the active power production during faults, which can increase the energy captured from the PV array. It is worth to point out that when the grid voltage dips, the DC side input current may not be equal to the output current, leading to the fluctuation of the DC-link voltage. In order to smooth the fluctuation, the item Ppv/Udc, reflecting the instantaneous current injecting into the DClink from the PV array, is used as the compensation, where
32
F. Yang et al. / Solar Energy 109 (2014) 24–35 Ia
(a)
1400
1200
(c) Strategy A Strategy B
Strategy B
Strategy A Strategy B
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I (A)
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q
Ia(A)
Iq 1000
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t(s)
(b)
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x 10
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Strategy B
4.5
Strategy B
dc
P(W)
4
U (V)
P
5
Udc
800
1.5
t(s)
750
3.5 3 2.5
Strategy A
Strategy A
2
700
1.5 1 0.5
650 0.5
1
1.5
t(s)
0.5
1
1.5
t(s)
Fig. 11. Simulation results for (a) Magnitude of the grid current (b) DC-link voltage (c) reactive current and (d) active power with 30% voltage dip (NonSTC).
Ppv is the instantaneous power injecting into the DC-link from the PV array and Udc is the voltage across the DClink capacitor. 4. Analysis of low voltage ride though strategies The complete PV system model as shown in Fig. 2 has been established and simulated in Matlab/Simulink. The components of the simulation model are built with standard electrical component blocks from the SimPowerSystems block in Matlab/Simulink library. The simulations are conducted on a 500 kW grid-connected PV system and the specific parameters of the studied system are listed in Table 1. For comparisons, two different control strategies of LVRT, the proposed method (named strategy A) and the conventional strategy using DC-link chopper circuit (named strategy B), are investigated not only for standard test condition (STC, the irradiation S is 1000 W/m2, the temperature T is 25 °C), but also for Non-STC (S = 800 W/m2, T = 15 °C).
4.1. ZVRT and LVRT in STC This section shows the performances of the PV system in STC. Three typical symmetrical three-phase short-circuit fault scenarios, which lead to the point of common coupling (PCC) voltage dropping to 0 for 150 ms, 30% and 70% for 625 ms, are investigated. Considering the worst situation, the PCC voltage drops to 0 at 1.5 s and lasts for 150 ms. The transient responses of the PV system with strategy A and B are shown in Fig. 7. Fig. 7 shows that these two control strategies can reduce the value of transient current and the DC-link voltage, and realize ZVRT. Obviously, with the proposed control strategy A, the PV system has better LVRT behaviors of the grid inverter current, DC-link voltage, reactive power and active power than the cases with the conventional strategy B. In Fig. 7(a) and (b), the over-current and the over-voltage with the control strategy A are significantly suppressed than the cases with the strategy B. Referring to Fig. 1(b), when the voltage drops to zero, the PV system is required
F. Yang et al. / Solar Energy 109 (2014) 24–35
to provide 100% reactive current into the grid. Hence, the PV system generates 1050A reactive current with the proposed method, as shown in Fig. 7(c), and the active power is zero in this situation as shown in Fig. 7(d). The situation in Fig. 8 shows a grid fault with 70% voltage drop and 625 ms duration. In Fig. 8(a) and (b), with the strategy A, the PV system has lower over-current and lower over-voltage than with the strategy B at the stage of voltage sag. The active and reactive power with the proposed and the conventional control strategy are shown in Fig. 8(c) and (d), respectively. According to the LVRT requirement as shown in Fig. 1(b), the converter should inject 100% reactive current into the grid when the voltage value is less than 50% of its normal value. Compared with the conventional control, the proposed control is able to provide corresponding reactive current, which is helpful for the voltage recovery. Due to 100% reactive current is needed with the proposed strategy, the active current is zero, resulting in zero active power. When the voltage drops 30% of its normal value, the simulation results are shown in Fig. 9. Fig. 9(a) and (b) show that with the proposed control strategy, the fluctuations of the inverter current and the DC-link voltage are significantly reduced than with the conventional strategy. It can be found in Fig. 9(c) that the proposed method can support the specified reactive current required in the E.ON code while the conventional method provides zero. Fig. 9(d) shows that the proposed strategy delivers less active power than the conventional method during the fault. The reason is that with the proposed method the PV system supplies the grid with the reactive current as required in the E.ON code. This will reduce the ability of the active power flowing through the inverter to the grid. Even so, the PV system can supply active power to the grid as much as possible within its limit.
33
provide the reactive current required in the grid code to help grid voltage recovery, meanwhile, supply the corresponding active power in Non-STC. From the simulation in this subsection, it can be found that the proposed LVRT control strategy is still effective when the actual environment, such as irradiation and temperature, varies. 5. Conclusion On the basis of the grid security requirement, the research focuses on the low-voltage ride-through control strategy of the two-stage three-phase photovoltaic system. The control strategy enables zero-voltage ride-through and could improve the low voltage ride through capability of the PV system. During the faults, the grid inverter can deliver the regulated reactive current and the active current as large as possible within its ability of power delivery to the grid. Furthermore, the new strategy also introduces the feed forward compensation to the DC-voltage controller so as to maintain a stable DC-link voltage in low voltage events. The simulation results show that the proposed control strategy could effectively protect the PV system from both over-voltage and over-current when low-voltage even zero-voltage dip occurs. Compared with the conventional protection, the new method performs a better transient behavior and can fulfill stringent grid code requirements during various low voltage events without additional device. Acknowledgement This work was supported by National Natural Science Foundation of China (No. 51207122).
4.2. ZVRT and LVRT in Non-STC Appendix A Taking into consideration that the PV array operating point varies with environmental influences, such as the irradiation and the temperature, the comparison of the two different control strategies of LVRT in Non-STC (S = 800 W/m2, T = 15 °C) is provided. Two scenarios have been adopted to verify the effectiveness of the proposed method: grid voltage drops 100% and 30% if fault lasts for 150 ms and 625 ms, respectively. When the voltage drops to zero at 1.5 s and lasts for 150 ms, the simulation results are shown in Fig. 10. It can be found that when the PV system operates in NonSTC, the proposed control strategy can also improve the ZVRT behavior and provide 100% reactive current to the grid. The situation in Fig. 11 displays a grid fault with 30% voltage drop and 625 ms duration. Fig. 11 shows that when operating in Non-STC, the PV system with the proposed control strategy still has better LVRT behavior than with the conventional strategy. The proposed control is able to
The parameters of all the PI controllers are tuned according to the typical II-type system by using the engineering design method in order to ensure better antidisturbance performance. Take the derivation process of the parameters of the PI compensators in the active current loop as an example. Considering the delay of signal sampling in the current loop (PWM switching period) and the small inertia characteristics of the PWM control, Ts presents the switching period and 0.5 Ts stands for the small inertia characteristics of PWM. Merging the small time constant Ts and 0.5 Ts and ignoring the resistance in the AC side of the grid inverter, the simplified structure is as shown in Fig. A.1. Kid and sid are the proportional gain and the integral constant of the PI controller, respectively. KPWM is the equivalent gain of PWM. From Fig. A.2, the open-loop transfer function of the current loop can be described as
34
F. Yang et al. / Solar Energy 109 (2014) 24–35 * iLd +
id
K id
s 1
id
s
K PWM
1
1.5Ts s +1
Ls
compensators have been revised based on the calculated value in order to realize better control.
iLd
-
References
Fig. A.1. Simplified structure of the active current loop.
U dc + *
Kv
v
s 1
0.75
1
s
(Tv 3Ts ) s +1
sC
v
U dc
Fig. A.2. Simplified structure of the voltage loop.
W oi ðsÞ ¼
K id K PWM sid s þ 1 sid L s2 ð1:5T s s þ 1Þ
ðA:1Þ
It can be seen that the inner current loop is a typical II-type system. In order to improve the current response speed as far as possible, the wide bandwidth hi is needed. In engineering, hi = sid/1.5Ts = 10. Thus, sid = 15Ts. According to the parameters tuning relationship of typical II-type system, we have K id K PWM hi þ 1 ¼ sid L 2s2id
ðA:2Þ
Therefore, the integral constant of the PI parameters can be computed by K id ¼
ðhi þ 1ÞL 2sid K PWM
ðA:3Þ
The same as the current loop, ignoring the disturbance of load current iL, the simplified structure of the voltage loop is as shown in Fig. A.2. Kv and sv are the proportional gain and the integral constant of the voltage PI controller, respectively. Ts is the switching period and Tv is the voltage sampling small inertia time constant. According to Fig. A.2, the open-loop transfer function of the voltage can be achieved. W ov ðsÞ ¼
0:75K v ðsv s þ 1Þ Csv s2 ððT v þ 3T s Þs þ 1Þ
Therefore, the bandwidth of the voltage loop is sv hv ¼ T v þ 3T s
ðA:4Þ
ðA:5Þ
Based on the parameters tuning relationship of typical II-type system, we have 0:75K v hv þ 1 ¼ 2 2 Csv 2hv ðT v þ 3T s Þ
ðA:6Þ
In engineering, hv is always set to 5. If Tv = Ts, the parameters of the voltage PI compensators can be obtained on the basis of Eqs. (A.5) and (A.6). Due to the approximation and simplification introduced in the design process, the actual parameters used in PI
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