Photovoltaic power generation is an intermittent power source. The integration of large-scale photovoltaic power stations will affect the power flow distribution of the grid, and large fluctuations may also threaten the frequency and voltage stability of the system. The model and parameters of photovoltaic power stations directly affect the accuracy of dynamic stability simulation analysis of power systems, and also have an impact on grid planning, operation, and the safety of grid-connected photovoltaic power stations. Only through the actual measurement of the model and parameters of photovoltaic power stations can the dispatching and operation department be provided with detailed and accurate models and parameters of grid-connected photovoltaic power stations, which plays an important role in the safe and stable operation of the system.
As an important part of a photovoltaic power station, the solar inverter should have certain low voltage ride-through capability, and can only be connected to the grid after passing the tests by relevant departments. At present, scholars at home and abroad have conducted in-depth research on the voltage ride-through control strategy of solar inverters. General Electric Company first proposed a simple photovoltaic power station power flow calculation model based on the power at the grid connection point, reflecting the equivalent power output characteristics of photovoltaic power generation. Our country has formulated the national standard GB/T 19964—2012 “Technical Regulations for Photovoltaic Power Stations Connected to Power Systems”, which specifies the technical requirements for grid connection of photovoltaic power stations in detail, and puts forward dynamic characteristic index requirements such as reactive current and active power during voltage ride-through. However, the standard only gives the technical indicators to be tested and does not give specific parameter detection methods. Parameter identification can provide a more accurate simulation model and control strategy parameters of grid-connected solar inverters.
In this paper, starting from the physical structure and general control logic of the solar inverter, combined with the simulation requirements of the power grid, the simplified requirements of electromechanical transient modeling are proposed. Based on this, the basic structure of the solar inverter model in the PSD-BPA electromechanical transient simulation program is analyzed. For the electromagnetic simulation model of the solar inverter provided by the manufacturer, detailed tests of low voltage ride-through and high voltage ride-through fault control characteristics are carried out. With a voltage fault step of 1%, detailed tests are carried out for low voltage ride-through and high voltage ride-through faults from 20% to 130%. Furthermore, considering the conditions under symmetrical and asymmetrical faults, the detailed characteristics of the solar inverter under all possible faults are obtained. Based on this, the control characteristics are analyzed, and the model parameters of PSD-BPA are identified. The simulation verification is carried out through the PSD-BPA program, which verifies the accuracy of the identified model parameters.
1. Photovoltaic power generation system model considering voltage ride-through characteristics
The transient stability model of a general photovoltaic power generation system in the PSD-BPA program contains multiple modules. The overall block diagram is shown in the following table description. The main modules include: (1) photovoltaic power generation model; (2) steady-state control module of the solar inverter, including normal active power control model and reactive power control model, active/reactive current limit model; (3) fault voltage ride-through module of the solar inverter, including high and low voltage state judgment model, fault ride-through active power control model, fault ride-through reactive power control model; (4) protection system module of the solar inverter. This research focuses on the fault ride-through power control model of the solar inverter.
1.1 Photovoltaic power generation model
The photovoltaic array is composed of multiple photovoltaic cells connected in series and parallel. The photovoltaic cell model can accurately express the I-V output external characteristics of the photovoltaic cell and be simplified according to the practical application parameters of the project. The photovoltaic array integration module is based on a single photovoltaic cell and is comprehensively designed and adjusted according to the series-parallel relationship of the single photovoltaic cell to express the output characteristics of the photovoltaic array.
First, the technical parameters of the photovoltaic cell are converted under actual temperature and light intensity conditions:
$$
\begin{aligned}
T’ &= T – T_{ref} \\
S’ &= \frac{S}{S_{ref}} – 1 \\
I’_{sc} &= I_{sc} \cdot \frac{S}{S_{ref}} \left(1 + aT’\right) \\
U’_{oc} &= U_{oc} \cdot \left(1 – cT’\right) \ln\left(e + bS’\right) \\
I’_{m} &= I_{sc} \cdot \frac{S}{S_{ref}} \left(1 + aT’\right) \\
U’_{m} &= U_{m} \cdot \left(1 – cT’\right) \ln\left(e + bS’\right)
\end{aligned}
$$
where \(I_{sc}\), \(V_{oc}\), \(I_{m}\), \(V_{m}\) are the short-circuit current, open-circuit voltage, maximum power point load current, and maximum power point load voltage, respectively. \(T\) is the photovoltaic cell temperature, \(S\) is the light intensity, and \(a\), \(b\), \(c\) are constants, with \(a=0.0015\,^{\circ}\mathrm{C}\), \(b=0.5\), \(c=0.0018\,^{\circ}\mathrm{C}\).
Then the following formula is used to calculate the photovoltaic cell current:
$$
I_L = I_{sc} \left[1 – C_1 \left( \exp\left(\frac{V}{C_2 V_{oc}}\right) – 1 \right) \right]
$$
$$
C_1 = \left(1 – \frac{I_m}{I_{sc}}\right) \exp\left(-\frac{V_m}{C_2 V_{oc}}\right)
$$
$$
C_2 = \left( \frac{V_m}{V_{oc}} – 1 \right) \left[ \ln\left(1 – \frac{I_m}{I_{sc}}\right) \right]^{-1}
$$
On the basis of the photovoltaic cell model, some corrections are made as follows:
$$
\begin{aligned}
I_{scc-AR} &= N_{sh} \cdot I_{scc} \\
I_{mm-AR} &= N_{sh} \cdot I_{mm} \\
U_{occ-AR} &= N_{se} \cdot U_{occ} \\
U_{mm-AR} &= N_{se} \cdot U_{mm}
\end{aligned}
$$
where \(I_{scc\_AR}\), \(I_{mm\_AR}\), \(U_{occ\_AR}\), \(U_{mm\_AR}\) are the short-circuit current, open-circuit voltage, maximum power point current, and maximum power point voltage of the photovoltaic array, respectively; \(N_{se}\) is the number of photovoltaic cells in series; \(N_{sh}\) is the number of photovoltaic cells in parallel.
1.2 Analysis of high and low voltage ride-through characteristics
The energy industry standard NB/T 32004—2018 “Technical Specifications for Photovoltaic Grid-connected Inverters” stipulates that large and medium-sized photovoltaic power stations should have certain high and low voltage ride-through capabilities when the grid is abnormal. During voltage ride-through, both active power and reactive power will change dramatically, which may cause the power system to lose stability. Therefore, during voltage ride-through, the grid-connected solar inverter needs to provide certain active and reactive power support. The dynamic characteristics of active and reactive power are shown in the following tables and formulas.
1.3 Mathematical model of the grid-connected solar inverter
1.3.1 Active power control strategy during voltage ride-through
After a voltage ride-through event occurs, the active power change process generally goes through three stages: the control process during the low voltage ride-through (segment A), the holding process after the low voltage ride-through ends (segment B), and the power recovery process (segment C). These three stages are controlled by different control modes. The control strategies of the three stages and the corresponding BPA-PSD commands are shown in Table 1.
| Segment | Command | Corresponding control |
|---|---|---|
| A (IP_FLG) | 0 | Specified current value |
| 1 | Initial current percentage | |
| 2 | Specified power value | |
| 3 | Initial power percentage | |
| B (IP_FLG2) | 0 | Specified current value |
| 1 | Initial current percentage | |
| 2 | Specified power value | |
| 3 | Initial power percentage | |
| C (IP_FLG3) | 0 | Immediate recovery |
| 1 | Constant slope rise | |
| 2 | Parabolic rise | |
| 3 | Fixed time slope rise |
During segment A, the calculation equation is as follows:
$$
\begin{aligned}
I_{P_{ref}} &= K_V \cdot V_t + K_I \cdot I_{P0} + I_{PSET}, \quad I_{P\_FLG}=1 \\
P_{ref} &= K_P \cdot P_0 + P_{SET}, \quad I_{P\_FLG}=2
\end{aligned}
$$
where \(I_{P0}\), \(V_t\), \(P_0\) are the initial active current, terminal voltage amplitude, and initial active power, respectively.
In segment B, the specified active current is calculated as:
$$
I_{P_{ref}} = \min\left(K_I \cdot I_{P0} + I_{PSET}, \quad I_{P0}\right), \quad I_{P\_FLG2}=0
$$
1.3.2 Reactive power control during and after voltage ride-through
Under normal conditions, the solar inverter generally does not output reactive power, or outputs a fixed reactive power. After entering the voltage ride-through state, the reactive power change process generally goes through three stages: the control process during the low voltage ride-through (segment D), the holding process after the low voltage ride-through ends (segment E), and the power recovery process (segment F). The control strategies of the three stages and the corresponding BPA-PSD commands are shown in Table 2.
| Segment | Command | Corresponding control |
|---|---|---|
| D (IQ_FLG1) | 0 | Calculate current according to voltage drop |
| 1 | Specified curve | |
| 2 | Specified reactive power | |
| 3 | Initial reactive current | |
| E (IQ_FLG2) | — | Specified reactive current |
| 0 | Immediately restore initial value | |
| 1 | Hold for a fixed time | |
| 2 | Exponential recovery | |
| F (IQ_FLG3) | 0 | Immediate recovery |
| 1 | Hold | |
| 2 | Slope recovery |
During segment D, the control equation is:
$$
\begin{aligned}
I_{Q_{ref}} &= K_V \cdot (V_{SET} – V_t) + K_I \cdot I_{Q0} + I_{QSET}, \quad I_{Q\_FLG1}=3 \\
Q_{ref} &= K_Q \cdot Q_0 + Q_{SET}, \quad I_{Q\_FLG1}=2
\end{aligned}
$$
where \(I_{Q0}\), \(Q_0\) are the initial reactive current and initial reactive power, respectively.
2. Symmetrical and asymmetrical fault characteristic testing of the solar inverter
From the above analysis, the fault ride-through model of the solar inverter is clear, but the parameters need to be determined according to the actual situation. In order to identify the parameters, it is necessary to conduct a comprehensive test of the fault control characteristics of the solar inverter. According to the Matlab simulation platform solar inverter model provided by a manufacturer, the low voltage ride-through and high voltage ride-through characteristics under symmetrical and asymmetrical faults are tested. In the test, the symmetrical and asymmetrical faults are respectively selected as three-phase short-circuit faults and two-phase short-circuit faults under small power operation, and the data are normalized.
After extracting the data, the low voltage ride-through and high voltage ride-through fault data are combined and divided into symmetrical and asymmetrical fault data sets, as shown in Tables 3 to 6.
| Case | Positive-sequence voltage | Active power | Reactive power | Active current | Reactive current |
|---|---|---|---|---|---|
| 1 | 0.071558 | 0.071558 | 0.071558 | 0.071558 | 0.071558 |
| 2 | 0.265627 | 0.000444 | 0.001983 | 0.282205 | 0.007464 |
| 3 | 0.401587 | 0.000194 | 0.004581 | 0.350683 | 0.011406 |
| 4 | 0.627894 | 0.000194 | 0.007342 | 0.337772 | 0.011693 |
| 5 | 0.903425 | 0.000212 | 0.983387 | 0.121117 | 1.088509 |
| 6 | 1.188283 | 0.000346 | 0.985720 | -0.047280 | 0.829533 |
| 7 | 1.277839 | 0.000587 | 0.984271 | -0.226150 | 0.434138 |
| Case | Positive-sequence voltage | Active power | Reactive power | Active current | Reactive current |
|---|---|---|---|---|---|
| 1 | 0.071860 | 0.002280 | 0.008600 | 0.082170 | 0.119710 |
| 2 | 0.265690 | 0.000250 | 0.002460 | 0.284620 | 0.009250 |
| 3 | 0.401560 | 0.000200 | 0.005030 | 0.350710 | 0.012530 |
| 4 | 0.627890 | 0.000190 | 0.007270 | 0.337780 | 0.011590 |
| 5 | 0.900570 | 0.000180 | 0.198420 | 0.124240 | 0.220330 |
| 6 | 1.187050 | 0.000350 | 0.197910 | -0.039600 | 0.166730 |
| 7 | 1.276640 | 0.000470 | 0.198440 | -0.222300 | 0.155440 |
| Case | Positive-sequence voltage | Active power | Reactive power | Active current | Reactive current |
|---|---|---|---|---|---|
| 1 | 0.362809 | 0.329424 | -0.049260 | 0.190974 | -0.135760 |
| 2 | 0.495584 | 0.263375 | -0.029250 | 0.262892 | -0.059020 |
| 3 | 0.594578 | 0.213880 | -0.015570 | 0.316415 | -0.026190 |
| 4 | 0.748527 | 0.131575 | 0.000197 | 0.268383 | 0.000264 |
| 5 | 0.936243 | 0.033642 | 0.985321 | 0.120586 | 1.052420 |
| 6 | 1.130007 | 0.065557 | 0.982656 | 0.062156 | 0.869602 |
| 7 | 1.189206 | 0.094632 | 0.977359 | -0.039720 | 0.821858 |
| Case | Positive-sequence voltage | Active power | Reactive power | Active current | Reactive current |
|---|---|---|---|---|---|
| 1 | 0.363182 | 0.329394 | -0.051240 | 0.189591 | -0.141080 |
| 2 | 0.495588 | 0.263373 | -0.028830 | 0.262819 | -0.058170 |
| 3 | 0.594577 | 0.213882 | -0.015320 | 0.316432 | -0.025760 |
| 4 | 0.748543 | 0.131576 | 0.000161 | 0.268381 | 0.000215 |
| 5 | 0.933531 | 0.033595 | 0.197353 | 0.123777 | 0.211405 |
| 6 | 1.125731 | 0.065810 | 0.196583 | 0.069561 | 0.174627 |
| 7 | 1.186799 | 0.097784 | 0.190591 | -0.037530 | 0.160593 |
3. Voltage ride-through control parameter identification and verification of the solar inverter
After identification, the parameters corresponding to the PSD-BPA active power control under symmetrical faults are shown in Table 7.
| Parameter | LVRT value | HVRT value |
|---|---|---|
| FLG1 | 2 | 1 |
| FLG1=1: Kp; FLG1=2: Kv | 0.000 | 1 |
| FLG1=1: /; FLG1=2: Ki | 0.090 | 0.000 |
| FLG1=1: Pset(MW); FLG1=2: IPset(A) | -27.1 | 0 |
| FLG2 | 1 | 0 |
| Ki | 0.400 | — |
| IPset(A) | 0 | — |
| TIM2 | 0.000 | 0 |
| FLG3 | 1 | 0 |
| Slope or time constant | 12.000 | — |
From the identified parameters in Table 7, it is easy to deduce that the control strategies of the three stages during low voltage ride-through, after low voltage ride-through, and power recovery are: initial current percentage, initial current percentage, and constant slope rise, respectively. During high voltage ride-through, the control strategies of the three stages are: specified power value, specified current value, and immediate recovery. Combined with equations (4) and (5), to adapt to the BPA simulation parameter settings, the identified parameters need to be further optimized. After least squares identification, the control strategy expression is:
$$
I_{P_{ref}} =
\begin{cases}
0.09 I_{p0} + 0.104, & 0.1 < V_t < 0.90 \\
P_0, & 0.90 < V_t < 1.2
\end{cases}
$$
Similarly, the PSD-BPA active power control parameters under asymmetrical faults are shown in Table 8.
| Parameter | LVRT value | HVRT value |
|---|---|---|
| FLG1 | 2 | 1 |
| FLG1=1: Kp; FLG1=2: Kv | 0.000 | 1 |
| FLG1=1: /; FLG1=2: Ki | 0.090 | — |
| FLG1=1: Pset(MW); FLG1=2: IPset(A) | -135.0 | 0 |
| FLG2 | 1 | 0 |
| Ki | 0.400 | — |
| IPset(A) | 0 | — |
| TIM2 | 0.000 | 0 |
| FLG3 | 1 | 0 |
| Slope or time constant | 12.000 | — |
From the table, it can be seen that the active power change control strategy under asymmetrical faults is the same as that under symmetrical faults. The control strategy expression is:
$$
I_{P_{ref}} =
\begin{cases}
0.09 I_{p0} + 0.518, & 0.1 < V_t < 0.93 \\
P_0, & 0.93 < V_t < 1.2
\end{cases}
$$
After identification, the PSD-BPA reactive power control parameters under symmetrical faults are shown in Table 9.
| Parameter | LVRT value | HVRT value |
|---|---|---|
| FLG1 | 3 | 3 |
| Kv | 1.501 | 1.610 |
| Ki | 0.000 | 0.000 |
| IQset(A) | 382.1 | 286.9 |
| Vset | 0.900 | 1.100 |
| FLG2 | 0 | 0 |
| FLG3 | 0 | 0 |
From Table 9, it is easy to deduce that the control strategies of the three stages during voltage ride-through, after low voltage ride-through, and power recovery are: initial reactive current, initial reactive current, and immediate recovery. Combined with equation (6), to adapt to the BPA simulation parameter settings, the identified parameters need to be further optimized. After least squares identification, the control strategy expression is:
$$
I_{Q_{ref}} =
\begin{cases}
-1.501 (0.9 – V_t) + 0.124, & 0.1 < V_t < 0.9 \\
-1.610 (1.1 – V_t) + 0.020, & 0.9 < V_t < 1.3
\end{cases}
$$
After identification, the PSD-BPA reactive power control parameters under asymmetrical faults are shown in Table 10.
| Parameter | LVRT value | HVRT value |
|---|---|---|
| FLG1 | 3 | 3 |
| Kv | 1.239 | 1.554 |
| Ki | 0.000 | 0.000 |
| IQset(A) | 457.7 | 269.3 |
| Vset | 0.900 | 1.100 |
| FLG2 | 0 | 0 |
| FLG3 | 0 | 0 |
From Table 10, it can be seen that the reactive power change control strategy under asymmetrical faults is the same as that under symmetrical faults. The control strategy expression is:
$$
I_{Q_{ref}} =
\begin{cases}
-1.239 (0.9 – V_t) + 0.173, & 0.1 < V_t < 0.93 \\
-1.554 (1.1 – V_t) + 0.075, & 0.93 < V_t < 1.3
\end{cases}
$$
Then the PSD-BPA software is used to simulate the above faults. The test results show that the error between the measured values and the simulated values is very small, which satisfies the error requirements in GB/T 32892—2016 “Test Procedures for Model and Parameters of Photovoltaic Power Generation Systems”, verifying the reliability of the identified parameters.
4. Conclusion
In order to accurately obtain the fault ride-through model parameters of the solar inverter, this paper proposes a related testing and model parameter identification method. Through simulation verification, the correctness of the method is confirmed, and the following conclusions are drawn:
(1) For the manufacturer’s packaged model of the solar inverter, when the structure and parameters are not clear or when it is not necessary to know its structure and parameters, the characteristics of the solar inverter under various types of faults that may occur in the power grid can be comprehensively mastered through extensive testing. A control strategy model under voltage ride-through conditions can then be established.
(2) By analyzing the relationship between the fault voltage and the fault reactive current obtained from the tests, the control model and parameters under low voltage ride-through and high voltage ride-through faults can be identified.
(3) Furthermore, by selecting consistent or similar models in the PSD-BPA program, practical model parameters can be fitted. The solar inverter control model under low voltage ride-through and high voltage ride-through faults, applicable to the voltage range from 0.1 p.u. to 1.4 p.u., can be obtained with high parameter accuracy and good adaptability.