Research on the Parameter Test and Identiﬁcation Method of Electromechanical Transient Model for PV Power Generation

: Model and parameters are the indispensable conditions for the simulation calculation of power systems with a high proportion of photovoltaic power generation. Conventional models of power electronic devices are di ﬃ cult to meet the requirement of power system electromechanical transient simulation, and the parameters are di ﬃ cult to obtain. Aiming at this problem, this paper proposes a structure of an electromechanical transient simulation model of a photovoltaic power station and designs a set of photovoltaic power generation transient characteristic test systems based on a fault simulation device. Through a disturbance test and model parameter identiﬁcation, the electromechanical transient simulation model and parameters of photovoltaic power generation are obtained. In this paper, based on the test system, the electromechanical transient characteristics of a certain type of photovoltaic inverter are modeled. The results show that the model can successfully describe the electromechanical transient characteristics of photovoltaic power generation, and the simulation results obtained based on the model parameters have a good ﬁtting degree compared with the measured curve.


Introduction
Model parameters are the basis of power system simulation calculations. With the continuous maturity of photovoltaic (PV) power generation technology and its promotion and application in the world, the proportion of PV power generation in the installed capacity of power system continues to increase. The model parameters of PV power generation also become an indispensable condition for the simulation calculation of power systems with a high proportion of PV power generation. Many scholars have carried out extensive and in-depth research on PV power generation modeling requirements applicable to power system simulation calculation. In reference [1], according to the four parameters provided by the manufacturer under the standard test conditions, two detailed methods for calculating the model parameters are given. In reference [2], a disturbance observation method based on uncertainty reasoning was proposed to realize maximum power point tracking (MPPT). In reference [3], a MPPT technique combining a prediction model with a disturbance observation algorithm is proposed. In reference [4], an effective strategy is presented to realize IGBT open-circuit fault diagnosis for closed-loop cascaded PV grid-connected inverters. In reference [5], an overview of MPPT methods for PV systems used in the Micro Grids of PV systems is presented. In reference [6], a method to improve the performance of a distribution system by optimizing volt-var function of a

Electromechanical Transient Model Structure
This paper mainly studied the mathematical model of the PV power station suitable for electromechanical transient simulation of the power system. Dynamic processes such as maximum power point tracking (MPPT) of inverter and switch tube modulation are not considered in the electromechanical transient modeling process of the PV power station. In the process of standardization of the parameters of the PV power generation unit, the reference capacity should be the total rated power of the inverter in the content of the PV power generation unit, and the reference voltage on the Direct Current (DC) side should be the standard working condition (solar irradiance S ref = 1000 W/m 2 , PV array working temperature T ref = 25 • C) under the working voltage of the maximum power point of PV array, the reference voltage on the alternating current (AC) side should be the rated voltage of the PV power generation unit boosted to the low voltage side.

Typical Structure of the PV Power Station
The PV power station consists of several PV power generation units, collector lines, step-up transformers in the station, reactive power compensation devices in the station, etc. The PV power generation unit is composed of PV array, inverter, cell step-up transformer, and so on. Specifically shown in Figure 1.
Electronics 2020, 9, x FOR PEER REVIEW 3 of 15 identification based on the test system, the model and parameters of the electromechanical transient model of PV power generation can be successfully fitted.

Electromechanical Transient Model Structure
This paper mainly studied the mathematical model of the PV power station suitable for electromechanical transient simulation of the power system. Dynamic processes such as maximum power point tracking (MPPT) of inverter and switch tube modulation are not considered in the electromechanical transient modeling process of the PV power station. In the process of standardization of the parameters of the PV power generation unit, the reference capacity should be the total rated power of the inverter in the content of the PV power generation unit, and the reference voltage on the Direct Current (DC) side should be the standard working condition (solar irradiance Sref = 1000 W/m 2 , PV array working temperature Tref = 25 °C ) under the working voltage of the maximum power point of PV array, the reference voltage on the alternating current (AC) side should be the rated voltage of the PV power generation unit boosted to the low voltage side.

Typical Structure of the PV Power Station
The PV power station consists of several PV power generation units, collector lines, step-up transformers in the station, reactive power compensation devices in the station, etc. The PV power generation unit is composed of PV array, inverter, cell step-up transformer, and so on. Specifically shown in Figure 1.
Step  Corresponding to the physical structure of the PV power station in Figure 1, the mathematical model of the PV power station is also composed of the PV power generation unit model and conventional power equipment element model [21]. The model parameters of the PV power generation unit should be obtained by means of actual measurement, and PV power generation units composed of PV square arrays and inverters of different types and capacities should be modeled, respectively.

Model Framework
The electromechanical transient calculation model of the PV power station is composed of multiple PV power generation unit models and conventional power equipment element models, as shown in Figure 2. The electromechanical transient model of the PV power generation unit consists of three parts [22]: (1) PV array model: simulates the nonlinear characteristics of PV array; (2) inverter model: simulates the grid-connected operation control characteristics of the inverter, including grid- Corresponding to the physical structure of the PV power station in Figure 1, the mathematical model of the PV power station is also composed of the PV power generation unit model and conventional power equipment element model [21]. The model parameters of the PV power generation unit should be obtained by means of actual measurement, and PV power generation units composed of PV square arrays and inverters of different types and capacities should be modeled, respectively.

Model Framework
The electromechanical transient calculation model of the PV power station is composed of multiple PV power generation unit models and conventional power equipment element models, as shown in Figure 2. The electromechanical transient model of the PV power generation unit consists of three parts [22]: (1) PV array model: simulates the nonlinear characteristics of PV array; (2) inverter model: simulates the grid-connected operation control characteristics of the inverter, including grid-connected interface models, control and protection models, etc.; (3) unit step-up transformer model. Among them, the inverter model is the core of electromechanical transient modeling.

PV Array Model
The PV array power output model simulates the photoelectric conversion characteristics of PV array under different environmental factors. The environmental quantity input is the solar irradiance S of the current working condition and the working temperature T of the current working condition. The input electrical quantity is the DC working voltage Udc of the PV array. The electrical quantity output is the PV array output current Ipv. According to the test parameters under standard test conditions, the characteristics of the PV array IV under any radiation intensity S and operating temperature T can be derived [8].

Inverter Control Model
The connection relationship of the three-phase grid-connected PV inverter is shown in Figure 3: The output apparent power ̃ of the inverter is [23]: The inverter control and protection model includes the steady-state operation control module and the transient control protection module, as shown in Figure 4.

PV Array Model
The PV array power output model simulates the photoelectric conversion characteristics of PV array under different environmental factors. The environmental quantity input is the solar irradiance S of the current working condition and the working temperature T of the current working condition. The input electrical quantity is the DC working voltage U dc of the PV array. The electrical quantity output is the PV array output current I pv . According to the test parameters under standard test conditions, the characteristics of the PV array IV under any radiation intensity S and operating temperature T can be derived [8].

Inverter Control Model
The connection relationship of the three-phase grid-connected PV inverter is shown in Figure 3: Electronics 2020, 9,

PV Array Model
The PV array power output model simulates the photoelectric conversion characteristics of PV array under different environmental factors. The environmental quantity input is the solar irradiance S of the current working condition and the working temperature T of the current working condition. The input electrical quantity is the DC working voltage Udc of the PV array. The electrical quantity output is the PV array output current Ipv. According to the test parameters under standard test conditions, the characteristics of the PV array IV under any radiation intensity S and operating temperature T can be derived [8].

Inverter Control Model
The connection relationship of the three-phase grid-connected PV inverter is shown in Figure 3: The output apparent power ̃ of the inverter is [23]: The inverter control and protection model includes the steady-state operation control module and the transient control protection module, as shown in Figure 4. The output apparent power S of the inverter is [23]: The inverter control and protection model includes the steady-state operation control module and the transient control protection module, as shown in Figure 4.  In steady-state operation, the inverter adopts active and reactive decoupling control, including DC voltage calculation module, active power control module, reactive power control module and output current calculation module, as shown in Figure 5.  In steady-state operation, the inverter adopts active and reactive decoupling control, including DC voltage calculation module, active power control module, reactive power control module and output current calculation module, as shown in Figure 5.  In steady-state operation, the inverter adopts active and reactive decoupling control, including DC voltage calculation module, active power control module, reactive power control module and output current calculation module, as shown in Figure 5. The DC voltage calculation module simulates the stable voltage of the DC capacitor of the inverter. The active power control module tracks the maximum power point voltage (or control command at plant-level) of the PV array, and outputs the inverter current active component Id. The block diagram of the active power control module with Udc as the controlled object is shown in Figure  6. Figure 6. Block diagram of active power control module.
The reactive power control module takes the reference value of reactive power as the control target and outputs the inverter current reactive component Iq, as shown in Figure 7.    In steady-state operation, the inverter adopts active and reactive decoupling control, including DC voltage calculation module, active power control module, reactive power control module and output current calculation module, as shown in Figure 5. The DC voltage calculation module simulates the stable voltage of the DC capacitor of the inverter. The active power control module tracks the maximum power point voltage (or control command at plant-level) of the PV array, and outputs the inverter current active component Id. The block diagram of the active power control module with Udc as the controlled object is shown in Figure  6. Figure 6. Block diagram of active power control module.
The reactive power control module takes the reference value of reactive power as the control target and outputs the inverter current reactive component Iq, as shown in Figure 7.    In steady-state operation, the inverter adopts active and reactive decoupling control, including DC voltage calculation module, active power control module, reactive power control module and output current calculation module, as shown in Figure 5. The DC voltage calculation module simulates the stable voltage of the DC capacitor of the inverter. The active power control module tracks the maximum power point voltage (or control command at plant-level) of the PV array, and outputs the inverter current active component Id. The block diagram of the active power control module with Udc as the controlled object is shown in Figure  6.  The output current calculation module calculates the output current vector of the inverter according to the current active component, reactive component, and grid voltage phase [23].
According to the requirements of GB/T 19,964 for the fault ride-through and recovery process of the PV power station, the dynamic reactive current injected into the grid by PV power station should meet certain requirements, and the active power restores to the pre-fault value at a certain rate after fault clearing. The variables and parameters of inverter protection module as shown in Figure 8, usually include control node voltage class, voltage, current, frequency limit, tolerance time, protection action time, etc., which can be used as a reference value according to the inverter setting value.
According to the requirements of GB/T 19,964 for the fault ride-through and recovery process of the PV power station, the dynamic reactive current injected into the grid by PV power station should meet certain requirements, and the active power restores to the pre-fault value at a certain rate after fault clearing.
The variables and parameters of inverter protection module as shown in Figure 8, usually include control node voltage class, voltage, current, frequency limit, tolerance time, protection action time, etc., which can be used as a reference value according to the inverter setting value.
Over-current protection, Over-voltage protection, Over and under frequency protection, Voltage unbalance protection, etc.  The output current calculation module refers to the definition in the steady-state operation control module.

Test Principle
The test principle of transient characteristic of PV power station is shown as in Figure 9.

Verification Conditions
(1) Power range: high power output state, P ≥ 0.8 Pp, P is the output active power of the PV power generation unit, Pp is the peak power of the PV power generation unit; intermediate power grade output state, 0.5 Pp ≤ P ≤ 0.7 Pp; low power output state, 0.1 Pp ≤ P ≤ 0.3 Pp.
(2) Fault type: the working conditions of the electromechanical transient model parameters of the PV power generation unit include a three-phase symmetric fault and a two-phase asymmetric fault. The output current calculation module refers to the definition in the steady-state operation control module.

Test Principle
The test principle of transient characteristic of PV power station is shown as in Figure 9.
According to the requirements of GB/T 19,964 for the fault ride-through and recovery process of the PV power station, the dynamic reactive current injected into the grid by PV power station should meet certain requirements, and the active power restores to the pre-fault value at a certain rate after fault clearing.
The variables and parameters of inverter protection module as shown in Figure 8, usually include control node voltage class, voltage, current, frequency limit, tolerance time, protection action time, etc., which can be used as a reference value according to the inverter setting value.
Over-current protection, Over-voltage protection, Over and under frequency protection, Voltage unbalance protection, etc.  The output current calculation module refers to the definition in the steady-state operation control module.

Test Principle
The test principle of transient characteristic of PV power station is shown as in Figure 9.

Verification Conditions
(1) Power range: high power output state, P ≥ 0.8 Pp, P is the output active power of the PV power generation unit, Pp is the peak power of the PV power generation unit; intermediate power grade output state, 0.5 Pp ≤ P ≤ 0.7 Pp; low power output state, 0.1 Pp ≤ P ≤ 0.3 Pp.
(2) Fault type: the working conditions of the electromechanical transient model parameters of the PV power generation unit include a three-phase symmetric fault and a two-phase asymmetric fault.   (4) restore the AC side voltage of the inverter to 1 p.u. until stable operation of the inverter.

AC Large Disturbance Test
(1) The model parameter test should be carried out when inverter output is within the high power output range; (2) exit the inverter MPPT control mode and enter the constant voltage control mode. The reference value of DC voltage is set to 1 p.u. to stable operation; (3) set the voltage drop of the AC side of the inverter to 0.85 p.u. until stable operation of the inverter, and set the voltage drop of the AC side of the inverter to 0.6, 0.4, 0.2, and 0 p.u. until stable operation of the inverter; (4) restore the AC side voltage of the inverter to 0.85 p.u. until stable operation of the inverter; (5) restore the AC side voltage of the inverter to 1 p.u. until stable operation of the inverter.

Preprocessing of Test Data
(1) Low-pass filter: due to the influence of the on-site test environment, the test data contained a large number of harmonics, which needed to be filtered. In this paper, a first-order low-pass filter was selected. The selection of filter parameters affects the amplitude and phase angle of the measured data. Therefore, the amplitude and phase angle difference caused by the filter must be considered when calculating the output power of the PV power generation unit according to the filtered voltage and current. The disturbance test data are the instantaneous values, and the previously processed data still have a high sampling rate (for example, 100 kHz), while the simulation step of power system transient calculation is millisecond class (for example, 20 ms). Therefore, the average value of the test data is calculated within a simulation step to obtain the test comparison data, and the test data are processed to per unit values.

Identification Method
According to the theory of system identification, identification methods can be divided into a classical identification method, modern identification method, and artificial intelligence identification method. Classical identification methods mainly include a convolution identification method, correlation identification method, and frequency domain FFT method etc. [24]. Modern identification methods mainly include a least square estimation method, maximum likelihood method, and Kalman filtering method, etc. Typical intelligent identification methods include genetic algorithm and immune Electronics 2020, 9, 1184 8 of 15 algorithm. In this paper, the least squares estimation method was adopted [25], which is based on the minimum sum of squares of the difference between the measured value z and the estimated valueẑ.
where x is the true value of the state variable; n is the number of state variables; h(x) is the measurement function; m is the number of measurements; H is a matrix m × n, and its element is h ij . The objective function is established according to the least squares criterion [25]: The estimatorx can be solved by differentiating the objective function and setting it to zero [25].

Model Simulation
The electromechanical transient model of the PV station was established in power system software. Before model simulation, the power system parameters included voltage, equivalent impedance, and short circuit capacity should be determined.

Model Evaluation
According to the time scale, the test and simulation data were processed in sections. Taking a large disturbance test on the AC side as an example, the data were divided into three sections [26].

•
Period A: before fault, 2 s before voltage disturbance is the beginning of period A, and the beginning time of voltage disturbance is the end of period A. • Period B: during the fault period, the end of period A is the beginning of period B, and the start of voltage disturbance clearing is the end of period B. • Period C: after the fault, the end of period B is the beginning of period C, and the 2 s after the active power of PV unit starts to output stably is the end of period C.
Xs and Xm were, respectively, used to represent the per-unit values of electric quantities provided by model simulation and experimental test. The sequence numbers of the first and last data obtained from the model simulation or experimental test in the corresponding interval are represented by K S_start , K M_start , K S_end , and K M_end , respectively. The deviation indexes of each interval were as follows [26]: • Average deviation of the steady state interval: F1.
• Average deviation of the transient interval: F2.
The weighted average total deviation of voltage, current, active power, and reactive power in the whole disturbance process were obtained by calculating the average deviation of each period. In this paper, the weights of the three intervals were 10% (period A), 60% (period B), 30% (period C).

Case Study
Based on the above research, a set of test platforms was designed, as shown in Figure 10. The system used a controllable DC power supply to simulate the V-I input characteristics of the PV array and connected the DC side of the inverter. The AC side of the inverter was connected to the power grid fault simulation device through a step-up transformer. The power grid fault simulation device connected/disconnected reactor X 1 and X 2 through circuit breakers S1 and S2 to simulate various fault disturbances of the power grid voltage. In order to reduce the impact on the power grid, a buffer reactance Z G was connected in a series between the grid fault simulation device and the grid. Two measuring points were set on the DC side and AC side of the inverter to collect DC side voltage, DC side current, AC side voltage, and AC side current. The measured data were used to identify the model parameters of the PV inverter.
 Average deviation of the transient interval: F2.
Maximum deviation of the steady state interval: F3.
The weighted average total deviation of voltage, current, active power, and reactive power in the whole disturbance process were obtained by calculating the average deviation of each period. In this paper, the weights of the three intervals were 10% (period A), 60% (period B), 30% (period C).

Case Study
Based on the above research, a set of test platforms was designed, as shown in Figure 10. The system used a controllable DC power supply to simulate the V-I input characteristics of the PV array and connected the DC side of the inverter. The AC side of the inverter was connected to the power grid fault simulation device through a step-up transformer. The power grid fault simulation device connected/disconnected reactor X1 and X2 through circuit breakers S1 and S2 to simulate various fault disturbances of the power grid voltage. In order to reduce the impact on the power grid, a buffer reactance ZG was connected in a series between the grid fault simulation device and the grid. Two measuring points were set on the DC side and AC side of the inverter to collect DC side voltage, DC side current, AC side voltage, and AC side current. The measured data were used to identify the model parameters of the PV inverter. The test items included a voltage small disturbance test and a voltage large disturbance test. Among them, the small disturbance test referred to the use of the power grid fault simulation device to change the grid-side voltage, the voltage range was 0.9~1.15 times the rated voltage, and tested whether the inverter could operate stably in the case of the small disturbance of the grid voltage. The large disturbance test meant that the grid side voltage dropped to 0~0.9 times the rated voltage, and it tested whether the inverter could maintain grid-connected operation and provide reactive current support to the grid when a serious short circuit fault occurred in the grid.

Parameter Identification under Small Disturbance Mode of the Grid Voltage
The rated power of the tested PV inverter was 500 kW, the grid-side rated line voltage was 315 V, and the working range of the DC side voltage was 500~850 V. Test device parameters: the shortcircuit capacity of the power grid fault simulation device was 2 MVA, and the reactance of the generating device was L1 + L2 = 200 mL; the rated capacity of the transformer was 2 MVA with a ratio of 10.5/0.315 kV, and the short-circuit voltage was 4%. The test steps were as follows: The test items included a voltage small disturbance test and a voltage large disturbance test. Among them, the small disturbance test referred to the use of the power grid fault simulation device to change the grid-side voltage, the voltage range was 0.9~1.15 times the rated voltage, and tested whether the inverter could operate stably in the case of the small disturbance of the grid voltage. The large disturbance test meant that the grid side voltage dropped to 0~0.9 times the rated voltage, and it tested whether the inverter could maintain grid-connected operation and provide reactive current support to the grid when a serious short circuit fault occurred in the grid.

Parameter Identification under Small Disturbance Mode of the Grid Voltage
The rated power of the tested PV inverter was 500 kW, the grid-side rated line voltage was 315 V, and the working range of the DC side voltage was 500~850 V. Test device parameters: the short-circuit capacity of the power grid fault simulation device was 2 MVA, and the reactance of the generating device was L 1 + L 2 = 200 mL; the rated capacity of the transformer was 2 MVA with a ratio of 10.5/0.315 kV, and the short-circuit voltage was 4%. The test steps were as follows: (1) Make the output of the inverter reach more than 0.7 p.u. of its rated output power; (2) After the inverter enters into steady-state operation, the circuit breaker S2 is closed through the grid fault simulation device, and makes the AC side voltage of the inverter drop to near 0.925 p.u.; The waveform of the grid voltage is shown in Figure 11. Since the unit power factor control was adopted in the test inverter, reactive power was not output in a normal operation and the control reactive current was 0, so there was no need to identify the parameters of the reactive controller. According to the grid voltage disturbance data, the data of the controller were identified. The identification results are shown in Table 1, and the fitted curve of the active current is shown in Figure 12.
(1) Make the output of the inverter reach more than 0.7 p.u. of its rated output power; (2) After the inverter enters into steady-state operation, the circuit breaker S2 is closed through the grid fault simulation device, and makes the AC side voltage of the inverter drop to near 0.925 p.u.; (3) The test data are the instantaneous values of DC voltage at measuring point 1 and AC voltage and current at measuring point 2. The voltage and current transformers are used to transmit the measurement signal to the multi-channel wave-recorder to ensure the synchronization of the test data of each channel in time.
The waveform of the grid voltage is shown in Figure 11. Since the unit power factor control was adopted in the test inverter, reactive power was not output in a normal operation and the control reactive current was 0, so there was no need to identify the parameters of the reactive controller. According to the grid voltage disturbance data, the data of the controller were identified. The identification results are shown in Table 1, and the fitted curve of the active current is shown in Figure  12.

Identification Parameters Damped Least Squares
Kd 0.00269 Td 0.11447 Figure 11. Grid voltage curve with small disturbance of grid voltage.  The identification curve shows that the active current simulation curve could fit the measured curve closely under the small disturbance of the grid voltage, and the identified parameters were also within a reasonable range, as shown in Table 2. The identification results verified the correctness and The identification curve shows that the active current simulation curve could fit the measured curve closely under the small disturbance of the grid voltage, and the identified parameters were also within a reasonable range, as shown in Table 2. The identification results verified the correctness and validity of the above theoretical analysis in the previous section. The test steps and data measuring points were the same as above. During the test, the voltage dropped to 0.63 p.u. of the rated voltage. The waveform of grid voltage is shown in Figure 13. According to the PV inverter fault ride-through control model mentioned above, the model parameters determined by the test data are shown in Table 3, and the fitting curves of active and reactive power current obtained are shown in Figures 14 and 15.   According to the PV inverter fault ride-through control model mentioned above, the model parameters determined by the test data are shown in Table 3, and the fitting curves of active and reactive power current obtained are shown in Figures 14 and 15. The identification curve shows that the active current component and reactive current component of the inverter output could fit the measured curve closelyunder the large disturbance of the grid voltage, and the identification parameters were within a reasonable range, as shown in Tables 4 and 5, which verified the correctness and effectiveness of the above test and identification methods.

Identification Parameters Damped Least Squares
parameters determined by the test data are shown in Table 3, and the fitting curves of active and reactive power current obtained are shown in Figures 14 and 15.   The identification curve shows that the active current component and reactive current component of the inverter output could fit the measured curve closelyunder the large disturbance of the grid voltage, and the identification parameters were within a reasonable range, as shown in Tables 4 and 5, which verified the correctness and effectiveness of the above test and identification methods.

Conclusions
This paper mainly studies the PV power station model suitable for electromechanical transient simulation of a power system. The research shows that the transient characteristics of PV power generation are mainly affected by the inverter control strategy and interface characteristics. Therefore, the inverter model is the core of the whole modeling work. In this paper, the electromechanical transient model structure of the PV inverter is established based on the time scale of electromechanical simulation and the control protection strategy of the PV inverter, and a model

Conclusions
This paper mainly studies the PV power station model suitable for electromechanical transient simulation of a power system. The research shows that the transient characteristics of PV power generation are mainly affected by the inverter control strategy and interface characteristics. Therefore, the inverter model is the core of the whole modeling work. In this paper, the electromechanical transient model structure of the PV inverter is established based on the time scale of electromechanical simulation and the control protection strategy of the PV inverter, and a model parameter identification method based on the transient characteristic test and test data fitting is proposed. Based on a certain test system, the test and parameter identifications are carried out in small and large disturbances of the grid voltage, respectively, in the paper. The results show that the parameters of the PV power generation model obtained through the test and identification can successfully fit the electromechanical transient characteristics, and have certain engineering practicability. In particular, it can provide basic models and parameters for power system security and stability simulation and control decision-making, including PV power stations, and improve the simulation efficiency on the premise of ensuring the accuracy of simulation results.
Author Contributions: This research was a collaborative effort between the authors. T.S. proposed the method framework of PV parameter identification, designed the experiments and wrote the paper. L.Q. realized the simulation model of the PV system in the software and performed the experiments. L.G. contributed analysis tool and reviewed the paper. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflicts of interest. Reactive current support coefficient of inverter in fault ride through