In the context of global decarbonization goals, renewable energy sources, particularly solar power, have seen rapid integration into power systems. By the end of 2021, the installed capacity of solar power in China reached 306 million kilowatts, accounting for 13.8% of the total national generation capacity, with a year-on-year growth of 20.9%. The solar inverter, as a core component of photovoltaic (PV) systems, plays a critical role in converting DC power from PV panels to AC power for grid connection. However, the increasing penetration of solar inverters poses challenges to grid stability due to their diverse control strategies and unknown parameters. Identifying the control modes and parameters of solar inverters is essential for accurate modeling and simulation, which underpins the secure operation of modern power systems.
Solar inverters operate under various control modes during steady-state and fault ride-through conditions. These modes significantly influence the dynamic behavior of the system. For instance, the steady-state power control block includes open-loop and PI control modes, while the voltage ride-through block encompasses strategies such as specified power, specified current, and pre-fault current control. The complexity arises because different manufacturers implement distinct control logics, and the parameters are often proprietary. Therefore, a holistic approach that simultaneously identifies control modes and parameters is necessary to capture the true characteristics of solar inverters.
This article presents an integrated identification strategy for the control modes and parameters of solar inverter electromechanical transient models. We focus on both steady-state operation and voltage ride-through scenarios, leveraging measurement data such as power, voltage, and current. Our methodology combines least-squares-based multiple linear regression for voltage ride-through sections and adaptive particle swarm optimization (PSO) for steady-state control sections. By validating the strategy with actual field data, we demonstrate its effectiveness in enhancing model accuracy and supporting grid stability analyses.
The electromechanical transient model of a solar inverter consists of several interconnected blocks. The steady-state power control block manages active and reactive power output under normal conditions. For active power, the control mode can be either open-loop (PFlag=1) or PI control (PFlag=2), as shown in the following transfer function representation for PI control:
$$ G_p(s) = K_{p,lp} + \frac{K_{i,lp}}{s} $$
where \( K_{p,lp} \) is the proportional gain and \( K_{i,lp} \) is the integral gain. The reactive power control block offers multiple modes: open-loop (QFlag=1), reactive/voltage coordination (QFlag=2), reactive PI control (QFlag=3), and constant reactive current (QFlag=4). The reference value selection includes constant power factor, fixed reactive power, and plant-level commands. The dynamic equations for reactive power control involve filters and time constants, such as:
$$ Q_{e,filt} = \frac{1}{1 + sT_{fltr}} Q_e $$
where \( T_{fltr} \) is the filter time constant.
During voltage ride-through events, such as low-voltage (LVRT) or high-voltage (HVRT) conditions, the solar inverter switches control blocks to maintain grid support. The LVRT active power control modes include steady-state control, specified power, specified current, and pre-fault current control. For specified current mode, the active current command \( I_{pLVRT} \) is computed as:
$$ I_{pLVRT} = K_{1,Ip,LV} U_t + K_{2,Ip,LV} I_{p0} + I_{pset,LV} $$
where \( U_t \) is the terminal voltage, \( I_{p0} \) is the pre-fault current, and \( K_{1,Ip,LV} \), \( K_{2,Ip,LV} \), and \( I_{pset,LV} \) are parameters to be identified. Similarly, the LVRT reactive power control follows specified current mode with:
$$ I_{qLVRT} = K_{1,Iq,LV} (U_{Lin} – U_t) + K_{2,Iq,LV} I_{q0} + I_{qset,LV} $$
where \( U_{Lin} \) is the LVRT threshold voltage. The HVRT control modes are analogous, with adjustments for overvoltage conditions. Additionally, current limiting constraints are applied to prevent overcurrent, defined by limits such as maximum total current \( I_{max} \) and maximum reactive current \( I_{qmax} \).
To identify the control modes and parameters, we propose a two-stage strategy. For the voltage ride-through block, we employ least-squares-based multiple linear regression. This method estimates parameters by minimizing the error between measured and calculated values. Consider the general linear model:
$$ z = b_0 + b_1 x_1 + b_2 x_2 + \cdots + b_n x_n $$
Given \( k \) sets of measurement data, we form matrices:
$$ \mathbf{Z} = \begin{bmatrix} z(1) \\ z(2) \\ \vdots \\ z(k) \end{bmatrix}, \quad \mathbf{X} = \begin{bmatrix} 1 & x_{11} & \cdots & x_{1n} \\ 1 & x_{21} & \cdots & x_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ 1 & x_{k1} & \cdots & x_{kn} \end{bmatrix} $$
The parameter vector \( \boldsymbol{\theta} = [b_0, b_1, \ldots, b_n]^T \) is estimated as:
$$ \hat{\boldsymbol{\theta}} = (\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \mathbf{Z} $$
For LVRT active power control in specified current mode, we use measurements of terminal voltage, pre-fault current, and active current during faults to solve for \( K_{1,Ip,LV} \), \( K_{2,Ip,LV} \), and \( I_{pset,LV} \). The control mode is determined by comparing errors across different mode hypotheses. For example, if the error for specified current mode is below a threshold (e.g., 0.1 p.u.), and lower than that for specified power mode, the specified current mode is selected.
For the steady-state control block, we use an adaptive PSO algorithm. PSO is a metaheuristic optimization technique inspired by swarm behavior. Each particle represents a candidate solution (i.e., a set of parameters), and its position is updated based on personal and global best positions. The velocity update equation is:
$$ v_{id}^{t+1} = w v_{id}^t + c_1 r_1 (p_{id} – x_{id}^t) + c_2 r_2 (g_d – x_{id}^t) $$
where \( w \) is the inertia weight, \( c_1 \) and \( c_2 \) are learning factors, \( r_1 \) and \( r_2 \) are random numbers, \( p_{id} \) is the personal best, and \( g_d \) is the global best. We enhance PSO with adaptive boundary adjustment: if the optimal solution includes parameter values at the search boundaries, we expand the boundaries to avoid local optima. For a parameter \( x \) with initial bounds [\( x_{min} \), \( x_{max} \)], if the optimal value \( x_{best} \) equals \( x_{max} \), we update \( x_{max} \) to \( 2x_{max} \); similarly, if \( x_{best} = x_{min} \), we set \( x_{min} \) to \( 0.5x_{min} \). This ensures thorough exploration for non-typical solar inverter parameters.
The identification process for steady-state active power control involves prioritizing sensitive parameters. Based on sensitivity analysis, parameters like \( K_{p,lp} \), \( K_{i,lp} \), and \( T_{ip} \) have higher impacts on output response. We use multiple data sets (e.g., from small disturbances or power reference changes) to iteratively refine parameters. For reactive power control, we similarly prioritize proportional and integral gains in PI modes or coordination coefficients.
We validate the integrated strategy using field data from a 500 kW centralized solar inverter. The testing environment included low-voltage ride-through and reactive power command change scenarios. Measurement data were recorded using a DEWE5000 power analyzer. For LVRT identification, we processed 12 data sets with voltage dips ranging from 0.05 to 0.8 p.u. The identified parameters for LVRT active power control in specified current mode were: \( K_{1,Ip,LV} = 0.045 \), \( K_{2,Ip,LV} = 0.5412 \), and \( I_{pset,LV} = 0.0211 \). For reactive power control: \( K_{1,Iq,LV} = 1.5015 \), \( K_{2,Iq,LV} = 1.1219 \), and \( I_{qset,LV} = 0.001 \). The active current recovery slope was identified as \( dI_{prec} = 0.975 \) p.u./s.
We simulated the solar inverter behavior in PSASP using these parameters and compared results with measured data. The tables below summarize key identification results and errors.
| Control Mode | Parameter | Identified Value | Error (p.u.) |
|---|---|---|---|
| Active Power: Specified Current | \( K_{1,Ip,LV} \) | 0.045 | 0.0002 |
| \( K_{2,Ip,LV} \) | 0.5412 | 0.001 | |
| \( I_{pset,LV} \) | 0.0211 | 0.0005 | |
| Reactive Power: Specified Current | \( K_{1,Iq,LV} \) | 1.5015 | 0.002 |
| \( K_{2,Iq,LV} \) | 1.1219 | 0.0015 | |
| \( I_{qset,LV} \) | 0.001 | 0.0001 |
| Control Block | Parameter | Identified Value | Sensitivity |
|---|---|---|---|
| Active Power PI Control | \( K_{p,lp} \) | 0.2002 | High |
| \( K_{i,lp} \) | 3.5000 | High | |
| Reactive Power Coordination | \( K_{p,lv} \) | 1.528 | Medium |
| \( K_{i,lv} \) | 4.975 | Medium |
The simulation results showed close alignment with measurements. For LVRT, the active power output during faults matched within 0.0054 p.u. average deviation, and reactive power within 0.0155 p.u., meeting standard requirements. For steady-state reactive power command changes, the maximum error was below 0.012 p.u., demonstrating the strategy’s accuracy. These outcomes highlight the robustness of our integrated approach in capturing the dynamic response of solar inverters.
Furthermore, we tested the strategy on high-voltage ride-through scenarios. Using synthetic data from PSASP, we identified HVRT control modes as specified power for active and specified current for reactive. The parameter errors were under 1%, confirming the method’s versatility. The current limiting parameters, such as \( I_{max} \) and \( I_{qmax} \), were deduced from data patterns where currents saturated, ensuring realistic constraints in the model.
Our integrated identification strategy offers several advantages. First, it simultaneously determines control modes and parameters, reducing the need for prior knowledge about the solar inverter. Second, the combination of least-squares regression and adaptive PSO leverages both linear efficiency and global optimization capabilities. Third, the validation with field data ensures practical applicability. This approach is crucial for grid operators to develop accurate models for stability studies, especially as solar inverter penetration grows.
In conclusion, we have developed and validated an integrated strategy for identifying control modes and parameters in solar inverter electromechanical transient models. By employing least-squares-based multiple linear regression for voltage ride-through blocks and adaptive particle swarm optimization for steady-state control blocks, we achieve high accuracy in parameter estimation and mode selection. Field data tests confirm that the strategy meets industry standards, providing a reliable foundation for modeling solar inverters in power system simulations. Future work could extend this approach to other renewable energy converters or integrate real-time identification for adaptive control.
The increasing complexity of modern grids necessitates advanced modeling techniques for solar inverters. Our strategy contributes to this by offering a systematic, data-driven method that enhances model fidelity and supports the stable integration of renewable energy. As solar power continues to expand, such tools will be indispensable for ensuring grid reliability and achieving decarbonization goals.