With the increasing integration of large-scale photovoltaic systems into power grids, the operational uncertainty of the grid has significantly risen. To accurately analyze the grid-connection characteristics of solar inverters, it is essential to establish precise simulation models. The accuracy of these models largely depends on the control parameters, which are often difficult to obtain directly due to manufacturer confidentiality. Therefore, parameter identification has become a critical approach to accurately derive these “black-box” control parameters. This paper addresses the challenge of identifying low voltage ride-through (LVRT) control modes and parameters for solar inverter electromechanical transient models. We propose a method based on the multi-objective differential evolution (MODE) algorithm to enhance modeling precision and facilitate accurate analysis of grid-connection characteristics.
The structure of a typical grid-connected photovoltaic system includes a solar array, a solar inverter, an LCL filter circuit, and the grid connection. Under normal operating conditions, the solar inverter employs a double closed-loop control strategy based on voltage vector orientation, consisting of an outer voltage loop and an inner current loop. Maximum power point tracking (MPPT) is used to maximize the conversion of solar energy into electrical energy, prioritizing the output of active power. During this process, the three-phase grid voltages \(u_{ga}\), \(u_{gb}\), \(u_{gc}\) and currents \(i_{ga}\), \(i_{gb}\), \(i_{gc}\) at the point of common coupling (PCC) are transformed into dq-axis components \(u_{gd}\), \(u_{gq}\) and \(i_{gd}\), \(i_{gq}\) using Park’s transformation. To achieve synchronized control between the grid current and voltage, a phase-locked loop (PLL) is utilized to accurately feedback the grid voltage phase \(\theta_{PLL}\). Thus, the tracking performance of \(\theta_{PLL}\) directly influences the grid-connection characteristics of the solar inverter.
The DC voltage \(u_{dc}\) is regulated by the outer voltage loop to generate the reference value for the d-axis current component \(i_{gd,ref}\), expressed as:
$$ i_{g,ref} = k_{P1}(u_{dc,ref} – u_{dc}) + k_{I1} \int (u_{dc,ref} – u_{dc}) dt $$
where \(k_{P1}\) is the proportional control coefficient of the voltage outer loop, \(k_{I1}\) is the integral control coefficient, and \(u_{dc,ref}\) is the reference DC voltage in kV. Under normal conditions, the q-axis current reference \(i_{gq,ref}\) is typically zero. The inner current loop control ensures that the output currents \(i_{gd}\) and \(i_{gq}\) rapidly and accurately follow their reference values, producing the dq-axis components of the reference voltage at the AC side of the solar inverter, \(u_{d,ref}\) and \(u_{q,ref}\), as follows:
$$ u_{d,ref} = u_{gd} – \omega L i_{gq} + k_{P2}(i_{g,ref} – i_{gd}) + k_{I2} \int (i_{g,ref} – i_{gd}) dt $$
$$ u_{q,ref} = u_{gq} + \omega L i_{gd} + k_{P3}(i_{g,ref} – i_{gq}) + k_{I3} \int (i_{g,ref} – i_{gq}) dt $$
Here, \(k_{P2}\) and \(k_{I2}\) are the proportional and integral control coefficients for the d-axis current inner loop, \(k_{P3}\) and \(k_{I3}\) are for the q-axis current inner loop, \(\omega\) is the angular frequency of the grid voltage in rad/s, and \(L\) is the filter inductance in mH.
During a short-circuit fault, the grid voltage deviates from the normal operating range, causing an imbalance between the inverter output power and the MPPT output power. This leads to overvoltage on the DC side, as described by:
$$ P_{PV} – P_{dc} = \frac{C}{2} \frac{du_{dc}^2}{dt} $$
where \(P_{PV}\) is the output power of the solar array in kW, and \(C\) is the DC-side capacitance in μF. To maintain grid-connected operation, it is crucial to switch the solar inverter to LVRT control strategies. To enhance reactive power output, the dynamic reactive current \(i_Q\) should satisfy:
$$ i_Q = K(u – u_{lin}) i_N $$
where \(u_{lin}\) is the LVRT threshold, \(u\) is the per-unit value of the inverter AC-side voltage, \(K\) is the ratio of reactive current change to voltage change, and \(i_N\) is the rated output current of the solar inverter in A. To sustain the grid connection of the photovoltaic system, swift and accurate switching of control strategies is essential. However, actual controllers cannot respond instantaneously due to inherent delays, during which the fault current is influenced by both the system’s steady-state control objectives and the prevailing fault conditions.
Moreover, voltage dips cause abrupt changes in the magnitude and phase of the grid voltage, triggering the PLL to re-synchronize, which significantly impacts the transient fault current. This process continues until the disturbance components decay and the current reaches a steady state. Given the long time-scale characteristics of the solar inverter electromechanical transient model, the parameter identification method employed in this study focuses on the steady state after the fault transient process, thus neglecting the effects of control delay and PLL on the identification results.
As the proportion of renewable energy in power systems increases, some regional grids exhibit weak grid characteristics with low short-circuit ratios (SCR). The integration of renewable energy into weak grids often results in poor system stability, which can lead to system instability in severe cases. Therefore, analyzing different SCR conditions is significant for optimizing control parameters and improving system stability.
During voltage sags, the solar inverter is required to prioritize the injection of reactive current \(i_Q\) to support the grid voltage, and within the total current range, consider the output of active current \(i_P\). Due to the influence of limiters, the actual values of \(i_P\) and \(i_Q\) are:
$$ i_{Q,cmd} = \min(i_{Q,LVRT}, i_{Q,max}) $$
$$ i_{P,cmd} = \min(i_{P,LVRT}, \sqrt{i_{max}^2 – i_{Q,cmd}^2}, i_{P,max}) $$
where \(i_{Q,cmd}\) is the reactive current output command, \(i_{Q,LVRT}\) is the LVRT reactive current command, \(i_{Q,max}\) is the upper limit of reactive current, \(i_{P,cmd}\) is the active current output command, \(i_{P,LVRT}\) is the LVRT active current command, \(i_{max}\) is the upper limit of total current, and \(i_{P,max}\) is the upper limit of active current.
The primary control modes for solar inverter electromechanical transient models during LVRT include specified power control and specified current control, as shown below:
$$ i_{P,LVRT} = k_{1,iP} u_t + k_{2,iP} i_{P0} + i_{P,set} $$
$$ i_{Q,LVRT} = k_{1,iQ} (u_t – u_{lin}) + k_{2,iQ} i_{Q0} + i_{Q,set} $$
where \(u_t\) represents the voltage sag depth, i.e., the grid voltage during the LVRT steady state; \(k_{1,iP}\) and \(k_{2,iP}\) are the LVRT active current coefficients 1 and 2; \(i_{P,set}\) is the LVRT active current setting; \(k_{1,iQ}\) and \(k_{2,iQ}\) are the LVRT reactive current coefficients 1 and 2; \(i_{Q,set}\) is the LVRT reactive current setting; and \(i_{P0}\) and \(i_{Q0}\) are the initial active and reactive currents, respectively.
Alternatively, for specified current control:
$$ i_{P,LVRT} = \frac{P_{LVRT}}{u_t} = k_P \frac{P_0}{u_t} + P_{set} $$
$$ i_{Q,LVRT} = \frac{Q_{LVRT}}{u_t} = k_Q \frac{Q_0}{u_t} + Q_{set} $$
where \(k_P\) is the LVRT active power coefficient, \(P_{set}\) is the LVRT active power setting, \(P_0\) is the pre-fault active power, \(P_{LVRT}\) is the active power during LVRT, \(k_Q\) is the LVRT reactive power coefficient, \(Q_{set}\) is the LVRT reactive power setting, \(Q_0\) is the pre-fault reactive power, and \(Q_{LVRT}\) is the reactive power during LVRT. Additionally, \(i_P\) can be controlled based on the pre-fault current \(i_{P0}\) and low-voltage current limiting.
To accurately identify the control parameters, it is necessary to extract key points from the LVRT response characteristics. As illustrated in a typical LVRT period division, points A, B, and C correspond to the pre-disturbance, disturbance, and post-disturbance stages, respectively. The disturbance period B and post-disturbance period C can be further divided into transient intervals B1 and C1, and steady-state intervals B2 and C2. The power and current averages in interval B2 are computed, with the key points for active power, reactive power, active current, and reactive current denoted as \(P_t\), \(Q_t\), \(i_{Pt}\), and \(i_{Qt}\), respectively. For example, \(i_{Pt}\) is calculated as:
$$ i_{Pt} = \frac{1}{b_2 – b_1} \int_{b_1}^{b_2} i_P(t) dt $$
Using the key points from measured cases, an identification dataset is established, and limited cases are excluded. From the equations above, the specified power mode requires control parameters such as power coefficients and power settings, while the specified current mode requires current coefficients and current settings. These parameters are identified using the dataset and the proposed method.
The parameter identification process involves the differential evolution (DE) algorithm, which includes steps such as population initialization, mutation, crossover, and selection, simulating multi-generational evolution of the population to obtain the individual with the best fitness. Unlike genetic algorithms (GA), DE utilizes differential information between individuals to expand the search range and avoid local optima. The specific steps are as follows:
1. Population Initialization: A random number \(r \in (0,1)\) is set, and an initial population \(T\) of size \(G\) is generated using typical values of the parameters to be identified:
$$ T = [T_1, T_2, \ldots, T_G]^T $$
$$ T_i = [x_{i1}, x_{i2}, \ldots, x_{in}] $$
$$ x_{ij} = x_j^{\min} + r (x_j^{\max} – x_j^{\min}) $$
where \(T_i\) is the parent individual \(i\) (\(i=1,2,\ldots,G\)), \(x_{ij}\) is the value of \(T_i\) in the j-th dimension (\(j=1,2,\ldots,n\)), \(n\) is the dimension of the parameters to be identified, \(x_j^{\max}\) is the upper bound of the j-th parameter, and \(x_j^{\min}\) is the lower bound.
2. Individual Mutation: Individuals \(T_a\), \(T_b\), and \(T_c\) are randomly selected from \(T\), with \(a\), \(b\), and \(c\) being distinct. The differential vector \(d\) between \(T_b\) and \(T_c\) is computed, and \(T_a\) is mutated to produce \(T_a^{(1)}\):
$$ d = T_b – T_c $$
$$ T_a^{(1)} = T_a + p_m d = T_a + p_m (T_b – T_c) $$
where \(p_m\) is the mutation operator.
3. Individual Crossover: A crossover probability \(p_c\) is set, and \(T_i\) (\(i \neq a,b,c\)) is crossed with \(T_a^{(1)}\), ensuring at least one dimension is selected, resulting in an updated \(T_a^{(1)}\). To enhance optimization speed, boundary conditions are applied to constrain \(T_a^{(1)}\):
$$ T_a^{(1)} = [x_{a1}^{(1)}, x_{a2}^{(1)}, \ldots, x_{an}^{(1)}] $$
$$ x_{aj}^{(1)} = \begin{cases}
x_j^{\min} & \text{if } x_{aj}^{(1)} < x_j^{\min} \\
x_{aj}^{(1)} & \text{if } x_j^{\min} \leq x_{aj}^{(1)} \leq x_j^{\max} \\
x_j^{\max} & \text{if } x_{aj}^{(1)} > x_j^{\max}
\end{cases} $$
4. Individual Selection: The fitness function \(J\) is used to compare \(T_a\) and \(T_a^{(1)}\), retaining the individual with higher fitness:
$$ J(T_i) = \max – \sum_{g=1}^{m} e_g $$
$$ T_a = \begin{cases}
T_a^{(1)} & \text{if } J(T_a^{(1)}) \geq J(T_a) \\
T_a & \text{if } J(T_a^{(1)}) < J(T_a)
\end{cases} $$
where \(J(T_i)\) is the fitness of \(T_i\), \(e_g\) is the residual of case \(g\), and \(m\) is the total number of cases.
5. The population \(T\) is updated based on the selection results, and the process returns to step 2. Each traversal of \(T\) is considered one iteration. The iteration stops when the objective function corresponding to the best individual in \(T\) converges.
Selecting appropriate \(p_m\) and \(p_c\) can effectively improve the accuracy and efficiency of the optimization results. To reflect population diversity, a larger \(p_m\) should be set in the early iterations to expand the search range and avoid local optima. In later iterations, as individual diversity decreases and population fitness approaches convergence, \(p_c\) can be increased to maintain diversity. Common methods like grid search and random search require manual selection of parameter combinations, reducing the possibility of finding the optimal configuration and resulting in low tuning efficiency. Therefore, adaptive adjustment of optimization operators based on population diversity is an effective approach. Information entropy, a common metric for measuring the purity of sample sets, where data confusion is proportional to entropy, can quantify the diversity of the population and its individuals.
As shown in the population initialization, \(T_i\) represents the parameters to be identified, so population diversity \(H(T)\) is expressed as:
$$ H(T) = -\sum_{j=1}^{n} \sum_{h=h_0}^{h_1} p(x_j = h) \log_2 p(x_j = h) $$
where \(x_j\) is the j-th parameter, \(p(x_j = h)\) is the probability that \(x_j\) takes the value \(h\), and \(h_0\) and \(h_1\) are the possible values of \(x_j\). Thus, adaptive \(p_m\) and \(p_c\) are expressed as:
$$ p_m = p_{m,\min} + (p_{m,\max} – p_{m,\min}) \frac{H(T)}{H_0(T)} $$
$$ p_c = p_{c,\max} – (p_{c,\max} – p_{c,\min}) \frac{H(T)}{H_0(T)} $$
where \(H_0(T)\) is the diversity of the initial population, \(p_{m,\max}\) and \(p_{m,\min}\) are the upper and lower bounds of mutation probability, and \(p_{c,\max}\) and \(p_{c,\min}\) are the upper and lower bounds of crossover probability.
To accurately identify the control modes and parameters of solar inverters under different LVRT conditions, a multi-objective identification strategy is implemented by incorporating non-dominated sorting into the DE algorithm, establishing an identification strategy based on the MODE algorithm. To ensure the adaptability of the identification results to different cases, the objective functions are defined as:
$$ J_1 = \min \sum_{g=1}^{m} e_g^2 $$
$$ J_2 = \min \max e_g $$
If \(T_a\) is in the feasible region \(R(T_b)\) of \(T_b\), then \(T_a\) dominates \(T_b\), and \(T_a\) is referred to as a non-dominated solution, while \(T_b\) is a dominated solution. If multiple non-dominated optimal solutions exist in the population, they can be mapped into the objective space formed by \(J_1\) and \(J_2\) to create a Pareto front (PF). Non-dominated sorting can stratify individuals in the population into multiple layers. In multi-objective optimization, the solutions on the PF are usually not unique, and the optimal solution needs to be selected based on practical considerations.
The steps of the MODE algorithm are as follows:
1. Traverse the initial population \(T\), and apply a set of constraints to newly generated individuals to improve optimization efficiency:
$$ J_1(T_i^{(1)}) < J_1(T_i) $$
$$ J_2(T_i^{(1)}) < J_2(T_i) $$
By generating a subpopulation \(T^{(1)}\) of size \(G\), the population size is expanded to \(2G\):
$$ T \cup T^{(1)} = [T_1, T_2, \ldots, T_G, T_1^{(1)}, T_2^{(1)}, \ldots, T_G^{(1)}]^T $$
2. Use the fast sorting method to stratify \(T \cup T^{(1)}\), denoted as \(s\) total layers, and the population is further divided into \([T_{best,1}, T_{best,2}, \ldots, T_{best,s}]\).
3. Sort \(J_1(T_{best,1}), J_1(T_{best,2}), \ldots, J_1(T_{best,s})\) and \(J_2(T_{best,1}), J_2(T_{best,2}), \ldots, J_2(T_{best,s})\) in descending order, and compute the crowding distances \(L_{i,1}\) and \(L_{i,2}\) of individual \(T_i\) for \(J_1\) and \(J_2\):
$$ L_{i,1} = \begin{cases}
\infty & \text{if } i = 1 \\
\frac{J_1(T_{i+1}) – J_1(T_{i-1})}{\max J_1 – \min J_1} & \text{if } 1 < i < z \\
\infty & \text{if } i = z
\end{cases} $$
$$ L_{i,2} = \begin{cases}
\infty & \text{if } i = 1 \\
\frac{J_2(T_{i+1}) – J_2(T_{i-1})}{\max J_2 – \min J_2} & \text{if } 1 < i < z \\
\infty & \text{if } i = z
\end{cases} $$
$$ L_i = L_{i,1} + L_{i,2} $$
where \(L_i\) is the crowding distance of \(T_i\).
4. Use \(L_i\) to sort the individuals in \([T_{best,1}, T_{best,2}, \ldots, T_{best,s}]\), select the top \(G\) \(T_i\) to form a new population \(T\), and record this as one update.
5. After multiple updates, the individuals in \(T\) will converge to \(T_{best,1}\). The overall parameter identification process is summarized in a flowchart.
To make the final decision, the fuzzy comprehensive evaluation method can be used to quantitatively express the objective functions, selecting the individual with the highest target satisfaction as the optimal solution. Target satisfaction \(y\) is expressed as:
$$ y = \frac{1}{2} \left( \frac{\max J_1 – J_1}{\max J_1 – \min J_1} + \frac{\max J_2 – J_2}{\max J_2 – \min J_2} \right) $$
After obtaining the optimal solution, the above method is applied to identify the parameters for various cases, such as symmetric and asymmetric faults under different power conditions. The identified control parameters for active and reactive power under different modes are substituted into the PSASP photovoltaic electromechanical transient model. For example, the simulation waveforms of cases under different control modes are compared.
Due to the complexity and variability of operating conditions, the LVRT control mode of solar inverters cannot be directly determined. Some researchers have proposed using identification errors for judgment, but this strategy focuses on the identification results of a single electrical quantity and fails to fully consider the comprehensive impact of power and current, posing certain limitations. Therefore, to accurately reflect the LVRT characteristics of the cases and the control effectiveness of the parameters, these factors are simultaneously included in the evaluation indicators:
$$ \beta_X = \frac{1}{K_{end} – K_{start} + 1} \sum_{k=K_{start}}^{K_{end}} \left| \frac{X_{LVRT}(k) – X_{cmd}(k)}{X_{cmd}(k)} \right| $$
$$ \beta_{X,\max} = \max \left| \frac{X_{LVRT}(k) – X_{cmd}(k)}{X_{cmd}(k)} \right| $$
where \(t\) is the test data point, \(K_{end}\) is the end sequence number, \(K_{start}\) is the start sequence number, \(\beta_X\) is the average deviation (where \(X = P, i_P, Q, i_Q\)), and \(\beta_{X,\max}\) is the maximum deviation. The maximum allowable values for \(\beta_X\) and \(\beta_{X,\max}\) are set to 0.1 and 0.15, respectively. Taking active control as an example, if the evaluation indicators under the specified current mode simultaneously satisfy \(\beta_P < 0.1\), \(\beta_{i_P} < 0.1\), \(\beta_{P,\max} < 0.15\), and \(\beta_{i_P,\max} < 0.15\), then the case is under specified current control. If \(i_{Pt} \approx i_{P0}\), it is controlled based on the pre-fault current, and cases not within the maximum allowable value range have no additional control. Similarly, the reactive control mode of the inverter can be determined.
Currently, grid-connected solar inverters commonly adopt grid-following modes based on PLL synchronization to measure grid phase information for synchronization with the grid. However, stability issues arise in weak grids. In contrast, grid-forming inverters employ power synchronization strategies similar to synchronous machines and exhibit voltage source characteristics externally, but they can cause extremely high fault currents during short circuits. To address this issue and maintain voltage support capability, researchers have proposed a combination of virtual impedance and hardware expansion methods for grid-forming control. Therefore, the above conclusions still hold certain reference significance for identifying control modes of grid-forming inverters: identify the parameters of the inverter under different control modes based on fault case characteristics, and use the parameters to verify the simulation effectiveness of the case under test, thereby determining the control mode.
To validate the effectiveness and adaptability of the proposed method in identifying control modes and parameters for solar inverter electromechanical transient models, hardware-in-the-loop simulations of actual solar inverter controllers were conducted based on the RT-LAB real-time simulation platform. LVRT case tests for three-phase and two-phase short-circuit faults were performed under different power conditions. This platform combines real controller hardware while retaining the controllability of digital simulation, aiding in a comprehensive analysis of solar inverter grid-connection characteristics.
The cases required for identification are shown in the table below, which includes both training and testing sets for three-phase and two-phase short-circuit faults under various active power conditions \(P_0\) and voltage levels \(u_t\).
| Case Type | \(P_0\) (pu) | \(u_t\) (pu) |
|---|---|---|
| Three-phase short-circuit training | 0.2, 1.0 | 0.35, 0.75 |
| Two-phase short-circuit training | 0.2, 1.0 | 0.35, 0.50, 0.75 |
| Three-phase short-circuit testing | 0.2, 1.0 | 0.50 |
| Two-phase short-circuit testing | 0.2, 1.0 | 0.20 |
Key points are extracted from the cases to establish an identification dataset, and the MODE algorithm is used to identify the LVRT control modes and parameters for \(i_P\) and \(i_Q\). With \(G=50\), the parameter solutions on the PF are denoted as layer 1. The distribution of the population \(T\) objective function during updates under specified current control and specified power control modes is illustrated. To decide the final result, the fuzzy comprehensive evaluation method is used to quantify the objective functions, selecting the individual with the highest target satisfaction as the optimal solution.
After obtaining the optimal solution, the method is applied to identify parameters for various cases, including symmetric and asymmetric faults, and the identified control parameters for active and reactive power under different modes are substituted into the PSASP photovoltaic electromechanical transient model. For instance, the simulation waveforms of cases under different control modes are compared. The evaluation indicators \(\beta_X\) and \(\beta_{X,\max}\) for specified power control and specified current control modes are calculated, and based on these, the control modes for active and reactive power are determined. For example, under specified power control, if \(\beta_P\), \(\beta_{i_P} < 0.1\) and \(\beta_{P,\max}\), \(\beta_{i_P,\max} < 0.15\), and the values are lower than those under specified current control, the active control mode is specified power control. Similarly, for reactive power, if \(\beta_Q\), \(\beta_{i_Q} < 0.1\) and \(\beta_{Q,\max}\), \(\beta_{i_Q,\max} < 0.15\) under specified current control, and the values are lower, the reactive control mode is specified current control.
To validate the effectiveness of the proposed multi-objective identification strategy, parameters are identified and verified based on the cases in the table. The average error \(I_1\) and maximum error \(I_2\) are used to analyze and evaluate the adaptability of the parameter identification results to different cases:
$$ I_1 = J_1 $$
$$ I_2 = J_2 $$
The comparison results between the DE algorithm and the proposed MODE algorithm are defined with specific symbols for active and reactive indicators under specified power and specified current control modes. The results show that for active evaluation indicators, compared to the DE algorithm, the MODE algorithm increases \(I_{1,iP}\) by 0.003, while decreasing \(I_{1,P}\), \(I_{2,P}\), and \(I_{2,iP}\) by 0.002, 0.033, and 0.090, respectively. For reactive evaluation indicators, the proposed method reduces \(I_{1,Q}\), \(I_{2,Q}\), \(I_{1,iQ}\), and \(I_{2,iQ}\) by 0.011, 0.042, 0.001, and 0.001, respectively, compared to the single-objective method. The results indicate that the proposed method achieves better identification results in the test set cases, and the multi-objective strategy improves the adaptability of control parameters to different cases.
To verify the identification accuracy of the proposed algorithm, the adaptive particle swarm optimization (APSO) algorithm, the non-dominated sorting genetic algorithm II (NSGA-II), and the multi-objective cuckoo search (MOCS) algorithm are combined with non-dominated sorting to form multi-objective problem-solving algorithms, and compared with the proposed MODE algorithm. The relationship between different SCR values and \(u_t\), \(i_{Qt}\) is analyzed. It is observed that under low short-circuit ratio (SCR=1.8) conditions, \(u_t\) for two cases increases by 31% and 20% compared to high short-circuit ratio (SCR=20), while \(i_{Qt}\) decreases by 21% and 27%. This indicates that under low short-circuit ratio conditions, the reactive current support capability is weaker, affecting the dynamic response and control capability of solar inverters during faults. As an important indicator for measuring system voltage support strength, SCR can be used to judge the system’s operating state, evaluate voltage support strength, and thereby control the impact of renewable energy grid integration, which is significant for ensuring the safe and stable operation of renewable energy grid-connected systems. Considering the impact of low short-circuit ratio conditions on LVRT key points, further verification of algorithm adaptability is needed.
For cases with SCR=1.8, two additional case sets are added, and the simulation results of the above algorithms are compared. The error percentages of the LVRT key points are used to measure the difference between measured and simulated values, comparing the accuracy of different algorithms. The results show that for active control parameters, the average errors of APSO, NSGA-II, MOCS, and MODE identification algorithms are 5.66%, 14.47%, 6.84%, and 3.78%, respectively. For reactive control parameters, the average errors are 1.56%, 2.60%, 3.72%, and 1.16%, respectively. This demonstrates that the proposed MODE algorithm effectively improves parameter identification accuracy.
In conclusion, addressing the difficulty in obtaining control modes and parameters for solar inverter electromechanical transient models, a method based on the MODE algorithm is proposed to identify control modes and parameters, aiming to enhance modeling precision and accurately analyze grid-connection characteristics. The case results lead to the following main conclusions:
1. Compared to the DE algorithm, the MODE algorithm’s identification results can accurately simulate case characteristics during LVRT, effectively improving parameter identification accuracy.
2. The proposed algorithm uses non-dominated sorting to optimize the population update process, maintaining parameter value diversity while improving search efficiency, reducing the risk of identification results falling into local optima.
3. Compared to APSO, NSGA-II, and MOCS algorithms, the MODE algorithm improves the adaptability of control parameters to different LVRT cases, with average errors for \(i_{P,LVRT}\) and \(i_{Q,LVRT}\) below 3.8% and 1.2%, respectively, enhancing identification efficiency and accuracy.
The proposed method provides a reliable approach for parameter identification of solar inverters, contributing to the development of precise simulation models and better understanding of grid-connection behaviors in modern power systems. Future work could explore the application of this method to other types of inverters and more complex grid conditions.