Distributed energy main body current injection optimization method and system for low-voltage distribution network

Abstract

The invention provides a distributed energy main body current injection optimization method and system for a low-voltage distribution network. The method comprises the following steps: S1, constructing an equivalent circuit model of a grid-connected IBR system; s2, constructing a constraint set of a current injection optimization model based on the constructed equivalent circuit model of the grid-connected IBR system; s3, by introducing an auxiliary variable, performing convex domain reconstruction on a non-convex constraint term in the constraint set of the current injection optimization model to form a complete current injection optimization model; and S4, solving the complete current injection optimization model under the condition of meeting the constraint set to obtain an optimal solution of the current reference injection value.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering technology, specifically to a method and system for optimizing the main current injection of distributed energy sources for low-voltage distribution networks, and more specifically to a method and system for optimizing inverter current reference injection values ​​for addressing three-phase voltage imbalance in power grids. Background Technology

[0002] The high penetration of distributed energy resources in modern power grids can exacerbate power quality problems in distribution networks. Among these problems, the persistent three-phase voltage imbalance at the point of common coupling (PCC) has attracted widespread attention. Three-phase voltage imbalance increases the risk of equipment damage and failure, and in severe cases, may cause distributed generation devices to disconnect from the grid. IEEE international standards recommend that power system design and operation limit the voltage unbalance factor (VUF) to within 3%. Static synchronous compensators (SMCs) and static reactive power compensators (SVCs) can typically be used to compensate reactive power and reduce voltage imbalance at the PCC. However, these dedicated power quality conditioning devices suffer from high installation and operating costs, low utilization rates, and poor flexibility. Therefore, utilizing the widespread distributed energy resources in distribution networks, i.e., inverter-based resources (IBRs), to address voltage imbalance at the PCC is more cost-effective.

[0003] From a power supply perspective, an IBR using current loop control essentially behaves as a controlled current source, such as... Figure 3 As shown, this characteristic can be used to adjust the current amplitude and phase injected into the grid by the IBR to provide reactive power support. Typically, the current injection reference value of the IBR can be obtained by multiplying the voltage deviation by a droop factor. However, using a fixed droop factor cannot maximize the voltage imbalance mitigation potential of the IBR, resulting in poor flexibility. Therefore, optimized current injection reference value solutions have attracted academic attention. Existing PCC voltage imbalance mitigation optimization models are mainly established from two dimensions: positive-sequence voltage support and negative-sequence voltage mitigation. Most of them use the steady-state three-phase current amplitude and the active (reactive) output value of the IBR as constraints in the optimization problem, only with slightly different optimization objectives: maximizing the positive-sequence voltage at the PCC and minimizing the negative-sequence voltage at the PCC, respectively.

[0004] To simultaneously regulate both positive-sequence and negative-sequence voltages at the PCC, this invention proposes an inverter current reference injection value optimization method and system for three-phase voltage imbalance mitigation in power grids. This method includes incorporating the steady-state amplitude of the three-phase current, the reactive power output of the IBR, and synchronization stability into the constraint set of the optimization model, and setting the optimization objective as the difference between the positive and negative-sequence voltages. By introducing auxiliary variables, the optimization model can be transformed into a convex optimization model. Therefore, compared to existing current injection reference optimization models, this invention can simultaneously mitigate voltage imbalances at the PCC from both positive-sequence and negative-sequence dimensions. Furthermore, the convex optimization problem ensures the optimality of the solution, allowing this invention to maximize the reactive power capacity of the IBR and minimize voltage imbalance at the PCC while satisfying physical constraints.

[0005] Guo, Yifei, et al. "Global optimality of inverter dynamic voltage support." IEEE Transactions on Power Systems 37.5 (2021): 3947-3957. This paper discloses a study on dynamic voltage support (DVS) strategies based on inverter resources (IBRs) under voltage dip conditions to improve low-voltage ride-through performance. The DVS problem is formulated as a non-convex optimization problem aiming to maximize the positive-sequence voltage magnitude at the point of common coupling (PCC) while satisfying current, active power, and synchronization stability constraints. Subsequently, optimization analysis was conducted to explore the global optimal solution analytically. This paper proposes an effective method to achieve global optimality of positive-sequence voltage support under symmetrical voltage dip conditions. By analyzing the relationship between the voltage at the PCC, the inverter output current, and the grid voltage phasors, the voltage support problem is constructed as a non-convex optimization problem, and its global optimal solution is divided into three cases, with closed-form solutions (implicit solutions) derived for each case. Its drawback lies in the fact that the model only considers positive-sequence voltage support and ignores negative-sequence voltage mitigation. This makes the optimization problem applicable only to symmetrical faults and not to asymmetrical faults, failing to reduce voltage imbalance at the PCC. Under asymmetrical fault conditions, it may lead to excessive three-phase current amplitude. The advantages of this invention are: 1) It considers both positive-sequence voltage support and negative-sequence voltage mitigation, making it more widely applicable; 2) It does not require a staged analytical method, but directly solves the optimal solution through a unified optimization problem, covering all three cases.

[0006] C. Zhao, D. Sun, X. Duan and H. Nian, "Current Reference Optimization for Inverter-Based Resources to Mitigate Grid Voltage Unbalance Factor," in IEEE Transactions on Power Systems, vol. 39, no. 4, pp. 6103-6106, July 2024, doi: 10.1109 / TPWRS.2024.3397030. This paper discloses that modern grid specifications require inverter-based resources (IBRs) to inject reactive current into the power system proportional to voltage drop to support voltage recovery during voltage faults. However, current reference values ​​calculated according to established grid specifications may not maximize the dynamic voltage support capability of IBRs. This paper proposes a novel current reference optimization method that achieves better voltage support performance compared to traditional current references. Current constraints for each phase of the IBR are added to the optimal voltage unbalance factor decay model (OAVUF). By changing the voltage orientation and replacing variables, the OAVUF model is reformulated as a quadratic cone problem. A case study was conducted using MATLAB / Simulink to verify the effectiveness of the proposed optimization method. This paper proposes an effective method for voltage support using an IBR under three-phase voltage imbalance conditions. Through coordinate system transformation and variable substitution, the IBR current reference solution problem is reformulated as a second-order cone optimization problem, and the optimal current reference value is then obtained through a solver. Its drawback is that this model only considers the active power output limit of the IBR, ignoring the reactive power output limit. The lack of reactive power constraints may lead to the obtained current reference value being unfeasible in actual operation. The advantages of this invention are: 1) It constructs a global optimization problem in a specified synchronous rotating coordinate system, eliminating the need for coordinate transformation; 2) It incorporates the available reactive power capacity of the IBR into the constraint set, thereby preventing the current reference from exceeding the controllable range, resulting in a more complete and reliable optimization model under actual operating conditions. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for optimizing the main current injection of distributed energy resources for low-voltage distribution networks.

[0008] The present invention provides a method for optimizing the main current injection of distributed energy resources in low-voltage distribution networks, comprising: Step S1: Construct the equivalent circuit model of the grid-connected IBR system; Step S2: Construct the constraint set of the current injection optimization model based on the equivalent circuit model of the grid-connected IBR system; Step S3: By introducing auxiliary variables, the non-convex constraint terms in the current injection optimization model constraint set are reconstructed into convex domains to form a complete current injection optimization model. Step S4: Under the condition of satisfying the constraint set, solve the complete current injection optimization model to obtain the optimal solution of the current reference injection value.

[0009] Preferably, the equivalent circuit model of the grid-connected IBR system in step S1 includes: (1) in, X = oh 0 L ; For the positive-sequence grid phasor at PCC, For the negative sequence power grid phasor at PCC. This refers to the positive sequence current phasor output by IBRIBR. The negative sequence current phasor output by the IBR; oh 0 represents the rotational angular frequency; The equivalent inductance of the power grid; It is an ideal voltage source in a positive-sequence network; It is an ideal voltage source in a negative sequence network; The equivalent resistance of the power grid. It is the imaginary unit.

[0010] Preferably, the constraint set in step S2 includes: Mapping the voltage and current phasors to the corresponding dq rotating coordinate system, and separating the real and imaginary parts, we obtain: (2) in, This represents the positive-sequence d-axis voltage at PCC. The equivalent positive-sequence d-axis voltage of the power grid. This refers to the positive-sequence d-axis current output by the IBR. This is the positive-sequence q-axis current output by the IBR. This is the positive-sequence q-axis voltage at PCC. This represents the equivalent positive-sequence q-axis voltage of the power grid. This is the negative sequence d-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The negative sequence d-axis current output by the IBR. This refers to the negative-sequence q-axis current output by the IBR. This is the negative sequence q-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The equivalent resistance of the power grid; X = oh 0 L , oh 0 represents the rotational angular frequency; The equivalent inductance of the power grid; The magnitudes of the positive and negative sequence voltages at PCC are expressed as: (3) Using the cone relaxation technique, equation (3) is restated as follows: (4) The magnitudes of the positive and negative sequence voltages at PCC are limited to non-negative values: (5) Under unbalanced operating conditions, the reactive power output value of the IBR is as follows: (6) Reactive power constraints, as shown in equation (7): (7) in, Q lim This is the maximum reactive power output of the IBR; The positive and negative sequence components of the three-phase current are derived through the Park transformation, as shown in equation (8): (8) in, These are the time-domain expressions for the positive-sequence three-phase output current of the IBR. These are the time-domain expressions for the negative-sequence three-phase output current of the IBR, respectively. It is a positive sequence phase; Based on equation (8), the expression for the three-phase current in the time domain is obtained; by setting... c = i p +2 π / 3 and apply Cauchy's inequality to eliminate variables i p Thus, the following inequality constraints are obtained: (9) (10) (11) in, I lim This indicates the maximum allowable steady-state phase current amplitude of the IBR.

[0011] Preferably, step S3 includes: Introducing auxiliary variables Z iBy substituting variables, equation (7) is rewritten as equation (12), which is composed of convex constraints such as hyperplane constraints and cone constraints. (12) in, , and The expression is as follows: (13) (14) (15); The complete current injection optimization model includes: (16).

[0012] Preferably, step S4 includes: under the condition of satisfying the constraint set, solving the current injection optimization model using the Gurobi solver to obtain four steady-state current reference values.

[0013] According to the present invention, a distributed energy source main current injection optimization system for low-voltage distribution networks includes: Module M1: Constructs the equivalent circuit model of the grid-connected IBR system; Module M2: Constructs a constraint set for the current injection optimization model based on the equivalent circuit model of the grid-connected IBR system; Module M3: By introducing auxiliary variables, the non-convex constraint terms in the constraint set of the current injection optimization model are reconstructed into convex domains to form a complete current injection optimization model; Module M4: Under the condition of satisfying the constraint set, solve the complete current injection optimization model to obtain the optimal solution of the current reference injection value.

[0014] Preferably, the equivalent circuit model of the grid-connected IBR system in module M1 includes: (1) in, X = oh 0 L ; For the positive-sequence grid phasor at PCC, For the negative sequence power grid phasor at PCC. This refers to the positive sequence current phasor output by IBRIBR. The negative sequence current phasor output by the IBR; oh 0 represents the rotational angular frequency; The equivalent inductance of the power grid; It is an ideal voltage source in a positive-sequence network; It is an ideal voltage source in a negative sequence network; The equivalent resistance of the power grid. It is the imaginary unit.

[0015] Preferably, the constraint set in module M2 includes: Mapping the voltage and current phasors to the corresponding dq rotating coordinate system, and separating the real and imaginary parts, we obtain: (2) in, This represents the positive-sequence d-axis voltage at PCC. The equivalent positive-sequence d-axis voltage of the power grid. This refers to the positive-sequence d-axis current output by the IBR. This is the positive-sequence q-axis current output by the IBR. This is the positive-sequence q-axis voltage at PCC. This represents the equivalent positive-sequence q-axis voltage of the power grid. This is the negative sequence d-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The negative sequence d-axis current output by the IBR. This refers to the negative-sequence q-axis current output by the IBR. This is the negative sequence q-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The equivalent resistance of the power grid; X = oh 0 L , oh 0 represents the rotational angular frequency; The equivalent inductance of the power grid; The magnitudes of the positive and negative sequence voltages at PCC are expressed as: (3) Using the cone relaxation technique, equation (3) is restated as follows: (4) The magnitudes of the positive and negative sequence voltages at PCC are limited to non-negative values: (5) Under unbalanced operating conditions, the reactive power output value of the IBR is as follows: (6) Reactive power constraints, as shown in equation (7): (7) in, Q lim This is the maximum reactive power output of the IBR; The positive and negative sequence components of the three-phase current are derived through the Park transformation, as shown in equation (8): (8) in, These are the time-domain expressions for the positive-sequence three-phase output current of the IBR. These are the time-domain expressions for the negative-sequence three-phase output current of the IBR, respectively. It is a positive sequence phase; Based on equation (8), the expression for the three-phase current in the time domain is obtained; by setting... c = i p +2 π / 3 and apply Cauchy's inequality to eliminate variables i p Thus, the following inequality constraints are obtained: (9) (10) (11) in, I lim This indicates the maximum allowable steady-state phase current amplitude of the IBR.

[0016] Preferably, the module M3 includes: Introducing auxiliary variables Z i By substituting variables, equation (7) is rewritten as equation (12), which is composed of convex constraints such as hyperplane constraints and cone constraints. (12) in, , and The expression is as follows: (13) (14) (15); The complete current injection optimization model includes: (16).

[0017] Preferably, the module M4 includes: under the condition of satisfying the constraint set, solving the current injection optimization model to obtain four steady-state current reference values ​​by including the Gurobi solver.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention provides an optimized current injection reference value solution method and system that effectively utilizes the widely available inverter resource IBR to address the three-phase voltage imbalance problem. 2. This invention adopts a novel current injection reference value optimization solution model, which maximizes the use of the reactive power capacity of the IBR to alleviate the three-phase voltage imbalance at the PCC while ensuring the safe and stable operation of the IBR. 3. This invention introduces auxiliary variables and performs equivalent substitution on the original bilinear constraints, thereby making the non-convex constraints convex and fundamentally avoiding the suboptimal solution problem caused by the bilinear terms. Therefore, the global optimal solution can be obtained directly using a commercial optimization solver. 4. This invention does not introduce a phase-locked loop structure, which helps to improve the overall stability of the system operation. Attached Figure Description

[0019] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the topology of a three-phase three-wire interconnected IBR.

[0020] Figure 2 This is a block diagram for dual-sequence current control.

[0021] Figure 3 This is a schematic diagram of the equivalent circuit of a grid-connected IBR.

[0022] Figure 4a to Figure 4b This is the voltage and current phasor diagram in a dual synchronous rotating coordinate system.

[0023] Figure 5 This is a schematic diagram of the system step response waveform in Case 1.

[0024] Figure 6 This is a schematic diagram of the system step response waveform in Case 2. Detailed Implementation

[0025] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0026] Example 1 The present invention provides a method for optimizing the main current injection of distributed energy resources in low-voltage distribution networks, comprising: Step S1: Construct the equivalent circuit model of the grid-connected IBR system; Specifically, the equivalent circuit model of the grid-connected IBR system in step S1 includes: (1) in,X = oh 0 L ; For the positive-sequence grid phasor at PCC, For the negative sequence power grid phasor at PCC. This refers to the positive sequence current phasor output by IBRIBR. The negative sequence current phasor output by the IBR; oh 0 represents the rotational angular frequency; The equivalent inductance of the power grid; It is an ideal voltage source in a positive-sequence network; It is an ideal voltage source in a negative sequence network; The equivalent resistance of the power grid. It is the imaginary unit.

[0027] Step S2: Construct the constraint set of the current injection optimization model based on the equivalent circuit model of the grid-connected IBR system; Specifically, the constraint set in step S2 includes: Mapping the voltage and current phasors to the corresponding dq rotating coordinate system, and separating the real and imaginary parts, we obtain: (2) in, This represents the positive-sequence d-axis voltage at PCC. The equivalent positive-sequence d-axis voltage of the power grid. This refers to the positive-sequence d-axis current output by the IBR. This is the positive-sequence q-axis current output by the IBR. This is the positive-sequence q-axis voltage at PCC. This represents the equivalent positive-sequence q-axis voltage of the power grid. This is the negative sequence d-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The negative sequence d-axis current output by the IBR. This refers to the negative-sequence q-axis current output by the IBR. This is the negative sequence q-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The equivalent resistance of the power grid; X = oh 0 L , oh 0 represents the rotational angular frequency; The equivalent inductance of the power grid; The magnitudes of the positive and negative sequence voltages at PCC are expressed as: (3) Using the cone relaxation technique, equation (3) is restated as follows: (4) The magnitudes of the positive and negative sequence voltages at PCC are limited to non-negative values: (5) Under unbalanced operating conditions, the reactive power output value of the IBR is as follows: (6) Reactive power constraints, as shown in equation (7): (7) in, Q lim This is the maximum reactive power output of the IBR; The positive and negative sequence components of the three-phase current are derived through the Park transformation, as shown in equation (8): (8) in, These are the time-domain expressions for the positive-sequence three-phase output current of the IBR. These are the time-domain expressions for the negative-sequence three-phase output current of the IBR, respectively. It is a positive sequence phase; Based on equation (8), the expression for the three-phase current in the time domain is obtained; by setting... c = i p +2 π / 3 and apply Cauchy's inequality to eliminate variables i p Thus, the following inequality constraints are obtained: (9) (10) (11) in, I lim This indicates the maximum allowable steady-state phase current amplitude of the IBR.

[0028] Step S3: By introducing auxiliary variables, the non-convex constraint terms in the current injection optimization model constraint set are reconstructed into convex domains to form a complete current injection optimization model. Specifically, step S3 includes: Introducing auxiliary variables Z i By substituting variables, equation (7) is rewritten as equation (12), which is composed of convex constraints such as hyperplane constraints and cone constraints. (12) in, , and The expression is as follows: (13) (14) (15); The complete current injection optimization model includes: (16).

[0029] Step S4: Under the condition of satisfying the constraint set, solve the complete current injection optimization model to obtain the optimal solution of the current reference injection value.

[0030] Specifically, step S4 includes: under the condition of satisfying the constraint set, solving the current injection optimization model using a Gurobi solver to obtain four steady-state current reference values.

[0031] The present invention also provides a distributed energy main current injection optimization system for low-voltage distribution networks. The distributed energy main current injection optimization system for low-voltage distribution networks can be implemented by executing the process steps of the distributed energy main current injection optimization method for low-voltage distribution networks. That is, those skilled in the art can understand the distributed energy main current injection optimization method for low-voltage distribution networks as a preferred embodiment of the distributed energy main current injection optimization system for low-voltage distribution networks.

[0032] This embodiment proposes a novel method and system for optimizing the IBR current injection reference value to maximize the utilization of the IBR's reactive power capacity, while ensuring the stable and safe operation of the IBR, thereby maximizing the mitigation of voltage imbalance at the PCC. The proposed current injection reference value optimization model encompasses physical constraints such as phase current amplitude constraints and reactive power output constraints, ensuring the safe and stable operation of the IBR. By introducing auxiliary variables, the nonlinear constraints in the optimization model are transformed into convex cone constraints and hyperplane constraints, ensuring the optimality of the solution. Setting an initial phase of 0 in the reference synchronous rotating coordinate system eliminates the need for a phase-locked loop, reducing the risk of system instability.

[0033] Example 2 Example 2 is a preferred example of Example 1. The present invention provides a distributed energy source current injection optimization method for low-voltage distribution networks, comprising: three-phase three-wire grid-connected IBR equivalent circuit description, constraint set construction of current injection optimization model, non-convex constraint transformation and construction of overall optimization model; The three-phase three-wire grid-connected IBR equivalent circuit includes: The topology and control block diagram of a three-phase three-wire grid-connected IBR are as follows: Figure 1 and 2 As shown; Figure 4a As shown, a synchronous rotating reference coordinate system with positive and negative sequences, both with an initial phase of zero, is used; that is, only two phases are considered in the controller, namely the positive sequence phase. i p = oh 0 t and negative sequence phase i n =- oh 0 t=-θ p , where subscript p / n These represent positive and negative order, respectively; oh 0 represents the rotational angular frequency. oh 0=2 πf 0, f 0 is the nominal frequency of the power grid. ；t For time; further, such as Figure 3 As shown, the equivalent circuit of a grid-connected IBR can be modeled as a controlled current source in steady state. The controlled current sources in the positive-sequence and negative-sequence networks are represented as follows: and ;in, This refers to the positive-sequence d-axis current output by the IBR. The imaginary unit, This refers to the positive-sequence q-axis current output by the IBR; The negative sequence d-axis current output by the IBR. This represents the negative-sequence q-axis current output by the IBR; according to Thevenin's theorem, in a positive-sequence network, the power grid is modeled as a series equivalent impedance. and ideal voltage source ;in, The equivalent resistance of the power grid. The equivalent inductance of the power grid, The equivalent positive-sequence d-axis voltage of the power grid. This represents the equivalent positive-sequence q-axis voltage of the power grid; correspondingly, in the negative-sequence network, the power grid is modeled as an ideal voltage source. The corresponding series equivalent impedance is ;in, This represents the equivalent negative-sequence d-axis voltage of the power grid. This represents the equivalent negative-sequence q-axis voltage of the power grid. According to Kirchhoff's voltage law, we can obtain equation (1). It can be seen that changing the current injected into the grid by the IBR can regulate the positive and negative sequence voltages at the PCC, thereby alleviating voltage imbalance.

[0034] (1) in, X = oh 0 L ; For the positive-sequence grid phasor at PCC, For the negative sequence power grid phasor at PCC. This refers to the positive sequence current phasor output by IBRIBR. This is the negative sequence current phasor output by the IBR.

[0035] The following sections will construct an optimization problem in a specified synchronous rotating coordinate system to solve for the optimal steady-state current injection reference value, in order to maximize the mitigation of voltage imbalance at the PCC. This optimization problem comprehensively considers the current amplitude of each phase and the constraints of the active and reactive power output limits of the IBR.

[0036] The constraint set construction includes: like Figure 4b As shown, by mapping the voltage and current phasors to a positive- and negative-sequence dq rotating coordinate system and separating the real and imaginary parts, we can obtain... (2) in, This represents the positive-sequence d-axis voltage at PCC. The equivalent positive-sequence d-axis voltage of the power grid. This refers to the positive-sequence d-axis current output by the IBR. This is the positive-sequence q-axis current output by the IBR. This is the positive-sequence q-axis voltage at PCC. This represents the equivalent positive-sequence q-axis voltage of the power grid. This is the negative sequence d-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The negative sequence d-axis current output by the IBR. This refers to the negative-sequence q-axis current output by the IBR. This is the negative sequence q-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The magnitudes of the positive and negative sequence voltages at PCC can be expressed as: (3) Using the cone relaxation technique, equation (3) can be reformulated as equation (4): (4) The magnitudes of the positive and negative sequence voltages at PCC are limited to non-negative values: (5) Under unbalanced operating conditions, the reactive power output value of the IBR is as follows: (6) Therefore, the reactive power constraint can be obtained, as shown in equation (7): (7) in, Q lim It is the maximum reactive power output of the IBR.

[0037] The positive and negative sequence components of the three-phase current can be derived through the Park transformation, as shown in equation (8).

[0038] (8) in, These are the time-domain expressions for the positive-sequence three-phase output current of the IBR. These are the time-domain expressions for the negative-sequence three-phase output current of the IBR. = oh 0 t . ( (As explained above) Based on equation (8), the expression for the three-phase current in the time domain can be obtained. Then, by setting... c = i p +2 π / 3 and by applying Cauchy's inequality, the variables can be eliminated. i p Thus, the following inequality constraints are obtained.

[0039] (9) (10) (11) in, I lim This indicates the maximum allowable steady-state phase current amplitude of the IBR; = i p +2 π / 3 (explained above).

[0040] The convex domain reconstruction of the non-convex constraint term includes: By observation, it can be seen that equation (7) is a non-convex constraint. Although it can be solved using a commercial solver, it may get stuck in a local optimum. Therefore, an auxiliary variable can be introduced. Z i By substituting variables, equation (7) can be rewritten as equation (12). Equation (12) consists of convex constraints such as hyperplane constraints and cone constraints.

[0041] (12) in , and The expression is as follows (13) (14) (15) Based on the foregoing analysis, the optimization problem can be formulated as follows: (16) All constraints in this optimization model are convex constraints, and four steady-state current reference values ​​can be obtained by solving with a commercial solver such as Gurobi. The four obtained current reference values ​​are defined for a specified dq coordinate system. Therefore, the resulting d-axis and q-axis current components should not be interpreted as active and reactive current components in the traditional sense. This does not affect control performance because their impact on the voltage at the PCC is fundamentally determined by phasor relationships, i.e., the magnitude and relative phase angle between the grid voltage, PCC current, and grid impedance. Under grid imbalance conditions, the actual power and reactive power injected by the IBR themselves contain second harmonic oscillation components. The optimization model regarding... Q The constraint refers to the average reactive power injected into the grid. While these oscillations can be suppressed by appropriately modifying the current reference value, such suppression measures are beyond the scope of this invention. The method proposed in this invention focuses on minimizing the voltage imbalance of the PCC by adjusting the injected positive-sequence and negative-sequence currents.

[0042] Example 3 Example 3 is a preferred example of Example 1. like Figure 1 and Figure 2 The grid-connected IBR system and control block diagram shown are modeled on the MATLAB / Simulink simulation platform. The parameters of the grid-connected IBR system are shown in Table 1. To verify the effectiveness of the above optimized model in the selected dq coordinate system, two case studies were conducted, and the corresponding operating conditions are shown in Table 2.

[0043] Table 1 Grid-connected IBR Parameter Table

[0044] Table 2 Operating Condition Settings

[0045] In Case 1, the upper limit of the phase current amplitude is set to 15A, and the average reactive power output of the IBR is limited to 2kVar. Solving the optimization problem yields the following optimal current reference values: I dp =2.44A, I qp =-5.59A, I dn =-3.95A, I qn=-10.14A. Optimization results show that the phase current amplitude constraint is activated, while the reactive power constraint is not activated. Figure 5 The system step response waveform using optimized current reference values ​​is shown. 0.5 seconds ago, I dp =10A, all other current reference values ​​are set to 0A. The reference value switches to the optimized value after 0.5 seconds and switches back to the original value after 0.8 seconds. From Figure 5 It can be observed that the steady-state current of phase B does indeed reach the preset amplitude limit (15A), while the average reactive power output remains below the limit (2kVar). This simulation result is completely consistent with the theoretical optimization result. Moreover, the voltage imbalance at PCC decreased from 11.11% to 1.57%.

[0046] Case 2 aims to further investigate the scenario where reactive power output constraints take effect. In this scenario, the average reactive power output is limited to 700Var. The phase current amplitude limit remains at 15A. Solving the optimization problem yields the following optimal current reference values: I dp =2.11A, I qp =-4.59A, I dn =-4.94A, I qn =-10.74A. Optimization results show that both phase current amplitude and reactive power constraints are activated simultaneously. Figure 6 The system step response waveform using optimized current reference values ​​is shown. 0.5 seconds ago, I dp =10A, all other current reference values ​​are set to 0A. The reference value switches to the optimized value after 0.5 seconds and switches back to the original value after 0.8 seconds. From Figure 6 It is evident that the steady-state current and average reactive power of phase B did indeed reach their preset limits. This observation is entirely consistent with the optimization results. Simultaneously, the voltage imbalance at PCC decreased from 21.43% to 9.32%. These results validate the effectiveness of the proposed optimization strategy. Furthermore, the steady-state operating point can be accurately solved and practically realized in a selected dq coordinate system with an initial phase of zero.

[0047] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0048] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for optimizing the main current injection of distributed energy resources in low-voltage distribution networks, characterized in that, include: Step S1: Construct the equivalent circuit model of the grid-connected IBR system; Step S2: Construct the constraint set of the current injection optimization model based on the equivalent circuit model of the grid-connected IBR system; Step S3: By introducing auxiliary variables, the non-convex constraint terms in the current injection optimization model constraint set are reconstructed into convex domains to form a complete current injection optimization model. Step S4: Under the condition of satisfying the constraint set, solve the complete current injection optimization model to obtain the optimal solution of the current reference injection value.

2. The method for optimizing the main current injection of distributed energy sources for low-voltage distribution networks according to claim 1, characterized in that, The equivalent circuit model of the grid-connected IBR system in step S1 includes: （1） in, X = ω 0 L ; For the positive-sequence grid phasor at PCC, For the negative sequence power grid phasor at PCC. This refers to the positive sequence current phasor output by IBRIBR. The negative sequence current phasor output by the IBR; ω 0 represents the rotational angular frequency; The equivalent inductance of the power grid; It is an ideal voltage source in a positive-sequence network; It is an ideal voltage source in a negative sequence network; The equivalent resistance of the power grid. It is the imaginary unit.

3. The method for optimizing the main current injection of distributed energy sources for low-voltage distribution networks according to claim 1, characterized in that, The constraint set in step S2 includes: Mapping the voltage and current phasors to the corresponding dq rotating coordinate system, and separating the real and imaginary parts, we obtain: （2） in, This represents the positive-sequence d-axis voltage at PCC. The equivalent positive-sequence d-axis voltage of the power grid. This refers to the positive-sequence d-axis current output by the IBR. This is the positive-sequence q-axis current output by the IBR. This is the positive-sequence q-axis voltage at PCC. This represents the equivalent positive-sequence q-axis voltage of the power grid. This is the negative sequence d-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The negative sequence d-axis current output by the IBR. This refers to the negative-sequence q-axis current output by the IBR. This is the negative sequence q-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The equivalent resistance of the power grid; X = ω 0 L , ω 0 represents the rotational angular frequency; The equivalent inductance of the power grid; The magnitudes of the positive and negative sequence voltages at PCC are expressed as: （3） Using the cone relaxation technique, equation (3) is restated as follows: （4） The magnitudes of the positive and negative sequence voltages at PCC are limited to non-negative values: （5） Under unbalanced operating conditions, the reactive power output value of the IBR is as follows: （6） Reactive power constraints, as shown in equation (7): （7） in, Q lim This is the maximum reactive power output of the IBR; The positive and negative sequence components of the three-phase current are derived through the Park transformation, as shown in equation (8): （8） in, These are the time-domain expressions for the positive-sequence three-phase output current of the IBR. These are the time-domain expressions for the negative-sequence three-phase output current of the IBR, respectively. It is a positive sequence phase; Based on equation (8), the expression for the three-phase current in the time domain is obtained; by setting... γ = θ p +2 π / 3 and apply Cauchy's inequality to eliminate variables θ p Thus, the following inequality constraints are obtained: （9） （10） （11） in, I lim This indicates the maximum allowable steady-state phase current amplitude of the IBR.

4. The method for optimizing the main current injection of distributed energy sources for low-voltage distribution networks according to claim 3, characterized in that, Step S3 includes: Introducing auxiliary variables Z i By substituting variables, equation (7) is rewritten as equation (12), which is composed of convex constraints such as hyperplane constraints and cone constraints. （12） in, , and The expression is as follows: （13） （14） （15）； The complete current injection optimization model includes: （16）。 5. The method for optimizing the main current injection of distributed energy sources for low-voltage distribution networks according to claim 1, characterized in that, Step S4 includes: under the condition of satisfying the constraint set, solving the current injection optimization model using the Gurobi solver to obtain four steady-state current reference values.

6. A distributed energy source main current injection optimization system for low-voltage distribution networks, characterized in that, include: Module M1: Constructs the equivalent circuit model of the grid-connected IBR system; Module M2: Constructs a constraint set for the current injection optimization model based on the equivalent circuit model of the grid-connected IBR system; Module M3: By introducing auxiliary variables, the non-convex constraint terms in the constraint set of the current injection optimization model are reconstructed into convex domains to form a complete current injection optimization model; Module M4: Under the condition of satisfying the constraint set, solve the complete current injection optimization model to obtain the optimal solution of the current reference injection value.

7. The distributed energy main current injection optimization system for low-voltage distribution networks according to claim 6, characterized in that, The equivalent circuit model of the grid-connected IBR system in module M1 includes: （1） in, X = ω 0 L ; For the positive-sequence grid phasor at PCC, For the negative sequence power grid phasor at PCC. This refers to the positive sequence current phasor output by IBRIBR. The negative sequence current phasor output by the IBR; ω 0 represents the rotational angular frequency; The equivalent inductance of the power grid; It is an ideal voltage source in a positive-sequence network; It is an ideal voltage source in a negative sequence network; The equivalent resistance of the power grid. It is the imaginary unit.

8. The distributed energy main current injection optimization system for low-voltage distribution networks according to claim 6, characterized in that, The constraint set in module M2 includes: Mapping the voltage and current phasors to the corresponding dq rotating coordinate system, and separating the real and imaginary parts, we obtain: （2） in, This represents the positive-sequence d-axis voltage at PCC. The equivalent positive-sequence d-axis voltage of the power grid. This refers to the positive-sequence d-axis current output by the IBR. This is the positive-sequence q-axis current output by the IBR. This is the positive-sequence q-axis voltage at PCC. This represents the equivalent positive-sequence q-axis voltage of the power grid. This is the negative sequence d-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The negative sequence d-axis current output by the IBR. This refers to the negative-sequence q-axis current output by the IBR. This is the negative sequence q-axis voltage at PCC. This represents the equivalent negative-sequence q-axis voltage of the power grid. The equivalent resistance of the power grid; X = ω 0 L , ω 0 represents the rotational angular frequency; The equivalent inductance of the power grid; The magnitudes of the positive and negative sequence voltages at PCC are expressed as: （3） Using the cone relaxation technique, equation (3) is restated as follows: （4） The magnitudes of the positive and negative sequence voltages at PCC are limited to non-negative values: （5） Under unbalanced operating conditions, the reactive power output value of the IBR is as follows: （6） Reactive power constraints, as shown in equation (7): （7） in, Q lim This is the maximum reactive power output of the IBR; The positive and negative sequence components of the three-phase current are derived through the Park transformation, as shown in equation (8): （8） in, These are the time-domain expressions for the positive-sequence three-phase output current of the IBR. These are the time-domain expressions for the negative-sequence three-phase output current of the IBR, respectively. It is a positive sequence phase; Based on equation (8), the expression for the three-phase current in the time domain is obtained; by setting... γ = θ p +2 π / 3 and apply Cauchy's inequality to eliminate variables θ p Thus, the following inequality constraints are obtained: （9） （10） （11） in, I lim This indicates the maximum allowable steady-state phase current amplitude of the IBR.

9. The distributed energy main current injection optimization system for low-voltage distribution networks according to claim 8, characterized in that, The module M3 includes: Introducing auxiliary variables Z i By substituting variables, equation (7) is rewritten as equation (12), which is composed of convex constraints such as hyperplane constraints and cone constraints. （12） in, , and The expression is as follows: （13） （14） （15）； The complete current injection optimization model includes: （16）。 10. The distributed energy main current injection optimization system for low-voltage distribution networks according to claim 6, characterized in that, The module M4 includes: under the condition of satisfying the constraint set, obtaining four steady-state current reference values ​​by solving the current injection optimization model through the Gurobi solver.

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