A power system reactive power optimization method and system based on adaptive power flow calculation

Abstract

This invention belongs to the field of power system optimization technology and provides a method and system for reactive power optimization of power systems based on adaptive power flow calculation. The method includes: obtaining adaptive power flow equations of the power system considering the complementary constraints of generator reactive power output and generator node voltage; constructing an iterative convergence criterion and a reactive power optimization model of the power system based on the obtained adaptive power flow equations; determining whether the obtained adaptive power flow equations of the power system have converged according to the constructed iterative convergence criterion; when the adaptive power flow equations have converged, solving the constructed reactive power optimization model of the power system using a variable ternary optimization algorithm to obtain the optimal control variables of the power system; substituting the obtained optimal control variables into the obtained adaptive power flow equations and repeatedly iterating until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization technology, specifically relating to a power system reactive power optimization method and system based on adaptive power flow calculation. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In the operation and dispatch of power systems, reactive power distribution, node voltage levels, and generator reactive power output status directly affect the system's voltage security, network loss level, and operational economy. With the large-scale integration of new energy sources, frequent changes in grid operation modes, and increased load volatility, the requirements for coordinated reactive power and voltage control in power systems are constantly increasing. How to reduce system active power losses or active power imbalances while satisfying power flow equations, voltage constraints, generator reactive power output constraints, transformer tap constraints, and reactive power compensation equipment switching constraints has become an important issue in the optimized operation of power systems.

[0004] Traditional AC power flow calculations typically pre-classify nodes into slack nodes, PV nodes, and PQ nodes based on their control characteristics. For generator nodes, when their reactive power is within limits, they are generally treated as PV nodes, maintaining the node voltage amplitude at a given reference value and calculating the corresponding reactive power output. When the calculated generator reactive power output exceeds the allowable range, the node needs to be switched from a PV node to a PQ node, and the reactive power output is fixed at the constraint boundary. However, this process relies on explicit node type determination and switching logic, which can easily lead to problems such as repeated node type switching, power flow non-convergence, or inconsistencies between the power flow solution and the actual reactive power constraints during iteration. Especially under heavy loads, insufficient reactive power support, or multiple generator nodes simultaneously approaching the reactive power output boundary, traditional methods struggle to smoothly describe the transition of generator nodes from voltage-controlled mode to reactive power-constrained mode, thus affecting the feasibility and convergence stability of subsequent optimization calculations.

[0005] Reactive power optimization problems in power systems typically fall under the category of mixed-integer nonlinear programming problems involving both continuous and discrete variables. Continuous variables include node voltage magnitudes, node phase angles, and generator reactive power output, while discrete variables include the tap positions of on-load tap-changing transformers and the number of reactive power compensation devices switching on and off. These problems are characterized by strong nonlinearity, high dimensionality, complex variable types, and tight constraint coupling. Directly applying traditional nonlinear optimization methods is susceptible to issues such as the feasibility of the initial point, the handling of integer variables, and the degree of nonlinearity in power flow constraints, leading to low solution efficiency, poor convergence, or solutions that do not meet actual operational constraints. Conversely, using general intelligent optimization algorithms for direct search may result in infeasible solutions or decreased search efficiency due to improper handling of the mixed continuous and integer variables, insufficient power flow verification, and discrete device out-of-bounds issues.

[0006] To address the aforementioned issues, existing reactive power optimization methods typically require additional processing logic to be designed separately between power flow calculation, node type switching, discrete variable handling, and optimization iteration correction. This separate processing approach not only increases the complexity of the algorithm but also easily leads to inconsistencies between the power flow calculation results and the optimization model: the control variables given by the optimization algorithm may cause generator reactive power or node voltage to exceed limits after being substituted into the AC power flow equations; and if the power flow calculation cannot provide a feasible initial state that satisfies the reactive power and voltage constraints, it will affect the normal execution of subsequent reactive power optimization algorithms.

[0007] Therefore, there is an urgent need for a power system reactive power optimization method that can unify and coordinate generator reactive power over-limit handling, node voltage constraints, discrete reactive power control equipment regulation, and power flow feasibility correction. Summary of the Invention

[0008] To address the aforementioned issues, this invention proposes a reactive power optimization method and system for power systems based on adaptive power flow calculation. The method achieves reactive power optimization of the power system through collaborative iteration of adaptive power flow calculation and variable ternary optimization algorithm. By alternating between adaptive power flow calculation and reactive power optimization, the power flow state is corrected after each optimization round, and the corrected feasible state is fed back to the next optimization round, thereby effectively improving the feasibility, stability, and engineering applicability of the reactive power optimization results.

[0009] According to some embodiments, the first aspect of the present invention provides a reactive power optimization method for power systems based on adaptive power flow calculation, employing the following technical solution: A reactive power optimization method for power systems based on adaptive power flow calculation includes: Obtain the adaptive power flow equations for the power system considering the complementary constraints of generator reactive power output and generator node voltage; Based on the obtained adaptive power flow equations of the power system, an iterative convergence criterion and a reactive power optimization model of the power system are constructed. The convergence criterion established by the iteration determines whether the obtained adaptive power flow equations of the power system have converged. When the adaptive power flow equation converges, the variable ternary dream optimization algorithm is used to solve the constructed power system reactive power optimization model to obtain the power system optimization control variables; The obtained optimized control variables are substituted into the acquired adaptive power flow equations, and the solution is iterated repeatedly until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

[0010] As a further technical limitation, the obtained adaptive power flow equations for the power system considering the complementary constraints of generator reactive power output and generator node voltage are as follows: ; ; in, , and These represent the active power balance equation, the reactive power balance equation, and the additional complementary constraint equation for the generator node, respectively. The additional complementary constraint equation reflects the relationship between whether the reactive power at that point reaches the upper limit and whether the voltage at that point can be maintained at the voltage reference value. and Represents a node The active power output and reactive power output of the generator at the location; and Representing nodes respectively Active and reactive loads at the location; It indicates the degree of imbalance in the system's active power caused by power loss; Represents a node The participation factor of the generator at the location in Automatic Generation Control (AGC); Represents the set of all nodes; The set of generator nodes in the representation is, i.e. A subset of; Indicates generator node The upper limit of the reactive power output of the generator at that location. This indicates the reference value (per unit) of the voltage at that node. For nodes Voltage amplitude at the location (per unit); The total number of all nodes. Represents a node With nodes Directly connected by a branch road, or ; and Representing nodes respectively Self-conductivity and self-susceptivity, and Representing nodes respectively With nodes Mutual conductance and mutual susceptance between them; Represents a node With nodes The phase angle difference between the voltage vectors.

[0011] Furthermore, the obtained adaptive power flow equations of the power system are condensed to obtain... ;in, This represents the set of all state variables to be solved; This represents the voltage phase angle vector of the load node. This represents the voltage phase angle vector of the generator node; This represents the voltage magnitude vector at the load node. Represents the voltage magnitude vector of the generator node; superscript This indicates that the node has a generator attached; such nodes belong to the set. ; superscript This indicates that the node does not have a generator connected to it and is a pure load node. Such nodes belong to the set. ; and All A subset of, and ; This represents the union of two sets. This indicates that the intersection of two sets is taken. This represents the empty set.

[0012] As a further technical limitation, the Newton-Raphson method is used to solve the obtained adaptive power flow equations, and the Newton iterative scheme and the Jacobian matrix for power flow calculation are obtained. The infinite norm of the mismatch value in the iterative formula of the obtained Newton iterative scheme is used to construct the iterative convergence criterion.

[0013] As a further technical limitation, when the adaptive power flow equation converges, the state variable information at convergence is used as the initial value for reactive power optimization; it is determined whether the total number of reactive power optimization iterations is greater than the number of iterations in the exploration phase; if not, the exploration phase is entered, a forgetting group is randomly assigned, and the memory strategy, information sharing, and forgetting and replenishment strategies are executed simultaneously; if so, the mining phase is entered, a fixed forgetting group is assigned, and the global optimal memory strategy, information sharing mechanism, and forgetting and replenishment strategy are executed; integer variables are ternary-valued to obtain decision variables; when the number of iterations is less than the maximum number of iterations, the number of iterations is incremented by 1, and the adaptive power flow calculation program is entered for power flow correction, before entering the next iteration cycle; if the number of iterations reaches the maximum number of iterations, the iteration is considered to have converged, and the power system optimization control variables are obtained.

[0014] As a further technical limitation, if the obtained adaptive power flow equations of the power system do not converge, then the adaptive power flow equations of the power system are calculated incorrectly, and the reactive power optimization of the power system is terminated.

[0015] According to some embodiments, the second aspect of the present invention provides a power system reactive power optimization system based on adaptive power flow calculation, employing the following technical solution: A reactive power optimization system for power systems based on adaptive power flow calculation includes: The acquisition module is configured to acquire the adaptive power flow equations of the power system that take into account the complementary constraints of generator reactive power output and generator node voltage. The building module is configured to construct an iterative convergence criterion and a reactive power optimization model of the power system based on the acquired adaptive power flow equations of the power system. The judgment module is configured to determine whether the acquired adaptive power flow equations of the power system have converged based on the constructed iterative convergence criterion. The solver module is configured to use the variable ternary dream optimization algorithm to solve the constructed power system reactive power optimization model when the adaptive power flow equation converges, and obtain the power system optimization control variables. The optimization module is configured to substitute the obtained optimized control variables into the acquired adaptive power flow equations and iterate repeatedly until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

[0016] According to some embodiments, a third aspect of the present invention provides a computer-readable storage medium, employing the following technical solution: A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of a power system reactive power optimization method based on adaptive power flow calculation as described in the first aspect of the present invention.

[0017] According to some embodiments, the fourth aspect of the present invention provides an electronic device, which adopts the following technical solution: An electronic device includes a memory, a processor, and a program stored in the memory and running on the processor. When the processor executes the program, it implements the steps in the reactive power optimization method for a power system based on adaptive power flow calculation as described in the first aspect of the present invention.

[0018] According to some embodiments, the fifth aspect of the present invention provides a computer program product, which adopts the following technical solution: A computer program product includes software code, wherein the program in the software code performs the steps of a power system reactive power optimization method based on adaptive power flow calculation as described in the first aspect of the present invention.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention combines adaptive power flow calculation with a variable ternary dream optimization algorithm for reactive power optimization in power systems. By introducing complementary constraints between generator reactive power output and node voltage into the AC power flow equations, generator nodes naturally exhibit PV characteristics (maintaining reference voltage) when reactive power is below the upper limit, and naturally transform into PQ characteristics (allowing voltage variation) when reactive power reaches the upper limit. This avoids the discontinuity and non-convergence problems caused by explicit switching of traditional PV / PQ nodes and provides a feasible initial solution for reactive power optimization. The dream optimization algorithm iteratively searches for reactive power optimization variables. A ternary processing mechanism is designed for integer control variables such as the tap changer of on-load tap-changing transformers and the number of switching groups of reactive power compensation equipment. This allows discrete control variables to participate in optimization in the form of changes relative to the previous iteration state, thereby improving search efficiency while maintaining integer feasibility.

[0020] This invention alternates between adaptive power flow calculation and reactive power optimization processes, which can correct the power flow state after each round of optimization and feed the corrected feasible state back to the next round of optimization, ultimately improving the feasibility, stability and engineering applicability of the reactive power optimization results. Attached Figure Description

[0021] The accompanying drawings, which form part of this embodiment, are used to provide a further understanding of this embodiment. The illustrative embodiments and their descriptions are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0022] Figure 1 This is a flowchart of a power system reactive power optimization method based on adaptive power flow calculation in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the probability mapping function tanh in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the collaborative iterative solution framework for adaptive power flow calculation and reactive power optimization in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the IEEE 14-node standard computational topology in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the active power loss convergence curve in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the generator node voltage variation curve in Embodiment 1 of the present invention; Figure 7 This is a schematic diagram of transformer tap position changes in Embodiment 1 of the present invention; Figure 8 This is a structural block diagram of a power system reactive power optimization system based on adaptive power flow calculation, as shown in Embodiment 2 of the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0025] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0026] In this invention, terms such as "upper," "lower," "left," "right," "front," "back," "vertical," "horizontal," "side," and "bottom" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used only to facilitate the description of the structural relationships of the various components or elements of this invention and do not specifically refer to any component or element in this invention. They should not be construed as limiting the invention.

[0027] In this invention, terms such as "fixed connection," "connected," and "linked" should be interpreted broadly, indicating a fixed connection, an integral connection, or a detachable connection; a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can determine the specific meaning of these terms in this invention based on the specific circumstances, and they should not be construed as limitations on this invention.

[0028] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0029] Example 1 Embodiment 1 of this invention introduces a reactive power optimization method for power systems based on adaptive power flow calculation.

[0030] like Figure 1 The method for reactive power optimization in power systems based on adaptive power flow calculation, as shown, includes: Obtain the adaptive power flow equations for the power system considering the complementary constraints of generator reactive power output and generator node voltage; Based on the obtained adaptive power flow equations of the power system, an iterative convergence criterion and a reactive power optimization model of the power system are constructed. The convergence criterion established by the iteration determines whether the obtained adaptive power flow equations of the power system have converged. When the adaptive power flow equation converges, the variable ternary dream optimization algorithm is used to solve the constructed power system reactive power optimization model to obtain the power system optimization control variables; The obtained optimized control variables are substituted into the acquired adaptive power flow equations, and the solution is iterated repeatedly until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

[0031] As one or more implementation methods, this embodiment constructs an adaptive power flow equation that considers the complementary constraints of generator reactive power output and generator node voltage, namely... ; ; in, , and These represent the active power balance equation, the reactive power balance equation, and the additional complementary constraint equation for the generator node, respectively. The additional complementary constraint equation reflects the relationship between whether the reactive power at that point reaches the upper limit and whether the voltage at that point can be maintained at the voltage reference value. and Represents a node The active power output and reactive power output of the generator at the location; and Representing nodes respectively Active and reactive loads at the location; It indicates the degree of imbalance in the system's active power caused by power loss; Represents a node The participation factor of the generator at the location in Automatic Generation Control (AGC); Represents the set of all nodes; The set of generator nodes in the representation is, i.e. A subset of; Indicates generator node The upper limit of the reactive power output of the generator at that location. This indicates the reference value (per unit) of the voltage at that node. For nodes Voltage amplitude at the location (per unit); The total number of all nodes. Represents a node With nodes Directly connected by a branch road, or ; and Representing nodes respectively Self-conductivity and self-susceptivity, and Representing nodes respectively With nodes Mutual conductance and mutual susceptance between them; Represents a node With nodes The phase angle difference between the voltage vectors.

[0032] Traditional power flow calculation methods assume that the voltage values ​​of PV nodes are fixed. When calculating the reactive power output of the generators at a PV node after the power flow calculation is completed, there may be cases where the limits are exceeded. In this case, the power flow solution is actually infeasible because the power flow calculation does not take into account the transformation process from PV nodes to PQ nodes. However, the adaptive power flow calculation proposed in this embodiment can naturally handle the transformation process between PV nodes and PQ nodes. For different load levels, the power flow solution it provides is definitely a practically feasible solution.

[0033] In actual power systems, PV node generators operate in a mode of constant active power output, constant voltage, and variable reactive power output. When the reactive power output of the node has not reached its upper limit, the node has sufficient reactive power regulation capability to maintain the voltage at that point at a constant reference value. When the reactive power output of the generator at the node reaches its upper limit, the reactive power cannot be increased further. Therefore, the voltage at the node cannot be maintained at the reference value and will drop due to insufficient reactive power. The operating mode of the generator at the node then switches to constant active power output, constant reactive power output, and variable node voltage operation; that is, the node changes from PV node to PQ node operation. Additional equations Its purpose is to provide a unified mathematical modeling description of the process by which a generator transitions from a PV node to a PQ node due to reaching its upper limit of reactive power output. This allows the equations to naturally incorporate this process into the power flow model during iteration, eliminating the need to separately handle the node type conversion process. Additional equations The modeling of the above process is transformed into a mathematical description, that is, when hour, , and when hour, Furthermore, this equality constraint does not cause the Newton-Raphson algorithm to diverge iteratively, and it has good convergence.

[0034] Furthermore, the introduction of this additional equation can provide a feasible initial value for reactive power optimization (ORPF) calculation in subsequent optimization, effectively ensuring the convergence of subsequent ORPF calculations. The specific role will be introduced later.

[0035] The above power flow equilibrium equations can be expressed in a condensed form, namely... ;in, This represents the set of all state variables to be solved; This represents the voltage phase angle vector of the load node. This represents the voltage phase angle vector of the generator node; This represents the voltage magnitude vector at the load node. Represents the voltage magnitude vector of the generator node; superscript This indicates that the node has a generator attached; such nodes belong to the set. ; superscript This indicates that the node does not have a generator connected to it and is a pure load node. Such nodes belong to the set. ; and All A subset of, and ; This represents the union of two sets. This indicates that the intersection of two sets is taken. This represents the empty set.

[0036] During system operation, the participation factor of Automatic Generation Control (AGC) is usually constant, expressed as: The vector AGC can be considered a constant after initialization and will not change in subsequent PF and OPF.

[0037] The above nonlinear equations are solved using the Newton-Raphson method. The iterative scheme of the Newton method is as follows: ; in, for The change in each element in the equation is signified. This indicates a variable whose value has changed. For a vector, it means that the vector is composed of the changes in the values ​​of each element of the original vector.

[0038] The Jacobian matrix for power flow calculation in this embodiment for Where (k) and (k+1) represent the iteration numbers. The elements in the first two rows and first four columns of the Jacobian matrix for power flow calculation are the same as those in the classic power flow calculation Jacobian matrix, which is the basis of the method and will not be elaborated here; however, the new elements introduced by the new additional formula... , and They are respectively: ; ; The infinite norm of the mismatch value in the Newton iteration scheme is used to construct the iterative convergence criterion, i.e. When the maximum absolute value of the elements in the mismatch is less than a sufficiently small positive constant ( The iteration is considered convergent when the maximum absolute value of the elements in the mismatch is greater than a sufficiently large positive constant. If the iteration reaches the limit of the number of iterations, it is considered that the iteration is diverging.

[0039] It should be noted that a sufficiently small positive constant... The value varies depending on the required convergence accuracy during the calculation, and the range is 10. -6 ~10 -3 .

[0040] The general reactive power optimization problem is a mixed-integer nonlinear programming problem. Insufficient reactive power and insufficient voltage support lead to increased active power losses. Therefore, active power loss is usually used as the objective function in reactive power optimization. For the adaptive power flow calculation model of the power system obtained in this embodiment, minimizing active power loss can be equivalently considered as minimizing... The power imbalance referred to can be minimized in each iteration as the objective function of this approximately linear optimization problem. That is, if the decrease in power imbalance is maximized in each iteration, then the model gradually approaches the optimal solution. ; ;in, and These represent the voltage phase angle vectors of the load node and the generator node, respectively. and These represent the voltage amplitudes at the load node and the generator node, respectively. Represents the reactive power output vector of the generator node; This represents a vector consisting of the tap positions of an on-load tap-changing transformer, and is an integer variable. This is a vector consisting of the operational status (i.e., the number of operational groups) of all reactive power compensation equipment, and it is an integer variable. This represents a vector composed of control variables.

[0041] The inequality constraints for this mixed-integer linear programming problem are: Voltage upper and lower limit constraints for generator nodes: ; Upper and lower limits of reactive power output of generator nodes: ; Voltage phase angle range constraints for generator nodes: ; Voltage upper and lower limits constraints for load nodes: ; Voltage phase angle range constraints at load nodes: ; The vertical adjustment range constraints of the reactive power compensation devices connected to the reactive power compensation device nodes in the system are integer variable constraints: ; Upper and lower limit constraints of transformer tap positions at nodes connected to the tap changer of on-load tap-changing transformers: Transformer tap positions are a series of integer values, for example... Therefore, transformer tap position variable It can also be an integer variable.

[0042] As one or more implementation methods, the dream optimization algorithm requires initial values ​​before optimization, whereby the initial values ​​are randomly selected from the upper and lower bounds of the decision variables, i.e. ;in, Represents the initial variable. and These are the upper and lower bounds of the decision variables mentioned above; is a random number, indicating that the initial decision variables are randomly selected from the feasible region, and the range of values ​​is... .

[0043] because For ease of description, this embodiment refers to each variable as a decision variable group. That is, the active power imbalance, the voltage phase angle of the load node, the voltage phase angle of the generator node, the voltage amplitude of the load node, the voltage amplitude of the generator node, the reactive power output of the generator node, the tap position of the on-load tap changer and the number of reactive power compensation equipment groups are respectively assigned to different decision variable groups, and each group contains several individual decision variables.

[0044] Expanding E, we get: Where NL represents the number of load nodes, NG represents the number of generator nodes, NT represents the number of nodes connected to the tap changer of the on-load tap changer, and NC represents the number of nodes connected to the reactive power compensation equipment. Since the quantities are inconsistent, in order to maintain the consistency of the matrix dimension, it is necessary to fill the last empty position of each decision variable group in matrix E with 0, and this method does not affect the iterative solution results.

[0045] During the exploration phase, this embodiment replicates the current state of each decision variable into NF groups based on the differences in memory capacity of each decision variable, serving as candidate solutions. The following update operation is performed on each group's individual decision variables: The optimal solution is found through continuous iteration; each iteration is considered as entering a dream state. Before each dream state, each decision variable group's individual decision variables know the best decision variable from the previous iteration; each individual randomly forgets some information after entering the dream state to fully simulate the actual dream state in the human brain; therefore, only the forgotten locations need to be updated during each iteration. The different memory capacities of each decision variable group determine the different forgetting capacities of that group's decision variables; the stronger the memory capacity, the fewer locations are forgotten. Parameters are used to... , , , , This means that in each iteration, the decision variables are updated sequentially from beginning to end, with the specific update strategy as follows: First, for each individual decision variable in each forgetting group, update its information using the value of the best decision variable from the previous iteration, resetting its value to the value of the best individual in the decision variable group. ;in, This indicates the value at the i-th position in the decision variable group, and the superscript (t+1) indicates that this iteration is t+1. This indicates the optimal value of the decision variable within the forgetting group at the t-th iteration.

[0046] Secondly, the forgetting and replenishment strategy is implemented, and the update formula for each decision variable is as follows: ; ;in, This represents the value of the decision variable at iteration (t+1). This is a random number factor, and its value is a random number between 0 and 1; The step size control factor is used to control the step size of the decision variables in the solution space; t is the current iteration number. The maximum number of iterations, This represents the maximum number of iterations during the exploration phase.

[0047] While implementing forgetting and replenishment strategies, an information-sharing mechanism is needed to enhance the ability of decision variables to escape local optima and allow them to search globally. This information-sharing mechanism allows each individual decision variable to randomly obtain information from other individuals in the forgetting group, with the update formula as follows: Where i is the number of the decision variable group, j is the number of the forgetting group, m is a random number between 1 and N, and N is a specified positive integer whose value range is greater than the number of decision variable groups.

[0048] Apart from the variables in the forget group, each decision variable can remember its best value in the previous iterations during the iteration process; while the variables in the forget group forget the best value information during the iteration process, which stimulates their self-organization and updating measures, supplementing information in their corresponding positions in order to gradually move closer to the optimal position. The information sharing mechanism allows each decision variable to obtain the value information of other decision variables, thus providing a reference for the update direction.

[0049] In this embodiment, during the mining phase, the forgetting random grouping strategy is no longer implemented. Instead, during each iteration update, the historically best value of a single decision variable is shared with the entire decision variable group, updating the value of each decision variable in the forgetting group. All decision variables in the same decision variable group have the same forgetting group dimension. When updating the memory of a single decision variable, its own information is updated using the best individual value from historical iterations, resetting its value information to the value of the best individual in the decision variable group. Afterwards, the forgetting and replenishment strategy is implemented, and the update formula adopts the humble decision variable update formula, which will not be repeated here.

[0050] The difference between the mining phase and the exploration phase lies in the fact that the vast majority of iterations are used in the exploration phase, while only a small portion are used in the mining phase. In this embodiment, the ratio of iterations between the exploration and mining phases is 9:1, i.e. Secondly, the optimal solution that can be obtained in the exploration phase is the optimal solution within the group, while the optimal information that can be obtained in the mining phase is the historical optimal solution. This shows that the exploration phase is responsible for exploring the breadth of the feasible domain, while the mining phase is responsible for mining the depth of the historical optimal solution, allowing the entire decision variable group to carry out relatively unified local refinement around the global optimum.

[0051] In this embodiment, the generator reactive power output, node voltage, and node phase angle are all continuous variables, which can be directly solved using the aforementioned dream optimization algorithm. However, the transformer tap position and the number of reactive power compensation equipment in operation are integer variables. Directly applying the algorithm will result in non-integer results, leading to an infeasible solution. Therefore, these integer variables must be discretized to integrate them into the aforementioned solution framework.

[0052] To maintain solution consistency, when selecting decision variables, the transformer tap position and the number of reactive power compensation equipment groups in operation are both selected based on their current tap position or number of groups in operation. This significantly increases the processing difficulty of the dream optimization algorithm; to reduce processing difficulty, this approach is not used in the algorithm. and Instead of using it as a decision variable, we use its change relative to the result of the previous iteration as the decision variable, i.e., denoted as and As a decision variable, its relationship with the original decision variable can be transformed using the following formula, i.e. ; .

[0053] At this point, before reaching the upper and lower boundaries, and There are three possible values ​​for , namely The ternary processing here is reflected in: In the single-step iteration of the aforementioned dream optimization algorithm, and We still treat them as continuous variables; after the t-th iteration, we execute the ternary value strategy for discrete variables, as follows: First, the continuous quantities obtained from the dream algorithm are probabilistically mapped according to the following rules: ;in, This indicates the state after the t-th iteration. and The corresponding continuous variables, This represents the probability value after mapping by the tanh function; the tanh function can map the numerical range to the interval [-1, 1], and its graph is shown below. Figure 2 As shown.

[0054] During the exploration phase, the specific formula for ternary processing of this probability is as follows: ;in, As a representative and Discretized three-valued variables; at the same time and The following additional constraints also need to be met, namely ; This processing method can guarantee and Discretized variables that meet the constraints.

[0055] During the mining phase, the preceding formula is still used to calculate the corresponding probabilities for continuous variables after the iteration is completed. However, when determining the ternary variable... Different strategies are employed at different times, specifically: ;in, This represents the optimal value in the historical iteration process. Let be a random variable taking values ​​between [0, 1]. Let `rand` be a random variable taking values ​​between [-1, 0]. `rand` represents the random value enclosed in curly braces. This ternaryization strategy indicates that when the probability is high, the variable... Choose to inherit the best value from the previous iteration; when the probability lies between two random variables, the variable... Then, a random selection is made from three feasible values; when the probability is low, the variable... We choose the opposite value of the historical iterative optimal value. This ternary strategy can explore the feasible region space while effectively ensuring that the variables are integers, and gradually approach the global optimum.

[0056] This embodiment mainly employs two parts: adaptive power flow calculation and reactive power optimization. The reactive power optimization algorithm is responsible for providing optimized decision variables based on the values ​​of the current state variables, while the adaptive power flow calculation is responsible for substituting the results of the optimal reactive power optimization into the AC power flow model for verification and error correction, and providing an initial feasible solution for the next reactive power optimization.

[0057] This embodiment introduces an adaptive power flow calculation that considers complementary constraints on generator reactive power output and generator node voltage in the power flow calculation. The purpose is to provide an initial solution within the feasible region for reactive power optimization. Since the power flow state given by reactive power optimization is not verified during the optimization iteration process, when this result is introduced into traditional power flow calculation, for generator nodes, if the node is defined as a PV node for solution, there is a probability of generator reactive power output exceeding the limit; if the node is defined as a PQ node for solution, voltage exceeding the limit will occur. The result of this power flow calculation will be used as the initial solution for the next reactive power optimization. If this initial solution is infeasible, subsequent integer variable ternary optimization will be impossible, leading to optimization failure. Therefore, introducing complementary constraints on generator reactive power output and generator node voltage in the power flow calculation can effectively ensure that the reactive power output and node voltage of generator nodes do not exceed the upper limit, providing a feasible initial solution for reactive power optimization.

[0058] like Figure 2 As shown, the specific solution process in this embodiment is as follows: (1) Initialization Input network information and AGC data, initialize node voltage amplitude and phase angle, and set the number of adaptive power flow calculation iterations (k) and the total number of reactive power optimization iterations t to 0.

[0059] (2) Adaptive power flow calculation The adaptive power flow equations are constructed using the above method, and the corresponding Jacobian matrix is ​​calculated. If the error does not meet the convergence criterion and has not reached the maximum number of iterations km, the iteration number is set to (k+1), and the next round of power flow calculation is performed. If the error is greater than the maximum error or the number of iterations reaches the maximum number of iterations, the adaptive power flow calculation is considered to be non-convergent, the calculation fails, and the process is terminated. If the error meets the convergence criterion, the adaptive power flow calculation is considered to be converged, the state variable information is saved, and it is used as the initial value for reactive power optimization.

[0060] (3) Reactive power optimization Determine if the total number of reactive power optimization attempts t is greater than the number of exploration phase attempts. If not, proceed to the exploration phase, then randomly assign forgetting groups according to the process, and execute memory strategies, information sharing, and forgetting and replenishment strategies; if yes, proceed to the mining phase, assign fixed forgetting groups, and execute the globally optimal memory strategy, followed by the information sharing mechanism and forgetting replenishment strategy; since the problem solved by this invention contains integer variables, after the above process is completed, it is necessary to perform integer variable ternary processing on the integer variables so as to obtain practically feasible decision variables; then determine whether the number of iterations has reached the maximum number of iterations. When the number of iterations is less than the maximum number of iterations, increment the number of iterations by 1, and enter the adaptive power flow calculation program for power flow correction, and then enter the next loop iteration; if the number of iterations reaches the maximum number of iterations, it is considered that the iteration has converged, the program ends and the optimal solution is output.

[0061] (4) The adaptive power flow calculation and the dream optimization algorithm with integer variable ternary transformation are performed alternately. The control variables generated by each round of dream optimization are substituted into the adaptive power flow equation to solve the problem and obtain the corrected state variables, i.e. the objective function value. The corrected feasible result is used as the initial state of the next round of iteration. The process continues until the model converges and the process ends.

[0062] Case Analysis The proposed method was tested using the IEEE 14-node standard test system, which consists of 14 nodes, 5 generators, 3 transformers, and 17 branches. All data are per-unit values, without units, and the base power is 100 MVA. The relevant topology is as follows: Figure 4 As shown in Table 1, the load data in this example is as follows.

[0063] Table 1. IEEE 14-node computational load

[0064] In this example, node 9 is equipped with reactive power compensation equipment, and its single-group compensation capacity and total number of groups that can be put into operation are shown in Table 2.

[0065] Table 2. Compensation capacity of a single reactive power compensation unit and the total number of units that can be put into operation.

[0066] The transformer parameters used in the example are shown in Table 3.

[0067] Table 3 Transformer Parameters

[0068] The upper and lower limits of generator reactive power and node voltage are shown in Table 4. All parameters are per-unit values ​​and have no unit.

[0069] Table 4 Upper and lower limits of generator reactive power and node voltage

[0070] The algorithm's maximum number of iterations is set to 16,000. The calculation results and iteration process are shown below: Depend on Figure 5 As can be seen, the active power imbalance continuously decreases and converges during the iteration process, indicating that the optimization strategy designed in this invention has taken effect. The active power loss decreases from the initial 0.0442839602142008 to 0.0315217252354264, the algorithm converges, and the reactive power optimization is successful.

[0071] Figure 6 and Figure 7 The changes in generator node voltage and transformer tap position were displayed separately, and no limit violations occurred, proving the effectiveness of the algorithm. Figure 7 Since the transformer tap position fluctuated during the 16,000 iterations, in order to make the iteration process easier to understand intuitively, a point was taken every 1,000 iterations in the graph for output observation, and adjacent points were connected linearly. In the later stage of the iteration, the transformer tap position tended to stabilize, which proved the convergence of the algorithm.

[0072] This embodiment combines adaptive power flow calculation with a variable ternary dream optimization algorithm for reactive power optimization of the power system. By introducing complementary constraints between generator reactive power output and node voltage in the AC power flow equations, generator nodes naturally exhibit PV characteristics that maintain the reference voltage when reactive power is below the upper limit, and naturally transform into PQ characteristics that allow voltage changes when reactive power reaches the upper limit. This avoids the discontinuity and non-convergence problems caused by explicit switching of traditional PV / PQ nodes and provides a feasible initial solution for reactive power optimization. The dream optimization algorithm iteratively searches for reactive power optimization variables. A ternary processing mechanism is designed for integer control variables such as the tap changer of on-load tap-changing transformers and the number of switching groups of reactive power compensation equipment. This allows discrete control variables to participate in optimization in the form of changes relative to the previous iteration state, thereby improving search efficiency while maintaining integer feasibility.

[0073] This embodiment alternates between adaptive power flow calculation and reactive power optimization, which can correct the power flow state after each round of optimization and feed the corrected feasible state back to the next round of optimization, ultimately improving the feasibility, stability and engineering applicability of the reactive power optimization results.

[0074] Example 2 Embodiment 2 of the present invention introduces a reactive power optimization system for power systems based on adaptive power flow calculation.

[0075] like Figure 8 The power system reactive power optimization system based on adaptive power flow calculation shown includes: The acquisition module is configured to acquire the adaptive power flow equations of the power system that take into account the complementary constraints of generator reactive power output and generator node voltage. The building module is configured to construct an iterative convergence criterion and a reactive power optimization model of the power system based on the acquired adaptive power flow equations of the power system. The judgment module is configured to determine whether the acquired adaptive power flow equations of the power system have converged based on the constructed iterative convergence criterion. The solver module is configured to use the variable ternary dream optimization algorithm to solve the constructed power system reactive power optimization model when the adaptive power flow equation converges, and obtain the power system optimization control variables. The optimization module is configured to substitute the obtained optimized control variables into the acquired adaptive power flow equations and iterate repeatedly until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

[0076] The detailed steps are the same as those of the reactive power optimization method for power systems based on adaptive power flow calculation provided in Example 1, and will not be repeated here.

[0077] Example 3 Embodiment 3 of the present invention provides a computer-readable storage medium.

[0078] A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in a power system reactive power optimization method based on adaptive power flow calculation as described in Embodiment 1 of the present invention.

[0079] The detailed steps are the same as those of the reactive power optimization method for power systems based on adaptive power flow calculation provided in Example 1, and will not be repeated here.

[0080] Example 4 Embodiment 4 of the present invention provides an electronic device.

[0081] An electronic device includes a memory, a processor, and a program stored in the memory and running on the processor. When the processor executes the program, it implements the steps in the reactive power optimization method for a power system based on adaptive power flow calculation as described in Embodiment 1 of the present invention.

[0082] The detailed steps are the same as those of the reactive power optimization method for power systems based on adaptive power flow calculation provided in Example 1, and will not be repeated here.

[0083] Example 5 Embodiment 5 of the present invention provides a computer program product.

[0084] A computer program product includes software code, wherein the program in the software code performs the steps of a power system reactive power optimization method based on adaptive power flow calculation as described in Embodiment 1 of the present invention.

[0085] The detailed steps are the same as those of the reactive power optimization method for power systems based on adaptive power flow calculation provided in Example 1, and will not be repeated here.

[0086] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0087] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0091] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

[0092] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. A reactive power optimization method for power systems based on adaptive power flow calculation, characterized in that, include: Obtain the adaptive power flow equations for the power system considering the complementary constraints of generator reactive power output and generator node voltage; Based on the obtained adaptive power flow equations of the power system, an iterative convergence criterion and a reactive power optimization model of the power system are constructed. The convergence criterion established by the iteration determines whether the obtained adaptive power flow equations of the power system have converged. When the adaptive power flow equation converges, the variable ternary dream optimization algorithm is used to solve the constructed power system reactive power optimization model to obtain the power system optimization control variables; The obtained optimized control variables are substituted into the acquired adaptive power flow equations, and the solution is iterated repeatedly until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

2. The reactive power optimization method for power systems based on adaptive power flow calculation as described in claim 1, characterized in that, The obtained adaptive power flow equations for the power system considering the complementary constraints of generator reactive power output and generator node voltage are as follows: ； ； in, , and These represent the active power balance equation, the reactive power balance equation, and the additional complementary constraint equation for the generator node, respectively. The additional complementary constraint equation reflects the relationship between whether the reactive power at that point reaches the upper limit and whether the voltage at that point can be maintained at the voltage reference value. and Represents a node The active power output and reactive power output of the generator at the location; and Representing nodes respectively Active and reactive loads at the location; It indicates the degree of imbalance in the system's active power caused by power loss; Represents a node The participation coefficient of the generator at the location in the automatic power generation control; Represents the set of all nodes; The set of generator nodes in the representation is, i.e. A subset of; Indicates generator node The upper limit of the reactive power output of the generator at that location. This indicates the reference value of the voltage at that node; For nodes Voltage amplitude at the location; The total number of all nodes. Represents a node With nodes Directly connected by a branch road, or ; and Representing nodes respectively Self-conductivity and self-susceptivity, and Representing nodes respectively With nodes Mutual conductance and mutual susceptance between them; Represents a node With nodes The phase angle difference between the voltage vectors.

3. The reactive power optimization method for power systems based on adaptive power flow calculation as described in claim 2, characterized in that, The obtained adaptive power flow equations of the power system are condensed to obtain... ;in, This represents the set of all state variables to be solved; This represents the voltage phase angle vector of the load node. This represents the voltage phase angle vector of the generator node; This represents the voltage magnitude vector at the load node. Represents the voltage magnitude vector of the generator node; superscript This indicates that the node has a generator attached; such nodes belong to the set. ; superscript This indicates that the node does not have a generator connected to it and is a pure load node. Such nodes belong to the set. ; and All A subset of, and ; This represents the union of two sets. This indicates that the intersection of two sets is taken. This represents the empty set.

4. The reactive power optimization method for power systems based on adaptive power flow calculation as described in claim 1, characterized in that, The adaptive power flow equations are solved using the Newton-Raphson method to obtain the Newton iterative scheme and the Jacobian matrix for power flow calculation. The infinite norm of the mismatch value in the iterative formula of the obtained Newton iterative scheme is used to construct the iterative convergence criterion.

5. The reactive power optimization method for power systems based on adaptive power flow calculation as described in claim 1, characterized in that, When the adaptive power flow equation converges, the state variable information at the time of convergence is used as the initial value for reactive power optimization; it is determined whether the total number of reactive power optimizations is greater than the number of times in the exploration phase; if not, the exploration phase is entered, forget groups are randomly assigned, and memory strategies, information sharing, and forgetting and replenishment strategies are executed simultaneously; if so, the mining phase is entered, fixed forget groups are assigned, and the global optimal memory strategy, information sharing mechanism, and forgetting and replenishment strategy are executed. Integer variables are ternary-valued to obtain decision variables. When the number of iterations is less than the maximum number of iterations, the number of iterations is incremented by 1, and the adaptive power flow calculation program is entered for power flow correction before entering the next iteration cycle. If the number of iterations reaches the maximum number of iterations, the iteration is considered to have converged, and the power system optimization control variables are obtained.

6. The reactive power optimization method for power systems based on adaptive power flow calculation as described in claim 1, characterized in that, If the obtained adaptive power flow equations of the power system do not converge, then the adaptive power flow equations of the power system are calculated incorrectly, and the reactive power optimization of the power system is terminated.

7. A reactive power optimization system for power systems based on adaptive power flow calculation, characterized in that, include: The acquisition module is configured to acquire the adaptive power flow equations of the power system that take into account the complementary constraints of generator reactive power output and generator node voltage. The building module is configured to construct an iterative convergence criterion and a reactive power optimization model of the power system based on the acquired adaptive power flow equations of the power system. The judgment module is configured to determine whether the acquired adaptive power flow equations of the power system have converged based on the constructed iterative convergence criterion. The solver module is configured to use the variable ternary dream optimization algorithm to solve the constructed power system reactive power optimization model when the adaptive power flow equation converges, and obtain the power system optimization control variables. The optimization module is configured to substitute the obtained optimized control variables into the acquired adaptive power flow equations and iterate repeatedly until the optimal control variables of the power system are obtained, thus completing the reactive power optimization of the power system based on adaptive power flow calculation.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of a power system reactive power optimization method based on adaptive power flow calculation as described in any one of claims 1-6.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the program, it implements the steps of a power system reactive power optimization method based on adaptive power flow calculation as described in any one of claims 1-6.

10. A computer program product, comprising software code, characterized in that, The program in the software code executes the steps of a power system reactive power optimization method based on adaptive power flow calculation as described in any one of claims 1-6.

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