Dispersed voltage control method for power system

Abstract

The invention relates to the field of electric power systems, and discloses an electric power system dispersed voltage control method, which comprises the following steps of: establishing a dynamic model of a voltage control unit, and constructing a system description for driving voltage state change by a control signal; defining an optimization objective function based on the dynamic model, wherein the optimization objective function is used for representing voltage deviation, reactive power deviation and control signal strength; introducing constraint conditions of voltage and reactive power into the optimization objective function to form a constrained optimization problem; in the optimization problem, disturbance factors are considered, an uncertainty model is established, and system dynamic expression containing disturbance terms is constructed; a gaming model is established based on policy dependencies between the control units. The distributed voltage control method is adopted, the control strategy can be adjusted in real time according to the actual situation of each voltage control unit, the control effect of optimizing voltage and reactive power is achieved, and excessive dependence on a single control center is avoided.

Description

Technical Field

[0001] The present invention relates to the field of power systems, and specifically to a decentralized voltage control method for power systems. Background Art

[0002] In our daily life, the stability of the power system is of crucial importance. Voltage fluctuations or unstable reactive power will directly affect the normal operation of power equipment, and may even cause equipment damage or power interruption. Therefore, voltage control in the power system needs to be precise and reliable.

[0003] The power system voltage control methods in the prior art usually adopt centralized control. This method collects data from the entire network through a control center, analyzes and processes it, and then formulates voltage control strategies. This method can effectively coordinate the entire network, but its core defect lies in the high requirements for data processing and response speed. It is easy to be limited by insufficient computing power and response speed, resulting in limited control effects. At the same time, the prior art also often uses simple optimization algorithms to adjust voltage and reactive power. Although these algorithms can handle basic control tasks, they often cannot achieve the optimal control effect in complex and dynamic power grid environments.

[0004] Although the prior art can ensure the basic stability of the power system in some cases, its defects are also very obvious. First, the centralized control mode is prone to poor control effects in emergencies due to excessive computing load or response delay. Second, there is a lack of sufficient coordination mechanisms between voltage control units, and they often can only operate independently, unable to effectively avoid conflicts or redundancies between strategies, resulting in low control efficiency. In addition, when dealing with load fluctuations and generation uncertainties, the existing methods often ignore the impact of disturbances, resulting in poor robustness of the system and inability to adapt to the rapid changes of the power grid. For this reason, those skilled in the art have proposed a decentralized voltage control method for power systems to solve the above problems. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a decentralized voltage control method for power systems, which solves the problems of heavy computing burden, poor real-time response and insufficient control coordination in the existing centralized voltage control method.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: A decentralized voltage control method for power systems includes the following steps:

[0007] Establish a dynamic model of the voltage control unit and construct a system description that drives the change of the voltage state with a control signal;

[0008] Define an optimization objective function based on the dynamic model to characterize voltage deviation, reactive power deviation and control signal strength;

[0009] Introduce the constraint conditions of voltage and reactive power into the optimization objective function to form a constrained optimization problem;

[0010] Consider the disturbance factors in the optimization problem and establish an uncertainty model to construct the system dynamic expression with disturbance terms;

[0011] Establish a game model based on the strategy dependence between control units, and define the multi-agent optimization structure through the form of non-cooperative game;

[0012] Solve the optimal control strategy under the game model and use it to drive each control unit to form a decentralized voltage control system.

[0013] Preferably, the establishment of the dynamic model of the voltage control unit includes:

[0014] Obtain the real-time voltage value and reactive power value of each voltage control unit;

[0015] Construct a dynamic equation including voltage variables, reactive power variables and control signal variables based on the form of non-linear functions;

[0016] Model each control unit as a non-linear differential equation system to characterize the influence of the control signal on the voltage change rate.

[0017] Preferably, the definition of the optimization objective function includes:

[0018] Set the reference voltage value and reference reactive power value of each voltage control unit;

[0019] Construct a weighted integral type performance index including the square term of voltage deviation, the square term of reactive power deviation and the square term of control signal;

[0020] Set a weight coefficient for each item, and the weight coefficient is used to adjust the influence proportion of each control objective on the total objective function.

[0021] Preferably, the introduction of the constraint conditions of voltage and reactive power includes:

[0022] Set the minimum allowable voltage and the maximum allowable voltage for each voltage control unit;

[0023] Set the minimum allowable reactive power and the maximum allowable reactive power for each voltage control unit;

[0024] Embed the above constraints as boundary conditions into the solution process of the optimization objective function.

[0025] Preferably, the disturbance factors include:

[0026] The disturbance term constructed based on the load change and the output uncertainty of the power generation side in the power grid;

[0027] The disturbance term is modeled as a time-varying Gaussian white noise process;

[0028] A disturbance term is introduced into the dynamic equation of the control unit to form a system dynamic expression containing a random term;

[0029] An optimization objective function containing an expected value is constructed to minimize the expectation of the performance index under random disturbances.

[0030] Preferably, the establishment of the game model includes:

[0031] Each voltage control unit is regarded as an independent decision-making entity;

[0032] An expected performance index function including its voltage deviation, reactive power deviation, and control signal is set for each control unit respectively;

[0033] A non-cooperative dynamic game structure is constructed on the premise that multiple control units influence each other;

[0034] According to the concept of Nash equilibrium, the strategy solution rules among multiple control units are defined.

[0035] Preferably, the solution of the optimal control strategy includes:

[0036] Based on the control objectives and constraints, the mathematical form of the optimization problem is constructed;

[0037] The distributed gradient descent algorithm or the Lagrangian dual algorithm is used for numerical solution of the optimal control strategy;

[0038] The optimization solver is deployed on the edge computing platform, and the control strategy is updated through real-time data feedback;

[0039] After the control strategy is generated, it is used to drive each control unit to adjust its output voltage and reactive power.

[0040] Preferably, the dynamic equation of the voltage control unit is:

[0041] The voltage state variable of each control unit is represented by the current voltage value;

[0042] The reactive power state variable is represented by the current output reactive power value;

[0043] The control input variable is the adjustment signal injected externally;

[0044] The control signal drives the change of the state variable, and the state evolution process is reflected through the differential expression.

[0045] Preferably, the specific structure of the optimization objective function is:

[0046] The first term is the square of the difference between the voltage deviation of each control unit and the reference value multiplied by the first weight coefficient;

[0047] The second term is the square of the difference between the reactive power deviation of each control unit and the reference value multiplied by the second weight coefficient;

[0048] The third term is the square of the amplitude of the control signal multiplied by the third weight coefficient;

[0049] The total objective function is the weighted sum of the above three terms after integration over a given time interval.

[0050] Preferably, the solution process of the Nash equilibrium includes:

[0051] Each control unit solves its own optimal response strategy when the strategies of other control units are fixed;

[0052] Iteratively update the strategies of all control units multiple times;

[0053] When the strategies of all control units no longer change, determine that the current strategy group constitutes the Nash equilibrium solution set.

[0054] The present invention provides a decentralized voltage control method for a power system. It has the following beneficial effects:

[0055] 1. The present invention adopts a decentralized voltage control method, which can adjust the control strategy in real time according to the actual situation of each voltage control unit, achieving the control effect of optimizing voltage and reactive power. Compared with the traditional centralized control method, the present invention avoids excessive dependence on a single control center and solves the problem of insufficient demand for complex calculations and real-time response in the traditional method.

[0056] 2. By constructing an optimization model of multiple control units based on game theory, the present invention enables each control unit to make independent decisions and coordinate with each other, achieving an improvement in control efficiency. Compared with the single optimization strategy lacking interaction and coordination in the prior art, the present invention solves the problem of insufficient coordination among multiple control units through the game model.

[0057] 3. The present invention adopts an optimization method introducing disturbance factors and uncertainty models, which can better cope with the influence of load fluctuations and generation uncertainties in the power grid, ensuring the stability and robustness of voltage and reactive power control. The prior art often ignores the actual influence of disturbances. The present invention considers disturbance factors in the control strategy, effectively improving the adaptability of the system.

[0058] 4. By combining the distributed optimization algorithm with the edge computing platform, the voltage control system of the present invention has efficient real-time computing and response capabilities, achieving the effect of rapid feedback and adjustment of control strategies. Compared with the traditional centralized computing method, the present invention solves the technical bottleneck of large-scale data processing and long response time, and improves the real-time performance and reliability of the system. Description of the Drawings

[0059] Figure 1 It is a schematic flow chart of the method of the present invention. Detailed Embodiments

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0061] Please refer to the attached Figure 1 , the embodiment of the present invention provides a method for decentralized voltage control of a power system, including the following steps:

[0062] S1. Establish a dynamic model of the voltage control unit and construct a system description that drives the voltage state change with a control signal;

[0063] Specifically, first, to achieve the autonomous adjustment ability of the decentralized voltage control system proposed by the present invention, it is necessary to establish a mathematical model at the system level that can accurately reflect the dynamic response characteristics of the control unit. This modeling process is not only the basis for control strategy design but also the core support for subsequent optimization solution and system response calculation. Therefore, in this step, by establishing the dynamic behavior model of each voltage control unit, a systematic description framework that drives the voltage state change with a control signal is constructed, providing the original dynamic support for the decentralized optimization of the entire control system.

[0064] In this embodiment, first, obtain the real-time operation state data of each voltage control unit in the power system, including but not limited to:

[0065] The current bus voltage amplitude, denoted as V i (t), with the unit of kilovolt (kV);

[0066] The current reactive power output, denoted as Q i (t), with the unit of megavolt-ampere reactive (MVAr);

[0067] The current control input signal, denoted as u i (t), and the unit depends on the specific control device (such as the amplitude of the output signal of the voltage controller).

[0068] Generally, the voltage control unit includes a Static Var Compensator (SVC), a Static Synchronous Compensator (STATCOM), shunt capacitor banks, voltage regulating transformers, etc. The above units are widely used to improve the regional voltage stability and the ability to regulate reactive power balance.

[0069] In a possible implementation, to accurately characterize the dynamic response relationship of the voltage state to the control input, a nonlinear differential equation is used to establish the dynamic mathematical model of the voltage control unit. Specifically, the system model can be expressed in the following form:

[0070]

[0071] Where: represents the change rate of the voltage of the i-th control unit; V i (t) is the voltage state variable of the unit at time t; Q i (t) is the reactive power state variable of the current output; u i (t) is the injected control input signal; f i (·) is the function mapping that defines the nonlinear response characteristics of the unit.

[0072] In some embodiments, the function f i (·) has the following specific structure:

[0073] f i (V i ,Q i ,u i )=α i ·u i (t)-β i ·Q i (t)+γ i ·sin(V i (t));

[0074] Where: α i represents the gain coefficient of the control input to the voltage rise, with the unit of kV / unit; β i represents the sensitivity coefficient of the reactive power to the voltage suppression effect; γ i is the internal nonlinear disturbance feedback coefficient of the system, used to simulate the coupling fluctuation effect in the network; sin(V i (t)) simulates the periodic disturbance or coupling oscillation feedback existing in some power systems.

[0075] As an option, to improve the adaptability and expandability of the modeling, hysteresis or inertia factors can be further introduced into the model. For example, the following dynamic expression with a first-order inertia link can be considered:

[0076]

[0077] where: τ i is the dynamic response time constant of the control unit, with the unit of seconds (s); g i (·) is the steady-state mapping function of the input-state, generally a linear or weakly non-linear function; V i (t) is the voltage state variable of the unit at time t; Q i (t) is the reactive power state variable of the current output; u i (t) is the injected control input signal.

[0078] This model form is applicable to describing control devices with slow regulation response in high-voltage transmission networks, such as large on-load tap-changing transformers, etc.

[0079] In the actual modeling process, there are often local couplings or boundary interactions between voltage control units. To improve the modeling accuracy, the state variables of adjacent units can be further introduced to construct a multi-input coupled dynamic model. The specific form is as follows:

[0080]

[0081] where: V i (t) is the voltage state variable of the unit at time t; Q i (t) is the reactive power state variable of the current output; u i (t) is the injected control input signal; represents the set of adjacent units that have a direct electrical connection or influence with the i-th control unit; V j (t) and Q j (t) represent the voltage and reactive power states of the adjacent units.

[0082] This coupled model reflects the state-dependent characteristics under the distributed control architecture.

[0083] Under the above modeling framework, the control signal u i (t) is regarded as an externally injected regulation variable. By adjusting its amplitude, the dynamic trajectory of the state variable can be directly changed, so as to achieve the regulation objectives of voltage and reactive power.

[0084] For the convenience of subsequent optimization solution and distributed deployment, the present invention preferably adopts an analytical non-linear function form in the model implementation, and determines each model parameter through on-site testing or simulation identification methods. The accuracy in the modeling stage will directly determine the response accuracy and stability of the control system in the implementation stage.

[0085] S2. Define an optimization objective function based on the dynamic model to characterize the voltage deviation, reactive power deviation and control signal strength;

[0086] Specifically, in order to achieve the optimal regulation of the distributed voltage control system, based on the established dynamic model of the voltage control unit, the present invention further constructs an optimization objective function to accurately measure the regulation efficiency of voltage, reactive power, and control signals. The main role of this optimization objective function is to comprehensively consider the voltage deviation, reactive power deviation, and control signal strength according to different requirements of the control objectives, so as to provide a clear performance evaluation criterion for the control algorithm. Through this optimization objective function, accurate regulation of the voltage control unit can be achieved, ensuring that the system reaches the optimal power dispatching effect under the premise of meeting various constraint conditions.

[0087] In this embodiment, first, based on the previously constructed dynamic model, an optimization objective function is defined. This objective function is mainly used to characterize the comprehensive regulation of voltage deviation, reactive power deviation, and control signal strength, so as to optimize the response speed and stability of the system in the subsequent control process. Specifically, the defined optimization objective function structure is as follows:

[0088]

[0089] Where: J is the optimization objective function, representing the weighted total objective of the control system within the given time interval [t 0 , t 1 ; W 1 , W 2 , W 3 are the weight coefficients of voltage deviation, reactive power deviation, and control signal strength respectively; V i (t) is the voltage state of the i-th control unit at time t; V ref,i is the reference voltage value of the i-th control unit; Q i (t) is the reactive power state of the i-th control unit at time t; Q ref,i is the reference reactive power value of the i-th control unit; u i (t) is the amplitude of the control signal of the i-th control unit; N is the total number of voltage control units.

[0090] Generally, in this optimization objective function, the square terms of voltage deviation and reactive power deviation reflect the error between the system and the desired target, and the square term of the control signal takes into account the influence of the magnitude of the system input signal on the system stability and response speed.

[0091] As an option, the reference voltage V ref,i and the reference reactive power Q ref,i of each control unit can be dynamically set through the historical operation data of the system or online calculation. For example, in the case of large load fluctuations, the reference voltage and reactive power values may be adjusted in a timely manner to adapt to the demand changes of the power grid.

[0092] Specifically, the optimized objective function is comprehensively evaluated through three parts of weighted integrals:

[0093] The first term describes the deviation between the voltage of the voltage control unit and the reference value at time t, reflecting the stability of the system voltage;

[0094] The second term describes the difference between the reactive power deviation and the reference value, which can reflect the accuracy of reactive power regulation;

[0095] The third term considers the magnitude of the control signal, avoiding the degradation or instability of the system performance that may be caused by too large or too small control signals.

[0096] Through these weighted terms, the optimized objective function can effectively consider multiple control objectives and adjust the priorities of different objectives by setting appropriate weight coefficients. For example, if the system requires higher voltage stability, the weight of W 1 can be appropriately increased; if reactive power balance is particularly important, the weight of W 2 can be increased.

[0097] In a possible implementation, the integral term in the objective function can be approximately calculated by numerical integration methods such as the trapezoidal method or Simpson's method. This can optimize the response of the control system in real time without increasing a large amount of computational complexity.

[0098] As an option, the optimized objective function can also be dynamically adjusted according to the real-time performance of the system. For example, when the power demand changes rapidly, the weight of the control signal can be temporarily increased to quickly respond to the load change; while under stable load conditions, the weights of the voltage and reactive power deviations can be increased to improve the long-term stability of the system.

[0099] S3. Introduce the constraint conditions of voltage and reactive power into the optimized objective function to form a constrained optimization problem;

[0100] Specifically, in the process of optimizing the voltage control system, in addition to the optimized objective function, the actual physical constraints of voltage and reactive power need to be considered to ensure the stability and safety of the system. Therefore, this step mainly focuses on introducing these constraint conditions, thereby transforming the optimization problem into a constrained optimization problem to ensure the optimal regulation of the system performance while satisfying the physical constraints of the power system.

[0101] In this embodiment, first, according to the physical characteristics and safe operation requirements of the voltage control unit, the constraint conditions of voltage and reactive power are set. These constraint conditions not only reflect the operation range of the control unit but also ensure that the system operation does not exceed the safety boundary, thus avoiding the situations of too high or too low voltage and reactive power exceeding the specified range. Specifically, the constraint conditions include the following aspects:

[0102] Set the minimum allowable voltage V min,i and the maximum allowable voltage V max,i for each voltage control unit, that is, for the i-th control unit, its voltage must satisfy:

[0103] V min,i ≤V i (t)≤V max,i ;

[0104] where: V i (t) represents the voltage value of the i-th control unit at time t.

[0105] These voltage limits are usually determined according to the design specifications of the system and the technical specifications of the equipment to avoid excessive voltage fluctuations from damaging the equipment and the power system.

[0106] Set the minimum allowable reactive power Q min,i and the maximum allowable reactive power Q max,i for each voltage control unit, that is, for the i-th control unit, its reactive power output must satisfy:

[0107] Q min,i ≤Q i (t)≤Q max,i ;

[0108] where: Q i (t) represents the reactive power output of the i-th control unit at time t.

[0109] These constraints on reactive power ensure that during the system operation, the output of the reactive power compensation equipment does not exceed its physical capacity and does not cause over-compensation or under-compensation of the system reactive power.

[0110] Generally, these constraint conditions are based on the actual needs of the power system and the equipment performance. Therefore, the optimization problem is not only to minimize or maximize the deviation between voltage, reactive power, and control signals in the objective function but also to consider these physical constraint conditions to ensure that the system operates in a safe and stable region.

[0111] As an option, to further enhance the stability and adaptability of the optimization results, the values of these constraints can also be dynamically adjusted according to the real-time grid load conditions. For example, when the system load is heavy, the maximum value constraints of voltage and reactive power can be appropriately relaxed to improve the flexibility of regulation; while when the load is light, the constraints can be tightened to ensure the stability of the power grid.

[0112] Specifically, when embedding these voltage and reactive power constraint conditions into the solution process of the optimization objective function, the actual optimization problem form is a constrained optimization problem with boundary conditions. Its mathematical model can be expressed as:

[0113]

[0114] Where: W 1 , W 2 , W 3 are the weight coefficients of voltage deviation, reactive power deviation and control signal strength respectively; V i (t) is the voltage state of the i-th control unit at time t; V ref,i is the reference voltage value of the i-th control unit; Q i (t) is the reactive power state of the i-th control unit at time t; Q ref,i is the reference reactive power value of the i-th control unit; u i (t) is the amplitude of the control signal of the i-th control unit; N is the total number of voltage control units; V min,i is the minimum allowable value of voltage; V max,i is the maximum allowable value of voltage; Q min,i is the minimum allowable value of reactive power; Q max,i The maximum allowable value of reactive power; subject to indicates that the constraint condition is.

[0115] In a possible implementation, these constraint conditions can be solved by classical constraint optimization methods such as the Lagrange multiplier method or the KKT conditions. By introducing the Lagrange multiplier, the constraint conditions can be incorporated into the objective function, thus obtaining an unconstrained optimization problem, and then solving this problem through a numerical optimization algorithm.

[0116] As an option, in some applications, if the constraint conditions are relatively complex or have inequality constraints, more advanced optimization algorithms such as Newton's method, genetic algorithm or particle swarm optimization (PSO) may be required for solution. These methods can better adapt to complex constraint conditions and obtain effective optimization results within a shorter calculation time.

[0117] S4. Consider disturbance factors in the optimization problem and establish an uncertainty model to construct a system dynamic expression containing disturbance terms;

[0118] Specifically, in the above steps, a dynamic model of the voltage control unit has been established, and a weighted optimization objective function including voltage deviation, reactive power deviation, and control signals has been constructed. At the same time, boundary constraints on voltage and reactive power have been introduced to form a constrained optimization problem. To further enhance the robustness of the system to uncertain factors in the actual operating environment, in this step, a perturbation modeling mechanism needs to be introduced to form a system expression structure with a random perturbation term, and the objective function is corrected accordingly, so as to construct an optimal control strategy with the ability to cope with uncertainties.

[0119] In this embodiment, to consider the unpredictable perturbation sources during the operation of the power grid, the perturbation term is first incorporated into the dynamic modeling of the voltage control system. The perturbation factors mainly come from load fluctuations on the load side and unpredictable changes in the power output of renewable energy sources (such as wind power and photovoltaic power) on the power generation side.

[0120] Specifically, the above perturbation terms are uniformly modeled as a time-varying random process, and this perturbation term is mathematically set as a Gaussian white noise process. Let the state variable of the i-th voltage control unit be denoted as x i (t), and its dynamic evolution model can be extended as:

[0121]

[0122] where: f i (x i (t), u i (t)) represents the deterministic dynamic function of the control unit; u i (t) is the control input of the i-th control unit; ξ i (t) represents the perturbation term, which satisfies the standard Gaussian white noise distribution, that is is a random process with a mean of 0 and a variance of 1; σ i (t) is the intensity function of the perturbation term corresponding to the i-th control unit, usually a time-varying real function, used to characterize the intensity level of the perturbation at different times.

[0123] Generally, the perturbation intensity σ i (t) can be estimated based on the historical operation data of the system or an empirical model, or can be dynamically obtained through an online identification method. This structure ensures that the model has higher practical adaptability, especially in operating scenarios where the power grid load fluctuates frequently or the proportion of new energy is relatively high.

[0124] To further counter the system response uncertainty caused by the above-mentioned random perturbations, it is necessary to transform the optimization objective function to enable it to handle performance metrics under random variables. Considering the statistical characteristics of Gaussian perturbations, an optimization objective function based on expectation is constructed to minimize the expected value of the system performance metric. The form of the revised optimization objective function is as follows:

[0125]

[0126] where: J t is the revised optimization objective function; represents the mathematical expectation of the random perturbation process; other parameter definitions are the same as in the previous steps, including: V i (t) is the actual voltage value, V ref,i is the reference voltage, Q i (t) is the reactive power, Q ref,i is the reactive power reference value, u i (t) is the control signal, W 1 , W 2 , W 3 are the weight coefficients; N is the total number of voltage control units.

[0127] In a possible implementation, the above optimization objective function can be approximately solved by the Monte Carlo simulation method, that is, by sampling the Gaussian white noise process multiple times, solving the objective function values respectively and taking their average value to estimate the expected function. This method has good adaptability and feasibility in engineering practice, especially suitable for complex models where the expected value cannot be calculated analytically.

[0128] As an option, to reduce the sensitivity of the system to instantaneous perturbation responses, a variance constraint of the perturbation term can also be introduced as an additional condition to limit the fluctuation range of the system state variables under perturbations. For example, it can be set that the system state variance shall not exceed a certain threshold δ, that is:

[0129] Var(V i (t)) ≤ δ V , Var(Q i (t)) ≤ δ Q ;

[0130] where: Var(·) represents the variance operation of the variable, δ V and δ Q are the upper limits of the variances of voltage and reactive power respectively; V i (t) is the voltage state of the i-th control unit at time t; Q i (t) is the reactive power state of the i-th control unit at time t.

[0131] Furthermore, to enhance the flexibility of system modeling, relevant high-order perturbation modeling methods can also be considered, such as Markov jump perturbation models or stochastic process models with memory characteristics, to more accurately reflect the time correlation and non-Gaussian characteristics of actual power grid perturbations. However, such extensions should be used with caution under specific conditions.

[0132] S5. Establish a game model based on the policy dependence between control units, and define a multi-agent optimization structure through the form of non-cooperative games;

[0133] Specifically, in the aforementioned steps, the modeling of introducing perturbation terms into the voltage control system has been completed, and an optimization objective function with an expected value has been constructed according to the uncertainty optimization method. The goal of this process is to ensure that the system can maintain stability and achieve optimal performance in the face of external perturbations. In this step, the accuracy and autonomy of the control strategy are further improved. Considering the policy dependence between voltage control units, a multi-agent optimization structure is described through a game model. Specifically, the framework of game theory is used to describe the interaction between different voltage control units, and the optimal strategy of each control unit is achieved through the form of non-cooperative games.

[0134] In this embodiment, each voltage control unit is first regarded as an independent decision-making agent, and an expected performance index function of voltage deviation, reactive power deviation, and control signal is set for each control unit. Specifically, the expected performance index function of the i-th control unit can be expressed as:

[0135]

[0136] where: J i is the expected performance index function of the i-th control unit; W 1i , W 2i , W 3i are weight coefficients related to the i-th control unit; V i (t) and Q i (t) are the voltage and reactive power of the i-th unit at time t, respectively; V ref,i and Q ref,i are their reference values; u i (t) is the control signal.

[0137] On the premise of the mutual influence of multiple control units, a non-cooperative dynamic game model is constructed. In this model, each control unit makes decisions based on its own performance index function in order to minimize its own performance error. However, due to the mutual influence between these control units, their strategy choices are not independent but interdependent. The optimization strategy of each control unit is affected by the behavior of other units, so a game model is needed to solve the optimal control strategy of each unit.

[0138] In general, this game model defines the strategy solution rules among multiple control units based on the concept of Nash equilibrium. Nash equilibrium is a stable strategy configuration where each participant (i.e., each control unit) has chosen its optimal strategy and, given the fixed strategies of other participants, cannot obtain a better result by unilaterally changing its strategy.

[0139] Specifically, each control unit solves its own optimal response strategy given the fixed strategies of other control units. This process can be achieved by solving the following optimization problem:

[0140]

[0141] where: The optimal control strategy of the i-th control unit in the current strategy environment; u -i (t) represents the control signals of all control units except the i-th control unit; J i (·) The objective function of the i-th control unit; u i (t) is the amplitude of the control signal of the i-th control unit.

[0142] Under this condition, the i-th control unit minimizes its performance index function by optimizing its control signal u i (t).

[0143] In a possible implementation, to solve the Nash equilibrium solution set, an iterative method can be used to gradually update the strategies of each control unit. Initially, the strategies of all control units can be randomly selected or set according to some empirical values. In subsequent iterative processes, each control unit continuously adjusts its strategy to minimize its expected performance index function. Through multiple iterative updates, it gradually approaches the Nash equilibrium solution, that is, the strategies of all control units no longer change.

[0144] As an option, to accelerate the convergence process, some optimization acceleration techniques can also be introduced, such as the accelerated gradient descent method or the population optimization strategy based on genetic algorithms, to speed up the process of finding the optimal strategy.

[0145] In some embodiments, to improve the robustness and adaptability of the system, the game structure among control units can also be extended. For example, a cooperative game framework can be considered, such that the control units are not just pure non - cooperative games, but rather cooperate in some form to optimize the overall system performance. This extension can effectively improve the overall performance of the system in specific application scenarios, especially when the coordination among multiple control units is more important.

[0146] By introducing the above game model, this embodiment ensures that in the voltage control system, each control unit can dynamically adjust its control strategy according to the interaction and finally converge to an optimal stable solution, which can ensure the optimization performance and stability of the system in the face of complex power grid environments and their disturbances.

[0147] S6. Solve the optimal control strategy under the game model and use it to drive each control unit to form a decentralized voltage control system.

[0148] Specifically, in the above steps, we have constructed a voltage control strategy based on the game model and ensured the optimal control strategy of each control unit through Nash equilibrium solution. Next, in order to apply these optimal control strategies to the voltage control system, the core of step S6 lies in solving and implementing these control strategies so that the system can adjust in real time and maintain optimal performance in the face of disturbances. This process includes constructing the mathematical form of the optimization problem based on the control objectives and constraints, using the distributed gradient descent method or the Lagrangian dual algorithm for solution, and updating the control strategy in real time through the edge computing platform.

[0149] In this embodiment, first, according to the objectives and constraints of the voltage control system, the mathematical form of the optimization problem is constructed. In order to achieve the optimal control of voltage deviation, reactive power deviation, and control signals, we have proposed the expected performance index function J of each control unit in the previous steps. i .

[0150] In the optimization problem, it is necessary to globally minimize the expected performance index functions of these control units to ensure that the system can achieve the optimal system performance under the cooperation of different voltage control units. Therefore, the mathematical form of the optimization problem can be expressed as:

[0151]

[0152] where: u -i (t) represents the control signals of all control units except the i-th control unit; J i (·) is the objective function of the i-th control unit; u i (t) is the amplitude of the control signal of the i-th control unit; N is the total number of voltage control units.

[0153] Generally, in order to solve this optimization problem, the distributed gradient descent algorithm or the Lagrangian dual algorithm is adopted. In the distributed gradient descent algorithm, each control unit locally calculates the gradient information of its objective function and adjusts its control signal u i (t) according to this information. This method does not require global communication and only needs to exchange local update information, so it has good scalability and real-time performance.

[0154] Specifically, the update rule of the gradient descent method is as follows:

[0155]

[0156] where: u i (t + 1) is the control signal of the i-th control unit at time t + 1; u i (t) is the control signal of the i-th control unit at time t; η is the learning rate, which is used to control the step size; is the objective function J of the i-th control unit i with respect to the control signal u i .

[0157] When using the Lagrangian dual algorithm, the constraint conditions of the problem are introduced through the method of Lagrange multipliers, and the original problem is relaxed to form a dual problem for solution. In this algorithm, by introducing the Lagrange multiplier λ i , the constraint conditions are optimized, thereby realizing the solution of the constrained optimization problem. For the constraint condition g i (u i ) ≤ 0, the Lagrangian form of the dual problem is:

[0158] L(u i , λ i ) = J i (u i ) + λ i ·g i (u i );

[0159] where: L(u i , λ i ) is the Lagrangian function; u i (t) is the control signal of the i-th control unit at time t; λ i is the Lagrange multiplier, indicating the influence of the constraint condition g i (u i ) on the objective function.

[0160] As an option, to improve the computational efficiency, the status data of each control unit can be obtained in real time through an edge computing platform, and the computing resources of the platform can be used for optimal solution. The platform updates the control strategy according to the real-time data of the control unit and transmits the updated control signal to each control unit through a feedback mechanism. This way can ensure that the system can respond to the changes in the power grid status in a timely manner and make adjustments during actual operation.

[0161] In a possible implementation, the edge computing platform, as the data and control center, processes the optimization problems of each control unit and adjusts the control strategy according to the real-time data feedback. Each control unit makes autonomous adjustments by obtaining the optimization results in real time, ensuring that the entire system achieves adaptive optimization of disturbances under the coordination of multiple control units.

[0162] Through this optimization process, ultimately each control unit will adjust its output voltage and reactive power according to the optimal control strategy, thereby achieving the optimal operation of the entire power grid system.

[0163] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for controlling distributed voltage in a power system, characterized in that: The following steps are involved: Establish a dynamic model of the voltage control unit and construct a system description of the voltage state change driven by the control signal; Based on the dynamic model, an optimization objective function is defined to characterize voltage deviation, reactive power deviation and control signal strength; Introducing constraints of voltage and reactive power into the optimization objective function to form a constrained optimization problem; Considering disturbance factors in the optimization problem and establishing an uncertainty model, constructing a system dynamic expression containing disturbance terms; A game model is established based on the strategic dependence between control units, and a multi-agent optimization structure is defined through a non-cooperative game form; The optimal control strategy is solved under the game model and used to drive each control unit to form a decentralized voltage control system.

2. A method for controlling distributed voltage in a power system according to claim 1, characterized in that: The step of establishing a dynamic model of the voltage control unit comprises: Obtain the real-time voltage value and reactive power value of each voltage control unit; Based on the nonlinear function form, a dynamic equation including voltage variables, reactive power variables and control signal variables is constructed; Each control unit is modeled as a nonlinear differential equation system to characterize the influence of the control signal on the voltage change rate.

3. A method for controlling distributed voltage in a power system according to claim 1, characterized in that: Defining the optimization objective function includes: Setting the reference voltage value and reference reactive power value of each voltage control unit; Constructing a weighted integral performance index including a square term of voltage deviation, a square term of reactive power deviation and a square term of control signal; A weight coefficient is set for each item, and the weight coefficient is used to adjust the influence ratio of each control target on the overall objective function.

4. A method for controlling distributed voltage in a power system according to claim 1, characterized in that: The constraints of the introduced voltage and reactive power include: Setting a minimum allowable voltage value and a maximum allowable voltage value for each voltage control unit; Setting a minimum allowable reactive power value and a maximum allowable reactive power value for each voltage control unit; The above constraints are embedded as boundary conditions into the solution process of the optimization objective function.

5. A method for controlling distributed voltage in a power system according to claim 1, characterized in that: The disturbance factors include: The disturbance term is constructed based on the load variation in the power grid and the uncertainty of the output on the generation side; The disturbance term is modeled as a time-varying Gaussian white noise process; Introduce disturbance terms into the dynamic equation of the control unit to form a system dynamic expression containing random terms; Construct an optimization objective function with expected value and minimize the expected performance index under random disturbance.

6. A method for controlling distributed voltage in a power system according to claim 1, characterized in that: The game model establishment comprises: Treat each voltage control unit as an independent decision-making entity; For each control unit, an expected performance index function including its voltage deviation, reactive power deviation and control signal is set respectively; Construct a non-cooperative dynamic game structure under the premise of multiple control units influencing each other; The strategy solving rules among multiple control units are defined based on the concept of Nash equilibrium.

7. A method for controlling distributed voltage in a power system according to claim 1, characterized in that: The solution of the optimal control strategy includes: Construct the mathematical form of the optimization problem based on control objectives and constraints; Use distributed gradient descent algorithm or Lagrangian dual algorithm to numerically solve the optimal control strategy; Deploy the optimization solver on the edge computing platform and update the control strategy through real-time data feedback; After the control strategy is generated, it is used to drive each control unit to adjust its output voltage and reactive power.

8. A method for controlling distributed voltage in a power system according to claim 2, characterized in that: The dynamic equation of the voltage control unit is: The voltage state variable of each control unit is represented by the current voltage value; The reactive power state variable is represented by the reactive power value currently output; The control input variable is the externally injected regulation signal; The control signal drives the change of state variables and reflects the state evolution process through differential expressions.

9. A method for controlling distributed voltage in a power system according to claim 3, characterized in that: The specific structure of the optimization objective function is: The first term is the square of the difference between the voltage deviation of each control unit and the reference value multiplied by the first weight coefficient; The second term is the square of the difference between the reactive power deviation of each control unit and the reference value multiplied by the second weight coefficient; The third term is the square of the control signal amplitude multiplied by the third weight coefficient; The overall objective function is the weighted sum of the above three items integrated over a given time interval.

10. A method for controlling distributed voltage in a power system according to claim 6, characterized in that: The process of solving the Nash equilibrium includes: Each control unit solves its own optimal response strategy when the strategies of other control units are fixed; Update the strategies of all control units in multiple iterations; When the strategies of all control units no longer change, it is determined that the current strategy group constitutes a Nash equilibrium solution set.

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