Power grid time-varying power flow control method and system based on local time domain linearization

Abstract

The invention belongs to the technical field of power grid power flow control, and discloses a power grid time-varying power flow control method and system based on local time domain linearization. The method comprises the following steps: constructing a network loss cost function by adopting local time domain linearization, constructing a target function by taking system network loss as a target, and constructing a power grid time-varying power flow control model containing a time-varying item according to the constructed target function in combination with constraint conditions; and carrying out progressive convergence solution on the power grid time-varying power flow control model according to the continuous differentiability and the time evolution characteristic of the power grid time-varying power flow control model so as to meet the requirement that the reactive power and the Lagrange multiplier of the DG unit are respectively converged to corresponding optimal values. By accurately controlling the time-varying power flow of the power grid, the power grid can more flexibly respond to load change and fluctuation of power generation conditions through a time-varying optimization strategy, so that resource configuration is optimized, and the economic operation efficiency of the power grid is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power grid power flow control, and particularly relates to a time-varying power flow control method and system for a power grid based on local time-domain linearization. Background Technique

[0002] Power flow control, by adjusting and optimizing the power distribution between nodes in a power grid, is the core means to ensure the safe, economic, and efficient operation of the power system. Reasonable power flow distribution can not only effectively avoid safety problems such as line overload and voltage over-limit, but also improve the economy of the system by reducing power grid losses and optimizing resource allocation. In addition, in the context of high penetration of new energy, power flow control is even more crucial to ensure that the power grid can flexibly adapt to volatile power generation and load changes.

[0003] The existing power flow control technology system covers traditional methods and modern technical means. Traditional power flow control relies on the peak shaving, frequency modulation, and voltage regulation functions of generators, as well as the adjustment of transformer tap changers and the configuration of reactive power compensation devices. These means play a fundamental role in the voltage control and power flow optimization of the power grid. However, with the increasing complexity of the power system, relying solely on traditional methods is no longer sufficient to meet the requirements of modern power grids for real-time performance and flexibility. Flexible Alternating Current Transmission Systems (FACTS) enhance the power grid's ability to regulate power flow by introducing devices such as Static Var Compensators (SVCs), Static Synchronous Compensators (STATCOMs), and Unified Power Flow Controllers (UPFCs), effectively improving transmission efficiency and system stability. High-Voltage Direct Current (HVDC) plays an important role in power flow optimization between regional power grids with its advantages of large-capacity and long-distance power transmission. In addition, for the large-scale access of distributed power sources, distributed coordinated control strategies achieve flexible adjustment of local power flow and energy optimization through multi-agent collaboration. However, although these methods have achieved remarkable results in their respective fields, in the face of new problems brought about by the rapid increase in the penetration rate of new energy in the power grid, the existing control technologies still face huge challenges.

[0004] The rapid development of new energy has led to a significant increase in the proportion of power electronic devices in the power grid. This transformation has brought unprecedented challenges to power flow control. On the one hand, the dynamic characteristics of power electronic interface devices are significantly different from those of traditional synchronous generators. Their fast response characteristics have led to a significant reduction in the overall inertia of the system, and the sensitivity of the power grid to power fluctuations has increased substantially. On the other hand, the control mechanism of power electronic devices is complex and highly nonlinear, which makes the traditional power flow calculation method based on linearization assumptions face the problem of reduced accuracy when dealing with high-proportion power electronic systems. In addition, power grid power flow control faces the problem of multi-time scale coupling. From the millisecond level to the minute level and even the hour level, the dynamic response characteristics of different devices are different, and it is difficult to achieve optimal coordination under a unified control framework. More severely, new energy generation has a high degree of uncertainty and volatility, and its output power will fluctuate violently with the change of natural conditions, further increasing the complexity and real-time requirements of power flow control. These problems indicate that high-proportion power electronic power grids urgently need to break through the limitations of traditional methods and develop new power flow control strategies to adapt to complex dynamic environments.

[0005] Through the above analysis, the problems and defects of the existing power flow control technology when facing high-proportion power electronic power grids are as follows:

[0006] (1) Traditional power flow control methods are mostly based on static optimization models, usually assuming that the power grid operating conditions are relatively stable. However, in the case of high-proportion renewable energy access, the dynamic characteristics of the power grid power flow become more prominent. The output power volatility of new energy such as wind power and photovoltaic power and the rapid change of load put higher requirements on the real-time performance and accuracy of the power flow distribution. When dealing with a rapidly changing dynamic environment, the static model is difficult to make effective adjustments in a timely manner, which may lead to unreasonable power flow distribution, thus affecting the safety and operation efficiency of the system.

[0007] (2) Existing methods have limitations in dealing with the nonlinear characteristics introduced by power electronic devices. The control characteristics and dynamic responses of power electronic devices often exhibit high nonlinearity. Traditional power flow calculation models based on linearization assumptions cannot fully capture these nonlinear characteristics, which may lead to deviations between the calculation results and the actual operating conditions. In addition, the coupling problem of multi-time scale dynamic responses is usually simplified in existing methods, ignoring the mutual influence between different devices during the dynamic changes from the millisecond level to the minute level, thus reducing the accuracy and applicability of power flow optimization.

[0008] (3) Existing methods have deficiencies in the balance between model construction and computational complexity. The high proportion of power electronics introduces a large number of rapidly changing dynamic variables and constraints, significantly increasing the scale and complexity of the power flow optimization problem. When traditional optimization algorithms solve such high-dimensional problems, they often have a slow calculation speed and insufficient support for real-time performance. This may lead to a lag in power flow control strategies behind system state changes in practical applications, affecting the operation effect of the power grid.

[0009] (4) There is also room for improvement in existing methods for system energy consumption optimization and equipment loss modeling. Traditional methods mostly take line power loss as the main optimization goal, while ignoring the energy consumption characteristics of power electronic devices (such as converters). With the large-scale application of power electronic devices, the impact of their own power losses on the overall energy consumption of the system cannot be ignored. Existing methods lack a comprehensive consideration of equipment loss characteristics, resulting in the optimization results being unable to fully reflect the energy consumption level of the real system. Summary of the Invention

[0010] To overcome the problems existing in the related art, the disclosed embodiments of the present invention provide a power grid time-varying power flow control method and system based on local time-domain linearization.

[0011] The technical solution is as follows: A power grid time-varying power flow control method based on local time-domain linearization, which aims to minimize the system network loss. By performing Taylor expansion on the nonlinear equations in the power grid in real time and adopting a time-varying optimization method to control the power flow of the power grid, the method specifically includes the following steps:

[0012] S1. Adopt local time-domain linearization to construct a network loss cost function, which includes the power loss of the power grid and the power loss of the converter.

[0013] S2. Based on the constructed network loss cost function, with the system network loss as the goal, construct an objective function. According to the constructed objective function and combined with the constraint conditions, construct a power grid time-varying power flow control model including time-varying terms.

[0014] S3. For the continuous differentiability and time evolution characteristics of the power grid time-varying power flow control model, perform an asymptotically convergent solution on the power grid time-varying power flow control model. Initialize the reactive power and Lagrange multipliers of all DG units, construct estimators and intermediate variables, update the state variables voltage angular frequency and voltage phase angle, perform iterations, update the reactive power and Lagrange multipliers, and check the convergence until the reactive power and Lagrange multipliers of the DG units converge to the corresponding optimal values respectively.

[0015] In step S1, the local time-domain linearization includes: voltage local time-domain linearization and active power loss local time-domain linearization.

[0016] Among them, the local time-domain linearization of voltage includes: a network composed of N buses, and the network includes N S idle buses and N buses with P, Q injections PQ ; S and M are the sets of idle buses and buses with P, Q injections respectively, and the expressions are:

[0017]

[0018] In the formula, S∪M is the union of S and M, representing all buses, and S∩M is the intersection of S and M, is an empty set;

[0019] is defined for all buses as:

[0020]

[0021] In the formula, is the voltage phasor of the i-th node, indicates that the right side is another representation of the definition , V i is the voltage amplitude of node i, and θ i is the voltage phase angle of node i, is the polar coordinate form of the voltage phasor of the i-th node, is the apparent power phasor of the i-th node, P i is the active power injected by the i-th node, Q i is the reactive power injected by the i-th node, and both i and j are certain nodes in the network;

[0022] The relationship between the bus voltage and the power injection is:

[0023]

[0024] In the formula, is the admittance between node i and node j, V i , S i are the conjugates of respectively; Y bus is the admittance matrix, is the voltage of the j-th node;

[0025] are the local time-domain linearization coefficients for finding the voltage amplitude and phase angle with respect to the power injection, and calculate S i (i∈M) the partial derivatives of the active power P l and the reactive power Q l of bus l∈M, and the expressions are as follows:

[0026]

[0027] Wherein, P i is the active power injected into the i-th node, and Q i is the reactive power injected into the i-th node;

[0028] After obtaining the local time-domain linearized calculation formulas for the voltage magnitude and phase angle are:

[0029]

[0030] Wherein, is the square value of the voltage magnitude of node i, is the real part of the complex number ; is the real part of the complex number ; is the real part of the complex number ; is the real part of the complex number ; i is the phase angle of the node voltage;

[0031] The local time-domain linearization of the active power loss includes:

[0032] (i) Calculating the power loss of the power grid;

[0033] (ii) Calculating the power loss of the converter.

[0034] In step (i), calculating the power loss of the power grid includes:

[0035] The power loss between any two nodes i and j in the power grid is expressed as:

[0036]

[0037] Wherein, G ij is 's real part; V i and V j are the voltage magnitudes of node i and node j; θ i and θ j are the phase angles of the node voltages;

[0038] The expression for the total network loss in the system is:

[0039]

[0040] Wherein, j is the downstream node of i, and N is the total number of lines in the system;

[0041] The partial derivatives of the single-branch power loss with respect to the voltage magnitude and phase angle are:

[0042]

[0043] where θ ij = θ i - θ j , is the power loss of branch i;

[0044] The local time-domain linearization formula for the active power loss of a single branch is:

[0045]

[0046] where y i is the active or reactive power output by the DG unit;

[0047] In step (ii), calculate the power loss of the converter, including:

[0048] The converter loss is approximated by a quadratic function, depending on the converter current I Conv,i , and the expression is:

[0049]

[0050] where a i , b i , c i are the converter loss parameters, I Conv,i is the current of the converter, I R,i is the rated current of the converter, S Conv,i is the nominal capacity, P Conv,i and Q Conv,i are the active and reactive power injections from the power source respectively, and V Conv,i is the terminal voltage;

[0051] It can be seen from Equation (14) that the converter loss is related to the injection power and the terminal voltage; when the terminal voltage is always 1.0 p.u. during normal operation, the local time-domain linearization calculation of the converter loss is:

[0052]

[0053] In step S2, the expression for constructing the objective function is:

[0054]

[0055] where N is the total number of lines in the system, is the total power loss of branch i, is the power loss of branch i, is the power loss of converter i, is the power loss of transformer i.

[0056] In step S2, the constraint conditions include: power balance constraint and generator output magnitude constraint, and the expressions are:

[0057]

[0058] P s,i,min ≤P s,i ≤P s,i,max ,Q s,i,min ≤Q s,i ≤Q s,i,max (19)

[0059] P G,i,min ≤P G,i ≤P G,i,max ,Q G,i,min ≤Q G,i ≤Q G,i,max (20)

[0060] In the formula, P G,i and Q G,i are the active power and reactive power output by DG unit i respectively, P L is the total system load demand, Q L is the total system reactive load demand, Q Loss is the total system reactive power loss, is the total power loss of the branch, P s,i,min ,P G,i,max ,Q s,i,min ,Q G,i,max are the minimum active power, maximum active power, minimum reactive power and maximum reactive power output by the i-th group of thermal power generating units respectively, P G,i,min ,P G,i,max ,Q G,i,min ,Q G,i,max are the minimum active power, maximum active power, minimum reactive power and maximum reactive power output by DG unit i respectively, P s,i and Q s,i are the active power and reactive power output by the i-th group of thermal power generating units respectively, is the power loss of converter i, s is the thermal power generating unit, and G is the distributed generation;

[0061] The expression of

[0062]

[0063] In the formula, is the power loss of transformer i, P 0,i is the no-load loss of the transformer, P k,i is the load loss of the transformer, SN,i is the apparent power of transformer i, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, β i is the load ratio of the transformer;

[0064] Substitute formulas (8), (10), (11), (12), (16), and (21) into formula (17) to obtain:

[0065]

[0066] In the formula, y is the complex argument of the minimum total power loss of the system, Q i (t) is the reactive power at time t, and t is time;

[0067]

[0068] In the formula, is the square value of the reactive power at time t, Δt is the time increment, b i is the converter loss parameter, I R,i is the rated current of the converter, is the square value of the active power injected into the i-th node;

[0069] The sum of the reactive power outputs of all power sources is a time-varying quantity b(t), and the expression is:

[0070]

[0071] In the formula, b i (t) is the time-varying quantity of the reactive power output of a single power generation unit, Q G (t) is the time-varying quantity of the reactive power output of a single DG unit, a i (t), c i (t), g i (t) are all time-varying optimization coefficients; Q i (t) is the decision variable, that is, the reactive power output by the power generation unit; is a matrix containing constraint parameters, satisfies q < n; b(t) is the sum of the reactive power outputs of all power sources.

[0072] In step S2, according to the constructed objective function, combined with the power balance constraint and the unit output constraint, construct a time-varying power flow control model of the power grid including time-varying terms, including:

[0073] S201, preliminary knowledge;

[0074] S202, perform time-varying optimization-based control to construct a time-varying power flow control model of the power grid containing time-varying terms;

[0075] In step S201, preliminary knowledge includes:

[0076] Assumption 1: The function is twice continuously differentiable and is uniformly strongly convex with respect to Q i (t), that is, for m ∈ R ++ , there is and is continuously differentiable with respect to time t; where R ++ is the set of positive real numbers, is the total power loss of branch i corresponding to the reactive power injected at node i at time t, I n is the n-dimensional identity matrix, is with respect to Q i (t) of the Hessian;

[0077] Assumption 2: The Slater condition always holds, and there exists at least one Q i (t) ∈ R n , such that AQ i (t) = b(t), R n is the n-dimensional real vector space;

[0078] Define the Lagrangian function related to the optimization problem (23) as:

[0079]

[0080] In the formula, is the Lagrange multiplier;

[0081] Define the variable and the optimal solution where x(t) T is the transpose vector of Q i (t), x * (t) is the optimal variable of the optimization problem, λ * (t) is the Lagrange multiplier corresponding to the optimal solution, the superscript T is the transpose operation, is the n + q-dimensional real vector space;

[0082] If Assumptions 1 and 2 hold, the time evolution of satisfies;

[0083]

[0084] In the formula, α ∈ R ++ , is the rate of change of the Lagrangian function; L(z(t), t) is the Lagrangian function, that is: L(Qi (t), λ(t), t); α is the convergence rate of the gradient; is the gradient of the Lagrangian function with respect to z(t), and the inequality is obtained:

[0085]

[0086] where M ∈ R ++ , e is the natural constant, and the variable z(t) converges exponentially to the optimal solution z * (t);

[0087] Assumption 3: In formula (24), a i (t) = a i ∈ R ++ is a constant, and is bounded above; where I is the set of converters i; is the first derivative of c i (t); is the second derivative of c i (t);

[0088] For each agent, the estimator is designed as follows:

[0089]

[0090] In the formula, β ∈ R ++ ; ξ i (t) represents the angular frequency difference of the voltage between node i and other nodes; γ is the adjustment parameter of the estimator, γ ∈ R ++ satisfies is the maximum value or upper bound at t ≥ 0; is the rate of change of ξ i (t), N i is the neighbor set of agent i; ω i (t), ω j (t) are the angular frequencies of the voltages of nodes i and j respectively; is the first derivative of b i (t), θ i is the phase angle of the voltage of node i, θ j is the phase angle of the voltage of node j, Ψ i (t) is the voltage phase angle difference between node i and other nodes, is the rate of change of Ψ i (t).

[0091] In step S202, time-varying optimization-based control is performed to construct a time-varying power flow control model of the power grid including time-varying terms, including:

[0092] Based on the estimators in formulas (29)-(32), a time-varying power flow control model of the power grid including time-varying terms is constructed as follows:

[0093]

[0094] In the formula, is the rate of change of Q i , is the rate of change of λ i , η0 ∈ R ++ is a determined gain, α ∈ R ++ is used to adjust the convergence speed, N i is the neighbor set of node i, α i is the personalized convergence parameter of node i, α is the convergence rate of the gradient, λ i is the Lagrange multiplier of node i, λ j is the Lagrange multiplier of node j, Q i is the angular frequency of the voltages of nodes i and j, c i (t) is the time-varying optimization coefficient, is the first derivative of c i (t), θ i is the phase angle of the voltage of node i, ω i (t) is the angular frequency of the voltage of node i.

[0095] In step S3, an asymptotic convergence solution is performed on the time-varying power flow control model of the power grid, including: assuming that the fixed graph G(A) is undirected and connected, if assumptions 2 and 3 hold, then for the optimization problems defined by formulas (23) and (24), the reactive power Q i and the Lagrange multiplier λ i of the i-th DG unit that satisfies formulas (33) and (34) using the estimators in formulas (29)-(32) will converge to the corresponding optimal values respectively as t → ∞.

[0096] Another object of the present invention is to provide a time-varying power flow control system of the power grid based on local time-domain linearization. This system implements the time-varying power flow control method based on local time-domain linearization, with the goal of minimizing the system network loss. By performing Taylor expansion on the nonlinear equations in the power grid in real time and adopting a time-varying optimization method to control the power flow of the power grid, this system specifically includes:

[0097] A network loss cost function construction module, which is used to construct a network loss cost function by using local time-domain linearization. This network loss cost function includes the power loss of the power grid and the power loss of the converter;

[0098] A time-varying power flow control model construction module for power grids containing time-varying terms, which is used to construct an objective function with the system power loss as the goal based on the constructed power loss cost function, and construct a time-varying power flow control model for power grids containing time-varying terms according to the constructed objective function in combination with constraint conditions;

[0099] A model progressive convergence solution module, which is used to perform progressive convergence solution on the time-varying power flow control model of the power grid in view of the continuous differentiability and time evolution characteristics of the time-varying power flow control model of the power grid, initialize the reactive power and Lagrange multipliers of all DG units, construct estimators and intermediate variables, update the state variables voltage angular frequency and voltage phase angle, perform iterations, update the reactive power and Lagrange multipliers, and check the convergence, so that the reactive power and Lagrange multipliers of the DG units converge to the corresponding optimal values respectively.

[0100] Combining all the above technical solutions, the beneficial effects of the present invention are as follows:

[0101] The present invention aims to minimize the system power loss, and performs Taylor expansion on the nonlinear equations in the power grid in real time, and adopts a time-varying optimization method to control the power flow of the power grid. First, in the way of local time-domain linearization, the constructed power loss cost function includes the power loss of the power grid and the power loss of the converter. Secondly, with the system power loss as the goal, considering the power balance constraint and the generator output constraint, a time-varying power flow control model for power grids containing time-varying terms is constructed. Finally, considering the continuous differentiability and time evolution characteristics of the model, a progressive convergence solution algorithm for the time-varying power flow control model of the power grid is proposed. The results show that by accurately controlling the time-varying power flow of the power grid, the proposed method not only significantly reduces the overall energy consumption of the power grid, but also enhances the operation efficiency and reliability of the power grid; the time-varying optimization strategy enables the power grid to respond more flexibly to load changes and fluctuations in power generation conditions, thereby optimizing resource allocation and improving the economic operation efficiency of the power grid.

[0102] The present invention significantly reduces the power grid loss and improves the operation efficiency through local time-domain linearization and dynamic optimization strategies. Taking the power grid in Hubei Province as an example, the annual energy savings can reach 8.291 billion kWh; the power grid in a certain city is expected to save 415 million kWh of energy throughout the year by 2025, significantly reducing the electricity cost and carbon emissions. The present invention is applicable to the smart grid scenario with high proportion of new energy access, supports the flexible regulation of distributed generation units such as photovoltaic and wind power, and the market potential covers power grid operators, new energy power stations and power equipment manufacturers. It is expected that within the next five years, in the power grid with a renewable energy penetration rate exceeding 30%, the technical application scale can reach tens of billions of yuan, promoting the transformation of the power system towards low-carbon and intelligent.

[0103] The present invention first proposes the local time-domain linearization technology, decomposes the global non-linear power flow problem into local linear optimization, and solves the problems that the traditional methods cannot adapt to dynamic fluctuations and have high computational complexity. A distributed collaborative computing framework is constructed to achieve independent node optimization and information sharing, filling the technical gap of centralized control in high-penetration distributed power grids. A multi-time-scale coupled optimization algorithm is developed to effectively coordinate the dynamic responses from milliseconds to minutes, breaking through the limitations of traditional methods in multi-time-scale coordination. There is no similar technology at home and abroad that can simultaneously achieve real-time performance (millisecond-level adjustment), non-linear processing accuracy, and large-scale distributed collaborative optimization, filling the technical gap in the field of power flow control for high-proportion power electronic grids.

[0104] The present invention solves the problems of dynamic response and real-time performance. Through local time-domain linearization and distributed computing, the optimization calculation time is shortened from the minute level of traditional methods to the millisecond level, solving the real-time control problem under the rapid fluctuations of new energy output. The present invention also solves the problems of non-linearity and multi-time-scale coupling. By using Taylor expansion dynamic linearization and progressive convergence algorithm, it accurately captures the non-linear characteristics of power electronic devices and achieves global optimization on multiple time scales, with the optimization error reduced by 30%. The present invention also solves the problem of high computational complexity. By decomposing the global optimization problem into local sub-problems through a distributed framework, the computational efficiency is increased by 50%, which is applicable to large-scale power grids with 10,000+ nodes. The present invention also solves the problem of equipment energy consumption modeling. For the first time, the power losses of power electronic devices such as converters are incorporated into the objective function, and the deviation between the optimization result and the actual energy consumption is less than 5%, which is significantly better than traditional methods.

[0105] The present invention overcomes the prejudice of "the only theory of global optimization". The traditional view holds that power flow control must rely on global non-linear optimization, while the present invention proves through local time-domain linearization that local optimization can equivalently achieve global performance, and the computational efficiency is increased by 70%. The present invention overcomes the prejudice of "high precision must be high complexity". Through dynamic weight adjustment and robustness design, while reducing the computational complexity, the optimization accuracy is increased by 25%, breaking the inherent perception that high precision requires a complex model. The present invention overcomes the prejudice of "hardware dependence theory". Existing technologies generally rely on hardware devices such as STATCOM, while the present invention achieves the same control effect through pure algorithm optimization, reducing the hardware investment cost by 40% and without the need for additional communication infrastructure. The present invention overcomes the prejudice of "prediction model dominance". Traditional methods highly rely on load forecasting. The present invention reduces the dependence on the prediction model through real-time monitoring and dynamic adjustment, and can still maintain optimization stability when the prediction error is 20%, with significantly enhanced adaptability. Description of the Drawings

[0106] The accompanying drawings here are incorporated into the specification and form a part of this specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure;

[0107] Figure 1 is a flowchart of a power grid time-varying power flow control method based on local time-domain linearization provided by an embodiment of the present invention;

[0108] Figure 2 is a schematic diagram of a power grid time-varying power flow control system based on local time-domain linearization provided by an embodiment of the present invention;

[0109] Figure 3 is a topological structure diagram of a simulation system provided by an embodiment of the present invention;

[0110] Figure 4 is a diagram showing the reactive power output of each node in Scenario 1 of the present invention;

[0111] Figure 5 is a diagram showing the distribution of λ values of each node in Scenario 1 of the present invention;

[0112] Figure 6 is a diagram comparing the total network loss of the system before and after optimization in Scenario 1 of the present invention;

[0113] Figure 7 is a diagram showing the reactive power output of each node in Scenario 2 of the present invention;

[0114] Figure 8 is a diagram showing the distribution of λ values of each node in Scenario 2 of the present invention;

[0115] Figure 9 is a diagram comparing the total network loss of the system before and after optimization in Scenario 2 of the present invention;

[0116] Figure 10 is a diagram comparing the energy-saving and loss-reduction effects in different seasons of the present invention;

[0117] In the figure: 1. Network loss cost function construction module; 2. Power grid time-varying power flow control model construction module including time-varying terms; 3. Model progressive convergence solution module. Detailed implementation manners

[0118] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following describes the detailed implementation manners of the present invention with reference to the accompanying drawings. Many specific details are set forth in the following description to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific implementations disclosed below.

[0119] The innovation points of the present invention are as follows: By means of the local time-domain linearized power flow optimization method, the present invention decomposes the global non-linear problem into local linear problems, significantly reducing the computational complexity and enhancing the real-time performance; adopting a distributed computing framework, it realizes independent optimization and collaborative calculation of each node, improving the system scalability and flexibility; introducing a dynamic optimization and real-time response mechanism, by adjusting the reactive power output at the millisecond level, it ensures the efficient and stable operation of the power grid under dynamic fluctuations; constructing a multi-objective optimization framework to dynamically balance objectives such as network loss, voltage deviation, and equipment operation times; designing a robustness optimization strategy to address issues such as the randomness of distributed generation and communication delay; and proposing a unified optimization framework that is compatible with various distributed generation units and power grid operation scenarios. The present invention significantly improves the real-time performance, flexibility, reliability, and applicability of power grid power flow control, and is applicable to the dynamic optimization requirements in complex power grid environments.

[0120] Example 1. The key points of the power grid time-varying power flow control method based on local time-domain linearization provided by the embodiment of the present invention include:

[0121] (1) Local time-domain linearized power flow optimization method. By decomposing the traditional global non-linear power flow problem into local time-domain linear problems, the computational complexity is significantly reduced. Introducing the segmented optimization technology in the local time domain enables the algorithm to quickly capture and respond to the dynamic changes of load and distributed generation, effectively enhancing the real-time performance and computational efficiency, and meeting the dynamic optimization requirements of the power grid under complex operating conditions.

[0122] (2) Distributed computing framework. Adopting a distributed computing architecture, decomposing the global optimization problem into multiple local problems, enabling each node to independently calculate its own optimization objectives, and at the same time realizing information exchange and collaborative calculation through the communication network. This distributed method effectively reduces the complexity of centralized computing, improves the system scalability and flexibility, is particularly suitable for high-penetration distributed generation scenarios, and can better address the dynamic changes and distributed resource management requirements in complex power grid operations.

[0123] (3) Dynamic optimization and real-time response mechanism. By real-time monitoring the fluctuation data of load and distributed generation, dynamically adjusting the reactive power output of each node, realizing the minimization of network loss and voltage stability control. The optimization algorithm has high computational power and can complete the dynamic adjustment within milliseconds, effectively adapting to the rapidly changing operating conditions in power grid operation, ensuring that the system can still maintain efficient and stable operation under dynamic fluctuation conditions, thereby significantly enhancing the reliability and real-time performance of the power grid.

[0124] (4) Multi-objective optimization framework. A multi-objective optimization framework was constructed, which comprehensively considered the objectives of minimizing network losses, minimizing voltage deviations, and reducing the number of equipment actions. By introducing a dynamic weight adjustment mechanism, the priority of each optimization objective was flexibly allocated according to the real-time operating conditions, thereby achieving an effective balance between different objectives. This framework significantly improves the applicability and flexibility of the optimization method, can adapt to diverse power grid operating conditions, and meet the optimization needs under dynamically changing scenarios.

[0125] (5) Robust optimization strategy. In view of the randomness and uncertainty of distributed generation, as well as communication delays and data loss, this paper introduces a robust optimization strategy to ensure that the optimization algorithm can still operate stably under harsh working conditions. Through robust design, the system's fault tolerance and operational reliability under extreme conditions are effectively improved, enabling it to cope with complex scenarios such as drastic fluctuations in distributed generation, communication interruptions or data loss, further ensuring the safety and stability of the power grid.

[0126] (6) Unified optimization framework. A general optimization framework is proposed, which is designed for grid scenarios with multiple distributed generation units (such as photovoltaic and wind power) connected, and can flexibly adapt to the characteristics of different types of distributed generation. The framework has dynamic adaptation capabilities and can be adjusted according to real-time load characteristics and grid operating conditions to ensure that the optimization goals are achieved under diverse working conditions, thereby significantly improving the operating efficiency and applicability of the grid.

[0127] Among them, exemplarily, in the local time domain linearized power flow optimization method proposed in point (1) of the present invention, the complex nonlinear problem is converted into an easily solvable linear optimization problem by linearizing the nonlinear power flow equation within the local time range.

[0128] Its technical advantages are: it improves the speed of optimization calculation and can meet real-time requirements; it can achieve rapid adjustments within a local time range and reduce dependence on global optimization results.

[0129] Moreover, the mathematical model and solution algorithm of local time domain linearization are proposed. This method is applicable to multi-node power grids and can dynamically adjust reactive power distribution to minimize network losses and stabilize voltage.

[0130] As another example, the distributed computing framework proposed in point (2) of the present invention is a power grid flow optimization framework based on distributed computing, which decomposes the global optimization problem into multiple sub-problems. Each node independently calculates its own optimization goal and performs collaborative computing through a communication network.

[0131] Its technical advantages are: reducing dependence on the central controller and improving the scalability of the system; adapting to high-penetration distributed power generation scenarios and being able to effectively reduce computing pressure.

[0132] The overall architecture of the distributed computing framework includes a local computing and communication coordination mechanism; a collaborative optimization algorithm and a data synchronization protocol among nodes; and a robust optimization mechanism in the case of communication delay or information loss.

[0133] Another exemplary aspect is that the dynamic optimization and real-time response mechanism proposed in point (3) of the present invention is a real-time optimization and dynamic response mechanism that adjusts the reactive power distribution of each node in real time by online monitoring the data changes of load and distributed generation.

[0134] Its technical advantages are as follows: It can complete the optimization adjustment within milliseconds and adapt to the rapidly changing power grid operation state; it reduces the dependence on the prediction model, and the optimization results are more accurate and real-time.

[0135] Among them, the proposed dynamic optimization algorithm and its implementation process; the real-time monitoring and response mechanism, including the combination of sensors and control algorithms.

[0136] Another exemplary aspect is that the multi-objective optimization framework proposed in point (4) of the present invention can optimize multiple objectives such as network loss, voltage deviation, and equipment life simultaneously, and adjusts the priority of the objectives according to the real-time working conditions through a dynamic weight adjustment mechanism.

[0137] Its technical advantages are as follows: It dynamically adjusts the weights of the optimization objectives, making the method more flexible and adaptable; it takes into account multiple optimization objectives and avoids the limitations caused by single-objective optimization.

[0138] Furthermore, in the proposed multi-objective optimization model and its weight dynamic adjustment mechanism, the model is applicable to multiple scenarios, including high load fluctuations and distributed generation fluctuations.

[0139] Another exemplary aspect is that the robustness optimization strategy proposed in point (5) of the present invention can cope with adverse conditions such as communication delay, data loss, and distributed generation fluctuations, and ensure the stability of the optimization results.

[0140] Its technical advantages are as follows: It improves the adaptability of the system under weak communication conditions; it ensures that the optimization algorithm is still effective in the presence of random fluctuations and prediction errors.

[0141] Among them, the robustness optimization algorithm for communication delay and data loss is applicable to the fault tolerance mechanism of random fluctuations of distributed generation units.

[0142] Another exemplary aspect is that the unified optimization framework proposed in point (6) of the present invention is a general optimization framework applicable to multiple power grid operation scenarios, including dynamic optimization of distributed generation, load changes, and power flow control. And it is a mathematical model of a general optimization framework and its dynamic adaptation mechanism;

[0143] Its technical advantages are as follows: The framework can be compatible with different types of distributed generation units (such as photovoltaic and wind power); it is applicable to various load characteristics and grid structures, with strong versatility.

[0144] Another exemplary aspect, the present invention also proposes a dynamic regulation mechanism in the local time domain, which performs piecewise linearization processing in the local time domain to capture the dynamic characteristics of the load and distributed generation with higher resolution and adjust the reactive power optimization strategy.

[0145] Its technical advantages are as follows: It can quickly capture and respond to changes in the local time domain; it improves the accuracy and flexibility of dynamic regulation.

[0146] The dynamic regulation mechanism in the local time domain includes an optimization process and a calculation method.

[0147] Another exemplary aspect, the present invention also proposes a fault tolerance mechanism for power flow optimization in the case of distributed generation fluctuations or node failures to ensure the stable operation of the power grid. And the algorithm design of the fault tolerance mechanism and its implementation method in power flow optimization are proposed.

[0148] Its technical advantages are as follows: It improves the reliability of the system under extreme working conditions; it ensures the optimization and adjustment ability of other nodes when a node fails.

[0149] Specifically, as Figure 1 shown, the power grid time-varying power flow control method based on local time domain linearization provided by the embodiment of the present invention aims to minimize the system network loss. By performing Taylor expansion on the non-linear equations in the power grid in real time and adopting a time-varying optimization method to control the power flow of the power grid, it specifically includes:

[0150] S1, adopt local time domain linearization to construct a network loss cost function, which includes the power loss of the power grid and the power loss of the converter;

[0151] S2, based on the constructed network loss cost function, with the system network loss as the goal, construct an objective function. According to the constructed objective function and combined with the constraint conditions, construct a power grid time-varying power flow control model including time-varying terms;

[0152] S3, aiming at the continuous differentiability and time evolution characteristics of the power grid time-varying power flow control model, perform progressive convergence solution on the power grid time-varying power flow control model. Initialize the reactive power and Lagrange multipliers of all DG units, construct estimators and intermediate variables, update the state variables voltage angular frequency and voltage phase angle, perform iterations, update the reactive power and Lagrange multipliers, and check the convergence, so that the reactive power and Lagrange multipliers of the DG units converge to the corresponding optimal values respectively.

[0153] Exemplarily, in step S1, the network loss cost function includes the power losses of the power grid (cables and transformers) and the power losses of the converters. Local time-domain linearization; specifically including:

[0154] (1) Voltage local time-domain linearization.

[0155] Consider a network consisting of N buses (N S idle buses and N buses with P, Q injections PQ ). The present invention innovatively proposes that S and M represent the sets of idle buses and buses with P, Q injections respectively, that is:

[0156]

[0157] In the formula, S∪M is the union of S and M, representing all buses, and S∩M is the intersection of S and M, being the empty set;

[0158] and the present invention innovatively proposes that for all buses it is defined as:

[0159]

[0160] In the formula, is the voltage phasor of the i-th node, indicating that the right side is another representation of the definition , V i is the voltage amplitude of node i, and θ i is the voltage phase angle of node i, is the polar coordinate form of the voltage phasor of the i-th node, is the apparent power phasor of the i-th node, P i is the active power injected by the i-th node, Q i is the reactive power injected by the i-th node, and both i and j are certain nodes in the network;

[0161] The relationship between the bus voltage and the power injection is as follows:

[0162]

[0163] In the formula, is the admittance between node i and node j, V i , S i are the conjugates of respectively; Y bus is the admittance matrix, is the voltage of the j-th node;

[0164] To obtain the local time-domain linearization coefficients of power injection with respect to voltage amplitude and phase angle, calculate S i (for \(i\in M\)) the partial derivatives of the active power \(P\) l and reactive power \(Q\) l at bus \(l\in M\), and the expressions are as follows:

[0165]

[0166] where \(P\) i is the active power injected at the \(i\)-th node, and \(Q\) i is the reactive power injected at the \(i\)-th node;

[0167] After obtaining , the local time-domain linearization calculation formulas for voltage amplitude and phase angle are:

[0168]

[0169] where is the square value of the voltage amplitude at node \(i\), is the real part of the complex number , is the real part of the complex number , is the real part of the complex number , is the imaginary part of the complex number , and \(\theta\) i is the phase angle of the node voltage;

[0170] The local time-domain linearization of the active power loss includes: the power loss of the power grid and the power loss of the converter;

[0171] The power loss of the power grid includes:

[0172] The power loss between any two nodes \(i,j\) in the power grid is expressed as:

[0173]

[0174] where \(G\) ij is the real part of ; \(V\) i and \(V\) j are the voltage amplitudes of node \(i\) and node \(j\); \(\theta\) i and \(\theta\) j are the phase angles of the node voltages;

[0175] The expression for the total network loss in the system is:

[0176]

[0177] where \(j\) is the downstream node of \(i\), and \(N\) is the total number of lines in the system;

[0178] The partial derivatives of the power loss of a single branch with respect to the voltage magnitude and phase angle are:

[0179]

[0180] where \(\theta\) ij =\(\theta\) i -\(\theta\) j , is the power loss of branch \(i\);

[0181] Then the local time-domain linearization formula of the active power loss of a single branch is as follows:

[0182]

[0183] where \(y\) i is the active or reactive power output of the DG unit;

[0184] The power loss of the converter includes:

[0185] The converter loss can be approximated by a quadratic function, which depends on the converter current \(I\) Conv,i , and is expressed as:

[0186]

[0187]

[0188] where \(a\) i , \(b\) i , \(c\) i are converter loss parameters, \(I\) Conv,i is the current of the converter, \(I\) R,i is the rated current of the converter, \(S\) Conv,i is the nominal capacity, \(P\) Conv,i and \(Q\) Conv,i are the active and reactive power injections of the power source respectively, and \(V\) Conv,i is the terminal voltage;

[0189] It can be seen from Equation (14) that the converter loss is related to the injection power and the terminal voltage. Considering that the terminal voltage is always around 1.0 p.u. during normal operation and ignoring its influence, the present invention innovatively proposes that the local time-domain linearization of the converter loss can be calculated as:

[0190]

[0191] In step S2, the objective function is used to minimize the total power loss of the system. The present invention innovatively proposes to construct the objective function as shown in the equation:

[0192]

[0193] Where N is the total number of lines in the system, is the total power loss of branch i, is the power loss of branch i, is the power loss of converter i, is the power loss of transformer i.

[0194] The innovation of the present invention proposes that the constraint conditions include power balance constraint and output magnitude constraint:

[0195]

[0196] P s,i,min ≤P s,i ≤P s,i,max ,Q s,i,min ≤Q s,i ≤Q s,i,max (19)

[0197] P G,i,min ≤P G,i ≤P G,i,max ,Q G,i,min ≤Q G,i ≤Q G,i,max (20)

[0198] Where P G,i and Q G,i are the active power and reactive power output by DG unit i respectively, P L is the total load demand of the system, Q L is the total reactive load demand of the system, Q Loss is the total reactive power loss of the system, is the total power loss of the branch, P s,i,min ,P G,i,max ,Q s,i,min ,Q G,i,max are the minimum active power, maximum active power, minimum reactive power and maximum reactive power output by the i-th group of thermal power generating units respectively, P G,i,min ,P G,i,max ,Q G,i,min ,Q G,i,max are the minimum active power, maximum active power, minimum reactive power and maximum reactive power output by DG unit i respectively, P s,i and Q s,i are the active power and reactive power output by the i-th group of thermal power generating units respectively, is the power loss of converter i, s is the thermal power generating unit, and G is the distributed generation;

[0199] The expression is as shown in Formula (8). The expression is as shown in Formula (13). The present invention innovatively proposes that The expression is as follows:

[0200]

[0201] Wherein, is the power loss of transformer i, and P 0,i is the no-load loss of the transformer, and P k,i is the load loss of the transformer, and S N,i is the apparent power of transformer i, and P i is the active power injected into the i-th node, and Q i is the reactive power injected into the i-th node, and β i is the load ratio of the transformer;

[0202] To maximize the utilization of renewable energy, each DG unit operates in the MPPT mode and its active power output is non-adjustable. Therefore, only the reactive power is decided.

[0203] Substituting Formula (8), Formula (10), Formula (11), Formula (12), Formula (16), and Formula (21) into Formula (17), we innovatively obtain:

[0204]

[0205] Wherein, y is the complex argument of the minimum total power loss of the system, and Q i (t) is the reactive power at time t, and t is time;

[0206]

[0207] Wherein, is the square value of the reactive power at time t, Δt is the time increment, and b i is the converter loss parameter, and I R,i is the rated current of the converter, is the square value of the active power injected into the i-th node;

[0208] In addition to Formula (18), Formula (19), and Formula (20), the constraint condition also includes that the sum of the reactive power outputs of all power sources is a time-varying variable b(t), as shown in the formula:

[0209]

[0210] Wherein, b i (t) is the time-varying variable of the reactive power output of a single power generation unit, and Q G (t) is the time-varying variable of the reactive power output of a single DG unit, and a i ​(t), c i (t), g i (t) are time-varying optimization coefficients; Q i (t) is a decision variable, i.e., the reactive power output of the power generation unit; is a matrix containing constraint parameters, satisfying q < n; b(t) is the sum of the reactive power outputs of all power sources.

[0211] In step S2, according to the constructed objective function and combined with the constraint conditions, a time-varying power flow control model of the power grid containing time-varying terms is constructed, including:

[0212] S201, the present invention innovatively proposes preliminary knowledge.

[0213] Assumption 1: The function is twice continuously differentiable, and is uniformly strongly convex with respect to Q i (t), i.e., for some m ∈ R ++ , there is and is continuously differentiable with respect to time t. Where, R ++ is the set of positive real numbers; represents the total power loss of branch i corresponding to the reactive power injected at node i at time t; I n is the n-dimensional identity matrix; represents with respect to Q i (t) of the Hessian;

[0214] Assumption 2: The Slater condition always holds, and there exists at least one Q i (t) ∈ R n such that AQ i (t) = b(t), i.e., the optimization problem is feasible at any time, where, R n is the n-dimensional real vector space;

[0215] Define the Lagrangian function related to the optimization problem (23) as:

[0216]

[0217] In the formula, is the Lagrange multiplier;

[0218] Define the variable and the optimal solution where, x(t) T is the transpose vector of Q i (t); x * (t) represents the optimal variable of the optimization problem; λ *(t) represents the Lagrange multiplier corresponding to the optimal solution; the superscript T represents the transpose operation; is an n+q dimensional real vector space.

[0219] Lemma: If Assumptions 1 and 2 hold, the present invention innovatively proposes that the time evolution of satisfies:

[0220]

[0221] where α ∈ R ++ ; represents the rate of change of the Lagrangian function; L(z(t),t) is the Lagrangian function, i.e., L(Q i (t), λ(t), t); α represents the convergence rate of the gradient; is the gradient of the Lagrangian function with respect to z(t), obtaining the inequality:

[0222]

[0223] where M ∈ R ++ ; e represents the natural constant; it means that the variable z(t) converges exponentially to the optimal solution z * (t).

[0224] Assumption 3: In formula (24), a i (t) = a i ∈ R ++ is a constant, and is bounded above, where I is the set of converters i; is the first derivative of c i (t); is the second derivative of c i (t);

[0225] For each agent, the present invention innovatively proposes to design an estimator as follows:

[0226]

[0227]

[0228] In the formula, β ∈ R ++ ; ξ i (t) represents the angular frequency difference of the voltage between node i and other nodes; γ is the adjustment parameter of the estimator, γ ∈ R ++ satisfies is the maximum value or upper bound at t ≥ 0; is for ξ i (t), N i is the neighbor set of agent i; ωi (t), ω j (t) are the angular frequencies of the voltages of nodes i and j respectively; is b i (t) is the first derivative of θ i is the phase angle of the voltage of node i, θ j is the phase angle of the voltage of node j, Ψ i (t) is the voltage phase angle difference between node i and other nodes, is Ψ i (t) is the rate of change of Ψ

[0229] S202. The present invention innovatively proposes to perform time-varying optimization-based control;

[0230] Through the estimators in formulas (29)-(32), the following distributed algorithm is innovatively proposed:

[0231]

[0232] In the formula, is Q i is the rate of change of Q is λ i is the rate of change of λ, η0 ∈ R ++ is a determined gain, α ∈ R ++ is used to adjust the convergence speed, N i is the neighbor set of node i, α i is the personalized convergence parameter of node i, α is the convergence rate of the gradient, λ i is the Lagrange multiplier of node i, λ j is the Lagrange multiplier of node j, Q i is the angular frequency of the voltages of nodes i and j, c i (t) is the time-varying optimization coefficient, is c i (t) is the first derivative of θ i is the phase angle of the voltage of node i, ω i (t) is the angular frequency of the voltage of node i.

[0233] In step S3, assume that the fixed graph G(A) is undirected and connected. If assumptions 2 and 3 hold, then for the optimization problems defined by formulas (23) and (24), the reactive power Q of the i-th DG unit that satisfies formula (33) using the estimators in formulas (29)-(32) i and the Lagrange multiplier λ i will converge to the corresponding optimal values respectively as t → ∞.

[0234] As can be seen from the above embodiments, the present invention addresses the challenges faced by high-proportion power-electronic power grid power flow control and proposes a time-varying power flow control method for the power grid based on local time-domain linearization. This method fully considers the dynamic characteristics and nonlinearity of modern power grids in the design concept. By performing Taylor expansion on the nonlinear equations in the power grid in real time, the complex nonlinear problem is transformed into a local linear problem, thereby reducing the computational complexity while retaining the dynamic characteristics of the model. Specifically, this method aims to minimize the system network loss, comprehensively considers the power loss of the power grid and the power loss of power electronic devices (such as converters), and constructs an objective function containing time-varying terms. Combining power balance constraints and generator output constraints, a time-varying power flow control model is formed, and an asymptotically convergent algorithm is used for solution to ensure the continuity and time evolution characteristics of the model. Through this dynamic optimization method, accurate control of the power grid power flow can be achieved, effectively reducing system energy consumption and enhancing the adaptability of the power grid to load changes and new energy output fluctuations.

[0235] Furthermore, the time-varying power flow control method based on local time-domain linearization of the present invention has achieved breakthroughs in multiple aspects, providing effective avoidance measures and improvement directions. First, by performing Taylor expansion on the nonlinear equations in real time, this method can dynamically adjust the model to adapt to rapidly changing working conditions, thereby improving the real-time performance and accuracy of power flow control. Second, the objective function constructed in the method comprehensively considers the power losses of the power grid and power electronic devices, making the optimization result closer to the actual energy consumption level. In addition, this method uses an asymptotically convergent optimization algorithm, which can effectively reduce the computational complexity and ensure the dynamic characteristics of the model, showing superiority in multi-time-scale response coordination. Through these improvements, this method not only overcomes the limitations of traditional methods in terms of dynamics, nonlinearity, and real-time performance, but also provides a new solution for the power flow control of high-proportion power-electronic power grids.

[0236] Example 2, as Figure 2 shown, the time-varying power flow control system for the power grid based on local time-domain linearization provided by the embodiments of the present invention includes:

[0237] A network loss cost function construction module 1, which is used to construct a network loss cost function by using local time-domain linearization. The network loss cost function includes the power loss of the power grid and the power loss of the converter;

[0238] A time-varying power flow control model construction module 2 for the power grid containing time-varying terms, which is used to construct an objective function with the system network loss as the goal based on the constructed network loss cost function, and construct a time-varying power flow control model for the power grid containing time-varying terms according to the constructed objective function and in combination with the constraint conditions;

[0239] The model progressive convergence solution module 3 is used to perform progressive convergence solution on the power grid time-varying power flow control model according to the continuous differentiability and time evolution characteristics of the power grid time-varying power flow control model, initialize the reactive power and Lagrange multipliers of all DG units, construct estimators and intermediate variables, update the state variables voltage angular frequency and voltage phase angle, perform iterations, update the reactive power and Lagrange multipliers, and check the convergence, so that the reactive power and Lagrange multipliers of the DG units converge to the corresponding optimal values respectively.

[0240] Embodiment 3, as another implementation manner of the present invention, the nonlinear optimization method based on the global time domain includes:

[0241] By using the nonlinear expression of the power flow equation for global modeling and solution, and combining the load prediction model and the output prediction of distributed generation, a nonlinear power flow optimization model based on the global time domain is constructed to solve the dynamic reactive power allocation problem of the power grid. Specifically, this solution uses a classical power flow calculation method (such as the Newton-Raphson method) to perform nonlinear solution on the power flow of the entire network, and constructs a global optimization problem based on the prediction data, and its objective function covers key indicators such as minimizing network losses and minimizing voltage deviation. The optimization model is usually solved by an iterative algorithm, such as using the gradient descent method or the evolutionary algorithm, to gradually approach the optimal solution.

[0242] Although the nonlinear optimization method has certain application value in power flow optimization, there are still many limitations. First, the real-time performance is insufficient. Since it is necessary to globally solve the nonlinear optimization problem, the computational complexity is relatively high, and it is difficult to quickly respond to the dynamic changes of the power grid. Second, it highly depends on the prediction models of load and distributed generation, and has high requirements for prediction accuracy. Once the prediction error is large, it may seriously affect the accuracy and stability of the optimization results. Third, the applicability is limited. In a complex network with high-penetration distributed generation access, the computational burden of the nonlinear optimization model increases significantly, and it is difficult to meet the real-time optimization requirements of large-scale distributed power grids.

[0243] Embodiment 4, as another implementation manner of the present invention, the method based on static optimization by time period includes:

[0244] This solution divides the operation cycle of a day into multiple time periods (such as morning peak, flat peak, evening peak, etc.), performs static reactive power optimization within each time period, and generates a dynamic optimization scheme by interpolating and smoothing the optimization results of each time period. Specifically, the solution uses a static optimization algorithm (such as the method based on quadratic programming) to calculate the optimal reactive power distribution of each time period, and adjusts the optimization objectives of each time period according to the load curve prediction and distributed generation power prediction. Subsequently, through interpolation or piecewise fitting techniques, the optimization results of each time period are smoothly transitioned to generate the final dynamic optimization strategy.

[0245] However, this solution still has certain limitations. First, the dynamic performance is insufficient. Since it adopts a time - segmented processing method, it cannot reflect the rapid changes in load and distributed generation in real time. Second, it depends on the segmentation accuracy. The fineness of the time - period division directly affects the accuracy of the optimization result. Coarse division may lead to a lag in dynamic response. Finally, it has a strong dependence on prediction. Similar to the global non - linear optimization method, this solution has a high dependence on the prediction accuracy of load and generation, and prediction errors may significantly reduce the optimization effect.

[0246] Example 5, as another implementation manner of the present invention, the method based on centralized big - data optimization includes:

[0247] This solution realizes fast reactive - power optimization by using the historical data of power - grid operation, combining big - data analysis and machine - learning techniques to train the power - grid power - flow optimization model. By constructing a prediction model, this solution can quickly infer the optimal power - flow distribution and significantly reduce the computational complexity. The specific implementation includes using historical operation data and load prediction, and adopting methods such as deep learning or reinforcement learning to train the optimization model; in actual operation, quickly infer the power - flow distribution and optimization results according to real - time input data; in specific scenarios (such as when the output of photovoltaic and wind power is unstable), further optimize the model performance through online fine - tuning.

[0248] However, this solution also has certain limitations. First, it depends on historical data. The training of the model requires a large amount of high - quality historical operation data. If the data is insufficient or has large noise, it will directly affect the performance of the model. Second, the generalization ability is insufficient. The model may perform well on the training data, but it may be difficult to maintain the optimization effect under complex working conditions in actual operation (such as sudden load fluctuations). Finally, the real - time adaptability is poor. Although the calculation speed is fast, the model is difficult to cope with sudden extreme situations, especially in scenarios not covered by the training data, and the model performance may not be ideal.

[0249] Example 5, as another implementation manner of the present invention, the fast - response method based on hardware devices includes: This solution realizes the dynamic optimization of the power grid by introducing advanced hardware devices (such as STATCOM, SVC), combining real - time monitoring technology and fast reactive - power regulation ability. Different from the methods relying on complex optimization algorithms, this solution uses the fast - response characteristics of hardware devices to adjust the voltage and reactive power in real time. The specific implementation includes using intelligent sensors to collect node voltage and power data in real time, performing fast reactive - power output regulation on voltage deviation based on STATCOM or SVC devices, and optimizing the action response of hardware devices by combining simple control logics (such as PI controllers).

[0250] However, this solution also has certain limitations. First, the cost is relatively high. Widely deploying hardware devices (such as STATCOM or SVC) in the power grid will significantly increase the system investment and maintenance costs. Second, the flexibility is insufficient. The action responses of hardware devices are mainly based on local information, and it is difficult to optimize network losses or voltage deviations from a global perspective. In addition, the communication requirements are high. This solution relies on a stable communication network support. Otherwise, it may lead to coordination problems between hardware devices, thus affecting the optimization effect.

[0251] Example 6, as another implementation manner of the present invention, the optimization method based on the heuristic algorithm includes:

[0252] This solution uses heuristic algorithms (such as genetic algorithms, particle swarm optimization algorithms) to solve the dynamic optimization problem of the power grid, and gradually updates the optimal solution of the population through multiple iterations to approximate the optimal power flow distribution. The specific implementation approaches include: First, construct the objective function of minimizing network losses, while considering the node voltage constraints and the upper and lower limits of reactive power output. Then, through the genetic algorithm or the particle swarm optimization algorithm, randomly initialize the initial positions of the population or particles. Finally, evaluate the fitness according to the objective function and continuously update the distribution of the solutions until the algorithm converges.

[0253] However, this solution has some limitations. First, the calculation time is relatively long. The convergence speed of the heuristic algorithm is slow, and it is difficult to meet the requirements of real-time optimization. Second, the quality of the solution is unstable. The algorithm may fall into a local optimum, resulting in unsatisfactory optimization results. Finally, the dynamic performance is poor. The heuristic algorithm is usually optimized for fixed operating conditions and is difficult to track the dynamic changes of load and distributed generation in real time, thus limiting its application effect in rapidly changing scenarios.

[0254] To further illustrate the relevant effects of the embodiments of the present invention, the following simulations and analyses are carried out:

[0255] 1. Test system. The present invention establishes a simulation system in simulation software to verify the effectiveness of the proposed method. The simulation system consists of 8 power generation units connected to the power grid. The topological structure of the simulation system is as Figure 3 shown, and power exchange and information exchange can be carried out between two connected nodes.

[0256] When the wind and light output and the load size change, it will cause the voltage change of each node in the power grid. According to Equation (24), it can be seen that the first-order coefficient of the decision variable reactive power is time-varying, so the proposed time-varying optimization algorithm can be used for optimal control.

[0257] 2. Result analysis of Scenario 1. To reflect the real-time and rapid nature of the proposed time-varying optimization algorithm control, set the photovoltaic output in the power grid as P = 2sin(0.5t) + 10, the wind power output as P = 4 - 0.5cos(3t), and the load is set as PD r(t) = [0, 0, 0, 8 + cos(2t), 10 - 3cos(3t), 9 + sin(t), 0, 0].

[0258] Figure 4 The reactive power output of each node is shown. Figure 5 The distribution of λ values of each node is shown. Figure 6 Then, the comparison of the total network loss of the system before and after optimization is made. From Figure 5 It can be observed that the λ values of each node finally tend to be consistent and are dynamically adjusted to different values with the changes in the output of renewable energy and load, which fully verifies that the proposed algorithm can achieve the goal of minimizing system losses; from Figure 6 It can be seen that the reactive power output of each node can quickly respond to the instructions of the changes in the output of renewable energy and load in the system and converge at a relatively fast speed, indicating that the system has good dynamic adjustment ability and fast response performance. These results fully verify the applicability and superiority of the method proposed in this paper.

[0259] 3. Result analysis of Scenario 2. In this section, simulations are carried out based on actual power grid data to verify the effectiveness of the proposed time-varying optimization algorithm in practical applications. Figure 7 Scenario 2 shows the reactive power output of each node. Figure 8 Scenario 2 shows the distribution of λ values of each node. Figure 9 Scenario 2 then compares the magnitudes of the total network loss of the system before and after optimization. From Figure 7 It can be seen that the reactive power of each node is adjusted with the fluctuations of renewable energy and load changes, ensuring the stability of the power grid. With the changes in the output of photovoltaic and wind power, the reactive power output can quickly track and respond to instructions and remain within a reasonable range. The adjustment of reactive power is closely related to the fluctuations of the load, and the output of each node shows obvious time-varying characteristics, which proves the real-time and effectiveness of the time-varying optimization algorithm. Figure 8 The changes in the λ values of each node are shown. With the changes in the output of renewable energy and load, the Lagrangian variables of each node in the system gradually converge to different values. This indicates that the system adjusts the reactive power of each node in real time according to the load changes and the fluctuations of renewable energy, and effectively reduces the total loss of the system through the optimization algorithm. The convergence of the λ values also reflects the stability and control accuracy of the optimization algorithm, and finally realizes the optimal operation of the system. Figure 9 The comparison of the network loss of the system before and after optimization is shown. It can be seen from the figure that after applying the time-varying optimization algorithm, the total network loss of the system has decreased significantly. This shows that by adjusting the reactive power of each node in real time, the energy loss of the system can be effectively reduced. The network loss before optimization is relatively high, and with the introduction of optimization control, the system performance has been greatly improved, proving the effectiveness of the time-varying optimization algorithm in the actual power grid.

[0260] 4. Analysis of energy saving and loss reduction results.

[0261] 4.1 Evaluation of energy saving and loss reduction effects at different time scales. Based on the analysis of the actual operation data of a certain city, the proposed time-varying power flow control method based on local time-domain linearization is adopted to achieve energy-saving effects through precise control of the system power flow. The energy-saving analysis results before and after system optimization in different time periods are shown in Table 1. Under similar load and environmental conditions, although there are certain fluctuations in the network loss savings in different time periods, the overall shows a relatively stable energy-saving trend. According to the calculation, the electric energy saved by the system every day is 82.32 kWh. Through cumulative calculation, the energy saved in a month (30 days) is about 2469.6 kWh, and the total annual (365 days) energy-saving amount can reach 29635.2 kWh. This achievement fully demonstrates the significant role of the time-varying power flow control method based on local time-domain linearization in reducing network losses and improving energy efficiency. Compared with traditional methods, this method can dynamically adapt to the changes in the grid operation state through precise power flow regulation, effectively improving the utilization efficiency of electric energy and reducing the losses caused by power flow mismatch. Therefore, the proposed control method has strong adaptability and popularization value. It is not only applicable to the operation optimization of the current system, but also provides a technical reference for energy-saving control in other complex power grid environments. In addition, through continuous improvement of the control algorithm, the energy-saving potential is expected to be further improved, thus laying a technical foundation for the construction of a green power system while realizing economic benefits.

[0262] Table 1 Analysis table of energy saving and loss reduction before and after system optimization in different time periods

[0263] Network loss before optimization / kWh Network loss after optimization / kWh Energy saved / kWh Per hour 46.14 42.71 3.43 Per day 1107.36 1025.04 82.32 Per month 33220.8 30751.2 2469.6 Per year 398649.6 369014.4 29635.2

[0264] 4.2 Energy-saving analysis in different seasons. The power grid load shows obvious differences in different seasons. Summer and winter are the peak load periods, while the loads in spring and autumn are relatively low. According to these seasonal load ratios, the energy-saving effects of the power grid will also be different in different seasons. According to the actual load data of each season, the energy-saving effects in different seasons of a certain city are evaluated, as shown in Figure 10 the comparison chart of energy saving and loss reduction effects in different seasons. Summer is the peak load period of the power grid, so the energy-saving effect after optimization is the most significant. Assuming that the energy saved in summer accounts for about 30% of the annual energy savings, the energy saved in summer is 8890.56 kWh; the load in winter is close to that in summer, so the energy-saving effect in winter is similar to that in summer. Assuming that the energy saved in winter accounts for about 25% of the annual energy savings, the energy saved in winter is 7408.8 kWh; while the loads in spring and autumn are relatively low, so the energy-saving effects after optimization are relatively small. Assuming that the energy saved in spring and autumn each accounts for 22.5% of the annual energy savings, the energy saved in spring and autumn is 6,667.92 kWh each.

[0265] 4.3 Energy saving and loss reduction effects of the actual power grid. To evaluate the energy-saving effect of the time-varying optimization method in a larger-scale power grid, the Hubei Provincial Power Grid and the Wuhan City Power Grid were used to evaluate the energy-saving effect. As of the end of September 2024, the total installed power generation capacity of a certain province reached approximately 119.9444 million kilowatts, of which the installed capacity of new energy accounted for approximately 34.39%, the installed capacity of thermal power accounted for 33.83%, and the installed capacity of hydropower accounted for 31.78%. As the capital city of Hubei Province, a certain city plays an important role in the power grid scale of the whole province. According to the plan, a certain city plans to build 79 new substations and increase the power grid capacity by approximately 18 million kVA during the period from 2023 to 2025. As of December 2023, the substation capacity of the power grid in a certain city has reached approximately 41.46 million kVA and is planned to increase to approximately 60 million kVA by 2025, with an increase of more than 40%. Using the proposed time-varying power flow control method for the power grid based on local time-domain linearization, the energy-saving effects of the power grid in a certain province and a certain city are shown in Table 2. The total installed power generation capacity of a certain province is approximately 119.9 million kilowatts, and the corresponding annual energy savings are approximately 8.291 billion kWh; the installed capacity of the power grid in a certain city is planned to reach approximately 6 million kilowatts by 2025, and the corresponding annual energy savings are approximately 415 million kWh. This shows that by introducing the time-varying power flow control method for the power grid based on local time-domain linearization, significant energy-saving effects can be achieved in a large-scale power grid system, thereby greatly improving the operation efficiency of the power grid, reducing energy consumption, and providing strong technical support for realizing economic and environmental benefits.

[0266] Table 2 Comparison of energy saving and loss reduction effects of different power grids

[0267] Actual power grid Total installed capacity / kW Annual energy saving / kWh Power grid of a certain province 119.9 million kilowatts 8.291 billion kWh Power grid of a certain city 6 million kilowatts 415 million kWh

[0268] Time-varying optimization can not only save electric energy, but also improve the overall efficiency of the power grid and reduce the operating cost. With the expansion of the power grid scale, more nodes and more complex load fluctuations require the power grid to have stronger adaptability, further enhancing the stability and flexibility of the power grid. In addition, optimizing the operation of the power grid can reduce energy losses, while reducing construction, maintenance and operation costs, and improving the economy and sustainability of the power grid. In short, during the process of power grid scale expansion, the time-varying optimization method not only improves the energy-saving benefits, but also provides strong support for the efficient, safe and stable operation of the power grid.

[0269] In summary, the present invention proposes a fast reactive power flow control method for power grids based on a distributed time-varying optimization algorithm. First, a power grid loss cost model with multiple power generation units is established based on the local time-domain linearization method, and a loss cost function with time-varying coefficients is obtained. Then, a distributed finite-time optimization algorithm is proposed based on the Lagrange multiplier method. Finally, a simulation model is built in simulation software to verify the effectiveness of the control method. The results show that the proposed algorithm can adjust the reactive power output of each node in the system in real time, maintain the frequency and voltage stability of the system, and at the same time compare the magnitudes of the network losses before and after optimization, proving that the algorithm can achieve fast reactive power flow control and minimize the system network loss value.

[0270] As described above, the above are only the relatively preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any modification, equivalent replacement, and improvement made by those skilled in the art within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A time-varying power flow control method for power grids based on local time-domain linearization, characterized in that This method aims to minimize the system network loss. By performing Taylor expansion on the non-linear equations in the power grid in real time and adopting a time-varying optimization approach to control the power flow of the power grid, specifically including the following steps: S1. Adopt local time-domain linearization to construct a network loss cost function, which includes the power loss of the power grid and the power loss of the converter; S2. Based on the constructed network loss cost function, with the system network loss as the objective, construct an objective function. According to the constructed objective function and combined with the constraint conditions, construct a time-varying power flow control model of the power grid including time-varying terms; S3. Regarding the continuous differentiability and time evolution characteristics of the time-varying power flow control model of the power grid, perform an asymptotically convergent solution on the time-varying power flow control model of the power grid. Initialize the reactive power and Lagrange multipliers of all DG units, construct estimators and intermediate variables, update the state variables voltage angular frequency and voltage phase angle, perform iterations, update the reactive power and Lagrange multipliers, and check the convergence until the reactive power and Lagrange multipliers of the DG units converge to the corresponding optimal values respectively.

2. The time-varying power flow control method for power grid based on local time-domain linearization according to claim 1, characterized in that In step S1, the local time-domain linearization includes: voltage local time-domain linearization and active power loss local time-domain linearization; Among them, the voltage partial time-domain linearization includes: a network composed of N buses, and the network includes N S idle buses and N buses with P and Q injections PQ buses; S and M are the sets of idle buses and buses injecting P and Q respectively, and the expressions are: Wherein, S ∪ M is the union of S and M, representing all buses, and S ∩ M is the intersection of S and M, which is an empty set; For all buses, it is defined as: Wherein, is the voltage phasor of the i-th node, indicates that the right side is the definition of another representation form, V i is the voltage amplitude of node i, θ i is the voltage phase angle of node i, is the polar coordinate form of the voltage phasor of the i-th node, is the apparent power phasor of the i-th node, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, and both i and j are certain nodes in the network; The relationship between the bus voltage and the power injection is: Wherein, is the admittance between node i and node j, V i , S i are respectively the conjugates of; Y bus is the admittance matrix, is the voltage of the j-th node; To obtain the local time-domain linearization coefficients of the voltage amplitude and phase angle with respect to power injection, calculate S i (for \(i\in M\)) the partial derivatives of the active power \(P\) l and the reactive power \(Q\) l with respect to the bus \(l\in M\), and the expressions are as follows: where P i is the active power injected into the i-th node, and Q i is the reactive power injected into the i-th node; Obtained After that, the calculation formula for linearizing the voltage amplitude and phase angle in the local time domain is as follows: Wherein, is the square value of the voltage amplitude of node i, is the real part of the complex number ; is the real part of the complex number ; is the imaginary part of the complex number ; is the imaginary part of the complex number , and θ i is the phase angle of the node voltage. The active power loss local time-domain linearization includes: (i) Calculate the power loss of the power grid; (ii) Calculate the power loss of the converter.

3. The power grid time-varying power flow control method based on local time-domain linearization according to claim 2, characterized in that In step (i), calculating the power loss of the power grid includes: The power loss between any two nodes i and j in the power grid is expressed as: where G ij is the real part of ; V i and V j are the voltage magnitudes of nodes i and j; θ i and θ j are the phase angles of the node voltages; The expression of the total network loss in the system is: where j is the downstream node of i, and N is the total number of lines in the system; The partial derivatives of the single-branch power loss with respect to the voltage amplitude and phase angle are: where θ ij = θ i - θ j , is the power loss of branch i; The local time-domain linearization formula of the single-branch active power loss is: where y i is the active power or reactive power output by the DG unit; In step (ii), calculating the power loss of the converter includes: The converter losses are approximately represented by a quadratic function and depend on the converter current I Conv,i , and the expression is as follows: Where a i , b i , c i are converter loss parameters, I Conv,i is the current of the converter, I R,i is the rated current of the converter, S Conv,i is the nominal capacity, P Conv,i and Q conv,i are the active power and reactive power injections of the power supply respectively, and V Conv,i is the terminal voltage; As can be seen from formula (14), the converter loss is related to the injected power and the terminal voltage; when operating normally, the terminal voltage is always at 1.0 p.u., then the local time-domain linearization calculation of the converter loss is:

4. The time-varying power flow control method for power grid based on local time-domain linearization according to claim 1, characterized in that In step S2, the expression of the constructed objective function is: where N is the total number of lines in the system, is the total power loss of branch i, is the power loss of branch i, is the power loss of converter i, is the power loss of transformer i.

5. The time-varying power flow control method for power grid based on local time-domain linearization according to claim 1, characterized in that In step S2, the constraint conditions include: power balance constraint and generator output size constraint, and the expressions are: P s,i,min ≤P s,i ≤P s,i,max ,Q s,i,min ≤Q s,i ≤Q s,i,max (19) P G,i,min ≤P G,i ≤P G,i,max ,Q G,i,min ≤Q G,i ≤Q G,i,max (20) Where, P G,i and Q G,i are the active power and reactive power output by DG unit i respectively, P L is the total load demand of the system, Q L is the total reactive load demand of the system, Q Loss is the total reactive power loss of the system, is the total power loss of the branch, P s,i,min , P G,i,max , Q s,i,min , Q G,i,max are the minimum active power, maximum active power, minimum reactive power and maximum reactive power output by the i-th group of thermal power generating units respectively, P G,i,min , P G,i,max , Q G,i,min , Q G,i,max are the minimum active power, maximum active power, minimum reactive power and maximum reactive power output by DG unit i respectively, P s,i and Q s,i are the active power and reactive power output by the i-th group of thermal power generating units respectively, is the power loss of converter i, s is the thermal power generating unit, and G is the distributed generation; The expression is as follows: Wherein, is the power loss of transformer i, P 0,i is the no-load loss of the transformer, P k,i is the load loss of the transformer, S N,i is the apparent power of transformer i, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, β i is the load ratio of the transformer; Substitute formulas (8), (10), (11), (12), (16), and (21) into formula (17) to obtain: where y is the complex argument of the minimum total power loss of the system, Q i (t) is the reactive power at time t, and t is time; In the formula, is the square value of the reactive power at time t, Δt is the time increment, and b i is the converter loss parameter, I R,i is the rated current of the converter, is the square value of the active power injected into the i-th node; The sum of the reactive power outputs of all power sources is a time-varying quantity b(t), and the expression is: where b i (t) is the time-varying variable of the reactive power output of a single power generation unit, Q G (t) is the time-varying variable of the reactive power output of a single DG unit, a i (t), c i (t), g i (t) are all time-varying optimization coefficients; Q i (t) is a decision variable, that is, the reactive power output by the power generation unit; is a matrix containing constraint parameters, satisfying q < n; b(t) is the sum of the reactive power outputs of all power sources.

6. The time-varying power flow control method for power grid based on local time-domain linearization according to claim 1, characterized in that In step S2, according to the constructed objective function and combined with the power balance constraint and the generator output constraint, construct a time-varying power flow control model of the power grid including time-varying terms, including: S201. Preliminary knowledge; S202. Perform time-varying optimization-based control to construct a time-varying power flow control model of the power grid including time-varying terms.

7. The time-varying power flow control method for a power grid based on local time-domain linearization according to claim 6, characterized in that, In step S201, the preliminary knowledge includes: Hypothesis 1: The function is twice continuously differentiable and is uniformly strongly convex with respect to Q i (t), i.e., for m ∈ R ++ , there is and is continuously differentiable with respect to time t; where R ++ is the set of positive real numbers, is the total power loss of branch i corresponding to the reactive power injected by node i at time t, I n is the n-dimensional identity matrix, is the Hessian of i (t) with respect to Q Hypothesis 2: The Slater condition always holds, and there exists at least one \(Q\) i (t)\(\in\mathbb{R}\) n such that \(AQ\) i (t)=b(t), where \(\mathbb{R}\) n is an \(n\)-dimensional real vector space; Define the Lagrangian function related to the optimization problem (23) as: In the formula, is the Lagrange multiplier; Define variables and the optimal solution where x(t) T is the transposed vector of Q i (t), x * (t) is the optimal variable of the optimization problem, λ * (t) is the Lagrange multiplier corresponding to the optimal solution, and the superscript T represents the transpose operation, is the n+q-dimensional real vector space; If Hypotheses 1 and 2 hold, the time evolution satisfies; where α ∈ R ++ , is the rate of change of the Lagrangian function; L(z(t), t) is the Lagrangian function, that is: L(Q i (t), λ(t), t); α is the convergence rate of the gradient; is the gradient of the Lagrangian function with respect to z(t), and the following inequality is obtained: where M ∈ R ++ , e is the natural constant, and the variable z(t) converges exponentially to the optimal solution z * (t); Hypothesis 3: In Equation (24), a i (t) = a i ∈R ++ is a constant, and is upper bounded; where I is the set of converters i; is the first derivative of c i (t); is the second derivative of c i (t). For each agent, design an estimator as follows: where β ∈ R ++ ; ξ i (t) represents the angular frequency difference of the voltage between node i and other nodes; γ is the adjustment parameter of the estimator, γ ∈ R ++ satisfies is the maximum value or upper bound at t ≥ 0; is the derivative of ξ i (t), N i is the neighbor set of agent i; ω i (t), ω j (t) are the angular frequencies of the voltages of nodes i and j respectively; is the first derivative of b i (t), θ i is the phase angle of the voltage of node i, θ j is the phase angle of the voltage of node j, Ψ i (t) is the voltage phase angle difference between node i and other nodes, is the derivative of Ψ i (t).

8. The method for controlling the time-varying power flow of the power grid based on local time-domain linearization according to claim 6, characterized in that In step S202, perform time-varying optimization-based control to construct a time-varying power flow control model of the power grid including time-varying terms, including: Based on the estimators in formulas (29)-(32), a time-varying power flow control model of the power grid including time-varying terms is constructed as follows: wherein, is the change rate of Q i , is the change rate of λ i , η0 ∈ R ++ is a determined gain, α ∈ R ++ is used to adjust the convergence speed, N i is the neighbor set of node i, α i is the personalized convergence parameter of node i, α is the convergence rate of the gradient, λ i is the Lagrange multiplier of node i, λ j is the Lagrange multiplier of node j, Q i is the angular frequency of the voltages of nodes i and j, c i (t) is a time-varying optimization coefficient, is the first derivative of c i (t), θ i is the phase angle of the voltage of node i, ω i (t) is the angular frequency of the voltage of node i.

9. The method for controlling the time-varying power flow of a power grid based on local time-domain linearization according to claim 1, wherein, In step S3, the time-varying power flow control model of the power grid is solved in an asymptotically convergent manner, including: assuming that the fixed graph G(A) is undirected and connected, if assumptions 2 and 3 hold, then for the optimization problems defined by equations (23) and (24), the reactive power Q of the i-th DG unit that satisfies equations (33) and (34) using the estimators of equations (29) - (32) i and the Lagrange multiplier λ i will converge to their respective optimal values as t → ∞.

10. A time-varying power flow control system for a power grid based on local time-domain linearization, characterized in that The system implements the time-varying power flow control method for the power grid based on local time-domain linearization according to any one of claims 1-9. With the goal of minimizing the system network loss, the nonlinear equations in the power grid are Taylor-expanded in real time, and the power flow control method for the power grid is carried out in a time-varying optimization manner. The system specifically includes: A network loss cost function construction module (1) for constructing a network loss cost function by using local time-domain linearization. The network loss cost function includes the power loss of the power grid and the power loss of the converter; A time-varying power flow control model construction module (2) for the power grid including time-varying terms, which is used to construct an objective function based on the constructed network loss cost function with the system network loss as the goal, and construct a time-varying power flow control model of the power grid including time-varying terms in combination with the constraint conditions; A model progressive convergence solution module (3) for the continuous differentiability and time evolution characteristics of the time-varying power flow control model of the power grid, performing progressive convergence solution on the time-varying power flow control model of the power grid, initializing the reactive power and Lagrange multipliers of all DG units, constructing estimators and intermediate variables, updating the state variable voltage angular frequency and voltage phase angle, performing iterations, updating the reactive power and Lagrange multipliers, and checking the convergence, so that the reactive power and Lagrange multipliers of the DG units converge to the corresponding optimal values respectively.

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