Active power distribution network flexible resource optimal operation method based on holomorphic embedding method

Abstract

This invention provides a method for optimizing the operation of flexible resources in active distribution networks based on the fully embedded method, comprising the following steps: 1) First, a model is established using photovoltaic, wind power generation devices, and energy storage as flexible resources in the distribution network, with the minimum voltage deviation rate and the minimum total daily network loss as the objective function; 2) Second, a power flow embedding model is constructed using the formula of the fully embedded method; a suitable embedding form is designed, and the analytical solution under the objective state is obtained through the Pad approximation analytical extension path; 3) Finally, the operating state of the flexible resources is optimized using the day-ahead forecast data of typical wind and solar power output and load power, and the fully embedded power flow calculation method is used to calculate the system power flow during the optimization process.

Description

Technical Field

[0001] This invention relates to the field of power flow calculation technology, and in particular to a method for optimizing the operation of active distribution network flexibility resources based on the fully embedded method. Background Technology

[0002] With the advancement of the national "dual-carbon" strategic goals, distributed resources, primarily photovoltaic (PV) power, are being extensively integrated into distribution networks, gradually forming distribution networks with high PV penetration. This has led to an increasingly prominent contradiction between voltage fluctuation issues and users' ever-increasing voltage quality requirements. Flexible resources are a crucial means of mitigating voltage fluctuation problems. The rational allocation and operation of flexible resources can improve voltage near the connection point, enhance power flow distribution within the system, and reduce line losses, thus playing a vital role in the efficient and economical operation of distribution networks and even the entire power system.

[0003] Power flow calculation is a fundamental analytical tool for power system planning and operation, and it forms the basis for solving optimal power flow problems. The process of solving power flow involves solving a system of nonlinear equations. This nonlinearity makes it difficult to directly address the optimization of flexible resource operation in active distribution networks. The high proportion of flexible resources makes the power generation capacity of the power system more dynamic and uncertain. Furthermore, the multi-timescale operation of the power system brought about by the introduction of flexible resources presents difficulties and challenges to power flow calculation, significantly reducing the efficiency of power flow solution.

[0004] Currently, the Newton-Raphson method is commonly used to solve nonlinear power flow equations in power systems. However, the NR method is widely recognized as being sensitive to initial value selection during power flow calculations. Furthermore, in large-scale power system power flow calculations or calculations involving the optimization of flexible resource operation states, it requires repeated updates and inverse operations of the Jacobi matrix, leading to increased computational load, slower computation speed, and the potential for singularity in the Jacobi matrix due to excessive iterations, resulting in non-convergence of the power flow calculation. Considering that complex and dynamic large-scale power grid system optimization problems often involve multiple objectives that are related and conflicting, suitable multi-objective optimization algorithms are needed. A suitable optimization method requires a trade-off between convergence speed, robustness, and algorithm complexity. In summary, robustly and efficiently solving multi-objective optimization problems involving flexible resources in large-scale power systems is challenging, exhibiting problems such as low solution efficiency, poor robustness, and cumbersome algorithms. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide an active distribution network flexibility resource optimization operation method based on the fully embedded method, which can more efficiently reduce the network loss of the power grid and achieve energy saving, environmental protection and low carbon emissions in the power system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for optimizing the operation of flexible resources in active distribution networks based on a fully embedded method, comprising the following steps:

[0007] 1) First, a model is established using photovoltaic, wind power generation devices, and energy storage as flexible resources of the distribution network. The objective functions are to minimize the voltage deviation rate and the total daily network loss of the system, and to establish a multi-objective flexible resource operation state optimization model.

[0008] 2) Next, the power flow embedding model is constructed using the formula of the fully embedded method; a suitable embedding form is designed to ensure that the power balance equation after fully embedded is meaningful under the target state; the initial solution at the initial state is solved; the recursive equation of the power series coefficient of voltage-power is proposed; and the analytical solution under the target state is obtained by performing an analytical extension path through the Pad approximation.

[0009] 3) Finally, using typical wind and solar power output and load power day-ahead forecast data, a multi-objective particle swarm optimization algorithm is used to optimize the operating status of flexible resources. At the same time, a fully embedded power flow calculation method is used to calculate the system power flow during the optimization process.

[0010] In a preferred embodiment, the multi-objective function is:

[0011] (1)

[0012] , These are the weighting coefficients;

[0013] Total daily network loss of the system:

[0014] (2)

[0015] In the formula: Let t represent the total network loss of the system, and t be the time identifier, where t=1,2,3. T, where T is the total number of moments; take =1h, T=24h; , Branch roads The resistance and current values; E is the set of branches;

[0016] Voltage deviation rate

[0017] (3)

[0018] In the formula, For nodes Voltage amplitude, denoted as , where is the expected voltage amplitude of the node; N is the total number of nodes in the system.

[0019] In a preferred embodiment, the constraints are specifically as follows:

[0020] a. Power flow constraints in the power system:

[0021] (4)

[0022] b. Branch flow constraints:

[0023] (5)

[0024] In the formula, It is the complex power of the PQ node. It is the active power of the PV node. This represents the given voltage amplitude at the PV node. This represents the setpoint voltage at the slack node; and It is a side road Power loss; and It is a side road Admittance and susceptance; It is a side road The susceptivity to ground; , , These are nodes and nodes Phase difference and nodes voltage amplitude and nodes voltage amplitude, It is a node and nodes The magnitude of the voltage vector difference between them;

[0025] When using the fully embedded method to calculate system power flow, the first step is to reconstruct the fully embedded model, which is then reconstructed as follows:

[0026] (6)

[0027] In the formula, , Indicates the node number; Represents the ()th node in the node admittance matrix , )element, and These are about nodes and Line admittance, node Earth-based self-acceptance;

[0028] In the initial state Below, we have an initial solution:

[0029] (7)

[0030] The recursive equation (8) is given below:

[0031]

[0032] (8)

[0033] In the formula, To specify the voltage magnitude for the slack node, For impulse functions, when hour, ;when hour, ; Let be a new holomorphic function. equal The reciprocal, ; ;

[0034] Based on the nth-order truncated power series of a holomorphic function, the analytic value is obtained by analytic extension through the Pad approximation. The Pad approximation is a rational polynomial approximation that can approximate the original function more accurately than the truncated Taylor series and can effectively expand the region of convergence.

[0035] hypothesis function ,in The Pad approximation can be expressed as:

[0036] (9)

[0037] Will Substituting into equation (9), when s=1, we can obtain the function value after Pad approximation; the function value satisfies the constraint equations (4) and (5).

[0038] In a preferred embodiment, node voltage constraints are applied:

[0039] (10)

[0040] In the formula, , They are nodes The upper and lower limits of voltage, For nodes Voltage;

[0041] Branch current constraints:

[0042] (11)

[0043] In the formula, , Branch roads The upper and lower limits of the current, branch road Current;

[0044] Node power constraints:

[0045] (12)

[0046] In the formula, and For impulse functions, when node When flexible resources are accessed, then and =1, otherwise and =0; It refers to the set of end nodes that start from in all branches of the distribution network; It refers to the branch circuits in the distribution network that are... It is the set of the first and last nodes at the end; A positive value indicates that the energy storage node is discharging, and a negative value indicates that the energy storage node is charging.

[0047] Output constraints of distributed power nodes:

[0048] (13)

[0049] Energy storage active and reactive power output constraints:

[0050] (14)

[0051] In the formula, and It is an energy storage node Active and reactive power injected by energy storage devices; and This represents the amount of electricity stored in the system at time t and the time following t; To improve the charging efficiency of energy storage systems, This refers to the discharge efficiency of the energy storage system.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) The fully pure embedding method, as a power flow solution method with non-iterative recursion, no dependence on the selection of initial points, and high computational efficiency, is organically combined with the particle swarm optimization algorithm with strong search capabilities and fast convergence capabilities. This can significantly improve the efficiency and accuracy of power flow calculation and optimization target convergence, without significantly increasing the complexity of the algorithm. It realizes flexible resource optimization operation that takes into account both operational economy and power quality.

[0054] (2) Using the holomorphic embedding method to replace the conventional power flow calculation method to solve the problem of optimizing the operation of flexible resources in the distribution network can avoid the disadvantage of repeated iterative updates of the Jacobi matrix in the traditional power flow calculation method. At the same time, it has the advantages of non-iterative recursive solution of the power series coefficients of holomorphic functions and non-initial value dependence of using a given feasible solution with actual physical meaning as the initial reference state. It significantly reduces the difficulty of solving the power flow of the flexible resource operation optimization model and improves the solution efficiency of the model.

[0055] (3) With the continuous in-depth research by researchers at home and abroad, the performance of the multi-objective particle swarm optimization algorithm has been continuously improved, and its application fields are also constantly expanding. Choosing this algorithm to deal with the optimal power flow problem is relatively mature to a certain extent. Attached Figure Description

[0056] Figure 1 This is a flowchart of the algorithm of a preferred embodiment of the present invention. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0059] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0060] A method for optimizing the operation of flexible resources in active distribution networks based on the fully embedded method, referencing Figure 1 This includes the following steps:

[0061] 1) First, a model is established using photovoltaic, wind power generation devices, and energy storage as flexible resources of the distribution network. The objective functions are to minimize the voltage deviation rate and the total daily network loss of the system, and to establish a multi-objective flexible resource operation state optimization model.

[0062] 2) Next, the power flow embedding model is constructed using the formula of the fully embedded method; a suitable embedding form is designed to ensure that the power balance equation after fully embedded is meaningful under the target state; the initial solution at the initial state is solved; the recursive equation of the power series coefficient of voltage-power is proposed; and the analytical solution under the target state is obtained by performing an analytical extension path through the Pad approximation.

[0063] 3) Finally, using typical wind and solar power output and load power day-ahead forecast data, a multi-objective particle swarm optimization algorithm is used to optimize the operating status of flexible resources. At the same time, a fully embedded power flow calculation method is used to calculate the system power flow during the optimization process.

[0064] Specifically:

[0065] Establish objective function

[0066] The optimization of the operation of flexible energy storage is a multi-objective, multi-constraint, and multi-dimensional problem. Taking into account the economy of the distribution network and power quality, the objective function is to minimize the total daily network loss and voltage deviation rate.

[0067] Constructing a multi-objective function:

[0068] (1)

[0069] , These are the weighting coefficients; other specific parameters are described below:

[0070] 1. Total daily network loss of the system

[0071] (2)

[0072] In the formula: Let t represent the total network loss of the system, and t be the time identifier, where t=1,2,3. T, where T is the total number of moments. For convenience, let's take... =1h, T=24h; , Branch roads The resistance and current values; E is the set of branches.

[0073] 2. Voltage deviation rate

[0074] (3)

[0075] In the formula, For nodes Voltage amplitude, denoted as , where is the expected voltage amplitude of the node; N is the total number of nodes in the system.

[0076] Constraints

[0077] (1)a. Power flow constraints in the power system:

[0078] (4)

[0079] b. Branch flow constraints:

[0080] (5)

[0081] In the formula, It is the complex power of the PQ node. It is the active power of the PV node. This represents the given voltage amplitude at the PV node. This represents the setpoint voltage at the balancing node. and It is a side road Power loss; and It is a side road Admittance and susceptance; It is a side road The susceptivity to ground; , , These are nodes and nodes Phase difference and nodes voltage amplitude and nodes voltage amplitude, It is a node and nodes The magnitude of the voltage vector difference between them.

[0082] When using the fully embedded method to calculate system power flow, the first step is to reconstruct the fully embedded model, which is then reconstructed as follows:

[0083] (6)

[0084] In the formula, , Indicates the node number; Represents the ()th node in the node admittance matrix , )element, and These are about nodes and Line admittance, node Earth-based self-acceptance;

[0085] In the initial state Below, we have an initial solution:

[0086] (7)

[0087] The recursive equation (8) is given below:

[0088]

[0089] (8)

[0090] In the formula, To specify the voltage magnitude for the slack node, For impulse functions, when hour, ;when hour, ; Let be a new holomorphic function. equal The reciprocal, ; .

[0091] Based on the above obtained nth-order truncated power series of the holomorphic function, the analytic value is obtained through analytic continuation using the Pad approximation. The Pad approximation is a rational polynomial approximation that can approximate the original function more accurately than the truncated Taylor series and can effectively expand the region of convergence.

[0092] hypothesis function ,in The Pad approximation can be expressed as:

[0093] (9)

[0094] Will Substituting into equation (9), when s=1, we can obtain the function value after Pad approximation. This function value satisfies the constraint equations (4) and (5).

[0095] (2) Node voltage constraints:

[0096] (10)

[0097] In the formula, , They are nodes The upper and lower limits of voltage, For nodes Voltage.

[0098] (3) Branch current constraints:

[0099] (11)

[0100] In the formula, , Branch roads The upper and lower limits of the current, branch road Electric current.

[0101] (4) Node power constraints:

[0102] (12)

[0103] In the formula, and For impulse functions, when node When flexible resources are accessed, then and =1, otherwise and =0; It refers to the set of end nodes that start from in all branches of the distribution network; It refers to the branch circuits in the distribution network that are... It is the set of the first and last nodes at the end; A positive value indicates that the energy storage node is discharging, while a negative value indicates that the energy storage node is charging.

[0104] Output constraints of distributed power nodes:

[0105] (13)

[0106] (5) Constraints on active and reactive power output of energy storage:

[0107] (14)

[0108] In the formula, and It is an energy storage node Active and reactive power injected by energy storage devices. and This represents the amount of electricity stored in the system at time t and the time following t. To improve the charging efficiency of energy storage systems, This refers to the discharge efficiency of the energy storage system.

[0109] The specific steps are as follows:

[0110] Step 1: Obtain the day-ahead predicted output of wind power and photovoltaic power generation, the data distribution of classical loads, the distribution network topology, and the node admittance matrix in the active distribution network.

[0111] Step 2: Solve the problem using a multi-objective particle swarm optimization (PSO) algorithm. The bird flock is represented by a particle swarm, and the distance between the birds and the food is represented by a fitness function. The particles fly at a certain speed in the search space. This flight speed is dynamically adjusted based on the flight experience of individuals and the group, continuously optimizing until an optimal fitness value is obtained. Taking an energy storage device as an example, the daily charging and discharging power of the energy storage device in the power distribution network is represented by the basic particles, specifically in the form of…

[0112] (15)

[0113] In the formula For particle swarm optimization, The first in the matrix line, number Column element, representing the energy storage device The particle in the first The charging and discharging power of the timing sequence. For the first in the matrix The fitness value of each particle is determined. Population initialization is performed in this step, including the size of the particle population, the position of each particle (the charging and discharging power of the energy storage device), its velocity (the direction and distance of particle movement in the search space), and the non-dominated solution states.

[0114] Step 3: Update the population size and the state of each particle in the population (position, velocity, non-dominated solution, etc.), and update the voltage-power state of each node in the distribution network.

[0115] Step 4: Use the fully embedded power flow calculation method to include all node voltages in the model as the unknowns. , The S of the PQ node and the Q of the PV node are reconstructed using fully pure embeddings. , , , s is the holomorphic embedding factor.

[0116] make (16)

[0117] As the initial solution for the holomorphic function recursion, it is substituted into equation (8), and the Taylor power series coefficients of the function to be solved are continuously obtained by recursively solving according to the recursive equation. After obtaining the coefficients of each order... and Then, the voltage and power values ​​are approximated using the Pad approximation rational fraction of equation (9).

[0118] (17)

[0119] Substituting s=1, we obtain the approximation result of the unknown quantity, and by comparing the given convergence accuracy, we determine the voltage value V of all nodes approximated, the complex power S of the PQ node, and the reactive power Q of the PV node.

[0120] Step 5: Based on the specific power flow distribution obtained by the pure embedding method in the previous step, calculate the average value of the network loss and the voltage deviation of all nodes in the system as the particle fitness of each particle at the current position.

[0121] Step 6: For each particle, compare its current fitness value with the fitness value corresponding to its individual historical best position (pbest). If the current fitness value is higher, then update the historical best position with the current fitness value.

[0122] Step 7: For each particle, compare its current fitness value with the fitness value corresponding to its global best position (gbest). If the current fitness value is higher, then update the global best position with the current fitness value.

[0123] Step 8: Update the speed of each individual, as follows:

[0124] (18)

[0125] In the formula , As a learning factor, It is a constant. , It is a random number that is uniformly distributed within the interval [0,1].

[0126] Step 9: Update the location of each individual, as follows:

[0127] (19)

[0128] Step 10: Compare the fitness of all particles, change the non-dominated solution state of the particles, find the particles in the first sequence of non-dominated solutions, and eliminate the dominated particles.

[0129] Termination condition judgment: When the number of iterations reaches the maximum number of iterations, if the condition is met, output the Pareto optimal solution; otherwise, jump to Step 3 and repeat the process.

Claims

1. A method for optimizing the operation of flexible resources in active distribution networks based on the fully embedded method, characterized in that... Includes the following steps: 1) First, a model is established using photovoltaic, wind power generation devices, and energy storage as flexible resources of the distribution network. The objective functions are to minimize the voltage deviation rate and the total daily network loss of the system, and to establish a multi-objective flexible resource operation state optimization model. 2) Next, the power flow embedding model is constructed using the formula of the fully embedded method; a suitable embedding form is designed to ensure that the power balance equation after fully embedded is meaningful under the target state; the initial solution at the initial state is solved; the recursive equation of the power series coefficient of voltage-power is proposed; and the analytical solution under the target state is obtained by performing an analytical extension path through the Pad approximation. 3) Finally, using typical wind and solar power output and load power day-ahead forecast data, the multi-objective particle swarm optimization algorithm is used to optimize the operation status of flexible resources. At the same time, the fully embedded power flow calculation method is used to calculate the system power flow during the optimization process. The specific constraints are as follows: a. Power flow constraints in the power system: (4) b. Branch flow constraints: (5) In the formula, It is the complex power of the PQ node. It is the active power of the PV node. This represents the given voltage amplitude at the PV node. This represents the setpoint voltage at the slack node; and It is a side road Power loss; and It is a side road Admittance and susceptance; It is a side road The susceptivity to ground; , , These are nodes and nodes Phase difference and nodes voltage amplitude and nodes voltage amplitude, It is a node and nodes The magnitude of the voltage vector difference between them; When using the fully embedded method to calculate system power flow, the first step is to reconstruct the fully embedded model, which is then reconstructed as follows: (6) In the formula, , Indicates the node number; Represents the ()th node in the node admittance matrix , )element, and These are about nodes and Line admittance, node Earth-based self-acceptance; In the initial state Below, we have an initial solution: (7) The recursive equation (8) is given below: (8) In the formula, To specify the voltage magnitude for the slack node, For impulse functions, when hour, ;when hour, ; Let be a new holomorphic function. equal The reciprocal, ; ; Based on the nth-order truncated power series of holomorphic functions, the analytical value is obtained by analytic continuation through the Pad approximation; hypothesis function ,in The Pad approximation is: (9) Will Substituting into equation (9), when s=1, we obtain the function value after Pad approximation; the function value satisfies the constraint equations (4) and (5).

2. The active distribution network flexibility resource optimization operation method based on the fully embedded method according to claim 1, characterized in that, The multi-objective function is: (1) , These are the weighting coefficients; Total daily network loss of the system: (2) In the formula: The total network loss is denoted by t, where t is the time period identifier, t=1,2,3. T, where T is the total number of time periods; take =1h, T=24h; , Branch roads The resistance and current values; E is the set of branches; Voltage deviation rate: (3) In the formula, For nodes Voltage amplitude, denoted as , where is the expected voltage amplitude of the node; N is the total number of nodes in the system.

3. The active distribution network flexibility resource optimization operation method based on the fully embedded method according to claim 1, characterized in that, Node voltage constraints: (10) In the formula, , They are nodes The upper and lower limits of voltage, For nodes Voltage; Branch current constraints: (11) In the formula, , Branch roads The upper and lower limits of the current, branch road Current; Node power constraints: (12) In the formula, and For impulse functions, when node When flexible resources are accessed, then and =1, otherwise and =0; It refers to the set of end nodes that start from in all branches of the distribution network; It refers to the branch circuits in the distribution network that are... It is the set of the first and last nodes at the end; A positive value indicates that the energy storage node is discharging, and a negative value indicates that the energy storage node is charging. Output constraints of distributed power nodes: (13) Energy storage active and reactive power output constraints: (14) In the formula, and It is an energy storage node Active and reactive power injected by energy storage devices; and This represents the amount of electricity stored in the system at time t and the time following t; To improve the charging efficiency of energy storage systems, This refers to the discharge efficiency of the energy storage system.

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