Evaluation Method for Integrated Frequency Support Capability of Active Distribution Networks Considering Power Flow Security

Abstract

This invention relates to an active distribution network comprehensive frequency support capability assessment method considering power flow safety, comprising the following steps: (1) keeping the original state space of the control variables unchanged, performing state space dimensionality upgrade processing on the disturbance variables, constructing an incompletely upgraded data-driven power flow model, performing data-driven training based on historical operating data of the distribution network, and estimating the incompletely upgraded data-driven power flow mapping matrix using the least squares method; (2) incorporating network power flow safety and the capacity of distributed power sources into the constraints, considering the system frequency change process, and establishing a distribution network frequency regulation capability assessment optimization model based on model prediction; (3) considering the frequency interaction characteristics between the distribution network and the main grid, performing alternating iterative calculations, solving the established distribution network frequency regulation capability assessment optimization model, and evaluating the overall maximum droop coefficient of the distribution network.

Description

Technical Field

[0001] This invention relates to the field of frequency regulation capability assessment technology for distribution networks, and more particularly to a method for assessing the comprehensive frequency support capability of active distribution networks that takes into account power flow security constraints. Background Technology

[0002] Existing research mainly focuses on the frequency regulation problem of large-scale renewable energy power plants directly connected to the transmission system, while less attention is paid to distribution networks containing a large number of controllable distributed power sources. Although the capacity of a single distributed resource is limited, the role of aggregated distributed power sources in participating in frequency regulation services for the power system cannot be ignored as the scale of access continues to increase. References [1-3] propose the idea of ​​using distributed power source clusters to provide frequency regulation auxiliary services for the power system. By adding additional control links to grid-connected converters, the external characteristics of synchronous generators are simulated, providing virtual inertia and virtual damping support for the power grid. References [4-6] use the concept and technology of virtual power plants to integrate different forms of distributed generation resources for integrated management and participate in the grid frequency regulation auxiliary services as a whole. However, the optimization and control strategies ignore the network architecture, that is, all frequency regulation control objects are regarded as located on the same electrical node, without considering the power flow constraints of the distribution network, which can easily lead to power flow exceeding the limit and pose serious safety hazards. Based on this, references [7-9] respectively present optimal frequency regulation control strategies for centralized and distributed virtual power plants in distribution networks. By coordinating and optimizing the active and reactive power of each distributed power source, these strategies ensure effective tracking of the active power setpoint at the feeder head while also considering voltage safety within the feeder. However, these methods still suffer from problems such as long optimization convergence time and susceptibility to local optima, inability to guarantee calculation accuracy due to approximate processing of power flow models, and safety hazards due to neglecting current constraints. New methods need to be explored for improvement.

[0003] In order to ensure the safe operation of the network power flow when participating in the frequency regulation ancillary services of the power grid, the active distribution network needs to assess its frequency regulation capability before the response period, calculate its maximum frequency regulation capability and submit it, and respond to the frequency regulation command fed back by the power grid in real time. Theoretically, by using the power flow model and frequency regulation characteristics of the distribution network to perform power flow calculations, and by comprehensively considering the constraints of safe operation and the capacity constraints of distributed generation, the maximum frequency regulation power of the distribution network can be accurately assessed and calculated. Specific assessment methods can be divided into random sampling and optimization calculation. References [10-11] use the Monte Carlo method to simulate a large number of power flow scenarios and assess and determine the feasible operating area of ​​the distribution network power based on the network operation constraints. However, this method is time-consuming, and as the number of assessment variables increases, it is difficult to capture extreme feasible points, which may lead to a more conservative assessment result.

[0004] In contrast, optimization-based methods can provide more accurate evaluation results. References [12-14] constructed an optimization model for evaluating the feasible power region of the distribution network based on the optimal power flow model. On this basis, the authors of reference

[15] obtained the maximum frequency regulation capability of the distribution network by evaluating the maximum frequency regulation active power output at different frequencies. However, the optimization algorithm does not reflect the time continuity between the operating variables, and the steady-state acquisition method of the frequency cannot effectively reflect the transient response of the system frequency in reality. In addition, since the frequency regulation capability of the distribution network is affected by the dynamic response process of the grid frequency, and the grid frequency changes with the frequency regulation capability of other frequency-supporting aggregation units in the grid. Therefore, the collaborative expansion characteristics of the frequency regulation capability boundary between the main grid and the distribution network need to be considered in the process of evaluating the frequency regulation capability of the distribution network. Secondly, since there are many nodes and distributed power sources in the distribution network and the dynamic characteristics are complex, the frequency regulation optimization model belongs to the non-convex non-deterministic polynomial problem, which is difficult to solve precisely analytically and requires a long computation time. Furthermore, since physical model-based analysis methods heavily rely on network model parameters, and medium- and low-voltage distribution networks often suffer from incomplete model parameters, they cannot guarantee high accuracy in practical applications.

[0005] With the continuous improvement of the power grid measurement system, data-driven methods that do not rely on the physical information of the system are widely used in power flow calculation of distribution networks. Reference

[16] uses convolutional neural networks to train historical data of distribution networks, establishes the mapping relationship between load patterns and optimal topology, and realizes efficient and rapid reconfiguration of distribution networks. Reference

[17] constructs a capsule network model and uses historical data to train the complex relationship between input features and scheduling strategies, which greatly shortens the calculation time of reactive power optimization of distribution networks. However, the above methods are detached from mathematical models and are difficult to reflect the internal relationship of the system. In some cases, it is difficult to guarantee the rationality of the output results. Unlike the above analysis methods, references [18-19] combine data-driven and optimization model linearization, and use linear regression methods to obtain power flow sensitivity parameters in the training data set, which greatly improves the solution efficiency. However, this linear data-driven method has the problem of insufficient accuracy due to its difficulty in adapting to the nonlinear characteristics of the distribution network after the access of high-power sources and loads with strong randomness.

[0006] In summary, current methods for assessing the frequency regulation capability of distribution networks still have certain shortcomings and deficiencies. Due to the large number of nodes and distributed generation sources in distribution networks, and the complexity of power flow models, traditional physical model-based frequency regulation capability assessment methods are difficult to solve analytically and heavily rely on the completeness and accuracy of network model parameters. Although data-driven neural network methods are widely used, they are detached from physical models, resulting in weak interpretability of the model outputs. Linear data-driven power flow models have low accuracy and cannot adapt to the highly nonlinear scenarios brought about by the high penetration rate of renewable energy integration.

[0007] Furthermore, due to the synchronicity of power system frequencies, the frequency regulation capability of a single distribution network varies with the frequency regulation capability of other frequency-supporting aggregation units in the power grid. Therefore, it is often impossible to accurately assess the frequency regulation capability of a single distribution network by only evaluating and calculating it individually.

[0008] Related literature:

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[0018]

[10] M.Heleno,R.Soares,J.Sumaili,R.J.Bessa,L.Seca,and M.A.Matos,“Estimation ofthe flexibility range in the transmission-distributionboundary,”in 2015IEEE Eindhoven PowerTech,Eindhoven,Netherlands:IEEE,Jun.2015,pp.1–6.

[0019]

[11] S.Riaz and P.Mancarella,“On Feasibility and Flexibility OperatingRegionsof Virtual Power Plants and TSO / DSO Interfaces,”in 2019 IEEE MilanPowerTech,Milan,Italy:IEEE,Jun.2019,pp.1–6.

[0020]

[12] F.Capitanescu,“TSO–DSO interaction:Active distribution networkpowerchart for TSO ancillary services provision,”Electric Power SystemsResearch,vol.163,pp.226–230,Oct.2018.

[0021]

[13] M.Sarstedt,L.Kluβ,J.Gerster,T.Meldau,and L.Hofmann,“SurveyandComparison of Optimization-Based Aggregation Methods for the DeterminationoftheFlexibility Potentials at Vertical System Interconnections,”Energies,vol.14,no.3,p.687,Jan.2021.

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[14] M.Kalantar-Neyestanaki,F.Sossan,M.Bozorg,and R.Cherkaoui,“Characterizing the Reserve Provision CapabilityArea ofActive DistributionNetworks:A Linear Robust Optimization Method,”IEEE Trans.Smart Grid,vol.11,no.3,pp.2464–2475,May 2020.

[0023]

[15] E.O.Kontis,A.R.D.Nozal,J.M.Mauricio,and C.S.Demoulias,“Provisionof Primary Frequency Response as Ancillary Service From ActiveDistributionNetworks to the Transmission System,”IEEE Trans.Smart Grid,vol.12,no.6,pp.4971–4982,Nov.2021.

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[16] Y.Yu,M.Yang,Y.Zhang,P.Ye,X.Ji,and J.Li,“Fast reconfigurationmethodof low-carbon distribution network based on convolutional neuralnetwork,”Front.Energy Res.,vol.11,p.1102949,Jan.2023.

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[17] W.Liao, J.Chen, Q.Liu, R.Zhu, L.Song, and Z.Yang, "Data-drivenReactivePower Optimization for Distribution Networks Using Capsule Networks," J.Mod.Power Syst.Clean Energy, vol.10, no.5, 2022.

[0026]

[18] H.Xu, ADDominguez-Garcia, VVVeeravalli, and PWSauer, "Data-Driven Voltage Regulation in Radial Power Distribution Systems," IEEETrans.Power Syst., vol.35, no.3, pp.2133–2143, May.2020.

[0027]

[19] H.Su, P.Li, P.Li, Summary of the Invention

[0028] To address the aforementioned issues, this invention constructs a two-layer control architecture for evaluating the frequency regulation capability of distribution networks based on an incomplete up-dimensional data-driven method. The cluster model training layer, through an incomplete up-dimensional mapping data-driven method, offline trains a sufficient amount of historical data to obtain a high-precision global power flow linear model, thus eliminating dependence on network line parameters. The online optimization evaluation layer utilizes the high-dimensional linear power flow model to transform the original, difficult-to-solve non-convex nonlinear evaluation model into an easily solvable linear evaluation model, significantly reducing computational time costs. Furthermore, considering the interactive characteristics of frequency regulation support capability between the distribution network and the main grid, this invention proposes an alternating iterative calculation method based on the linear evaluation model, achieving a full evaluation of the distribution network's frequency regulation support capability. The technical solution is as follows:

[0029] A method for evaluating the integrated frequency support capability of an active distribution network considering power flow security includes the following steps:

[0030] (1) Keep the original state space of the control variables unchanged, perform state space dimensionality upgrade processing on the disturbance variables, construct an incompletely upgraded data-driven power flow model, perform data-driven training based on historical operation data of the distribution network, and estimate the incompletely upgraded data-driven power flow mapping matrix by the least squares method.

[0031] (2) Incorporating network power flow safety and distributed generation capacity into the constraints, and considering the system frequency change process, a model-based prediction-based optimization model for the frequency regulation capability of the distribution network is established. The method is as follows: The goal of the frequency regulation capability assessment is to maximize the overall droop coefficient of the distribution network under the premise of ensuring the safe operation of network voltage and current; the time-coupled algebraic equation of the system frequency response is obtained through differential discretization; when the frequency deviation exceeds the dead zone, each distributed generation in the distribution network provides active power support through its own droop characteristics; the voltage amplitude of each node and the current amplitude of each line are calculated to determine that the power flow inside the distribution network is within a safe and reasonable range, and to avoid voltage and current exceeding the limits; the power of each photovoltaic unit needs to meet the capacity limit, and the energy storage unit needs to meet the power and energy capacity constraints.

[0032] (3) Considering the frequency interaction characteristics between the distribution network and the main network, perform alternating iterative calculations to solve the established distribution network frequency regulation capability evaluation optimization model and evaluate the overall maximum droop coefficient of the distribution network.

[0033] Furthermore, the method for step (1) is as follows:

[0034] The basic form of the power flow equation is as follows:

[0035] y = Mx' lift (1)

[0036] Where y represents the output variable, M represents the linearized power flow mapping matrix, and x' lift This represents an incomplete dimensionality increase in the input variable;

[0037] The power flow independent variable is further divided into control variable u and disturbance variable x. The control variable u is the optimization variable in the optimization problem, while the disturbance variable x is the uncontrolled independent variable in the optimization problem. The original state space of the control variable remains unchanged, and the state space of the disturbance variable is upgraded to a higher dimension, thereby constructing an incomplete upgraded power flow model.

[0038] Incomplete dimensionality increase of input variable x' lift Represented as:

[0039]

[0040] The incompletely upgraded data-driven power flow mapping relationship is expressed as follows:

[0041]

[0042] Where u represents the control variable, x represents the disturbance variable, and x lift ψ(x) represents the input variable for increasing the dimension, M0 and M1 are block matrices of M with different decompositions of the input variable, i.e., M = [M0 M1];

[0043] Based on historical operation data of the distribution network, data-driven training is performed, and the incompletely upgraded data-driven power flow mapping matrix is ​​estimated using the least squares method. The calculation formula is as follows:

[0044] M = [M0M1]

[0045]

[0046] in, Represents the Moore-Penrose inverse of the matrix;

[0047] Based on the perturbation variable x, a dimension-up operation function ψ(x) is established for the perturbation variable. This function consists of n scalar functions ψ i (x) constitutes, that is:

[0048] ψ i (x)=f lift (xc i (5)

[0049]

[0050] Among them, f lift Represents the expansion form of a function in higher dimensions, c i This represents the extended i-th basis vector, whose values ​​are selected from random values ​​within the range of the distribution network input variables, x. i c represents the i-th element in x. ij Represents c i The j-th element in the expression, where K is the dimension of the input variable x.

[0051] Furthermore, in step (2), the control variable u is selected as the active power P of a controllable distributed power source. DG and reactive power Q DG The disturbance variable is the uncontrollable node load active power P. load and no Q load ,but:

[0052] u = [P] DG Q DG ] T (7)

[0053] x = [P] load Q load ] T (8)

[0054] The purpose of power flow calculation is to obtain the node voltage and line current amplitude, and the output variable is taken as y = [V m ,I L ] T Then the power flow equation is:

[0055]

[0056] The optimization objective of the distribution network frequency regulation capability assessment optimization model established in step (2) can be:

[0057] The goal of frequency regulation capability assessment is to maximize the overall droop coefficient of the distribution network while ensuring the safe operation of network voltage and current. The optimized objective function is expressed as follows:

[0058]

[0059]

[0060]

[0061] ΔQ=(ΔQ 1 , …, ΔQ t , …, ΔQ T (13)

[0062]

[0063]

[0064]

[0065] Where t is the moment of the primary frequency regulation process, T is the total number of time points; H is the total number of reactive power regulation time points; n and m represent the number of photovoltaic and energy storage units included in the distribution network, respectively. K represents the overall droop coefficient of the distribution network. f It is an (m+n)×1 column vector containing the droop coefficients for photovoltaics and energy storage; ΔQ t and These are column vectors composed of the reactive power regulation values ​​of the DERs at time t and optimization point h, respectively; ΔQ represents the reactive power regulation sequence of each DER within the optimization period, consisting of T ΔQ values. t The resulting (m+n)×T matrix.

[0066] The constraints of the distribution network frequency regulation capability evaluation optimization model established in step (2) can be:

[0067] When the power generation and load power of a power system are unbalanced, the system frequency will change. The time-coupling algebraic equation of the system frequency response obtained through differential discretization is as follows:

[0068]

[0069]

[0070]

[0071] Where t1 represents the discrete frequency point, T1 represents the discrete time interval, and ΔP g This indicates the change in the active power output of the synchronous generator system. and f represents the overall droop coefficient of the distribution network and the new energy power station, respectively. n Indicates the system's rated frequency. Represents the current system frequency; R is the static droop coefficient of the governor, T0 is the equivalent inertial time constant of the turbine, α is the characteristic coefficient of the turbine, and H... sys The system inertia coefficient, ΔP L Indicates the power fluctuation of the system load;

[0072] When the frequency deviation exceeds the dead zone, each distributed power source in the distribution network provides active power support through its own droop characteristics, as shown in the following formula:

[0073]

[0074]

[0075] in, and These represent the active power of photovoltaics and energy storage, respectively. and These represent the initial active power of photovoltaic and energy storage, respectively. and These are the droop coefficients for photovoltaics and energy storage, respectively;

[0076] Calculate the voltage amplitude of each node and the current amplitude of each line to determine that the power flow within the distribution network is within a safe and reasonable range, and to avoid voltage and current exceeding limits, as shown in the following formula:

[0077]

[0078] V min ≤V m ≤V max (twenty three)

[0079] I L ≤I max (twenty four)

[0080] Among them, V m and I L Let P represent vectors consisting of node voltage magnitudes and line current magnitudes, respectively. pv and P ESS Let Q represent the vector consisting of photovoltaic active power and energy storage active power. pv and Q ESS V represents a vector consisting of photovoltaic reactive power and energy storage reactive power. max and V min I represents the upper and lower limits of the voltage at the distribution network nodes, respectively. max Indicates the upper limit of the current in each line;

[0081] The power output of each photovoltaic unit must meet the capacity limit, as expressed in the following formula:

[0082]

[0083] in, S represents the maximum active power output of the i-th photovoltaic unit; i,pv This corresponds to the rated capacity of the i-th photovoltaic unit;

[0084] Each energy storage unit must meet the constraints of energy quantity and power capacity, as shown in the following formula:

[0085]

[0086]

[0087]

[0088] in, The energy storage capacity connected to the i-th node at the current moment; and These are the corresponding energy storage charging power and discharging power; η charge and η discharge These represent the charge / discharge efficiency; Δt is the optimization time interval. and These are the upper limits of the charging and discharging power of energy storage; Indicates charging and discharging of energy storage, and introduces... The constraint means that at any given moment, energy storage can only be in one of three states: charging, discharging, or neither charging nor discharging. This is the limit for the amount of energy stored.

[0089] Furthermore, the method for step (3) is as follows:

[0090] 1) Under the scenario where the power system droop coefficient and disturbance negative power are determined, solve the established distribution network frequency regulation capability evaluation optimization model, evaluate the overall maximum droop coefficient of the distribution network, and report the results to the main grid;

[0091] 2) After receiving the evaluation results of the distribution network, the main grid side updates the overall droop coefficient of the regional power grid and reissues it to the distribution network;

[0092] 3) Determine whether the convergence condition of formula (29) is met. If it is met, the evaluation ends. If it is not met, repeat the above process 1)-2).

[0093]

[0094] in, ε represents the value of the maximum overall droop coefficient of the distribution network at the t-th iteration, and ε is the convergence criterion value.

[0095] This invention enables rapid and accurate assessment of the frequency regulation support capability of a distribution network without relying on physical network parameters. Compared with existing technologies, this invention has the following advantages:

[0096] (1) A two-layer control architecture is proposed. The power flow linear mapping model is trained offline, and the linear MPC optimization evaluation model is constructed to calculate the frequency regulation capability online. It does not depend on the completeness of the network model and the accuracy of the parameters. It can realize the high-precision and rapid evaluation of the frequency regulation capability of the distribution network and has higher application value in practical engineering.

[0097] (2) A linear evaluation calculation method based on incomplete dimensionality-upgrading linear regression is proposed. This method utilizes Koopman theory to upgrade the dimensionality of the perturbation variables, fitting the nonlinear characteristics of the system in a high-dimensional space. This transforms the evaluation model from a difficult-to-solve high-dimensional nonlinear equation system into an easily solvable linear equation system. The established linear evaluation optimization model is simple to solve and converges quickly, making it more suitable for online control compared to traditional physical-based models.

[0098] (3) A method for alternating iterative calculation based on an incomplete up-dimensional mapping linear evaluation optimization model is proposed. This invention delves into the interaction characteristics between the distribution network and the main grid, considers the entire process of system frequency change and the correlation between the extreme droop slope of the distribution network and the overall droop slope of the main grid, effectively utilizes the frequency regulation support capability of the distribution network, and achieves accurate evaluation calculation. Attached Figure Description

[0099] Figure 1 This is a flowchart of the active distribution network primary frequency regulation control method proposed in this invention.

[0100] Figure 2 This is a simulation example of the 10kV distribution network topology diagram used in this invention.

[0101] Figure 3 This is a comparison chart of the droop coefficient iterative evaluation results of the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the non-iterative data-driven linearization method in scenario 1.

[0102] Figure 4 This is a comparison chart of the droop coefficient iterative evaluation results of the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the non-iterative data-driven linearization method in scenario 2.

[0103] Figure 5 The radar chart shows the droop coefficient of distributed power sources in scenario 1, comparing the proposed method with the proportional allocation method, particle swarm optimization, particle swarm optimization with parameter errors of 10% and 20%, and a data-driven linearization method without iterative calculation.

[0104] Figure 6 The radar chart shows the droop coefficient of distributed power sources in scenario 2, comparing the proposed method with the proportional allocation method, particle swarm optimization, particle swarm optimization with parameter errors of 10% and 20%, and data-driven linearization method without iterative calculation.

[0105] Figure 7 This is a comparison chart of the frequency variation curves of the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the data-driven linearization method without iterative calculation in scenario 1.

[0106] Figure 8 This is a comparison chart of the frequency variation curves of the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the data-driven linearization method without iterative calculation in scenario 2.

[0107] Figure 9 This is a comparison chart of the current distribution in scenario 1 between the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the data-driven linearization method without iterative calculation.

[0108] Figure 10 This is a comparison chart of the current distribution in scenario 2 between the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the data-driven linearization method without iterative calculation.

[0109] Figure 11This is a comparison chart of the voltage distribution in scenario 1 between the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the data-driven linearization method without iterative calculation.

[0110] Figure 12 This is a comparison chart of the voltage distribution in scenario 2 between the proposed method, the proportional allocation method, the particle swarm optimization method, the particle swarm optimization method with parameter errors of 10% and 20%, and the data-driven linearization method without iterative calculation.

[0111] Table 1 shows the system parameters and control parameters of the method of the present invention.

[0112] Table 2 shows the comparison of computation time between the proposed method and the particle swarm optimization method in scenarios 1 and 2.

[0113] Table 3 compares the power flow capacity utilization of the proposed method, particle swarm optimization (PSO), PSO with parameter errors of 10% and 20%, data-driven linearization method without iterative computation, and the evaluation results based on the proposed method in scenarios 1 and 2, with the results distributed proportionally. Detailed Implementation

[0114] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0115] 1. A Data-Driven Power Flow Modeling Method Based on Incomplete Dimensionality Upgrading

[0116] The essence of Koopman's data-driven theory is state-space transformation. By collecting a large amount of synchronous historical operational data, linear regression fitting training is performed in the increased-dimensional state space to obtain a high-dimensional linear mapping relationship between input and output variables. The non-linear mapping relationship from input variable x to output variable y established through the dimensionality increase method is shown below:

[0117]

[0118] In the formula, x and y are the input and output variables, respectively, ψ(x) is the dimension-upgrading function of the input vector x, and matrix M is the linear mapping matrix from the upgraded input variables to the output variables. Theoretically, the above equation only holds strictly when the dimension-upgrading function ψ(x) is infinite-dimensional. However, in practical applications, simply increasing the Koopman operator to a certain dimension is sufficient to obtain good mapping accuracy. When using the dimension-upgrading function to increase the dimension by n, it can be viewed as consisting of n scalar functions ψ i (x) constitutes, that is

[0119] ψ i (x)=f lift (xc i (2)

[0120] In the formula, c i Let i be the i-th basis vector of the elevation. The base can be any random number within the range of variable values. lift The dimension-raising function can take many forms. This invention uses a polyharmonic dimension-raising function with high computational efficiency, as follows:

[0121]

[0122] Where, x i c is the i-th element in x. ij For c i The j-th element in the expression, where K is the dimension of the input variable x.

[0123] Therefore, based on a sufficient amount of historical distribution network operation data, the value of the linear power flow matrix M can be estimated using the least squares method to obtain the upgraded linear power flow equation. Assuming the historical sample set used for training contains S time-section data points, the input variable sample set is defined as... and the output variable sample set is Specifically, it can be represented as

[0124]

[0125]

[0126] Based on the above samples, the linearized power flow matrix M can be obtained as follows:

[0127]

[0128] in, Represents the Moore-Penrose inverse of the matrix.

[0129] Because fully upscaling data-driven models involve state-space upscaling transformations of all power flow variables, the power flow model is represented as a nonlinear equation for all variables. The complex upscaling function makes it difficult to solve analytically the optimization model using power flow as a constraint, hindering practical applications. Therefore, this invention further establishes a data-driven power flow mapping model based on incomplete upscaling.

[0130] Considering the selectivity of data-driven dimensionality-upgrading variables, power flow independent variables can be divided into control variables *u* and disturbance variables *x'*. Control variable *u* serves as the optimization variable in the optimization problem, while disturbance variable *x'* is the uncontrolled independent variable. Only the state space of the disturbance variable is upgraded to accommodate the nonlinear characteristics of the system. The control variable remains in its original state space to ensure its linear characteristics under power flow constraints, facilitating optimization solutions. The power flow mapping model established based on the incomplete dimensionality-upgrading data-driven method can guarantee power flow mapping accuracy while remaining unaffected by the accuracy of model parameters, and can also be applied to the rapid solution of optimization problems.

[0131] Therefore, the incompletely upgraded data-driven power flow mapping relationship can be expressed as follows:

[0132]

[0133] In the frequency regulation capability evaluation and optimization model of the distribution network established in this invention, the highly nonlinear power flow physical model of the distribution network can be replaced by equation (6) as the power flow constraint. The control variables are the active and reactive power of controllable distributed sources, then u=[P DG Q DG ] T Among them, P DG =[P pv ,P ESS ] T Q DG =[Q pv Q ESS ] T If the disturbance variable is chosen to be the uncontrollable node load power, then x = [P] load Q load ] T The purpose of power flow calculation is to obtain the node voltage and line current amplitude, and to take the output variable y = [V m ,I L ] T Then the power flow equation is:

[0134]

[0135] 2. Data-driven linear evaluation model for frequency regulation capability of distribution networks

[0136] By utilizing a power flow linear model obtained through an incomplete up-dimensional data-driven method, this invention constructs an optimization model for evaluating the frequency regulation capability of distribution networks that is independent of network parameters. This avoids complex mechanistic analysis and modeling processes and transforms the nonlinear optimization problem into a linear optimization problem, significantly reducing the computational burden. The specific expression of the evaluation optimization model is as follows:

[0137] for all 1≤h≤H,

[0138]

[0139]

[0140]

[0141] Y h =M0U h +M1X lift h (9-d)

[0142] U h =[P pv h ,P ESS h ,Q pv h ,Q ESS h ] T (9-e)

[0143] X h =[P load h ,Q load h ] T (9-f)

[0144] X lift h [X h ,ψ(X t )] T (9-g)

[0145] Y h [V m h ,I L h ] T (9 o'clock)

[0146]

[0147]

[0148] Y min ≤Y h ≤Y max (9-k)

[0149] U min ≤U h ≤U max (9-l)

[0150] In the formula, h represents the time within the optimization period, and t represents the time in the frequency prediction calculation. and f represents the initial active power of photovoltaic and energy storage, respectively. n This refers to the system's rated frequency. and These are the droop coefficients for photovoltaics and energy storage, respectively; Y max ,Y min U represents the upper and lower limits of the distribution network node voltage and line current, respectively. max U min These represent the upper and lower limits of active power for photovoltaic and energy storage, respectively.

[0151] 3. Iterative evaluation process of alternating primary and secondary components

[0152] To fully assess the maximum frequency regulation capability of the distribution network, it is necessary to consider the frequency interaction characteristics between the distribution network and the main grid and perform alternating iterative calculations. The specific assessment process can be summarized as follows: 1) Under the scenario where the power system droop coefficient and disturbance negative power are determined, alternating iterations are performed within formula (9) to assess the overall maximum droop coefficient of the distribution network and report the results to the main grid. 2) After receiving the assessment results from the distribution network, the main grid updates the overall droop coefficient of the regional power grid and reissues it to the distribution network. 3) Determine whether the convergence condition of formula (10) is met. If it is met, the assessment ends; if not, repeat the above process 1)-2).

[0153]

[0154] in ε represents the value of the maximum overall droop coefficient of the distribution network at the t-th iteration, and ε is the convergence criterion value.

[0155] In the frequency regulation capability assessment and optimization control, the system frequency change curve is calculated using the regional overall droop coefficient and inertia coefficient issued by the main grid. The evaluation optimization model is solved based on the power flow linear mapping matrix M and the current real-time operating data. The distribution network evaluation results are reported to the main grid for iterative calculation, continuously updating the regional grid overall droop coefficient until convergence, thereby evaluating the maximum droop coefficient of the distribution network. Throughout the optimization control process, since the power flow linear mapping matrix M does not require repeated training and calculation, and the online evaluation optimization model is an easily solvable linear model, the speed requirement for distribution network frequency regulation capability assessment can be met. The overall process of active distribution network frequency regulation capability assessment based on incomplete up-dimensional data is as follows: Figure 1 As shown.

[0156] 4 Case Analysis

[0157] To verify the effectiveness and correctness of the evaluation method proposed in this invention, a simulation model was established in Matlab / Simulink software as follows: Figure 2 The simulation model of the 82-node distribution system shown is illustrated. In this example, distributed power sources include photovoltaics and energy storage, with total installed capacities of 4.68MW and 3.4MW, respectively. The system's base voltage is 10kV, the first node is the slack node, and the upper and lower limits of the node voltage are 1.08pu and 0.92pu, respectively, with a line current upper limit of 0.16pu. Given that the simulation model established in this invention represents only a typical example among many distribution networks in a large power grid, to highlight the correlation between the frequency regulation support capability of the distribution network and the overall frequency regulation support capability of the main grid, this invention equates the large power grid to a small power grid. This can be understood as multiple distribution networks being aggregated into the main grid in a real-world scenario. Specific system and control parameters are shown in Table 1.

[0158] In actual operation, the distribution network can be divided into four frequency regulation conditions: 1) frequency drop when the distribution network feeds back active power; 2) frequency rise when the distribution network absorbs active power; 3) frequency rise when the distribution network feeds back active power; and 4) frequency drop when the distribution network absorbs active power. In conditions 3 and 4, the frequency regulation power flows in the opposite direction to the original power, resulting in relatively stable power flow. The frequency regulation capability of the distribution network is often limited by the rated capacity of distributed generation sources and can be directly and easily calculated. However, in conditions 1 and 2, the frequency regulation power flows in the same direction as the original power. During a single frequency regulation process, the power flow easily reaches its limit, and the frequency regulation capability of the distribution network is often limited by the power flow carrying capacity of the grid structure, requiring optimization calculations using optimal power flow. Therefore, conditions 1 and 2 are the main research scenarios of this invention, where the total net load active power corresponding to the distribution network feeding back and absorbing active power are -1.9767MW and 1.6796MW, respectively.

[0159] To verify the superiority of this method, it is compared and analyzed with the proportional allocation method (PA), particle swarm optimization (PSO), PSO with parameter errors of 10% and 20% (PSO & 10% PE and PSO & 20% PE), and non-iterative data-driven linearization (NDL). The performance of different methods in terms of evaluation results, solution performance, actual frequency regulation effect, and power flow distribution is compared. The particle swarm algorithm adopts the standard form, with a maximum inertia weight w. max =1.5, minimum inertia weight w min =0.2, particle swarm size N=100, number of iterations T=200, learning factors s1 and s2 are both 0.7.

[0160] Table 1

[0161]

[0162]

[0163] Table 2

[0164]

[0165] Table 3

[0166]

[0167] Example 1

[0168] The five methods described above—MDL, PA, PSO, PSO&10%PE, and PSO&20%PE—were iteratively run 10 times to obtain the maximum droop coefficient evaluation curves for operating conditions 1 and 2. Figure 3 and Figure 4 Incorporate the NDL evaluation results. Figure 5 and Figure 6 A radar chart for the corresponding operating conditions is provided, depicting the distribution of the droop coefficient for each distributed generation after descending order processing. It can be seen that the MDL method proposed in this invention yields the largest maximum droop coefficient, followed by the PSO, NDL, and PA methods. When line parameters contain errors, the frequency regulation capability boundary predicted by the PSO method deviates from the actual boundary, leading to errors in the droop coefficient evaluation results. Calculations show that, using the PA method's evaluation results as a reference, the MDL method expands the feasible region of the distributed generation droop coefficient by an average of 198.67%, verifying that the proposed power optimization evaluation scheme based on optimal power flow is superior to the simple proportional allocation evaluation scheme.

[0169] Example 2

[0170] Table 2 compares the number of convergence iterations and the computation time per optimization evaluation between the PSO and MDL methods under conditions 1 and 2. It can be seen that, since the evaluation optimization model based on physical model parameters is a high-dimensional nonlinear problem, the traditional PSO method requires multiple iterations to update particle velocity and position in the solution space. Each iteration involves a large amount of computation, resulting in a long solution time for the evaluation model. Furthermore, each evaluation calculation is prone to falling into different local optimum traps, failing to meet convergence requirements and exhibiting poor practicality. In contrast, the MDL method of this invention, through incomplete dimensionality-upgrading linearization mapping, transforms the original, difficult-to-solve nonlinear evaluation optimization model into an easily solvable linear evaluation model, significantly improving computation time and convergence performance.

[0171] Example 3

[0172] Figure 7 and Figure 8The maximum droop factor and reactive power command of each distributed generation source determined using different evaluation methods are presented for operating conditions 1 and 2, respectively, along with the actual system frequency response of the distribution network participating in PFR. It can be seen that the MDL method and PSO method have the best frequency regulation performance, followed by the NDL method, while the PA method has the worst performance. Calculations show that compared to the PA method, the MDL method improves the frequency stability by 0.0093Hz and 0.0147Hz in operating conditions 1 and 2, respectively.

[0173] Example 4

[0174] The maximum droop factor in a distribution network typically occurs when the power flow just reaches the safe operating boundary. To more intuitively illustrate the power flow situation corresponding to maximum frequency regulation capability, Figure 9 , Figure 10 , Figure 11 and Figure 12 The current and voltage curves for different evaluation methods at the peak frequency in operating conditions 1 and 2 are presented respectively. It can be seen that in operating conditions 1 and 2, the PA method, limited by node voltage, struggles to fully assess the actual maximum droop factor. The MDL method, however, optimizes the allocation of distributed power sources, rationally distributing power flow and transforming the boundary factor of the droop factor limit from the less capable node voltage to the more capable line current, thus improving the frequency regulation support capability of the distribution network. Compared to the MDL method, the voltage and current under the NDL method did not reach their maximum rated values. This is because the system frequency response is affected by the update of the current main grid frequency regulation capability assessment results, leading to a more conservative result for the NDL method, which only performs a single assessment. The PSO method heavily relies on the accuracy of model parameters; when line parameters have errors of 10% and 20%, severe voltage exceedances occur, jeopardizing the operational safety of the distribution network. Furthermore, distributing the MDL assessment results proportionally resulted in severe voltage and current exceedances in the PFR. This demonstrates the optimization effect of the MDL method on network power flow in frequency regulation capability assessment.

[0175] Example 5

[0176] from Figure 9 and Figure 10 As can be seen, except for the PA method, the frequency modulation capability under other evaluation methods is limited by the current capacity of the main line. Considering... Figure 9 and Figure 10The most severe overcurrent is shown in Table 3, which presents the actual current capacity utilization rate under different evaluation methods. It can be seen that compared to other evaluation methods, the MDL and PSO methods achieve full utilization of current capacity at the cost of a very small violation rate, thereby releasing the maximum frequency regulation support capacity of the distribution network. The reason for the relatively small current violation is that the PSO method typically uses soft constraints when handling inequality constraints in the optimization model, allowing for minor violations of inequality constraints. The slight violation phenomenon in the MDL method is related to the overfitting problem inherent in data-driven approaches. In practical engineering, solving this problem only requires adding a reasonable power flow safety threshold during the evaluation process. Furthermore, it is worth noting that since the line parameters of low-voltage distribution networks are often difficult to obtain accurately in practice, the PSO method will inevitably have a larger power flow violation rate. Therefore, the MDL method of this invention, which does not rely on model parameters and has a shorter computation time, is more suitable for practical scenarios.

Claims

1. A method for evaluating the integrated frequency support capability of an active distribution network considering power flow security, comprising the following steps: (1) Keep the original state space of the control variables unchanged, perform state space dimensionality upgrade processing on the disturbance variables, construct an incompletely upgraded data-driven power flow model, perform data-driven training based on the historical operation data of the distribution network, and estimate the incompletely upgraded data-driven power flow mapping matrix by the least squares method. (2) Incorporate network power flow security and distributed power capacity into the constraints, consider the system frequency change process, and establish a model-based prediction-based optimization model for the frequency regulation capability of the distribution network. The method is as follows: The goal of the frequency regulation capability assessment is to maximize the overall droop coefficient of the distribution network under the premise of ensuring the safe operation of network voltage and current. The time-coupled algebraic equations of the system frequency response are obtained by differential discretization; When the frequency deviation exceeds the dead zone, each distributed power source in the distribution network provides active power support through its own droop characteristics. Calculate the voltage amplitude of each node and the current amplitude of each line to determine that the power flow within the distribution network is within a safe and reasonable range, and to avoid voltage and current exceeding limits; the power of each photovoltaic unit needs to meet the capacity limit, and the energy storage units need to meet the power and energy capacity constraints. The optimization objective of the established distribution network frequency regulation capability assessment optimization model is as follows: The goal of frequency regulation capability assessment is to maximize the overall droop coefficient of the distribution network while ensuring the safe operation of network voltage and current. The optimized objective function is expressed as follows: (10) (11) (12) (13) (14) (15) (16) Where t is the moment of a single frequency modulation process, and T is the total number of time points; This represents the total number of reactive power adjustment time points. and These represent the quantity of photovoltaic and energy storage components included in the distribution network, respectively. This refers to the overall droop coefficient of the distribution network. It is The column vector contains the droop coefficients for photovoltaics and energy storage; and They are respectively from the first The reactive power adjustment at time point h and the optimization point h form a column vector; This indicates the reactive power adjustment sequence of each DER within the optimization cycle, which is composed of... indivual Composition 1-order matrix; (3) Considering the frequency interaction characteristics between the distribution network and the main network, perform alternating iterative calculations to solve the established distribution network frequency regulation capability evaluation optimization model and evaluate the overall maximum droop coefficient of the distribution network.

2. The method for evaluating the integrated frequency support capability of an active distribution network according to claim 1, characterized in that, The method for step (1) is as follows: The basic form of the power flow equation is as follows: (1) in, The output variable is represented by M, which represents the linearized power flow mapping matrix. This represents an incomplete dimensionality increase in the input variable; The independent variable of the tidal current is further divided into control variables. and disturbance variables Among them, control variables As optimization variables in optimization problems, and perturbation variables To optimize the uncontrolled independent variables in the problem, while keeping the original state space of the control variables unchanged, the state space of the disturbance variables is upgraded to a higher dimension, thereby constructing an incomplete upgraded power flow model. Incomplete dimensionality upgrade of input variables Represented as: (2) The incompletely upgraded data-driven power flow mapping relationship is expressed as follows: (3) in, Represents control variables. Represents the perturbation variable. Represents input variables for increasing dimensionality. Represents a dimension-increasing function. and yes The block matrix of different decompositions of the input variables, i.e. ; Based on historical operation data of the distribution network, data-driven training is performed, and the incompletely upgraded data-driven power flow mapping matrix is ​​estimated using the least squares method. The calculation formula is as follows: (4) in, Represents the Moore-Penrose inverse of the matrix; According to the disturbance variable Establish a function for increasing the dimensionality of the perturbation variable. This function is... scalar functions Composition, namely: (5) (6) in, Represents the expansion form of a function in higher dimensions. Representing the expansion of the first A basis vector, whose values ​​are selected from random values ​​within the range of input variables of the distribution network. represent The j-th element in represent The first in One element, Input variables The dimension of.

3. The method for evaluating the integrated frequency support capability of an active distribution network according to claim 2, characterized in that, In step (2), control variables Select the active power of a controllable distributed power source. and reactive power The disturbance variable is the uncontrollable node load active power. and no merit ,but: (7) (8) The purpose of power flow calculation is to obtain the node voltage and line current amplitudes and take the output variables. Then the power flow equation is: (9)。 4. The method for evaluating the integrated frequency support capability of an active distribution network according to claim 2, characterized in that, The constraints of the frequency regulation capability evaluation optimization model of the distribution network established in step (2) are as follows: When the power generation and load power of a power system are unbalanced, the system frequency will change. The time-coupling algebraic equation of the system frequency response obtained through differential discretization is as follows: (17) (18) (19) in, Represents discrete points of frequency. Represents discrete time intervals. This indicates the change in the active power output of the synchronous generator system. and These represent the overall droop coefficients of the distribution network and the new energy power station, respectively. Indicates the system's rated frequency. Indicates the current system frequency; This is the static droop coefficient of the speed governor. Let be the equivalent inertial time constant of the turbine. For turbine characteristic coefficients, Represents the system's inertia coefficient. Indicates the power fluctuation of the system load; When the frequency deviation exceeds the dead zone, each distributed power source in the distribution network provides active power support through its own droop characteristics, as shown in the following formula: (20) (21) in, and These represent the active power of photovoltaics and energy storage, respectively. and These represent the initial active power of photovoltaic and energy storage, respectively. and These are the droop coefficients for photovoltaics and energy storage, respectively. Calculate the voltage amplitude of each node and the current amplitude of each line to determine that the power flow within the distribution network is within a safe and reasonable range, and to avoid voltage and current exceeding limits, as shown in the following formula: (22) (23) (24) in, and These represent vectors composed of node voltage magnitudes and line current magnitudes, respectively. and This represents a vector consisting of photovoltaic active power and energy storage active power. and This represents a vector consisting of photovoltaic reactive power and energy storage reactive power. and These represent the upper and lower limits of the voltage at the distribution network nodes, respectively. Indicates the upper limit of the current in each line; The power output of each photovoltaic unit must meet the capacity limit, as expressed in the following formula: (25) in, Representing the The maximum active power output of the photovoltaic unit; For the corresponding number Rated capacity of the photovoltaic unit; Each energy storage unit must meet the constraints of energy quantity and power capacity, as shown in the following formula: (26) (27) (28) in, For the current moment The amount of energy stored at the node; and These are the corresponding energy storage charging power and discharge power. Electric power; and These are the charge and discharge efficiencies, respectively. To optimize the time interval; and These are the upper limits of the charging and discharging power of energy storage; Indicates charging and discharging of energy storage, and introduces... The constraint means that at any given moment, energy storage can only be in one of three states: charging, discharging, or neither charging nor discharging. This is the limit for the amount of energy stored.

5. The method for evaluating the integrated frequency support capability of an active distribution network according to claim 1, characterized in that, The method for step (3) is as follows: 1) Under the scenario where the power system droop coefficient and disturbance negative power are determined, solve the established distribution network frequency regulation capability evaluation optimization model, evaluate the overall maximum droop coefficient of the distribution network, and report the results to the main grid; 2) After receiving the evaluation results of the distribution network, the main grid side updates the overall droop coefficient of the regional power grid and reissues it to the distribution network; 3) Determine whether the convergence condition of formula (29) is met. If it is met, the evaluation ends. If it is not met, repeat the above process 1)-2). (29) in, This represents the value of the maximum overall droop coefficient of the distribution network at the t-th iteration. This is the convergence criterion value.

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