Method for analyzing active and reactive coupling characteristics of power distribution network

Abstract

The invention discloses a method for analyzing active and reactive coupling characteristics of a power distribution network, and relates to the technical field of power distribution networks. S1, analyzing the active and reactive power regulation capability of the multi-flexibility resources of the active power distribution network; s2, researching a power distribution network linearization load flow calculation method considering load voltage static characteristics and PV nodes; and S3, carrying out linear load flow calculation and active-reactive coupling characteristic analysis and research on the power distribution network. According to the active and reactive coupling characteristic analysis method for the power distribution network, a distributed generator is used as a controllable and adjustable power supply to participate in the operation scheduling of the optimal power flow of the power distribution network, and the global optimization of the resources of the active power distribution network is realized through the coordinated scheduling of numerous resources in the active power distribution network; the safety, reliability, quality, economical efficiency and friendliness indexes of system operation are improved, and the key problems of overvoltage, wind curtailment, light curtailment, power blockage, line loss and the like of the active power distribution network are solved.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, specifically to a method for analyzing the active and reactive power coupling characteristics of power distribution networks. Background Technology

[0002] In recent years, the rapid development of renewable energy power generation technology has provided new opportunities for improving the ecological environment, optimizing energy allocation, and achieving sustainable development. It has also provided new solutions for addressing global warming, energy shortages, and environmental pollution. However, when photovoltaic and wind power are connected to the distribution network on a large scale, their power fluctuations, combined with load power fluctuations, can cause frequent voltage fluctuations at distribution network nodes, which can even seriously threaten the power quality and reliability of the entire distribution network. The randomness and volatility of renewable energy power generation need to be given greater attention in grid planning and operation.

[0003] To overcome the above-mentioned defects, the prior art (Chinese patent with publication number CN116452025A and publication date of 2023-07-18) provides a method for evaluating the voltage-reactive coupling characteristics of a regional distribution network's collection point. By selecting a large amount of historical operating data and simulation results, including the topological structure characteristic model of the regional distribution network at different times, the correlation between distributed power sources and loads within the regional distribution network, and the values ​​of collection point voltage and reactive current under different grid disturbances, a coupling relationship between the regional distribution network's collection point voltage and reactive current is established in the form of a coefficient table. Finally, based on the established mathematical coupling model of regional distribution network collection point voltage-reactive current, the internal topology of the regional distribution network, the operating conditions of power sources and loads, and the magnitude of the collection point voltage under grid disturbances can be determined, and the reactive current value of the regional distribution network can be calculated. Existing technology two (Chinese patent CN105006845B, published on 2017-05-03) discloses a multi-stage scheduling method for decoupling active and reactive power of distributed generation in a distribution network. The steps include: in intraday rolling stage scheduling, correcting the day-ahead scheduling of the distribution network to obtain the intraday active power output of the distributed generation; based on the coupling relationship between the active and reactive power of the distributed generation, determining the range of reactive power output of the distributed generation through the active power output obtained from the intraday rolling stage scheduling, thus achieving decoupling of active and reactive power output; and incorporating the active and reactive power outputs of the distributed generation into the real-time optimized scheduling of the distribution network. The technical solution provided by this invention can achieve decoupling of active and reactive power of distributed generation in the optimized scheduling of the distribution network, and considers the reactive power output of distributed generation in the optimized scheduling of the distribution network. This can effectively reduce the operating costs of the distribution company, reduce the adverse impact of load forecast uncertainty on the distribution network, and improve the safety and stability of the distribution network operation.

[0004] The aforementioned institutions, through the established mathematical coupling model of voltage-reactive current at the collection point of the regional distribution network, can understand the internal topology of the regional distribution network, the operation of power sources and loads, and the magnitude of the collection point voltage under grid disturbances. They can then calculate the reactive current value of the regional distribution network. However, in actual use, with the increase in the types of nodes in the system, traditional power flow calculation methods are difficult to apply to distribution networks containing distributed generators, resulting in the inability to meet the requirements for fast power flow calculation and analysis of distribution networks containing distributed generators. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the active and reactive power coupling characteristics of distribution networks, in order to solve the problem mentioned in the background art that the increase in the number of node types in the system makes it difficult for traditional distribution network power flow calculation methods to be applied to distribution networks containing distributed generators, thus failing to meet the requirements for fast power flow calculation and analysis of distribution networks containing distributed generators.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for analyzing the active and reactive power coupling characteristics of a distribution network, the method comprising the following steps;

[0007] S1. Analyze the active and reactive power regulation capabilities of multiple flexible resources in an active distribution network;

[0008] S2. Research on linearized power flow calculation method for distribution networks considering static characteristics of load voltage and PV nodes;

[0009] S3. Research on linear power flow calculation and active-reactive coupling characteristics analysis of distribution network;

[0010] S4. Theory and practice of linear power flow calculation and active-reactive coupling characteristic analysis of distribution network;

[0011] S5. Research on Distributed Resource Modeling and Distribution Network Power Flow Calculation Methods.

[0012] Furthermore, the flexibility resources of the active distribution network in S1 include the optimized scheduling of energy storage systems. The optimized scheduling of energy storage systems can provide a rapid response when there is an imbalance between power supply and demand, smooth load fluctuations, and improve the stability and reliability of the power grid.

[0013] Furthermore, the research on linear power flow calculation and active-reactive coupling characteristics analysis of the distribution network in S3 includes the analysis of the active-reactive coupling mechanism of the active distribution network and a detailed analysis of the active-reactive regulation capability of adjustable resources in the active distribution network in combination with the grid connection methods of various controllable resources.

[0014] Furthermore, the research on linear power flow calculation and active-reactive coupling characteristics analysis of the distribution network in S3 also includes classifying distributed generators into PV type and non-PV type, and using linear power flow calculation and node sensitivity analysis methods to analyze the active and reactive power regulation capabilities of adjustable resources in the active distribution network.

[0015] Furthermore, the distributed generators and energy storage systems with reactive power regulation capabilities participate as continuous reactive power sources in the optimized scheduling of multi-source coordination in the active distribution network.

[0016] Furthermore, the theory and practice of the S4 distribution network linear power flow calculation and active-reactive coupling characteristic analysis study include linear power flow calculation to obtain load power changes and distribution network voltage monitoring.

[0017] Furthermore, the voltage monitoring of the distribution network can accelerate the rate of coordinated and optimized operation and scheduling of the active and reactive power of the distribution network.

[0018] Furthermore, the research on S5 distributed resource modeling and power flow calculation methods for distribution networks includes a correlation analysis model of source-load-storage interaction and system regulation capacity.

[0019] Furthermore, the correlation analysis model between the source-load-storage interaction and the system regulation capacity mainly uses a two-dimensional domain interval of energy storage, flexible load regulation capacity and system new energy consumption level as indicators to evaluate the system regulation capacity.

[0020] Furthermore, the correlation analysis model between the source-load-storage interaction and the system regulation capability is combined with the static characteristics of the load voltage in S2 and the distributed power sources and distributed generators to achieve the linearization of the power flow equations.

[0021] Compared with the prior art, the beneficial effects of the present invention are:

[0022] 1. The core value of active distribution networks lies in: through the coordinated control technology of source-grid-load-storage, distributed generators participate in the optimal power flow operation and scheduling of the distribution network as controllable and adjustable power sources. By coordinating and scheduling numerous resources in the active distribution network, global optimization of active distribution network resources is achieved, ensuring the coordinated operation, positive interaction, and comprehensive and efficient utilization of numerous resources. This improves the safety, reliability, quality, economy, and friendliness of system operation, and solves key problems such as overvoltage, wind curtailment, solar curtailment, power congestion, and line losses in active distribution networks.

[0023] Furthermore, reactive power compensation planning is an important approach to address the negative impacts of renewable energy grid integration on the distribution network. Through reasonable reactive power planning, it is possible to maintain system reactive power balance, reduce reactive power flow, and lower active power losses, thereby ensuring voltage quality and improving economic efficiency. The main objectives of reactive power compensation planning include reducing economic costs, improving voltage quality, maximizing voltage stability margin, and enhancing the absorption capacity of renewable energy.

[0024] Furthermore, linear power flow calculations can quickly determine the changes in node voltage and network losses caused by load power variations. The more accurate linear power flow calculation method for distribution networks enables precise monitoring of distribution network voltage quality, thereby accelerating the rate of coordinated and optimized operation and scheduling of active and reactive power in the distribution network and improving the voltage quality of the distribution network.

[0025] 2. This project proposes a correlation analysis model between source-load-storage interaction and system regulation capacity. A two-dimensional domain interval describing the regulation capacity of energy storage, flexible loads, and the system's renewable energy absorption level is used as an indicator to evaluate the system's regulation capacity. Addressing the shortcomings of existing linear power flow calculation methods for distribution networks, and in order to meet the needs of rapid analysis and real-time optimization of distribution networks, a highly versatile and accurate power flow calculation method for distribution networks is proposed.

[0026] Furthermore, considering the static characteristics of load voltage and distributed generation / generators, the constant power load and distributed generator models are represented as quadratic functions related to node voltages. Optimal values ​​for each coefficient of the function are obtained through curve fitting techniques, ultimately achieving linearization of the power flow equations. The proposed method can achieve high-precision approximation of the power flow model without iteration. Attached Figure Description

[0027] Figure 1 This is a schematic diagram related to the research content of this invention.

[0028] Figure 2 This is a schematic diagram of the power distribution line model of the present invention.

[0029] Figure 3 This is a diagram illustrating the interactive mechanism of the active distribution network "source-grid-load-storage" according to the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Example 1: As Figure 1-3 The technical solution presented addresses the challenge of adapting traditional power flow calculation methods to distribution networks with distributed generators due to the increasing number of node types in the system. This results in the inability to perform rapid power flow calculation and analysis on distribution networks with distributed generators. The solution discloses a method for analyzing the active and reactive power coupling characteristics of distribution networks. Specifically, S1 analyzes the active and reactive power regulation capabilities of multiple flexible resources in active distribution networks. The flexible resources in S1 include the optimized scheduling of energy storage systems, which can provide rapid response to power supply and demand imbalances, smooth load fluctuations, and improve the stability and reliability of the power grid. S2 studies the distribution network linear power flow considering the static characteristics of load voltage and PV nodes. Personalized power flow calculation method; S3, linear power flow calculation and active-reactive coupling characteristic analysis of distribution network; the S3 linear power flow calculation and active-reactive coupling characteristic analysis of distribution network includes analysis of the active-reactive coupling mechanism of active distribution network, and detailed analysis of the active-reactive regulation capability of adjustable resources in active distribution network in combination with grid connection methods of various controllable resources; the S3 linear power flow calculation and active-reactive coupling characteristic analysis of distribution network also includes classifying distributed generators into PV type and non-PV type, and analyzing the active-reactive regulation capability of adjustable resources in active distribution network using linear power flow calculation and node sensitivity analysis methods; the distributed generators and energy storage systems with reactive power regulation capability participate as continuous reactive power sources in the multi-source coordinated optimization scheduling of active distribution network.

[0032] In this example, the optimized scheduling of the energy storage system can provide a rapid response when there is an imbalance between power supply and demand, smooth load fluctuations, and improve the stability and reliability of the power grid. Regarding the reactive power output problem of the energy storage system, reactive power compensation equipment can be used to optimize reactive power, improve voltage stability, reduce grid losses, and improve the efficiency of power transmission and distribution.

[0033] The integration of distributed generators into the distribution network increases the number of node types in the system, making traditional power flow calculation methods difficult to apply to distribution networks containing distributed generators. Furthermore, the active and reactive power in the distribution network and the active and reactive power output of adjustable resources are strongly coupled, leading to several irrationalities in optimization methods for decoupling and controlling active and reactive power, which to some extent affects the safe and economical operation of the system. This project first analyzes the active and reactive power coupling mechanism of active distribution networks. Based on simulation analysis of the distribution system, it verifies the necessity and practicality of joint optimization of active and reactive power in ensuring the economic and safety aspects of system operation. Secondly, it conducts a detailed analysis of the active and reactive power regulation capabilities of adjustable resources in active distribution networks, combining various grid connection methods for controllable resources. This provides a foundation for establishing a multi-source coordinated scheduling model for active distribution networks. Fast power flow calculation and analysis are performed on distribution networks containing distributed generators to quickly determine the rate of change of node voltage and network losses caused by load power variations, providing technical support for subsequent configuration schemes.

[0034] Linear power flow calculation methods for distribution networks can quickly determine the changes in node voltage and network losses due to load power variations. To meet the need for rapid analysis of distribution systems, this project adopts a linear power flow calculation method for distribution networks incorporating distributed generators. First, Taylor series expansion techniques are used to simplify the traditional distributed generator power flow calculation model, reducing the distributed generator output power to a quadratic function of voltage. The error of the simplified distributed generator model is then tested. Next, various types of distributed generators are categorized into PV and non-PV types. Combined with the proposed linear power flow equations, a linear power flow calculation method for distribution networks incorporating distributed generators is derived.

[0035] The power at each node in a distribution network can be expressed using node voltage and admittance; that is, the polar coordinate form of the node power equation can be expressed as:

[0036]

[0037] In the formula: i and j represent the node numbers in the distribution network (i,j=1,2,3…n);

[0038] These represent the active power and reactive power generated by the power source at node i, respectively. , These represent the active power and reactive power of the load at node i, respectively. , These represent the total injected active power and reactive power at node i, respectively. Let be the voltage amplitude at node i; The voltage phase angle difference between node i and node j; , These are the real and imaginary parts of the admittance matrix, respectively.

[0039] The power flow calculation models for PQ-type distributed generators, PI-type distributed generators, and PQ(V)-type distributed generators can be simplified as follows:

[0040]

[0041] In the formula: , , These are all constants, and their values ​​differ for different types of distributed generators.

[0042] Then, linear power flow calculation and node sensitivity analysis are used to analyze the active and reactive power regulation capabilities of adjustable resources in the active distribution network. This project incorporates distributed generators and energy storage systems with reactive power regulation capabilities as continuous reactive power sources into the multi-source coordinated optimization scheduling of the active distribution network, so as to fully utilize their reactive power regulation capabilities, provide reactive power support for the system, optimize the system power flow distribution, and improve voltage levels. In actual systems, when the control variable (independent variable) undergoes a small change, the system's state variable (dependent variable) changes accordingly. The method of obtaining the sensitivity of the dependent variable to the independent variable by studying the differential relationship between variables is called the sensitivity method. This project uses voltage sensitivity index and network loss sensitivity index to analyze the impact mechanism of active and reactive power in the distribution network on node voltage and network loss.

[0043] The node voltage equation can be expressed as:

[0044]

[0045] In the formula, n is the number of nodes in the distribution network. Let be the voltage at node i. Inject active power into node j. Inject reactive power into node j. This represents the impedance of branch ij.

[0046] Example 2: Figure 1-3 The technical solution presented addresses the following problem: This method for analyzing the active and reactive power coupling characteristics of a distribution network discloses the theory and practice of linear power flow calculation and active-reactive power coupling characteristic analysis of the distribution network. The theory and practice of linear power flow calculation and active-reactive power coupling characteristic analysis of the S4 distribution network include calculating load power changes through linear power flow calculation and monitoring the distribution network voltage. The distribution network voltage monitoring can accelerate the rate of coordinated and optimized operation and scheduling of active and reactive power in the distribution network.

[0047] In this example, power flow calculation is an electrical calculation widely used in power system analysis, optimization configuration and operation, and planning and design. The calculation results reflect the operating status of the system. In distribution networks, it can calculate the voltage and power values ​​corresponding to nodes and branches using known network parameters. With the grid connection of distributed generation sources and the characteristics of distribution networks that differ from transmission networks, traditional power flow calculation methods are no longer applicable. To meet the requirements for rapid power flow calculation and analysis of distribution networks containing distributed generators, it is urgent to find an efficient linear power flow calculation method for distribution networks. Linear power flow means that the calculation process does not require iterative calculations; it directly solves a set of linear algebraic equations. Through linear power flow calculation, the changes in node voltage and network losses caused by load power variations can be quickly obtained. Therefore, researching a more universal and accurate linear power flow calculation method for distribution networks can achieve precise monitoring of distribution network voltage quality, thereby accelerating the rate of coordinated optimization of active and reactive power operation and scheduling in distribution networks and improving the voltage quality of distribution networks.

[0048] The impedance ratio in a distribution network differs from that in a transmission network; it is larger in the distribution network, resulting in weaker active-reactive power decoupling. Therefore, when studying distribution network optimization, the impact of active power must be considered in addition to reactive power. Furthermore, the strong coupling between active and reactive power in the distribution network and the active and reactive power output of adjustable resources leads to several irrationalities in optimization methods for decoupling and controlling active and reactive power, which to some extent affects the safe and economical operation of the system. Therefore, it is necessary to verify the necessity and practicality of joint optimization of active and reactive power in the distribution network in ensuring the economic efficiency and safety of system operation.

[0049] In summary, due to the nonlinear characteristics of power flow calculation, the problem of optimizing the allocation of flexible resources in distribution networks is a mixed-integer nonlinear nonconvex problem, which is difficult to solve directly. Therefore, it is necessary to develop linear power flow calculation methods applicable to optimization to reduce the difficulty of solving the model. Active distribution network fast power flow calculation can quickly determine the changes in node voltage and network losses caused by load power variations, thus analyzing the impact of power changes on node voltage. Meanwhile, due to the large resistance and reactance ratio (R / X) of distribution lines, simple reactive power control is insufficient to solve the voltage fluctuation problem caused by active power fluctuations from distributed generators and loads. Furthermore, the active and reactive power in the distribution network are strongly coupled with the active and reactive power output of adjustable resources, leading to several irrationalities in optimization methods for decoupling active and reactive power control. This, to some extent, affects the safe and economical operation of the system. Only by comprehensively considering the distribution of active and reactive power in the distribution network can efficient voltage control be achieved. Therefore, it is necessary to study the fast power flow calculation method for active distribution networks, combine the grid connection methods of various controllable resources to analyze the active-reactive power regulation capability of adjustable resources in active distribution networks, analyze the active-reactive power coupling mechanism of active distribution networks, and provide a foundation for the establishment of an active-reactive power coordinated optimization scheduling model that takes into account the participation of multiple flexible resources in active distribution networks.

[0050] Reactive power compensation planning is an important approach to address the negative impacts of renewable energy grid integration on the distribution network. Through reasonable reactive power planning, it is possible to maintain system reactive power balance, reduce reactive power flow, and lower active power losses, thereby ensuring voltage quality and improving economic efficiency. The main objectives of reactive power compensation planning include reducing economic costs, improving voltage quality, maximizing voltage stability margin, and enhancing the absorption capacity of renewable energy.

[0051] Example 3: Figure 1-3 The technical solution presented addresses the following problem: This method for analyzing the active and reactive power coupling characteristics of a distribution network discloses research on distributed resource modeling and distribution network power flow calculation methods. The S5 distributed resource modeling and distribution network power flow calculation method research includes a correlation analysis model of source-load-storage interaction and system regulation capability. This correlation analysis model primarily uses a two-dimensional domain interval of energy storage, flexible load regulation capability, and the system's renewable energy absorption level as indicators to evaluate system regulation capability. This correlation analysis model of source-load-storage interaction and system regulation capability, in conjunction with the load voltage static characteristics and distributed power sources / generators in S2, achieves linearization of the power flow equations.

[0052] In this example, power flow calculation, as the foundation of distribution system analysis, calculates the operating status of each node in the system based on the network structure and given data (mainly load power and line impedance) to determine whether the system is operating stably, safely, and reliably. With the increasing integration of distributed generators into the distribution network, the original distribution network containing only PQ nodes and a reference node now includes PV, PI, and PQ nodes. This increase in node types makes traditional power flow calculation methods difficult to apply to distribution networks with distributed generators. Therefore, there is an urgent need to find an efficient linear power flow calculation method for distribution networks to meet the requirements for rapid power flow calculation and analysis of distribution networks with distributed generators. Simultaneously, since the active and reactive power in the distribution network are strongly coupled with the active and reactive power output of adjustable resources, it is necessary to analyze the active and reactive power coupling mechanism of the active distribution network to provide a foundation for subsequent strategies involving multiple flexible resources in active and reactive power coordinated scheduling. This project proposes a correlation analysis model between source-load-storage interaction and system regulation capability, using a two-dimensional domain interval describing the regulation capability of energy storage, flexible loads, and the system's renewable energy absorption level as indicators to evaluate the system's regulation capability. To address the shortcomings of existing linear power flow calculation methods for distribution networks and to meet the needs of rapid analysis and real-time optimization of distribution networks, a general and highly accurate power flow calculation method for distribution networks is proposed. Considering the static characteristics of load voltage and distributed generation (DG) and generators, the constant power load and DG models are represented as quadratic functions related to node voltages. Optimal values ​​for the coefficients of these functions are obtained through curve fitting techniques, ultimately achieving linearization of the power flow equations. The proposed method can achieve a high-precision approximation of the power flow model without iteration.

[0053] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the active and reactive power coupling characteristics of a distribution network, characterized in that: The method includes the following steps; S1. Analyze the active and reactive power regulation capabilities of multiple flexible resources in an active distribution network; S2. Research on linearized power flow calculation method for distribution networks considering static characteristics of load voltage and PV nodes; S3. Research on linear power flow calculation and active-reactive coupling characteristics analysis of distribution network; S4. Theory and practice of linear power flow calculation and active-reactive coupling characteristic analysis of distribution network; S5. Research on Distributed Resource Modeling and Distribution Network Power Flow Calculation Methods.

2. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 1, characterized in that: The flexibility resources of the active distribution network in S1 include the optimized scheduling of energy storage systems. The optimized scheduling of energy storage systems can provide a rapid response when there is an imbalance between power supply and demand, smooth load fluctuations, and improve the stability and reliability of the power grid.

3. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 2, characterized in that: The research on linear power flow calculation and active-reactive coupling characteristics analysis of the distribution network in S3 includes the analysis of the active-reactive coupling mechanism of the active distribution network and a detailed analysis of the active-reactive regulation capability of adjustable resources in the active distribution network in combination with the grid connection methods of various controllable resources.

4. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 3, characterized in that: The research on linear power flow calculation and active-reactive coupling characteristics analysis of distribution networks in S3 also includes classifying distributed generators into PV type and non-PV type, and using linear power flow calculation and node sensitivity analysis methods to analyze the active and reactive power regulation capabilities of adjustable resources in active distribution networks.

5. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 4, characterized in that: The distributed generators and energy storage systems with reactive power regulation capabilities participate as continuous reactive power sources in the optimized scheduling of multi-source coordination in the active distribution network.

6. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 5, characterized in that: The theoretical and practical research on linear power flow calculation and active-reactive coupling characteristic analysis of the S4 distribution network includes linear power flow calculation to obtain load power changes and voltage monitoring of the distribution network.

7. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 6, characterized in that: The voltage monitoring of the distribution network can accelerate the speed of coordinated and optimized operation and scheduling of the active and reactive power of the distribution network.

8. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 7, characterized in that: The research on S5 distributed resource modeling and power flow calculation methods for distribution networks includes a correlation analysis model of source-load-storage interaction and system regulation capacity.

9. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 8, characterized in that: The correlation analysis model between the source-load-storage interaction and the system regulation capacity mainly uses a two-dimensional domain interval of energy storage, flexible load regulation capacity and system new energy consumption level as indicators to evaluate the system regulation capacity.

10. The method for analyzing the active and reactive power coupling characteristics of a distribution network according to claim 9, characterized in that: The correlation analysis model between the source-load-storage interaction and the system regulation capability, together with the static characteristics of the load voltage in S2 and the distributed power sources and distributed generators, achieves the linearization of the power flow equations.

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