CN112134309A

CN112134309A - Novel partitioning method suitable for distributed voltage control of power distribution network

Info

Publication number: CN112134309A
Application number: CN202010948950.2A
Authority: CN
Inventors: 高红均; 阮贺彬; 刘俊勇; 刘友波; 向月
Original assignee: Sichuan University
Current assignee: Sichuan University
Priority date: 2020-09-10
Filing date: 2020-09-10
Publication date: 2020-12-25

Abstract

The invention relates to the technical field of power distribution networks, and aims to provide a novel partitioning method suitable for distributed voltage control of a power distribution network, which is used for establishing a voltage control model of an active power distribution network aiming at the minimum loss of a power distribution network region to be researched and the minimum deviation of a node voltage amplitude value, establishing a network partitioning method for distributed control of the active power distribution network, dividing the power distribution network region main network system into a plurality of sub-regions, quantizing and calculating a complexity function by decision variables and the number of constraints in the sub-regions, adding an auxiliary power generation source to each sub-region of a boundary in a boundary bus by combining a partitioning method between two adjacent sub-regions, establishing a distributed coordination model, solving the distributed coordination model by a distributed solving method based on Lagrangian dual relaxation, coordinating and updating boundary variables to obtain the optimal decision result of the power distribution network to be researched according to local information exchange between the sub-regions of the boundary, and limiting the output of the power of the photovoltaic generator set and the wind generator set.

Description

Novel partitioning method suitable for distributed voltage control of power distribution network

Technical Field

The invention relates to the technical field of distributed power distribution, in particular to a novel partitioning method suitable for distributed voltage control of a power distribution network.

Background

In recent years, with the development of distributed power sources such as Wind Turbine Generation (WTG) and Photovoltaic Generation (PVG), the structure of an active power distribution network has become more and more complex. The high permeability of Distributed Generation (DGs) can have a large negative effect on voltage, and how to effectively coordinate the DGs to control the voltage becomes an important problem to be solved in an active power distribution network. In addition, the centralized optimization method is widely applied to voltage control, but a large bottleneck is often encountered in the calculation of a large-scale practical power distribution network. Distributed voltage control is therefore a promising direction of research in active power distribution networks. In order to realize effective distributed control, a reasonable network division method also has important significance for realizing distributed control of voltage.

Conventionally, On Load Tap Changers (OLTC), Capacitor bank regulators (CBs) and Static Var Compensators (SVC) have been considered as effective control measures to prevent voltage violations, while DGs only operate at a fixed power factor to provide voltage support. However, if these mechanical devices are operated frequently to prevent voltage violations caused by the intermittent output of the DGs, their life will be greatly shortened. Therefore, the distributed power supply can be used in a distribution network in the aspect of relieving frequent voltage out-of-limit and can be used as a special measure for voltage control in an active distribution network. The learner defines four operating points to describe the current limits of the DGs, and approximates the capacity curve of the DGs using a polygon to which these points are connected. In addition, in order to deal with the voltage regulation loss caused by the impact of the photovoltaic generator set, the Turitsyn et al obtains an optimal scheme by comparing different design schemes of the control system for managing the reactive power generated by the photovoltaic inverter. However, in previous studies, the coupling limits of the active and reactive power of the PVG and the WTG were not considered, and the proposed four operating points were also difficult to preset. In practical applications, the distribution network may reduce voltage fluctuations by absorbing reactive power from the DGs. Therefore, a more elaborate model of the DGs capacity curve needs to be built for voltage control to reduce voltage fluctuations. In addition, Energy Storage Systems (ESSs) can perform effective voltage control by changing the power distribution of the active power distribution network. Therefore, considering the influence of the fine capacity curve of the DGs and the regulation of ESSs in the active power distribution network has great significance for establishing an effective voltage control strategy.

Moreover, access of DGs and other large-scale active control devices to a practical power distribution network poses a great technical challenge (such as computational burden) to traditional centralized voltage control. The multi-period voltage centralized control model is actually a large-scale space-time coupling scheduling problem, and brings huge challenges to the calculation amount. Moreover, the centralized algorithm is not suitable for the plug and play function required by the future development of the active power distribution network. The distributed control method can effectively overcome the defects of the traditional centralized voltage control scheme and is beneficial to the effective coordination of the DGs and other controllable devices. The reasonable network division is the premise of distributed voltage control of the active power distribution network, and the network division method divides the whole power distribution network into a plurality of sub-regions and is characterized in that the relationship between internal nodes is strong, and the relationship between nodes of different sub-regions is weak. The existing dividing methods comprise a K-mean method, a spectral clustering method, an immune algorithm, a complex network theory and the like. But the longest optimization time among the partitioned sub-problems determines the computational efficiency of the whole model. Therefore, in order to improve the calculation efficiency, the calculation complexity should be considered. The computational complexity needs to be analyzed from the number of multiplication and addition operations in the optimization process according to the number of decision variables and the number of constraint conditions in the optimization model. Therefore, a new network partitioning method considering computational complexity and power balance is needed to obtain the optimal partitioning of distributed voltage control in the active power distribution network.

In past studies, many algorithms including an Alternating Direction Multiplier Method (ADMM), an Ancillary Problem Principle (APP), and a lagrangian dual relaxation Method have been applied to coordinate adjacent regions. Wang et al developed an ADMM method based on consistency, solving the problem of multi-zone coordinated network constraint unit combination in a distributed manner. However, the calculation efficiency of the ADMM algorithm is closely related to the selection of the penalty factor, and the convergence speed of the APP algorithm is sensitive to the selection of the auxiliary function parameters. The Lagrange dual relaxation method can overcome the defects, and a penalty factor or an auxiliary function parameter does not need to be selected by using the Lagrange dual relaxation method. In summary, the distribution network distributed voltage optimization control model based on the novel partition method is an important technology in the operation optimization research of the distribution network.

Disclosure of Invention

The invention aims to provide a novel partitioning method suitable for distributed voltage control of a power distribution network, a reasonable network partitioning result of the power distribution network is obtained, and a coordination method on different areas of a connecting line is utilized, so that different areas on the same connecting line in the power distribution network can be quickly coordinated, the efficiency of voltage optimization control of the power distribution network is improved, and the network loss is reduced;

the technical scheme adopted by the invention is as follows: a novel partitioning method suitable for distributed voltage control of a power distribution network comprises the following steps:

step 1: establishing a voltage control model of the active power distribution network with the aim of minimizing the total network loss and the node voltage amplitude deviation of the power distribution network area to be researched through the flow constraint of the second-order cone relaxation, and executing the step 2;

step 2: establishing a network partition method for active distribution network distributed control by establishing a modular function of electrical distance, dividing a distribution network area main network system into a plurality of sub-areas by the network partition method, wherein a decision variable and the number of constraints in each divided sub-area are used for quantitatively calculating a complexity function, and executing the step 3;

and step 3: adding an auxiliary power generation source to each sub-region of the boundary in a boundary bus by combining a partition method between two adjacent sub-regions, establishing a distributed coordination model, and executing the step 4;

and 4, step 4: solving the distributed coordination model by a distributed solving method based on Lagrange dual relaxation, coordinating and updating the boundary variables according to local information exchange between the boundary subregions to obtain an optimal decision result of the power distribution network to be researched, limiting the output of the power of the photovoltaic unit and the wind generating unit according to the optimal decision result, and ending.

Preferably, in step 1, capacity curves of the photovoltaic unit and the wind turbine generator are respectively established for the power distribution network to be researched, and feasible sub-areas of the photovoltaic unit and the wind turbine generator are limited through the capacity curves and the capacities of the stator and the rotor.

Preferably, in step 1, the process of establishing the voltage control model of the active power distribution network is as follows:

step 31: the objective function of the voltage control model is to minimize the network loss and the deviation of the bus voltage, and the objective function is

Where ij represents the positive power flow direction from node i to node j, E is the line set, B is the node set, r_ijRepresenting the resistance of branch ij, I_ij，tRepresenting the current, V, of branch ij during time period t_i，tRepresenting the value of the voltage at the node i,

and

representing the square of the branch current and the square of the node voltage, x, respectively_ijDenotes the reactance, g, of the ij branch_jAnd b_jRespectively representing the conductance and susceptance of the node j to the ground; p_j，tAnd Q_j，tRespectively representing active power injection and reactive power injection at a node j in a time period t;

step 32: by a second order cone relaxation technique, an expression is obtained

And

respectively representing the wind power, the photovoltaic power and the active power injected from the transformer substation of the node j in the period t;

respectively representing reactive power injected from the transformer substation at the node j in the time period t; the reactive power of the capacitor bank connected in parallel with the node j in the time period t, wind power and photovoltaic power generation is respectively used

To represent;

and

representing the active load and the reactive load of a node j in a period t; p_ij，tAnd Q_ij，tRepresenting the active and reactive power flows of the branch ij in the period t, and executing a step 33;

step 33: when the voltage at the primary side is fixed, the transformer is a node of the voltage control model, the output limit of the active power and the reactive power of the wind turbine generator is determined by the stator current and the rotor current of the wind turbine generator, and the feasible subregion of the wind turbine generator is

The feasible sub-region of the active and reactive power output of the photovoltaic unit is

Wherein the content of the first and second substances,

for the apparent power upper limit of the wind turbine generator, the maximum power factor and the predicted active power are expressed by gamma

The upper limit of the apparent power of the photovoltaic unit.

7. Preferably, in step 3, the specific content of the network partitioning method includes the following steps:

step 41: decomposing a total network system into N^PEach non-overlapping subarea, the connection line between the subareas is ij, an auxiliary generator is respectively added at the boundary nodes i and j of each subarea, and the power output of the auxiliary generator is P_ijAnd Q_ijThe power balance constraint of the boundary node is

Wherein E is^tie-lineRepresenting the branch connecting border nodes i and j, step 42 is performed;

step 42: calculating the electrical distance between two adjacent nodes, wherein the electrical distance between the node i and the node j in the network node is

Wherein the electrical distance is defined as measuring the closeness of the relationship between two nodes, step 43 is performed;

step 43: and combining the two subregions to obtain a new subregion, calculating the comprehensive index, adopting a combination result with the maximum comprehensive index, and stopping combination operation when the comprehensive index value reaches the maximum value so as to obtain the optimal number of the subregions.

Preferably, in the step 2, the complexity function is calculated by,

wherein ω is_mAnd ω_nAre each T_mAnd T_nWeight of (a), ω_m＝1，ω_n＝0，T_mRepresenting the number of multiplications, T, in a complexity function model_nAnd representing the times of addition and subtraction operations in the complexity function model.

Preferably, in step 2, the working process of the network partitioning method is as follows:

step 61: each independent sub-area is a node, and the comprehensive index of the sub-area is calculated

Step 62 is executed;

step 62: selecting a sub-region as an a region, randomly selecting a sub-region from other regions except the a region as a b region, combining the a region and the b region to form a new sub-region, and calculating the change of the comprehensive target of the new sub-region

In the calculation, the maximum positive value is adopted as

As an updated composite index

And step 63: repeating step 62 by using the new sub-region in step 63 as a separate node; until no nodes can be merged, go to step 64;

step 64: comprehensive index

When the maximum value is reached, the partitioning process stops, and the current partitioning scheme is the best partitioning result.

Compared with the prior art, the invention has the beneficial effects that:

(1) respectively establishing capacity curves of the photovoltaic unit and the wind turbine generator, limiting the feasible power domains of the photovoltaic unit and the wind turbine generator by using the capacity curves and the stator and rotor capacities, and considering the functions of the photovoltaic unit and the wind turbine generator in operation optimization of a distribution network;

(2) a novel network partitioning method considering computational complexity and power balance is introduced by utilizing a modularization function based on electrical distance, wherein the computational complexity is quantified by using decision variables and the quantity of constraints of each region (benefit subject) as the premise of distributed optimization operation of a power distribution network.

(3) Introducing a coordination method between two adjacent beneficial agents, and adding an auxiliary power generation source to each agent of the boundary in a boundary bus so as to better solve a distributed coordination model;

(4) the distributed solving method based on Lagrange dual relaxation does not need any central coordination, only needs local information exchange among boundary interest correlators, and carries out rapid coordination and updating on boundary variables to obtain an optimal decision result.

Drawings

FIG. 1 is a flow chart of a power distribution network partition distributed voltage control optimization;

FIG. 2 is a capacity curve for a wind turbine;

FIG. 3 is a capacity curve of a photovoltaic unit;

FIG. 4 is a decomposition of two adjacent sub-region branches;

FIG. 5 is a schematic view of each sub-area auxiliary generator;

FIG. 6 is a result of network partitioning for an IEEE-33 node system;

FIG. 7 is a distributed algorithmic dual gap for an IEEE-33 node system;

FIG. 8 is a comparison of voltage deviation results with and without a capacity curve;

FIG. 9 is a comparison of voltage deviation results with and without ESS;

FIG. 10 is a comparison of the effect of voltage squared with or without ESS;

FIG. 11 is a topology of an actual 152-node system;

FIG. 12 is a distributed algorithmic dual gap for a practical 152-node system;

FIG. 13 is a topology of an IEEE-8500 node system;

FIG. 14 is a dual gap for a distributed algorithm in an IEEE-8500 node system.

Detailed Description

The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to fig. 1 to 14 of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, but not all embodiments. All other implementations made by those of ordinary skill in the art based on the embodiments of the present invention are obtained without inventive efforts.

In the description of the present invention, it is to be understood that the terms "counterclockwise", "clockwise", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate orientations or positional relationships based on those shown in the drawings, and are used for convenience of description only, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be considered as limiting.

Example 1:

a novel partitioning method suitable for distributed voltage control of a power distribution network comprises the following steps:

It is worth to be noted that, in the step 1, capacity curves of the photovoltaic unit and the wind turbine generator are respectively established for the power distribution network to be researched, and feasible sub-areas of the photovoltaic unit and the wind turbine generator are limited through the capacity curves and the stator and rotor capacities.

It should be noted that, in the step 1, the process of establishing the voltage control model of the active power distribution network is as follows:

and

step 32: by a second order cone relaxation technique, an expression is obtained

And

To represent;

and

Wherein the content of the first and second substances,

The upper limit of the apparent power of the photovoltaic unit.

Preferably, in step 3, the specific content of the network partitioning method includes the following steps:

Preferably, in the step 2, the complexity function is calculated by,

Step 62 is executed;

In the calculation, the maximum positive value is adopted as

As an updated composite index

step 64: comprehensive index

Example 2:

in the invention, an objective function is minimized network loss and bus voltage deviation, namely:

where F refers to the objective function of the model, T is the total time period,

representing the total network loss during the time period t and ij representing the positive power flow direction from node i to node j. E is the line set and B is the node set. r is_ijRepresenting the resistance of branch ij, I_ij，tRepresenting the current, V, of branch ij during time period t_i，tRepresenting the value of the voltage at node i. The power flow constraint (2) is usually used for a branch power flow model, an expression (2d) is formed after a second-order cone relaxation technology is adopted,

and

representing the square of the branch current and the square of the node voltage, respectively. Wherein, (j) is the node set with j as the power outflow node, and pi (j) is the node set with j as the power inflow node. x is the number of_ijDenotes the reactance, g, of the ij branch_jAnd b_jRespectively, the conductance and susceptance of node j to ground. P_j，tAnd Q_j，tRespectively representing the active and reactive power injection at node j during the time period t.

And

and respectively representing the active power injected from the wind power, the photovoltaic and the transformer substation of the node j in the period t.

Respectively representing the reactive power injected from the substation at node j during the time period t. the reactive power of the capacitor bank connected in parallel with the node j in the time period t, wind power and photovoltaic power generation is respectively used

To indicate.

And

and the real load and the reactive load of the node j in the period t are represented. P_ij，tAnd Q_ij，tRepresenting the active and reactive power flows of branch ij during time t.

In the formula (I), the compound is shown in the specification,

and

are the current squared lower and upper limits of branch ij.

And

is the lower and upper voltage square limits at node j.P _ij，tAnd

representing the lower and upper active power limits for branch ij.Q _ij，tAnd

representing the upper and lower reactive power limits of the ij branch.

The transformer can be modeled as a node, assuming that the voltage of the primary side is fixed. Therefore, the voltage of the secondary side having the OLTC can be adjusted.

Wherein B is^OLTCIs a collection of nodes that are populated with OLTCs,

is a constant value.

Is a discrete variable that represents the square of the adjustable ratio of OLTC, i.e. the square of the ratio of the grid side voltage to the substation side voltage, and can be expressed as:

wherein, SR_jIs the maximum gear that the OLTC can adjust at node j,

and

is a variable from 0 to 1. In equation (5b), the discrete gear is expressed by the square of the change in the OLTC adjustment ratio. The first inequality in equation (5c) is used to ensure that the total number of adjustments does not exceed

While the range of the adjustment gear is determined by the other inequality of equation (5 c). Equation (5d) represents the constraint of substation power injection.

In the present invention, assuming that the reactive power of each group of CBs is the same, the constraint condition of the CBs is similar to that of the OLTC, that is:

wherein B is^CBIs a group of nodes that are parallel connected capacitor banks,

is a discrete variable, representing the number of switched capacitor banks,

reactive compensation for each group.

And

is a 0-1 variable representing the state of the switched capacitor bank.

Represents the upper limit of the number of times of switching in the T period, and

representing an upper limit for the number of switch sets.

The actual active power output of the WTG cannot exceed the predicted active power

As shown in formula (7 a):

the limits of the active and reactive power output of a WTG are defined by its stator and rotor currents (apparent power ceiling)

) To decide. Fig. 1 shows the feasible range of WTG output.

Like WTGs, PVGs need to take into account predicted output and converter capacity for active and reactive power. In addition, the formula (8c) also considers the harmonic loss, the maximum power factor is represented by gamma, and the predicted active power

Apparent power ceiling

Figure 2 shows the feasible range of PVG forces.

Wherein, B^ESSFor the group of nodes to which the energy storage system is connected,

and

are 0-1 state variables respectively representing charge and discharge states,

and

represents the upper limit of charge and discharge, E_j,tIndicating that the energy storage system is storing an amount of electricity,

and

the upper and lower energy storage limits of the energy storage system are shown,

and

represents a charge-discharge coefficient.

It is worth mentioning that (2) the network partition method of distributed voltage control

In this section, we propose a novel network partitioning method, which considers the computation complexity and power balance in addition to the electrical distance, and provides a precondition for the distributed voltage control of the subsequent active power distribution network.

1) Method for decomposing a branch between two adjacent sub-regions

Suppose a network system is decomposed into N^PThe associated variables also need to be decoupled for non-overlapping sub-areas, such as the tie line ij connecting sub-areas 1 and 2 in fig. 3.

In order to solve the model (i.e. local model) of each sub-area more conveniently, an auxiliary generator is added to each boundary node i and j of each sub-area, as shown in fig. 4.

Thus, the power P exchanged by two adjacent sub-areas_ijAnd Q_ij(omitting the time index t) is the power output of the auxiliary generator, the power balance constraints of the boundary nodes (taking node i of subregion 1 as an example) are updated to (10a) and (10 b).

Wherein E is^tie-lineRepresenting the branch connecting the border nodes i and j.

The power loss on each border leg is then negligible, since the loss on the link is of a very small order of magnitude for the entire network. In the current research, the decomposition method of the boundary variable mainly comprises a branch tearing method and a node decoupling method. We apply the branch tear method here because of the different characteristics of the nodes. Moreover, the network loss of the tie lines between different areas is too small to have an effect on the calculation results of the whole network. Zheng et al propose a distributed algorithm to solve the problem of economic operation of multiple zones in an active power distribution network, which proves that ignoring network loss on the tie line does not have a large impact on the calculation result of the whole network. The following two equations can ensure that the switching power of any sub-region is equal to the adjacent sub-region.

2) Electrical distance

The voltage sensitivity is utilized to reflect the voltage response characteristics of DG injected power of different nodes in the network, and a basis is provided for evaluating the electrical distance.

According to a load flow calculation correction equation based on a Newton-Raphson method, the linear relation between all node voltage changes and injected power can be obtained

Wherein, is Δ V^pilotRepresenting the variation of the injected power as a function of deltap and deltaq. B is^YAnd G^YRespectively the real and imaginary parts of the admittance matrix. Thus, the active voltage sensitivity J^PAnd reactive voltage sensitivity J^QCan be expressed as

J^P＝[(B^Y+Q)(G^Y-P)^-1(B^Y-Q)+(G^Y+P)]^-1 (12a)

J^Q＝-[(G^Y-P)(B^Y+Q)^-1(G^Y+P)+(B^Y-Q)]^-1 (12b)

By utilizing voltage sensitivity, the correlation of voltage changes between node i and node j in the network can be treated as

Thus, the electrical distance can be expressed as:

the electrical distance is symmetrical, since it is defined as measuring the closeness of the relationship between two nodes. The relationship between nodes i and j or nodes j and i is the same.

In previous studies, the number of partitions was pre-specified, but this was not sufficient to obtain optimal results for the distributed model. Here we consider all nodes to be independent from the beginning and then merge the sub-regions. Any two sub-regions are combined into a new sub-region to calculate the composite index according to equations (15), (16), (21) and (22), and the combination result with the maximum composite index value is used. When the composite index value reaches the maximum value, the combining operation is stopped, and the optimal partition number is obtained. The distributed network takes a subregion as a node, a connection is established between two nodes, and the weight of the connection is calculated according to a modular function:

thus, the modularization function is:

when node i and node j are in the same sub-region, (i, j) ═ 1; otherwise, (i, j) ═ 0.

3) Power balancing

However, when the power grid is partitioned, the situation that the DG units of each partition are unbalanced in number needs to be avoided, and the situation that the power generation amount in the area is insufficient or too large cannot occur. Therefore, when dividing the network, we need the power balance index to judge the reactive or active power balance capability of DG in each sub-area.

Suppose a network is divided into N^PSub-region, power balance can be expressed as:

wherein N is^PIs the number of partitions

And

the active and reactive requirements of the a-zone, respectively.

4) Complexity of calculation

The longest optimization time in all sub-problems is generally used as the calculation time of the whole problem, so in practice, the accurate calculation time of each sub-problem also affects the overall calculation efficiency. Therefore, in the network division, the computation time of each sub-area should be considered, and the function of the computation complexity may be determined according to the number of constraints and decision variables. That is, the computational complexity may be analyzed in terms of the number of decision variables and the number of constraints. For clarity, we use the following form of model to obtain a function of computational complexity.

s.t. Δy_∞＝S_NΔu_∞(17b)

Wherein u is_∞Representing input variables related to linear constraints. u. of_MRepresenting the input variables associated with the second order cone constraint of the optimization model. u denotes all input variables. y is_∞Is a set of output variables, y, related to a linear constraint_MIs the set of output variables in the optimization model that are associated with the second order cone constraints. Δ represents the variation of these variables.

Equation (17a) represents the objective function of the optimization model (i.e., equation (1)). Equation (17b) is an equality constraint of the optimization model (e.g., equations (2a) - (2c) and (2e) - (2 f)). Equations (17c) and (17d) are inequality linear constraints (e.g., equations (3) - (4)) on decision variables (u and y). Equations (17e) and (17f) are second order cone constraints on the decision variables (u and y) (e.g., equations (2d), (5d), (7b), and (8 b)).

The above constraints associated with linear constraints can be represented in matrix form as follows:

because the coefficient matrix of the linear equation is a three-diagonal positive definite matrix, the coefficient matrix is processed by adopting a Gaussian elimination method. Therefore, the number of multiplication calculations related to the linear constraint is as follows

T_m(∞)＝5x_∞-4 (19a)

The number of computations associated with the second order cone constraint may be estimated approximately twice the number of computations associated with the linear constraint. Therefore, the number of multiplication operations of the entire optimization model can be estimated approximately as follows:

T_m＝10x_M+5x_∞-12 (19b)

the number of addition and subtraction operations associated with the linear constraint is:

T_n(∞)＝3x_∞-3 (19c)

therefore, the number of addition and subtraction operations of the whole optimization model can be estimated approximately as follows:

T_n＝6x_M+3x_∞-9 (19d)

wherein x is_∞Representing a matrix of input variables Deltau associated with a linear constraint_∞The dimension of (a); x is the number of_MRepresenting the matrix of input variables Deltau associated with a second order cone constraint_MThe dimension of (a); t is_m(∞)And T_n(∞)Respectively representing the times of multiplication and addition operations related to linear constraint; t is_mAnd T_nRespectively representing the times of multiplication and addition operations of the whole optimization model.

In summary, the computational complexity can be calculated as:

wherein ω is_mAnd ω_nAre each T_mAnd T_nThe weight of (c). In a simulation program, it takes more time to perform multiplication than to perform addition. Therefore, here we only count the number of multiplications to estimate the amount of simplified computation. That is, ω _m1 and ω_n＝0。

5) Comprehensive index

Since the modularity functions, power balancing and computational complexity are in different orders of magnitude, the results of the network partitioning method will be affected by the largest order of magnitude if they are not normalized. Thus, the ranges for these three indices should be normalized to [0,1], as follows:

ρ in (21a) and (21b) is defined in all possible partition results^PAnd ρ^QA minimum value and a maximum value. When this network partitioning method is employed, all nodes are initially treated as independent sub-areas, which can be merged. When the composite index reaches a maximum, the merge will stop. Therefore, equations (21a) and (21b) do not affect the computational aspect of the network partitioning method. The composite index can be expressed as:

wherein

Representing the most computationally complex values in all sub-regions. When in use

When the maximum value is reached, the optimal segmentation result is obtained.

6) Network partitioning step

The network division comprises the following specific steps:

step 1: each node is set as an independent nodeSub-region, calculating comprehensive index

Step 2: for the a-region, the b-region is randomly selected from the other regions, forming a new sub-region of the a-region and b-region combination (this step starts with all regions, i.e. the algorithm is parallel). Then, the variation of the composite index for each merged result is calculated

The maximum positive value is used in the calculation

The combined result of (1). Then, the comprehensive index is updated

And step 3: and (3) taking the newly formed sub-area as a single node, and repeating the step 2 to realize the partitioning process and obtain a new partitioning result.

And 4, step 4: when no node can be merged, the comprehensive index

(3) Distributed coordination model and solving algorithm for voltage control

In this section, we apply a distributed algorithm based on lagrangian dual relaxation to coordinate the boundary variables. After applying the variable splitting method, the models (1) - (9) can be transformed into a number of sub-problems, as follows:

s.t. g_a(x_a)≥0,a＝1,2,...,N^P (23b)

h_a1(x_a)＝0,a＝1,2,...,N^P (23c)

h_a2(x_a,x_b∈a)＝0,a＝1,2,...,N^P (23d)

if ij∈E^tie-line∩j∈B^a∩i∈B^b (23d)

wherein f is_a(x_a) Is the objective function of sub-region a; g_a(x_a) More than or equal to 0 is an inequality constraint related to the internal parameters of the sub-region a only; h is_a1(x_a) 0 is an equality constraint related only to the internal parameters of sub-region a; h is_a2(x_a,x_b∈a) 0 is the equality constraint of the coupling relationship of sub-region a to the adjoining sub-region b; e^tie-lineRepresenting branches with boundary nodes i and j; x is the number of_b∈aIs the boundary power variable in region b, but there must be a branch directly connecting regions a and b.

The model (25) is regarded as a problem. Based on Lagrange dual relaxation theory, the compression coupling constraint is relaxed into an objective function to form a Lagrange function of each sub-region, which is as follows:

wherein λ is_aIs h_a2(x_a,x_b∈a) An equality-constrained relaxation vector multiplier of 0. Vector lambda_aIs non-negative.

Thus, by minimizing the Lagrangian function L (x) for each sub-region_a,λ_a) The model (23a) may be equivalent to a plurality of subproblems.

s.t. g_a(x_a)≥0 (25b)

h_a1(x_a)＝0 (25c)

λ_a≥0 (25d)

The objective function of the model (25) can then be expressed as:

in each dual sub-problem, the internal variable x_aIs a decision variable and also requires other external determination of constants coupled with internal variables in the two boundary subregions

Thus, when the lagrange multiplier λ a is given, the internal model of the subproblem model can be expressed specifically as follows:

s.t. g_a(x_a)≥0 (27b)

h_a1(x_a)＝0 (27c)

according to the model (27), each subproblem is computed in parallel to obtain each subarea x_aThe corresponding result of. Then, based on the obtained variable value x_aAnd

the lagrange multiplier λ a for each region is updated with the sub-gradient algorithm described in the next section. By exchanging and coordinating boundary variables

A global optimization result may be obtained. It is noted that in the calculation of the sub-problem in each sub-area a, only the boundary information of the adjacent sub-area connected to the sub-area a is needed, i.e. the result of the sub-problem does not need to be sent to all other sub-areas. Let model (28) be a dual problem:

the external model of equation (26) is a maximization objective function

And (5) performing iterative updating on the Lagrangian multiplier lambda a by adopting a sub-gradient algorithm. The expression for the (n + 1) th iteration is as follows:

wherein

Is the step size, s_a ⁽ⁿ⁾Constraining h for relaxation of model (26) in nth iteration_a2(x_a,x_b∈a) The direction of the secondary gradient of (a) can be expressed as:

where C and D are positive constants. Due to h_a2(x_a,x_b∈a) 0 stands for expression (10c), so each sub-region only needs to send the tie-line power flow information to the neighboring sub-region, i.e. the schedule in each sub-region does not need to be sent to all other sub-regions. We can also find this feature from equation (29 b).

For a set of solutions in each iteration

The absolute dual gap G for the original and dual problem is as follows:

according to the dual optimal theorem, if G is 0, then

Is the optimal solution of the original dual problem.

It is worth noting that an example analysis was performed on the improved IEEE-33 node and actual 152 node system to demonstrate the effectiveness of the proposed model. These experiments were performed by cplex 12.6.0 using Matlab R2016a on a personal computer with an Intel kernel (i5, 3.20GHz) and 8GB of memory.

(1) IEEE-33 node test system

The apparent power limit of the photovoltaic is 0.3 MVA. The ESS is installed on

nodes

16 and 33 with a charge-discharge power limit of 0.3MW and a capacity limit of 0.15MWh and 1.5MWh, respectively.

1) Distributed algorithm efficiency based on Lagrange dual relaxation

By applying the network partitioning method in the second section (ω)_m＝1，ω_n0), the result of the network division can be obtained as shown in fig. 5.

Figure 6 shows the dual gap at each iteration of the distributed algorithm in the IEEE-33 node test system. It can be seen that the optimal solution of the ortho-duality problem (G ═ 0) can be found in 96 iterations, with the dual gap for the first iteration being significantly larger than the dual gap for the last iteration (96 iterations). After 45 iterations, the convergence rate increases significantly because the solver finds a solution that is close to the optimal solution, accelerating convergence to this direction. Therefore, the distributed algorithm can be effectively applied to the distributed voltage control strategy proposed by the invention.

2) Comparison of different network partitioning methods

In this subsection, we compare the results of different network partitioning methods. The modularity function, power balance and computational complexity are three indicators considered herein, so we compared the results of two other approaches that do not consider power balance and computational complexity. When different network partitioning methods are compared, they produce different partitioning results. Therefore, the calculation time and the iteration number of the voltage control model under different network division methods are different.

TABLE 1 comparison of calculated time for different network partitioning methods

Method of producing a composite material	Number of iterations	Time/s
			Partitioning method provided herein	96	4.008
Partitioning method without considering computational complexity	98	4.833
			Partitioning method without considering power balance	112	4.664
Irrespective of network partitioning	-	5.461

As can be seen from table 1, the distributed voltage control calculation efficiency using the network partitioning method proposed by the present invention is better than that of the network partitioning method without considering the calculation complexity. This is because when the model is implemented in a distributed manner, the longest time spent by a sub-region in order to get the computation time, excluding the elapsed time of communication between adjacent sub-regions, is considered as the computation time in each iteration. Therefore, the calculation time of the network division method provided by the invention is superior to that of the network division method without considering the calculation complexity.

In addition, the partitioning method without considering power balance maximizes the number of iterations when obtaining the distributed voltage control result. This is because more complex power exchange requirements between adjacent sub-zones (due to insufficient power generation) result in more iterations when coordinating different sub-zones. Therefore, the network partitioning method provided by the invention needs the least calculation time and iteration times. In addition, it can be seen that the centralized voltage control model takes more time to obtain the optimal solution due to the large amount of calculation. In summary, the network partitioning method provided by the present invention is more suitable for distributed applications.

3) Effect of DG Capacity Curve on Voltage control

The influence of the DG capacity curve on the voltage control was analyzed. The results of the voltage deviation with/without the capacity curve are shown in fig. 7, with other conditions remaining unchanged (e.g., also considering ESS).

As can be seen from fig. 7, the voltage deviation can be significantly reduced after considering the capacity curve of DG. This is because the wind turbines and PVGs can share part of the reactive compensation requirements. In addition, the reactive power generated by the DG can be consumed locally, and long-distance transmission is avoided, so that the voltage deviation is reduced. Therefore, it is important to consider the capacity curves of the wind turbine generator and the PVG in the voltage control.

4) Effect of ESS on Voltage control

This subsection also analyzes the effects of ESS on voltage control, and with other conditions remaining unchanged (e.g., also considering the DG capacity curve), FIG. 8 shows the voltage deviation results with/without ESS.

It can be seen from fig. 8 that the voltage deviation is greatly reduced when considering the ESS, also because the local ESS is advantageous to avoid remote power transmission.

While, as shown in fig. 9, when considering ESS, the square of the voltage magnitude at node 17 remains at the upper limit of 1.1236p.u. during 16-18 h. However, without consideration of the ESS, a voltage violation occurs at node 17. This is because during this time interval the voltage magnitude at node 17, which would otherwise be connected to the PVG, is about to reach its upper limit, at which time any additional PV power injection would cause the voltage to go out of limit. In this case, the charging and discharging power of the local ESS can effectively reduce the injection power of the PVG, thereby avoiding voltage collision. Therefore, ESS facilitates efficient voltage control.

(2) Actual 152-node system

This subsection tests the model using a real system containing 152 nodes. The topology of the system is shown in fig. 10.

The system parameters are shown in table 2, and the network partitioning results are shown in table 3:

TABLE 2 actual 152-node System parameters

TABLE 3 partitioning results for actual 152-node systems

Region(s)	Node point	Region(s)	Node point	Region(s)	Node point
						Region 1	{6-11}	Region 6	{47-53}	Region 11	{91-99}
Region 2	{1-5,12-15}	Region 7	{54-62}	Region 12	{100-108}
						Region 3	{16-24}	Region 8	{63-71}	Region 13	{109-123}
Region 4	{25-37}	Region 9	{73-75}	Region 14	{124-128,142-152}
						Region 5	{38-46}	Region 10	{76-90}	Region 15	{129-141}

It is worth noting that fig. 11 shows that the dual gap of the distributed algorithm in the actual system can be converged in 167 iterations, and the distributed voltage control calculation time of the method in the actual system is also minimum compared with other network division methods. Therefore, the distributed algorithm based on the Lagrangian dual relaxation and the proposed network partitioning method can also be applied to a practical system containing more nodes and branches.

It is worth mentioning that it is possible to show,

TABLE 4 comparison of computation times for different network partitioning methods

Method of producing a composite material	Number of iterations	Time/s
			Partitioning method provided herein	167	14.669
Partitioning method without considering computational complexity	171	16.452
			Partitioning method without considering power balance	224	15.979
Irrespective of network partitioning	-	80.788

It is worth pointing out that, (3) IEEE-8500 node test system

The IEEE-8500 node test system is used to validate the proposed model. The system has larger load or nonlinearity, and proves the superiority of the model. The topology of the system is shown in fig. 12.

As shown in fig. 13, the distributed algorithm applied to the IEEE-8500 node system has a double gap in each iteration that can converge in 561 iterations. In addition, table 5 also shows that the computation time for distributed voltage control using this partitioning method is also minimal in this system compared to other network partitioning methods, which can reduce the computation time by half;

TABLE 5 comparison of computation times for different network partitioning methods

Method of producing a composite material	Number of iterations	Time/s
			Partitioning method provided herein	561	23.871
Partitioning method without considering computational complexity	623	50.379
			Partitioning method without considering power balance	824	31.294
Irrespective of network partitioning	-	276.416

In summary, the implementation principle of the embodiment is as follows: and establishing a voltage control model with the minimum total network loss and the minimum node voltage amplitude deviation as targets based on the power flow constraint of Second Order Cone Relaxation (SOCR). Wherein we limit the feasible range of PVG and WTG power using the capacity curve and stator-rotor capacity, respectively. Then, a novel network division method considering calculation complexity and power balance is provided by utilizing a modular function based on the electrical distance, and the novel network division method is used as the premise of distributed control of the active power distribution network. And quantifying the calculation complexity by using the number of decision variables in the optimization model and constraint conditions. And finally, establishing a distributed model based on Lagrangian dual relaxation, wherein the model does not need any central coordination and only needs to exchange local information between the boundary sub-regions. The exchange power between the border sub-regions is set as a border variable, which can be equivalently regarded as the power injection of the auxiliary power supply when local optimization is performed.

Claims

1. A novel partitioning method suitable for distributed voltage control of a power distribution network is characterized by comprising the following steps:

2. The novel zoning method suitable for the distributed voltage control of the power distribution network according to claim 1, wherein in the step 1, capacity curves of the photovoltaic units and the wind turbine units are respectively established for the power distribution network to be researched, and feasible subregions of the photovoltaic units and the wind turbine units are defined by the capacity curves and the capacities of the stators and the rotors.

3. The novel partitioning method for distributed voltage control of a power distribution network according to claim 1, wherein in step 1, the process of establishing the voltage control model of the active power distribution network is as follows:

and

step 32: by a second order cone relaxation technique, an expression is obtained

And

To represent;

and

Wherein the content of the first and second substances,

The upper limit of the apparent power of the photovoltaic unit.

4. The novel partitioning method for distributed voltage control of a power distribution network according to claim 1, wherein in step 3, the specific content of the network partitioning method includes the following steps:

5. The novel partitioning method for distributed voltage control of power distribution network according to claim 1, wherein in step 2, the complexity function is calculated as,

6. The novel partitioning method suitable for distributed voltage control of the power distribution network according to claim 1, wherein in the step 2, the network partitioning method works as follows:

step 61: each independentThe sub-region is a node, and the comprehensive index of the sub-region is calculated

Step 62 is executed;

In the calculation, the maximum positive value is adopted as

As an updated composite index

step 64: comprehensive index