CN111490552B - A reactive power optimization method for distribution network - Google Patents

Abstract

A reactive power optimization method of a power distribution network aims at a power distribution network comprising SNOP and DG, a reactive power optimization model taking the minimum system active network loss and reactive power exchange with an upper power network as objective functions is established, the gear of an OLTC is optimized in a first stage, the action frequency constraint condition of the OLTC is ignored, the gear of an on-load voltage-regulating transformer OLTC in each period is solved by utilizing a mixed integer particle swarm algorithm, the gear of the on-load voltage-regulating transformer OLTC in each period in one day is obtained by adopting a clustering algorithm, the active network loss and the reactive power are optimized in a second stage, the gear of the on-load voltage-regulating transformer OLTC in each period in one day is used as a known value, and the active power of a first converter VSC1, the reactive power of a second converter VSC2 and the reactive power of a distributed power source DG in an intelligent soft switch SNOP are solved by adopting a standard particle swarm algorithm. The invention can optimize reactive power distribution of the power distribution network and reduce network loss, and has better convergence and optimizing capability.

Description

A Reactive Power Optimization Method for Distribution Network

technical field

The invention relates to a two-stage reactive power optimization method for a distribution network considering the adjustment capabilities of SNOP and DG.

Background technique

With the access of distributed generation (DG) to the traditional distribution network, the current situation that the voltage of the radial distribution network drops along the power point to the branch terminal node is changed, and the control variable of reactive power voltage is doubled. In recent years, the intelligent soft switch (Soft Normally Open Point, SNOP) installed on the tie line of the distribution network has made it more difficult to solve the reactive power optimization problem of the distribution network. With the continuous improvement of DG penetration rate and the wide application of SNOP devices, it is of practical significance to carry out research on reactive power optimization of distribution network considering the reactive power adjustment capabilities of SNOP and DG.

Contents of the invention

The invention provides a distribution network reactive power optimization method, which performs two-stage reactive power optimization for a distribution network including SNOP and DG, can optimize the reactive power distribution of the distribution network and reduce network loss, and has better convergence and optimization capabilities.

In order to achieve the above object, the present invention provides a distribution network reactive power optimization method. Aiming at the distribution network including intelligent soft switch SNOP and distributed power supply DG, a reactive power optimization model with the system active network loss and the minimum reactive power exchange power with the upper power grid as the objective function is established, and the reactive power optimization model is optimized in two stages. The first stage optimizes the gear position of the on-load tap changer OLTC, ignoring the constraints of the limit of the number of operations of the on-load tap changer OLTC within a day. In the second stage, the active network loss and reactive power are optimized, and the gear position of the on-load tap changer OLTC in each period of the day is taken as a known value, and the standard particle swarm optimization algorithm is used to solve the active power of the first converter VSC1, the reactive power of the first converter VSC1, the reactive power of the second converter VSC2, and the reactive power of the distributed power supply DG in the intelligent soft switch SNOP.

The stated objective function is:

In the formula, f is the fitness value, P _t,loss is the active network loss at time t, P _0,loss is the initial active network loss of the system at peak load, P _t,ref and Q _t,ref are the active power and reactive power provided by the upper grid at time t, respectively; n is the research time period; Ω _DG is the reactive power combination of distributed power supply DG, and Ω _SOP is the active and reactive power combination of intelligent soft switch SNOP;

The constraints are:

System power flow constraints: f(P _i ,Q _i ,U _i )＝0

Node voltage constraints: U _i,min ≤U _i ≤U _i,max

Branch flow constraints:

The power constraints of the smart soft-switching SNOP:

P ₁ (t)+P ₂ (t)=0

In the formula, P ₁ (t) and Q ₁ (t) are the active power and reactive power of the first converter VSC1 in the intelligent soft switching SNOP in the period t; P ₂ (t) and Q ₂ (t) are the active power and reactive power of the second converter VSC2 in the intelligent soft switching SNOP in the period t; S _1max and S _2max are the capacities of the two converters in the intelligent soft switching SNOP;

Power constraints of distributed power generation DG:

In the formula, are the actual active power and reactive power of the i-th distributed power generation DG, respectively, where The value of depends on the fan and photovoltaic resources corresponding to the distributed power generation DG; θ _min is the angle corresponding to the minimum power factor of the distributed power generation DG;/> is the capacity of the distributed power supply DG;

The gear adjustment limit constraints of the on-load tap changer OLTC:

TC _min ≤TC _t ≤TC _max ∩TC∈Z

N _TC ≤ N _TCmax

In the formula, P _i and Q _i are the total active power and reactive power injected by node i, U _i is the voltage of node i, U _i,min and U _i,max are the minimum and maximum allowable voltages of node i, I _ij and I ij, _max are the current amplitude and the upper limit of the current amplitude of the branch between node i and node j, TC _t is the gear position of the on-load tap changer OLTC at time t, TC _min and TC _max are the minimum gear and the maximum gear of the on-load tap changer OLTC, Z is An integer set, N _TC and N _TCmax are the actual number of actions and the maximum allowable number of actions of the on-load tap changer OLTC in one day, respectively.

The method for optimizing the OLTC gear of the on-load tap changing transformer in the first stage includes the following steps:

Step S2.1, initialize population size, number of iterations, initial position and speed of particles, limit value of particle position and speed limit, encode the gear position of the on-load tap changer OLTC, the active power P ₁ of the first converter VSC1 of the intelligent soft switch SNOP, the reactive power Q ₁ and Q ₂ of the first converter VSC1 and the second converter VSC2, and the reactive power of the distributed power supply DG;

Set particle position limits:

The maximum and minimum particle positions representing the OLTC gear position of the on-load tap changer are set to TC _max and TC _min respectively, the maximum and minimum particle positions representing the active power P ₁ (t) of the intelligent soft switch SNOP are S _1max and -S _1max respectively, the maximum and minimum particle positions representing the reactive power Q ₁ (t) of the intelligent soft switch SNOP are respectively S _1max and -S _1max , representing the maximum particle position of the intelligent soft switch SNOP reactive power Q ₂ (t) and the minimum values are S _2max and -S _2max respectively, indicating that the maximum and minimum particle positions of the reactive power Q _DG of the distributed power generation DG are respectively and />

Set particle velocity limit range: [-0.2×(maximum position-minimum position), 0.2×(maximum position-minimum position)];

Step S2.2, decode the position of the particle into the gear position of the on-load tap changer OLTC and the active power P ₁ of the first converter VSC1 of the intelligent soft switch SNOP, the reactive power Q ₁ and Q ₂ of the first converter VSC1 and the second converter VSC2, and the reactive power of the distributed power supply DG, and perform power flow calculation to make it meet the system power flow constraints, node voltage constraints and branch power flow constraints, and calculate the fitness value of each particle according to the objective function;

Step S2.3, counting the extreme value of the individual particle and the extreme value of the group, the extreme value of the individual particle is the historical minimum value of the fitness value of the particle, and the group extreme value is the historical minimum value of all particles;

Step S2.4, update the position and velocity of the particle swarm, and correct the updated position and velocity according to the integer constraint, particle position limit and particle velocity limit;

The position update and velocity update formulas are as follows:

In the formula, c ₁ and c ₂ are the weights of the local optimization direction and the global optimization direction; r ₁ and r ₂ are random numbers between two [0-1]; and /> The position and velocity of the id particle for the nth iteration, /> is the individual extremum of the id particle in the nth iteration, and p _ngd is the population extremum in the nth iteration;

Step S2.5, judging whether the number of iterations has been reached, if not, jump to step S2.2, if satisfied, go to step S2.6;

Step S2.6, counting the stalls of the on-load tap changer OLTC in each time period, each stall is initialized as a cluster, and the adjacent clusters of the same stall are merged into one cluster, and the number of clusters after the merging is N _TC ;

Step S2.7, calculating the value of the evaluation function of each adjacent two clusters after merging, and selecting the scheme with the smallest evaluation function for merging;

The clustering evaluation function f _cluster is defined as follows:

In the formula, K is the number of clusters, and its value is the maximum allowable number of operations of the on-load tap changer OLTC N _TCmax , J _i is the i-th cluster, TC _t is the gear position of the cluster J _i at time t, and TC _i is the gear position of the i-th cluster, and its value is equal to the average value of all gears in the cluster and rounded up to the nearest integer;

Step S2.8, if the number of clusters N _TC ≤ N _TCmax after merging, go to step S2.9, otherwise continue to step S2.7;

Step S2.9, calculate the average value of the gears in each cluster, round the corresponding integer to be the gear of the on-load tap changer OLTC in the corresponding time period, and calculate the value of the clustering evaluation function.

The method for optimizing active network loss and reactive power in the second stage includes the following steps:

Step S3.1, initialize the population size, number of iterations, initial particle position and velocity, particle position limit and velocity limit, and encode the active power P ₁ of the first converter VSC1 of the smart soft switch SNOP, the reactive power Q ₁ and Q ₂ of the first converter VSC1 and the second converter VSC2, and the reactive power of the distributed power supply DG;

Set particle position limits:

The maximum and minimum particle positions representing the OLTC gear position of the on-load tap changer are set to TC _max and TC _min respectively, the maximum and minimum particle positions representing the active power P ₁ (t) of the intelligent soft switch SNOP are S _1max and -S _1max respectively, the maximum and minimum particle positions representing the reactive power Q ₁ (t) of the intelligent soft switch SNOP are respectively S _1max and -S _1max , representing the maximum particle position of the intelligent soft switch SNOP reactive power Q ₂ (t) and the minimum values are S _2max and -S _2max respectively, indicating that the maximum and minimum particle positions of the reactive power Q _DG of the distributed power generation DG are respectively and />

Set particle velocity limit range: [-0.2×(maximum position-minimum position), 0.2×(maximum position-minimum position)];

Step S3.2, decode the position of the particle into the gear position of the on-load tap changer OLTC and the active power P ₁ of the first converter VSC1 of the intelligent soft switch SNOP, the reactive power Q ₁ and Q ₂ of the first converter VSC1 and the second converter VSC2, and the reactive power of the distributed power supply DG, and perform power flow calculation to make it meet the system power flow constraints, node voltage constraints and branch power flow constraints, and calculate the fitness value of each particle according to the objective function;

Step S3.3, counting the extreme value of the individual particle and the extreme value of the group, the extreme value of the individual particle is the historical minimum value of the fitness value of the particle, and the group extreme value is the historical minimum value of all particles;

Step S3.4, updating the position and velocity of the particle swarm, and correcting the updated position and velocity according to the integer constraint, particle position limit and particle velocity limit;

The position update and velocity update formulas are as follows:

In the formula, c ₁ and c ₂ are the weights of the local optimization direction and the global optimization direction; r ₁ and r ₂ are random numbers between two [0-1]; and /> The position and velocity of the id particle for the nth iteration, /> is the individual extremum of the id particle in the nth iteration, and p _ngd is the population extremum in the nth iteration;

Step S3.5, judging whether the number of iterations is reached, if not, jump to step S3.2, if satisfied, the particle position corresponding to the population extremum is the optimal solution.

Aiming at the distribution network including SNOP and DG, the present invention establishes a reactive power optimization model with the minimum active network loss of the system and the minimum reactive power exchanged with the upper-level power grid as the objective function, and takes the limit of the number of operations of the on-load tap changer OLTC in one day as a constraint condition, and performs two-stage optimization on the reactive power optimization model. The first stage optimizes the gear position of the OLTC, and the second stage optimizes active network loss and reactive power.

Description of drawings

Figure 1 is a typical structure diagram of an intelligent soft switch SNOP.

Fig. 2 is a schematic diagram of the operating range of the converter VSC in the intelligent soft switch SNOP.

Fig. 3 is a flowchart of a reactive power optimization method for a distribution network provided by the present invention.

Fig. 4 is a schematic diagram of an improved IEEE33 node system in an embodiment of the present invention.

Fig. 5 is a graph showing load fluctuations, fan and photovoltaic output in an embodiment of the present invention.

Fig. 6 is a diagram of OLTC gear change in an embodiment of the present invention.

Fig. 7 is the optimization result of the objective function in one embodiment of the present invention.

Fig. 8 is a schematic diagram of the optimization result of the SNOP control variable in an embodiment of the present invention.

Fig. 9 is a schematic diagram of the optimization results of DG control variables in an embodiment of the present invention.

Fig. 10 is a schematic diagram of the convergence of the particle swarm optimization algorithm in an embodiment of the present invention.

Detailed ways

A preferred embodiment of the present invention will be specifically described below with reference to FIGS. 1 to 10 .

Due to the fluctuation of loads and resources such as wind turbines and photovoltaics, the reactive power optimization problem needs to solve the optimization results in different time periods, and at the same time, it should meet the time correlation, such as the limit on the number of shifts of the on-load tap changer (OLTC) in a day. In terms of the objective function, the main considerations are the minimum network loss, the optimal economy of reactive power generation, the minimum operation risk, and the combination of these objectives. Relevant studies have shown that accessing SNOP in the distribution network can significantly increase the voltage level of the load point and reduce the network loss, which plays an important role in reactive power optimization. The difficulty of reactive power optimization of distribution network with SNOPs and DGs is to coordinate the active and reactive power of multiple SNOPs and DGs, and at the same time, it should satisfy the optimization of multiple time scales.

The traditional closed-loop design and open-loop operation of distribution network, the radial network realizes the network structure reconstruction during normal operation and load transfer under fault state through tie switches. The SNOP can replace the tie switch to realize the exchange of active power between the two feeders and provide a certain voltage and reactive power support. A typical structure of a SNOP is shown in Figure 1. The reactive power optimization problem belongs to the scenario of normal operation. In this embodiment, SNOP adopts the PQ-V _dc Q control mode, and there are three control variables: the active power output P ₁ flowing from the first converter VSC1 to the second converter VSC2, and the reactive power Q ₁ and Q ₂ of VSC1 and VSC2 .

P ₁ (t)+P ₂ (t)=0(1)

In the formula, P ₁ (t) and Q ₁ (t) are the active power and reactive power of the first converter VSC1 in the SNOP in the t period; P ₂ (t) and Q ₂ (t) are the active power and reactive power of the second converter VSC2 in the SNOP in the t period; S _1max and S _2max are the capacities of the two converters in the SNOP.

The distributed power generation connected to the grid through the converter can not only provide active power, but also emit or absorb reactive power according to the needs of system operation. Converters can achieve reactive power output through active power reduction, and large-capacity converters can also achieve additional reactive power support without losing active power output. The power grid operation unit generally requires that the converter-type distributed power generation connected to the grid can achieve leading or lagging operation, and the power factor should be continuously adjustable within the range of [cosθ _min , 1]. Capacity of Distributed Power Converter Should meet /> In the formula, /> is the maximum active power of the i-th DG. The operation constraints of distributed power generation are shown in mathematical expressions (4) and (5), and the capacity constraints of its converters are the same as equation (2).

In the formula, are the actual active power and reactive power of the i-th distributed power generation DG, respectively, where The value of depends on the fan and photovoltaic resources corresponding to DG; θ _min is the angle corresponding to the minimum power factor allowed by distributed power generation.

The reactive power optimization of the distribution network needs to consider minimizing the active network loss of the system. At the same time, the distribution network should meet the principle of "reactive power local balance", that is, the reactive power exchanged between the root node of the distribution network and the upper-level power grid should be as small as possible.因此，如图3所示，本发明提供了一种配电网无功优化方法，针对包含SNOP和DG的配电网，建立以系统有功网损和与上级电网无功交换功率最小为目标函数的无功优化模型，将有载调压变压器OLTC一天内动作次数限制作为约束条件，对无功优化模型进行两阶段优化，第一阶段优化OLTC的档位，忽略OLTC的动作次数约束条件，利用混合整数粒子群算法求解各个时段有载调压变压器OLTC的档位，采用聚类算法得到有载调压变压器OLTC的动作方案，即得到OLTC一天各个时段的档位，第二阶段优化有功网损与无功功率，将有载调压变压器OLTC一天各个时段的档位作为已知值，采用标准粒子群算法求解SNOP与DG的运行状态，即VSC1的有功功率P ₁ 、VSC1和VSC2的无功功率Q ₁和Q ₂ 、DG的无功功率Q _DG 。

Specifically, the present invention comprises the following steps:

Step S1, establishing a reactive power optimization model with the objective function of the system active network loss and the minimum reactive power exchanged with the upper-level power grid, wherein the active power P _SOP and reactive power Q _SOP of the SNOP, the reactive power Q _DG of the DG, and the gear position TC of the on-load tap changer transformer (OLTC) are control variables.

In order to achieve the unification of dimensions, the two objectives are processed per unit, that is, the nominal value is divided by the reference value to obtain the per unit value with a unit of 1. The constructed objective function can be expressed as:

In the formula, f is the fitness value, P _t,loss is the active network loss at time t, P _0,loss is the initial active network loss of the system at peak load, P _t,ref and Q _t,ref are the active power and reactive power provided by the upper power grid at time t, respectively; n is the research time period, and in this embodiment, the research interval is hours, so n=24; Ω _DG is the reactive power combination of DG, and Ω _SOP is the active and reactive power combination of SNOP. In summary, the first part of formula (6) is the ratio of the real-time network loss to the initial active network loss, and the second part is the ratio of the absolute value of the reactive power and the apparent power provided by the superior power grid.

Q _DG is to represent the reactive power of a certain DG, focusing on expressing that this value is a variable; Ω _DG is the combination of reactive power of each DG in the solution that minimizes the objective function f, emphasizing that this value is the optimization variable of the objective function. When the objective function is optimal, it is a series of specific values. One is a single variable and the other is a set of variables.

P ₁ refers to the active power of VSC1 of a specific SNOP, Q ₁ and Q ₂ refer to the reactive power of VSC1 and VSC2 of a specific SNOP, and the set of the two is Q _SOP . Ω _SOP refers to the set of active and reactive power of multiple SNOPs, that is, the set of _PSOP and Q _SOP of multiple SNOPs.

Constraint conditions mainly consider system power flow constraints (see formula (7)), node voltage constraints (see formula (8)), branch power flow constraints (see formula (9)), SNOP and DG operation constraints (see formulas (1)-(5)), gear adjustment restrictions (see formulas (10)-(11)).

f(P _i ,Q _i ,U _i )＝0 (7)

U _i,min ≤U _i ≤U _i,max (8)

TC _min ≤TC _t ≤TC _max ∩TC∈Z (10)

N _TC ≤ N _TCmax (11)

In the formula, P _i and Q _i are the total active power and reactive power injected by node i, U _i is the voltage of node i, U _i,min and U _i,max are the minimum and maximum allowable voltages of node i, I _ij and I _ij,max are the current amplitude and the upper limit of the current amplitude of the branch between node i and node j, TC _t is the OLTC gear at time t, TC _min and TC _max are the minimum gear and the maximum gear of OLTC, Z is an integer set, N _TC and N _TCmax They are the actual number of actions and the maximum allowed number of actions of OLTC in one day, respectively.

The reactive power optimization model established above is a mixed integer programming problem (MIP) with time coupling.

During reactive power optimization, the gear position of OLTC and SNOP have a coupling relationship with the reactive power output of DG. In order to deal with the limitation of the number of operations of OLTC in a day, that is, the constraint condition (11), a two-stage reactive power optimization method is adopted.

Step S2, the first stage of optimization, ignoring the constraint condition (11), using the mixed integer particle swarm optimization algorithm to solve the optimization scheme of each time period, clustering the number of OLTC stalls in each time period, and obtaining the OLTC action plan for the whole day.

Encode the gear position of OLTC, the active power P ₁ of VSC1, the reactive power Q ₁ and Q ₂ of VSC1 and VSC2, and the reactive power Q _DG of DG, and use the mixed integer particle swarm optimization algorithm to calculate the gear position of OLTC at each time period. The position update and speed update formulas are as follows:

In the formula, c ₁ and c ₂ are the weights of the local optimization direction and the global optimization direction; r ₁ and r ₂ are random numbers between two [0-1]; and /> The position and velocity of the id particle for the nth iteration, /> is the individual extremum of the id particle in the nth iteration, and p _ngd is the population extremum in the nth iteration. Set the maximum and minimum particle positions according to formulas (1)-(5) and (10), specifically: the maximum and minimum particle positions representing the on-load tap-changing transformer (OLTC) gear TC are set to TC _max and TC _min respectively, the maximum and minimum particle positions representing the SNOP active power P ₁ (t) are S _{1max and -S 1max respectively, and the maximum and minimum particle positions representing the SNOP reactive power Q 1 (t) are S 1max and -S 1max respectively , indicating that the maximum and minimum particle positions of SNOP reactive power Q 2 (t) are S 2max and -S 2max , respectively , indicating that the} maximum and minimum particle positions of _DG reactive power Q 2 (t) are /> and />

The above calculation can obtain the gear position of OLTC in each time period. By adjusting the gear value at some time, the overall number of actions can meet the restriction conditions, and the clustering algorithm is used to achieve this purpose. The clustering evaluation function f _cluster is defined as follows:

In the formula, K is the number of clusters, which can be the maximum allowable number of actions of OLTC N _TCmax , J _i is the i-th cluster, TC _t is the gear at time t in cluster J _i , and TC _i is the gear of the i-th cluster, and its value is equal to the average value of all gears in the cluster and rounded up to the nearest integer.

Further, the first-stage optimization specifically includes the following steps:

Step S2.1, population initialization. Initialize the population size, number of iterations, particle initial position and velocity, particle position limit and velocity limit. The particle position limit is set according to formulas (1)-(5) and (10), and the particle speed limit range is [-0.2×(maximum position-minimum position), 0.2×(maximum position-minimum position)].

When initializing the initial position of the particle, encode the gear of OLTC, the active power P ₁ of VSC1, the reactive power Q ₁ and Q ₂ of VSC1 and VSC2, and the reactive power Q _DG of DG. The first value of the particle position represents the OLTC gear, the second value represents the P ₁ of VSC1 of SNOP1, and so on, that is, to determine the physical meaning of each value of the particle position is the encoding process, and the value range of each value of the particle position can be determined after this is determined, that is, the particle position limit.

Step S2.2. Decode the position of the particle into the position of the OLTC and the operating state of SNOP and DG (the operating state of SNOP and DG is the active power P ₁ of VSC1, the reactive power Q ₁ and Q ₂ of VSC1 and VSC2, and the reactive power of DG), and perform power flow calculation to satisfy the constraints (7)-(9). Calculate the fitness value of each particle according to formula (6).

Step S2.3, counting individual extreme values and group extreme values of particles. After each iteration of the particle swarm algorithm, the fitness value of each particle can be calculated through formula (6). The extreme value of the individual particle is the historical minimum value of the fitness value of the particle after each iteration, and the group extreme value is the historical minimum value of all particles.

Step S2.4, update the position and velocity of the particle swarm according to formulas (12) and (13). Corrects the updated position and velocity based on integer constraints, position limits, and velocity limits.

Step S2.5, judging whether the convergence condition is met (set the convergence condition as whether the number of iterations is reached), if not, jump to step S2.2, and if yes, proceed to step S2.6.

Step S2.6: Count the stalls of OLTC in each time period, initialize each stall as a cluster, merge adjacent clusters of the same stall into one cluster, and count the number of clusters after merging as N _TC .

Step S2.7. Calculate the evaluation function value of each adjacent two clusters after merging according to formula (14), select the solution with the smallest evaluation function to merge, and if there are multiple solutions, randomly select one solution to merge.

Step S2.8, if the number of clusters N _TC ≤ N _TCmax after merging, go to step S2.9, otherwise continue to step S2.7.

Step S2.9. Calculate the average value of the gears in each cluster, round up the corresponding integer to be the gear of the OLTC in the corresponding time period, and calculate the value of the clustering evaluation function.

Note that the clustering process (step S2.6 to step S2.9) can be run multiple times, and the optimal clustering scheme is selected according to the final clustering evaluation function value.

Step S3, the second stage of optimization, takes the OLTC gear as a known value, and uses the standard particle swarm optimization algorithm to solve the running status of SNOP and DG.

The second stage of optimization specifically includes the following steps:

Step S3.1, population initialization. Initialize the population size, number of iterations, particle initial position and velocity, particle position limit and velocity limit. The particle position limit is set according to formulas (1)-(5) and (10), and the particle speed limit range is [-0.2×(maximum position-minimum position), 0.2×(maximum position-minimum position)].

When initializing the initial position of the particle, the active power P ₁ of VSC1 , the reactive power Q ₁ and Q ₂ of VSC1 and VSC2 , and the reactive power Q _DG of DG are encoded.

Step S3.2. Decode the position of the particle into the operating state of SNOP and DG (the operating state of SNOP and DG is the active power P ₁ of VSC1, the reactive power Q ₁ and Q ₂ of VSC1 and VSC2, and the reactive power of DG), and perform power flow calculation to satisfy the constraints (7)-(9). Calculate the fitness value of each particle according to formula (6).

Step S3.3, counting the extreme values of individual particles and group extreme values. After each iteration of the particle swarm algorithm, the fitness value of each particle can be calculated through formula (6). The extreme value of the individual particle is the historical minimum value of the fitness value of the particle after each iteration, and the group extreme value is the historical minimum value of all particles.

Step S3.4, update the position and velocity of the particle swarm according to formulas (12) and (13). The updated position and velocity are corrected according to the position and velocity limits.

Step S3.5, judging whether the convergence condition is satisfied (set the convergence condition to whether the number of iterations is reached), if not, jump to step S3.2, if satisfied, the particle position corresponding to the extreme value of the group is the optimal solution, decoded into the parameter values of SNOP and DG in the distribution network, and these parameter values are the optimal control variables.

The standard particle swarm optimization algorithm is used to solve the problem, and the steps are similar to the steps S2.1 to S2.5 of the first-stage optimization process, the difference is that integer constraints are not considered.

As shown in Figure 4, in one embodiment of the present invention, the improved IEEE33 node system is adopted, the allowable voltage range is [0.9, 1.1], node 1 is connected to the OLTC, the adjustable gear is ±8, each gear can be adjusted by 1.25%, and the allowable number of actions of the OLTC tap is set to 6 times a day. The tie line is replaced by two SNOPs, the tie line from node 12 to node 22 is replaced by SNOP1, and the tie line from node 25 to node 29 is replaced by SNOP2. The load fluctuations, fan and photovoltaic output curves are shown in Figure 5, where the load is the residential load, and the peak load is concentrated between 19:00-23:00. The specific parameters of SNOP and DG are shown in Table 1. The capacity of the two converters VSC of SNOP is 300kVA, and the power factor of DG is continuously adjustable in the range of [0.9, 1]. When the system does not consider SNOP and DG and the tap is not adjusted, the original network loss is 202.7kW at peak load.

Table 1

SNOP(VSC1--VSC2) Fan (WT) Photovoltaic (PV) Location 12-22, 25-29 10, 16, 30 7, 13, 27 capacity 300kVA--300kVA 500kW 400kW

In the particle swarm optimization algorithm, the population size is 100, the number of iterations is 80 generations, and c ₁ =c ₂ =2. If the particle position range is [x _min , x _max ], then the particle velocity range is set to [-0.2(x _max -x _min ),0.2(x _max -x _min )].

OLTC stall optimization: In the first stage of optimization, the original stalls of OLTC at each time period are shown as dotted lines in Figure 6. The stalls are affected by fluctuations in wind turbine and photovoltaic resources and load conditions. For example, 7:00-17:00 wind turbines and photovoltaic resources are relatively abundant, and the load is at an intermediate level. In order to better absorb new energy, the overall stalls are lower. Calculated by the clustering algorithm, the minimum value of f _cluster is 5. Correspondingly, the gear position at 5 o’clock is lowered by 2 gears, 7 o’clock is raised by 1 gear, 17 o’clock is lowered by 1 gear, and 18 o’clock is raised by 1 gear. The OLTC gears after clustering are shown by the solid line in Figure 6.

Active network loss and reactive power optimization: In the second stage of optimization, through the cooperation of SNOP and DG, the optimization of the objective function is realized, and the optimization result is shown in Figure 7. It can be seen from the dotted line in the figure that the network loss has been reduced at all times, the lowest dropped to 3.53% (time 10), and even at the peak load (time 21) it was reduced to 94.9%. The overall loss reduction effect is more obvious when the load is small and the wind turbine and photovoltaic resources are abundant. For example, the network loss has been reduced by more than 80% from 1:00 to 17:00. It can be seen from the dotted horizontal line in the figure that the ratio of reactive power and apparent power exchanged with the upper-level grid as a whole is small, and the value range is [0, 0.335], that is, the reactive power exchanged with the upper-level grid is small, and the corresponding power factor interval is [0.942, 1]. From 7:00 to 16:00, the reactive power exchanged with the upper-level power grid is basically equal to 0. During this period, the wind turbine and photovoltaic resources are relatively abundant, which provides sufficient reactive power output, realizes the local balance of reactive power, and reduces the active power loss caused by the transmission of reactive power in the upper-level power grid.

The control variables corresponding to the above optimization results are shown in Figure 8 and Figure 9. The active power transmitted by SNOP is from the small numbered node to the large numbered node as the positive direction, and the corresponding side of the small numbered node is VSC1. It can be seen from Figure 8 that the active power transmitted in SNOP changes its direction with the load, wind turbine and photovoltaic resources. For example, the active power of SNOP1 flows from node 22 to node 12 at 7:00-16:00, and the direction of active power is opposite at other times. The two VSCs corresponding to the two SNOPs emit reactive power at all times. It can be seen from Figure 9 that both wind turbines and photovoltaics emit reactive power, and the reactive power emitted most of the time is consistent with the active power of DG in Figure 5. Only PV2 connected to node 13 and WT2 connected to node 16 reduce the reactive power output due to sufficient reactive power at the peak time of wind turbines and photovoltaic resources, as shown by the horizontal line in the middle of the dot and the dotted line with squares in Figure 9, respectively.

Single-time cross-section analysis and convergence analysis: Take 12:00 as an example. At this time, the total active power of the load is 2.48MW, the reactive power is 1.53MVAr, the active power from a single photovoltaic is 294.9kW, and the active power from a single fan is 298.3kW. The convergence of the second-stage particle swarm optimization algorithm at this moment is shown in Figure 10. The algorithm quickly approaches the optimal value in the first eight iterations, and converges at the 15th iteration, which has good optimization ability and convergence.

The minimum allowable power factor of DG is 0.9, then the maximum reactive power that can be emitted or absorbed by photovoltaics and wind turbines at this moment is 142.8kVAr and 144.5kVAr respectively. At this moment, the active network loss is 10.1kW, and the reactive power provided by the superior grid is 0.0kVAr. The optimal combination of the output power of SNOP and DG is shown in Table 2, and the bold part in the table is the upper limit. The results show that based on the load, fan and photovoltaic resources at 12:00, when the objective function is formula (6), the reactive power generated by SNOP and DG is not as high as possible, but should be balanced locally and compensated nearby.

Table 2

The access of SNOP and DG increases the difficulty of solving the reactive power optimization problem of distribution network, and at the same time, it can greatly optimize the operation state of distribution network by setting reasonable targets. The objective function of the model established by the present invention is to minimize the system network loss and exchange reactive power with the upper-level power grid, and fully consider the operation constraints of SNOP and DG and the constraints of OLTC tap position and the like. The two-stage reactive power optimization method is used to solve the above model, and the improved IEEE33 node system is used as a calculation example to verify. The results show that the control of the SNOP equipment is flexible, and the cooperation with the DG can optimize the reactive power distribution of the distribution network and reduce the network loss. The optimization method provided by the invention has better convergence and optimization capabilities.

In future research, reactive power optimization problems in distribution networks including multi-terminal SNOP can be carried out. In addition, the economic research of SNOP is relatively lacking at present, and the optimal configuration and operation of SNOP in the whole life cycle can be carried out to solve the most economical SNOP installation quantity, capacity and location.

Although the content of the present invention has been described in detail through the above preferred embodiments, it should be understood that the above description should not be considered as limiting the present invention. Various modifications and alterations to the present invention will become apparent to those skilled in the art upon reading the above disclosure. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims (1)

1. A reactive power optimization method for a power distribution network is characterized by establishing a reactive power optimization model taking the minimum system active network loss and the minimum reactive power exchange power with an upper power network as objective functions for the power distribution network comprising an intelligent soft switch SNOP and a distributed power source DG, performing two-stage optimization on the reactive power optimization model, optimizing the gear of an on-load voltage-regulating transformer OLTC in the first stage, and ignoring the on-load voltage-regulating transformer OLTC

Solving the gear of the on-load voltage-regulating transformer OLTC in each period by utilizing a mixed integer particle swarm algorithm under the constraint condition of action frequency limitation in one day, obtaining the gear of the on-load voltage-regulating transformer OLTC in each period in one day by adopting a clustering algorithm, optimizing active network loss and reactive power in the second stage, taking the gear of the on-load voltage-regulating transformer OLTC in each period in one day as a known value, and solving the active power of the first converter VSC1, the reactive power of the second converter VSC2 and the reactive power of the distributed power source DG in the intelligent soft switch SNOP by adopting a standard particle swarm algorithm;

the objective function is as follows:

wherein f is a fitness value, P _t,loss Is the active network loss at the time t, P _0,loss For the initial active network loss of the system at peak load, P _t,ref And Q _t,ref Active power and reactive power provided by an upper power grid at t time respectively; n is the study period; omega shape _DG Reactive power combination, Ω for distributed power supply DG _SOP Active and reactive power combinations for intelligent soft switching SNOP;

the constraint conditions are as follows:

and (3) constraint of system tide: f (P) _i ,Q _i ,U _i )＝0

Node voltage constraint: u (U) _i,min ≤U _i ≤U _i,max

Branch tidal current constraint:

power constraint of intelligent soft switch SNOP:

P ₁ (t)+P ₂ (t)＝0

wherein P is ₁ (t) and Q ₁ (t) is the active power and reactive power of the first converter VSC1 in the t-period intelligent soft switch sno; p (P) ₂ (t) and Q ₂ (t) is the active power and reactive power of the second converter VSC2 in the t-period intelligent soft switch SNOP; s is S _1max And S is _2max The capacity of two converters in the intelligent soft switch SNOP;

power constraint of distributed power DG:

in the middle of，The actual active power and reactive power of the i-th distributed power source DG, respectively, wherein +.>The value of (1) depends on the condition of the fan and the photovoltaic resource corresponding to the distributed power supply DG; θ _min Allowing an angle corresponding to the minimum power factor for the distributed power supply DG; />Is the capacity of the distributed power source DG;

gear adjustment limit constraint for on-load step-down transformer OLTC:

TC _min ≤TC _t ≤TC _max ∩TC∈Z

N _TC ≤N _TCmax

wherein P is _i 、Q _i Total active and reactive power injected for node i, U _i For the voltage of node i, U _i,min And U _i,max For minimum and maximum allowed voltages of node I, I _ij And I _ij,max For the current amplitude and upper current amplitude limit of the branch between the node i and the node j, TC _t For the gear position of an on-load voltage regulating transformer OLTC at time t, TC _min And TC _max For the minimum gear and the maximum gear of the on-load voltage regulating transformer OLTC, Z is an integer set, N _TC And N _TCmax The actual action times and the maximum allowed action times of the on-load voltage regulating transformer OLTC in one day are respectively;

the first-stage method for optimizing the on-load voltage-regulating transformer OLTC gear comprises the following steps:

step S2.1, initializing population size, iteration number, particle initial position and speed, particle position limit and speed limit, active power P of first converter VSC1 of intelligent soft switch SNOP for gear of on-load voltage regulating transformer OLTC ₁ Reactive power of the first converter VSC1 and the second converter VSC2Rate Q ₁ And Q ₂ Coding reactive power of the distributed power supply DG;

setting particle position limit values:

particle position maximum and minimum values representing on-load voltage regulating transformer OLTC gear TC are respectively set as TC _max And TC _min Representing the active power P of the intelligent soft switch SNOP ₁ The maximum and minimum values of the particle position of (t) are S _1max and-S _1max Representing intelligent soft switch SNOP reactive power Q ₁ The maximum and minimum values of the particle position of (t) are S _1max and-S _1max Representing intelligent soft switch SNOP reactive power Q ₂ The maximum and minimum values of the particle position of (t) are S _2max and-S _2max Reactive power Q representing distributed power source DG _DG The maximum and minimum values of the particle positions of (2) are respectively And->

Setting a particle speed limit range: [ -0.2× (position maximum-position minimum), 0.2× (position maximum-position minimum) ];

step S2.2 decoding the position of the particles into the gear of the on-load step-up transformer OLTC and the active power P of the first converter VSC1 of the intelligent soft switch SNOP ₁ Reactive power Q of the first converter VSC1 and the second converter VSC2 ₁ And Q ₂ Reactive power of the distributed power supply DG is subjected to load flow calculation, so that the reactive power meets system load flow constraint, node voltage constraint and branch load flow constraint, and the fitness value of each particle is calculated according to an objective function;

s2.3, counting extremum and population extremum of individual particles, wherein the extremum of the individual particles is the historical minimum value of fitness value of the particles, and the population extremum is the historical minimum value of all the particles;

s2.4, updating the position and the speed of the particle swarm, and correcting the updated position and speed according to integer constraint, particle position limit and particle speed limit;

the location update and velocity update formulas are as follows:

wherein, c ₁ 、c ₂ Weights for the local and global optimization directions; r is (r) ₁ 、r ₂ Two [0-1 ]]Random numbers in between;and->Position and velocity of the id-th particle for the nth iteration, < >>For the individual extremum, p, of the nth iteration, the id-th particle _ngd The population extremum is the nth iteration;

step S2.5, judging whether iteration times are reached, if not, jumping to step S2.2, and if so, executing step S2.6;

step S2.6, counting gears of the on-load voltage-regulating transformer OLTC in each period, initializing each gear into one cluster, combining clusters adjacent to the same gear into one cluster, and counting the combined clusters as N _TC ；

S2.7, calculating an evaluation function value after combining each two adjacent clusters, and selecting a scheme with the minimum evaluation function for combining;

evaluation function f of clustering _cluster The definition is as follows:

wherein K is a cluster number, and the value is N which is the maximum allowable action times of an on-load voltage regulating transformer OLTC _TCmax ，J _i For the ith cluster, TC _t For clustering J _i Shift position at middle t moment, TC _i The value of the gear is equal to the average value of all gears in the ith cluster and is rounded nearby;

step S2.8, merging and then determining the clustering number N _TC ≤N _TCmax The step is skipped to the step S2.9, otherwise, the step S2.7 is continued;

s2.9, calculating an average value of gears in each cluster, rounding the corresponding integer to be the gear of the on-load voltage-regulating transformer OLTC in the corresponding time period, and calculating a cluster evaluation function value; the second-stage active power loss and reactive power optimizing method comprises the following steps:

step S3.1, initializing population size, iteration number, particle initial position and velocity, particle position limit and velocity limit, active power P of first converter VSC1 of intelligent soft switch SNOP ₁ Reactive power Q of the first converter VSC1 and the second converter VSC2 ₁ And Q ₂ Coding reactive power of the distributed power supply DG;

setting particle position limit values:

representing intelligent soft switch SNOP active power P ₁ The maximum and minimum values of the particle position of (t) are S _1max and-S _1max Representing intelligent soft switch SNOP reactive power Q ₁ The maximum and minimum values of the particle position of (t) are S _1max and-S _1max Representing intelligent soft switch SNOP reactive power Q ₂ The maximum and minimum values of the particle position of (t) are S _2max and-S _2max Reactive power Q representing distributed power source DG _DG The maximum and minimum values of the particle positions of (2) are respectivelyAnd->Setting a particle speed limit range: [ -0.2× (position maximum-position minimum), 0.2× (position maximum-position minimum)]；

Step S3.2 decoding the position of the particles into the gear of the on-load step-up transformer OLTC and the active power P of the first converter VSC1 of the intelligent soft switch SNOP ₁ Reactive power Q of the first converter VSC1 and the second converter VSC2 ₁ And Q ₂ Reactive power of the distributed power supply DG is subjected to load flow calculation, so that the reactive power meets system load flow constraint, node voltage constraint and branch load flow constraint, and the fitness value of each particle is calculated according to an objective function;

s3.3, counting extremum and population extremum of individual particles, wherein the extremum of the individual particles is the historical minimum value of fitness value of the particles, and the population extremum is the historical minimum value of all the particles;

s3.4, updating the position and the speed of the particle swarm, and correcting the updated position and speed according to integer constraint, particle position limit and particle speed limit;

the location update and velocity update formulas are as follows:

wherein, c ₁ 、c ₂ Weights for the local and global optimization directions; r is (r) ₁ 、r ₂ Two [0-1 ]]Random numbers in between;and->Position and velocity of the id-th particle for the nth iteration, < >>For the individual extremum, p, of the nth iteration, the id-th particle _ngd The population extremum is the nth iteration;

and S3.5, judging whether the iteration times are reached, if not, jumping to the step S3.2, and if so, judging that the particle positions corresponding to the population extremum are the optimal solutions.