CN107229809B - SPD (Surge protective device) optimal configuration method in power plant low-voltage power distribution system based on particle swarm optimization - Google Patents
SPD (Surge protective device) optimal configuration method in power plant low-voltage power distribution system based on particle swarm optimization Download PDFInfo
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Abstract
The invention discloses a particle swarm algorithm-based SPD optimal configuration method in a power plant low-voltage power distribution system, which comprises the steps of constructing an optimization function which takes the position of the ith SPD as a parameter and the minimum comprehensive failure rate as a target, solving the optimization function by adopting the particle swarm algorithm to obtain the optimal solution of the distance from n SPDs to a certain device, and determining the positions of the n SPDs; the method applies the particle swarm optimization to SPD positioning, can comprehensively consider the configuration method of the voltage protection level and the electrical distance, and can reduce the number of SPDs to the maximum extent on the premise of meeting the requirement of the impact voltage resistance of protected equipment.
Description
Technical Field
The invention relates to the technical field of lightning protection of a low-voltage power distribution system of a power plant, in particular to an optimal configuration method of a Surge Protection Device (SPD) in the low-voltage power distribution system of the power plant based on a particle swarm algorithm.
Background
With the stricter lightning protection requirements of power electronic related equipment, Surge Protection Devices (SPD) are installed to limit instantaneous overvoltage on a line, and the over-current on a bleeder line becomes one of the important links of the modern lightning protection technology. The good surge protection scheme not only depends on the quality of the surge protector itself, but also has a great relationship with the configuration and selection of the surge protector. Even if the surge protector itself is good, if the surge protector is not used properly or configured properly, not only the good protection effect cannot be achieved, but also the malfunction may occur, and even a certain level of device may explode.
For the configuration of the SPD in the low-voltage system, the existing international and domestic application standards are inconsistent, some important problems such as protection distance, interstage cooperation, backup overcurrent protection and the like are not clearly specified, and the configuration of the SPD has certain randomness. At present, the number of SPD levels in a low-voltage system is large, the spreading range is wide, the number of devices is large, the investment is large, a lot of troubles are brought to maintenance, and the workload of engineering design and construction stages is large. There are numerous devices in a power plant low voltage power distribution system and in most cases a lightning strike event is a small probability event. Therefore, under the condition of ensuring the safety of the equipment with a certain probability, the optimal positioning of the SPDs is determined, the protection distance of each SPD is fully utilized, the configuration number of the SPDs is optimized, certain economic benefit is brought, and the method has important significance for practical engineering application.
Disclosure of Invention
The invention aims to solve the problems and provides an SPD optimal configuration method in a power plant low-voltage power distribution system based on a particle swarm algorithm.
In order to achieve the purpose, the invention adopts the following specific scheme:
the SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm algorithm comprises the following steps:
(1) if there are m devices to be protected in the low voltage distribution network, including: device 1, device 2, … …, device m; the number of SPDs to be positioned is n, the acceptable failure rate is R, the length of the cable is S, and the electrical distance from the xth SPD to the equipment 1 is lxX is 1, 2, …, n, according to lxDetermining the position of the xth SPD;
(2) calculating the failure rate r of each device;
(3) carrying out linear weighting on the fault rate of each device to obtain a comprehensive fault rate R;
(4) constructing location l with the xth SPDxAn optimization function taking the minimum comprehensive failure rate R as a target is taken as a parameter;
(5) and solving the optimization function by adopting a particle swarm algorithm to obtain an optimal solution of the distance from the n SPDs to a certain device, thereby determining the positions of the n SPDs.
Further, in the step (2), the failure rate r of each device is specifically:
wherein, VkIs a lightning overvoltage, Pb(Vk) For devices at overvoltage VkProbability of flashover under influence, p0(Vk) As a function of the probability density of the overvoltage distribution.
Further, the device is in overvoltage VkProbability of flashover occurring under action Pb(Vk) The method specifically comprises the following steps:
probability density function p of overvoltage distribution0(Vk) The method specifically comprises the following steps:
wherein, V50％And σjMathematical expectations and standard deviations of the device insulation discharge voltage, respectively; vaAnd σgRespectively the mathematical expectation and the standard deviation of the lightning overvoltage.
Further, in the step (3), the comprehensive failure rate R specifically is:
wherein r isyAs failure rate of the device y, αyIs a weight of the failure rate of device y.
Further, in the step (4), the constructed objective function is specifically:
wherein R is the comprehensive failure rate lxIs the electrical distance of the xth SPD to the device 1.
Further, the specific method in the step (5) comprises the following steps:
1) initialization: randomly generating the position and speed of the particles in a solution interval [0, S ] of the problem space;
2) evaluating the particles, namely evaluating the applicable value of the optimization function for each particle;
3) updating the optimal: calculating the best position the particle experiences; calculating the best positions of all particles in the population, namely the global best positions;
4): particle updating: evolving the speed and position of the particle according to the result of 3);
5): judging an ending condition, and if the comprehensive fault rate meets the fault rate requirement or evolves to a preset maximum iteration number, ending the calculation; otherwise, returning to 2), and continuing;
6): obtaining a group of optimal solutions after the algorithm is finished, wherein1，l2，…，lnI.e. the distance of the n SPDs to a device, so that the location of the n SPDs can be determined.
Further, in the step 1), if the size of the population is set to be N, the following matrix is randomly generated
Wherein, { lijI is 1, 2, …, N, j is 1, 2, …, N represents the position of i particle in the group as j, vijIs the speed corresponding to it, both in the interval 0, S]Uniformly distributed random numbers.
Further, in the step 2), for each particle lijAnd (4) performing simulation calculation on the lightning wave invasion by adopting MATLAB simulation software at the determined corresponding n SPD positions to obtain the lightning overvoltage distribution of each node in the network.
Further, in the step 3), the best position pbest experienced by the particle is calculatedi(t)＝(li1，li2，…，linThat is, the location that the particle has experienced with the best fitness, is determined by：
Wherein pbesti(t) is the position of best fitness experienced by the particle, R (l)1(t+1)，l2(t+1)，…，ln(t+1))、R(pbesti(t)) are all particle fitness.
Further, in the step 3), the best positions that all particles in the population have undergone are specifically:
Gbesti(t)＝min{R(pbest1(t)，pbest2(t)，…，pbestN(t))}；
wherein R (pbest)1(t)，pbest2(t)，…，pbestN(t)) is the particle fitness.
The invention has the beneficial effects that:
(1) the invention theoretically calculates, analyzes and determines the position of the SPD, converts the positioning of the SPD into the optimal problem which takes the failure rate of equipment as a target function and the electrical distance from the SPD to the equipment as a parameter, and seeks the optimal solution by utilizing the particle swarm algorithm. Has very important significance for solving the practical engineering problem.
(2) Although the invention only solves the positioning problem of the SPD, the voltage protection level and the electrical distance are comprehensively considered in the calculation process.
(3) The invention converts the multi-objective function into the single objective function through weighting, and the importance and the danger degree of each device and the main protection of which device the SPD to be positioned is can be reflected by the corresponding weight.
(4) The particle swarm algorithm is simple in rule, easy to implement, free of operations of crossing and variation of the genetic algorithm, high in convergence speed and suitable for the optimal problem with few parameters. The algorithm is very suitable for the optimization problem researched by the invention, which only has the distance between the SPD and the protected equipment as a parameter and has the minimum failure rate.
Drawings
FIG. 1 is a flow chart of an SPD optimal configuration method in a power plant low-voltage power distribution system based on a particle swarm algorithm.
The specific implementation mode is as follows:
the invention is described in detail below with reference to the accompanying drawings:
the invention discloses an SPD optimal configuration method in a power plant low-voltage distribution system based on a particle swarm algorithm. The method applies the particle swarm optimization to SPD positioning, can comprehensively consider the configuration method of the voltage protection level and the electrical distance, and can reduce the number of SPDs to the maximum extent on the premise of meeting the requirement of the impact voltage resistance of protected equipment.
The specific method of the invention is shown in fig. 1, and specifically comprises the following steps:
the number of devices to be protected in the low-voltage distribution network is m (device 1, device 2 … … device m), n SPD protections are required to be positioned, and the acceptable failure rate is R0The cable length is S, and the electrical distance l from the xth SPD to the device 1xAs a parameter
(x is 1, 2, …, n), then lxL is more than or equal to 0xS is less than or equal to lxThe determined xth SPD position calculates the failure rate of each device
VkIs a lightning overvoltage, Pb(Vk) For devices at overvoltage VkProbability of flashover under influence, p0(Vk) As a function of the probability density of the overvoltage distribution.
Wherein, V50％And σjRespectively, the mathematical expectation (commonly known as 50% discharge voltage) and standard deviation of the device insulation discharge voltage; vaAnd σgThe mathematical expectation and standard deviation of lightning overvoltage are respectively taken as 3% and 10%.
The failure rate of each device is linearly weighted to obtain the comprehensive failure rate R,
wherein r isyAs failure rate of the device y, αyThe weight of the failure rate of the device y can be determined according to the importance, danger degree and the like of each device, and if the SPD to be positioned is used for mainly protecting a certain device, the corresponding weight of the device can be set to be the maximum.
Constructing location l with ith SPDxAnd (3) as a parameter, representing the SPD positioning problem as an optimal problem by using an optimization function with the minimum comprehensive fault rate R as a target:
solving the optimization function by adopting a particle swarm algorithm to obtain an optimal solution of the distance from the n SPDs to a certain device, thereby determining the positions of the n SPDs, and the method specifically comprises the following steps:
step (1): initialization: randomly generating the position and speed of the particles in a solution interval [0, S ] of the problem space;
setting the size of the population as N, then generating the following matrix randomly
Wherein { lijI is 1, 2, …, N, j is 1, 2, …, N represents the position of i particle in the group as j, vijIs the speed corresponding to it, both in the interval 0, S]Uniformly distributed random numbers.
Step (2): evaluation of particles evaluation of the applicability of the optimization function for each particle
1) For each particle lijAnd (4) performing simulation calculation on the lightning wave invasion by adopting MATLAB simulation software at the determined corresponding n SPD positions to obtain the lightning overvoltage distribution of each node in the network.
2) Calculating the equipment failure rate r of each equipment according to the formula (3-1)iWeighting according to the formula (3-4) to obtain the comprehensive failure rate r, namely each particle lijIs a suitable value of (c).
And (3): updating the optimal: calculating the best position experienced by the particle
pbesti(t)＝(li1，li2，…，lin) I.e. the position that the particle has experienced the best fitness, is determined by
Computing the best positions experienced by all particles in the population, i.e. the global best positions
Gbesti(t)＝min{R(pbest1(t)，pbest2(t)，…，pbestN(t))}
And (4): particle updating: the velocity and position of the particles were evolved according to equations (3-5) and (3-6).
And (5): judging the end condition, and ensuring that the fitness of the target function is good enough (the comprehensive fault rate meets the fault rate requirement that R is less than or equal to R)0) Or evolving to the preset maximum iteration number, otherwise, returning to the step (2) and continuing to perform.
And (6): obtaining a group of optimal solutions after the algorithm is finished, wherein1，l2，…，lnI.e. the distance of the n SPDs to a device, so that the location of the n SPDs can be determined.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (8)
1. A SPD optimal configuration method in a power plant low-voltage power distribution system based on a particle swarm algorithm is characterized by comprising the following steps:
(1) if there are m devices to be protected in the low voltage distribution network, including: device 1, device 2, … …, device m; the number of SPD protection needing positioning is n, and the acceptable failure rate is R0The cable length is S and the electrical distance from the xth SPD to the device 1 is lx1, 2,.. n, followed by lxDetermining the position of the xth SPD;
(2) calculating the failure rate r of each device, specifically:
r＝∫0 ∞Pb(Vk)p0(Vk)du
wherein, VkIs a lightning overvoltage, Pb(Vk) For devices at overvoltage VkProbability of flashover under influence, p0(Vk) Is a probability density function of the overvoltage distribution;
(3) carrying out linear weighting on the fault rate of each device to obtain a comprehensive fault rate R;
(4) constructing location l with the xth SPDxAs a parameter, an optimization function with the minimum comprehensive failure rate R as a target is constructed by the following specific steps:
wherein R is the comprehensive failure rate lxIs the electrical distance of the xth SPD to device 1;
(5) and solving the optimization function by adopting a particle swarm algorithm to obtain an optimal solution of the distance from the n SPDs to a certain device, thereby determining the positions of the n SPDs.
2. The SPD optimal configuration method in power plant low-voltage power distribution system based on particle swarm optimization algorithm according to claim 1, wherein the equipment is in overvoltage VkProbability of flashover under actionPb(Vk) The method specifically comprises the following steps:
probability density function p of overvoltage distribution0(Vk) The method specifically comprises the following steps:
wherein, V50％And σjMathematical expectations and standard deviations of the device insulation discharge voltage, respectively; vaAnd σgRespectively the mathematical expectation and the standard deviation of the lightning overvoltage.
3. The SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm optimization algorithm according to claim 1, wherein in the step (3), the comprehensive failure rate R specifically is as follows:
wherein r isyAs failure rate of the device y, αyIs a weight of the failure rate of device y.
4. The SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm optimization algorithm according to claim 1, wherein the specific method in the step (5) comprises the following steps:
1) initialization: randomly generating the position and speed of the particles in a solution interval [0, S ] of the problem space;
2) evaluation of particles: evaluating the applicable value of the optimization function for each particle;
3) updating the optimal: calculating the best position the particle experiences; calculating the best positions of all particles in the population, namely the global best positions;
4): particle updating: evolving the speed and position of the particle according to the result of 3);
5): judging an ending condition, and if the comprehensive fault rate meets the fault rate requirement or evolves to a preset maximum iteration number, ending the calculation; otherwise, returning to 2), and continuing;
6): obtaining a group of optimal solutions after the algorithm is finished, wherein1，l2，...，lnI.e. the distance of the n SPDs to a device, so that the location of the n SPDs can be determined.
5. The SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm optimization algorithm according to claim 4, wherein in the step 1), if the size of the group is set to be N, the following matrix is randomly generated
Wherein, { lijI 1, 2, N, j 1, 2, N represents the position of the i particle in the population as j, vijIs the speed corresponding to it, both in the interval 0, S]Uniformly distributed random numbers.
6. The SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm optimization algorithm according to claim 4, wherein in the step 2), for each particle lijAnd (4) performing simulation calculation on the lightning wave invasion by adopting MATLAB simulation software at the determined corresponding n SPD positions to obtain the lightning overvoltage distribution of each node in the network.
7. The SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm optimization algorithm according to claim 4, wherein in the step 3), the best position pbest that the particle experiences is calculatedi(t)＝(li1，li2，...，lin) I.e. the position that the particle has experienced the best fitness, is determined by:
wherein pbesti(t) is the position of best fitness experienced by the particle, R (l)1(t+1)，l2(t+1)，...，ln(t +1)) is the particle fitness.
8. The SPD optimal configuration method in the power plant low-voltage power distribution system based on the particle swarm optimization algorithm according to claim 4, wherein in the step 3), the best positions that all the particles in the group experience are specifically:
Gbesti(t)＝min{R(pbest1(t)，pbest2(t)，...，pbestN(t))}；
wherein R (pbest)1(t)，pbest2(t)，...，pbestN(t)) is the particle fitness.
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