CN116187165A - Power grid elasticity improving method based on improved particle swarm optimization - Google Patents

Power grid elasticity improving method based on improved particle swarm optimization Download PDF

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CN116187165A
CN116187165A CN202211681551.XA CN202211681551A CN116187165A CN 116187165 A CN116187165 A CN 116187165A CN 202211681551 A CN202211681551 A CN 202211681551A CN 116187165 A CN116187165 A CN 116187165A
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饶淦
王立功
江旭旭
陶然
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China Three Gorges University CTGU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
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    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
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Abstract

A power grid elastic lifting method based on an improved particle swarm algorithm is used for researching a line fault model under the influence of typhoon load, analyzing the influence condition of typhoon on line meteorological load, and calculating the line fault probability by combining the actual bearable load capacity of a line. On the basis, a fault scene is selected by utilizing the system information entropy and is used as a typical scene of a distributed power supply site selection model. And establishing and optimally solving a distributed power supply site selection model considering the line fault rate. Aiming at different typical scenes which possibly occur, the distributed power supply site selection position meeting various constraints and maximizing the elasticity of the power grid is obtained by using the proposed method; and the distributed power supply location and volume-fixing planning model is optimized and solved through an improved multi-target particle swarm algorithm, so that the toughness of the power distribution network is greatly improved.

Description

Power grid elasticity improving method based on improved particle swarm optimization
Technical Field
The invention belongs to the field of power systems, and particularly relates to a power grid elasticity improving method based on an improved particle swarm algorithm.
Background
Modern power systems tend to be interconnected for greater safety and economic benefits, the subsystems in a large power grid are more closely related, and the structure and the running state of the interconnected power grid are more complex due to the electromagnetic relationship of multiple voltage levels and alternating current and direct current mixing. As the power industry market progresses, the operating conditions, stability margins, backup capacity, and strain capacity for emergencies of the power system will also change. Based on the attention to energy crisis and environmental protection, various clean energy sources are greatly developed in various countries in recent years, and the introduction of distributed energy sources in various scales brings more uncertainty factors to the operation of a power system, so that the scheduling control of the power system faces more serious challenges. Under the influence of the factors, the faults occurring on the local power grid can cause malignant cascade reactions due to artificial or natural reasons, and finally large-area power failure accidents are generated.
The existing patents related to elastic lifting of a power grid mainly comprise:
patent application number/patent number of power transmission line and energy storage planning system collaborative planning modeling method considering elastic power grid restoring force improvement: 202210398654.9 in order to improve the restoring force of the elastic power system, a three-layer robust collaborative planning model is provided: the first layer model is a mathematical model for selecting an electric power system operator to determine the capacity expansion scheme and construction cost of a power transmission network and an energy storage system and the operation cost of the electric power system; the second layer model is a mathematical model of damage quantity predicted values of the power transmission line and the generator under extreme natural disasters; the third layer of model is a mathematical model for selecting the operation cost and the load shedding cost brought by an electric power system operator in the worst scene of an extreme natural disaster through optimal scheduling and load shedding, and the system operation scheme meeting the requirements is obtained through optimal solution of the model, so that the system operation cost is minimized. Patent application number/patent number of 'a high-elasticity power grid source and network load storage multi-element collaborative optimization control method': 202111001591.0 discloses a source network load storage multi-element collaborative optimization control method of a high-elasticity power grid, which comprises the steps of firstly, a multi-element collaborative optimization control model; analyzing the response performance characteristics of the demand side, and establishing a demand side response scheduling model to realize coordinated scheduling and effective interaction of supply and demand sides of the power grid; analyzing the energy storage unit characteristic building model to analyze the constraint quantity of the power grid side; establishing a MOPSO-based collaborative optimization control method based on the control model, and establishing an objective function and a multi-objective optimization model; the source network load storage collaborative optimization scheduling problem is solved efficiently through MOPSO, and the feasibility of multi-objective optimization scheduling is well guaranteed by setting an updating strategy of a non-inferior solution set, so that various resources of the source network load storage are reasonably scheduled, and the running economy of a power grid is improved. Patent application number of 'toughness comprehensive evaluation method and system of distribution network': 202111059384.0A comprehensive evaluation method and system for a power distribution network are disclosed, aiming at six categories of key characteristics of an elastic power grid, three functions of situation awareness, disturbance response and self-lifting capacity of the power distribution network are focused, a comprehensive evaluation system which is more comprehensive and refined under the elastic requirement can be established, and the accuracy and reliability of an evaluation result are improved.
The patent considers the elastic lifting method of the power transmission network under natural disasters, considers source network charge storage multielement collaborative optimization control, but does not consider scene complexity of large-scale faults caused by the natural disasters, and does not consider the conditions of influence of line fault rate on a distributed power supply site selection model, change of a distribution network topological structure and the like. Based on the above analysis, the deficiencies of the prior art patents are specifically as follows:
(1) The influence mechanism model of natural disasters on the power system is not considered.
(2) The influence of the line fault rate on the distributed power supply site selection model is not researched enough.
(3) The situation that the network topology of the power distribution network changes after being affected by natural disasters is not considered.
Disclosure of Invention
In view of the technical problems in the background art, the power grid elasticity improving method based on the improved particle swarm optimization provided by the invention considers the influence mechanism model of natural disasters on the power system, and solves the distributed power source location and volume-fixing planning model through the improved multi-objective particle swarm optimization, so that the toughness of the power distribution network is greatly improved.
In order to solve the technical problems, the invention adopts the following technical scheme:
an electric network elasticity improving method based on an improved particle swarm algorithm comprises the following steps:
step 1: analyzing the influence condition of typhoons on the meteorological load of the line by considering the line fault model under the influence of typhoons, and calculating the line fault probability by combining the load capacity which can be born by the line actually; then, a fault scene is selected by utilizing the system information entropy and is used as a typical scene of a distributed power supply site selection model; the decomposition steps are as follows:
step 1.1: determining the wind speed and the wind direction of each point in the influence range according to the wind field model;
step 1.2: establishing a relational expression of the outage rate of the power transmission line and the effective wind speed;
step 1.3: segmenting the power transmission line, and establishing an outage rate expression of a certain section of power transmission line with the length of L;
step 1.4: obtaining a system entropy value under a scene according to the probability of unreliable operation of the line;
step 2: establishing and optimally solving a distributed power supply site selection model considering the line fault rate; the decomposition steps are as follows:
step 2.1: establishing a distributed power supply site selection model objective function considering element failure rate;
step 2.2: establishing a constraint condition of a distributed power supply site selection model considering element failure rate;
step 2.3: considering the situation that wind and photoelectricity cannot be used as a standby power supply to be added into a power grid under typhoon disaster conditions, taking an energy storage system as a power generation source to provide electric energy for reconstruction of a post-disaster power distribution network;
step 2.4: optimizing and solving a distributed power supply site selection model by adopting a multi-target particle swarm algorithm based on an improved population updating and fitness strategy;
step 2.5: performing iterative optimization;
step 2.6: recalculating the adaptation value, deleting the inferior solution with small adaptation degree in the new population, and ensuring that the number of individuals of the new population does not exceed the maximum capacity of the new population;
step 2.7: and establishing a functional expression between a toughness evaluation index under the action of typhoons, duration time of the power distribution network influenced by typhoons, an expected load curve of the power distribution system during normal operation, an actual load curve of the power distribution system during fault operation under the action of typhoons and an actual power failure condition.
Preferably, in step 1.1, the wind speed and wind direction of each point in the influence range are determined according to the wind field model, where the expression is:
Figure BDA0004015508240000031
wherein x and y are actual coordinates of the section of transmission line; mu (mu) x (t) and mu y (t) is the actual coordinates of the typhoon center at time t; a is that 1 And A 2 Respectively two maximum wind speed coefficients, sigma 1 Sum sigma 2 For the corresponding attenuation coefficient, the two parameters satisfy A 1 >A 2 ，σ 1 >σ 2 The method comprises the steps of carrying out a first treatment on the surface of the Beta (t) is the included angle between the power transmission line and the wind direction.
Preferably, in step 1.2, the relationship between the outage rate of the transmission line and the effective wind speed is represented by using the following exponential function model:
Figure BDA0004015508240000032
wherein: v (V) d The wind speed is designed for the power transmission line; lambda (lambda) p (t) is the unit length outage rate of the power transmission line, and the unit is 1/(50 km.h); model parameters a and b can be obtained from statistical analysis of historical data.
Preferably, in step 1.3, the outage rate expression of a section of the power transmission line with the length L is:
λ(t)＝λ p (t)L (3)
in step 1.4: obtaining a system entropy value under a scene according to the probability of unreliable operation of the line:
Figure BDA0004015508240000041
wherein Ω B Representing a distribution line set; p is p i,t The failure rate of the element i at the time t; z i,t Indicating whether element i fails at time t; omega i Representing element value weights; and selecting a scene with the system entropy value in a proper range as a typical scene of the distributed power supply site selection model to perform optimization solution.
Preferably, in step 2.1, the distributed power location model objective function considering the component failure rate is expressed as:
Figure BDA0004015508240000042
wherein y is i Represents a 0-1 decision variable, represents whether node i builds a distributed power supply, and if so, y i Taking 1, otherwise taking 0; t is the considered period length; s, N is a scene set and a node set, respectively; omega i The weight coefficient of the load i;
Figure BDA0004015508240000043
active load power to restore power to node i in the presence s;
Figure BDA0004015508240000044
wherein: r is the discount rate; k is the service life of the equipment; c (C) T 、C Y Respectively representing investment cost and operation cost; x is x i Active capacity for accessing distributed power; n (N) b The number of branches in the system; line G b Representing the line b impedance; u (U) i 、U j 、δ ij Representing the actual voltage amplitude and phase angle difference at nodes i, j.
Preferably, in step 2.2, the constraint comprises:
constraint 1): a distributed power supply number constraint, the formula of which is:
Figure BDA0004015508240000045
wherein N represents a set of all distributed power supply candidate nodes; p represents the maximum number of distributed power supplies that can be built;
constraint 2): the tidal current constraint comprises the following formula:
Figure BDA0004015508240000046
Figure BDA0004015508240000047
p in the formula i 、Q i Representing the active and reactive power injected into node i, respectively; p (P) DGi 、Q DGi Injecting active power and reactive power of a node i into a distributed power supply; p (P) Li 、Q Li Active power and reactive power of the node i are flown out for the load; v (V) i 、V j Node voltages respectively representing nodes i and j; g ij And B ij The real part and the imaginary part of the node admittance matrix respectively; θ ij The voltage phase difference between the node i and the node j is obtained;
constraint 3): the active and reactive power output constraint of the distributed power supply is as follows:
P DGmin ≤P DGi(t) ≤P DGmax (10)
Q DGmin ≤Q DGi(t) ≤Q DGmax (11)
p in the formula DGi(t) Active power of node i at time t for distributed power supply, P DGmax And P DGmin The upper limit and the lower limit of active power are respectively output by the distributed power supply; q (Q) DGmax 、Q DGmin Upper and lower limits of the active power output for DG respectively；
Constraint 4): node voltage constraint, its formula is:
V imin ≤V i(t) ≤V imax (12)
wherein the node voltage constraint represents all node voltages V i(t) Must be maintained within a specific range, the node voltage amplitude is taken to be [0.90,1.10 ]]Between them;
constraint 5): the radial topological constraint of the power distribution system is as follows:
(Q N ) T Q N ＝(Q L ) T Q L +Q island (13)
in which Q island Representing the island number in a power distribution system, Q N ＝[q n (1),…,q n (n)]、Q L ＝[q l (1),…,q l (n)]Represents an n-dimensional recovery decision vector, q n And q l When 1 is taken, the node is changed and the feeder line is recovered;
constraint 6): the power reserve constraint is as follows:
Figure BDA0004015508240000051
Figure BDA0004015508240000052
in omega island Representing the number of nodes contained in the island;
Figure BDA0004015508240000053
and->
Figure BDA0004015508240000054
Respectively representing the upper limits of active and reactive output of the distributed power supply; c (C) a And C r The standby ratio of active power and reactive power is respectively represented; p (P) D (i) And Q D (i) Representing the load active and reactive power.
Preferably, in step 2.3, the stored energy is storedThe system is in t E [0, T ]]Active force P ge (i, t) and active load P ue (i, t) should satisfy:
0≤P ge (i,t)≤P ge (i) (16)
0≤P ue (i,t)≤P ue (i) (17)
wherein P is ge (i) And P ue (i) The rated power generation and charging power of the energy storage system are shown.
Preferably, in step 2.4, a multi-objective particle swarm algorithm based on an improved population update and fitness strategy is adopted to optimally solve a distributed power supply site selection model; taking a distributed power supply installation node as a position of a particle, randomly generating an initial position and a speed of the particle with the dimension of 90×4 and the value interval of [0, 33] in a constraint condition range, and setting the particle population size pop=90 and the maximum iteration number gen=100; calculating network loss by adopting a forward push back substitution tide calculation method, and calculating a current particle adaptation value;
the iterative formula of the n+1 step of the power distribution network power flow forward push back substitution power flow algorithm is as follows:
Figure BDA0004015508240000061
the forward calculation formula of the node i is as follows:
Figure BDA0004015508240000062
wherein n is the iteration number; r is (r) ki The impedance of branch ki;
Figure BDA0004015508240000063
and->
Figure BDA0004015508240000064
For branch k i Power loss; />
Figure BDA0004015508240000065
And
Figure BDA0004015508240000066
for flowing through branch k i Is set, is provided. P (P) Di And Q Di A load of a node i which is not considered to be a load voltage characteristic;
the calculation formula of the back-push of the voltage of the node i is as follows:
Figure BDA0004015508240000067
Figure BDA0004015508240000068
in the middle of
Figure BDA0004015508240000069
Is the branch ki current; />
Figure BDA00040155082400000610
Is the conjugate of the complex voltage of node k; (r) ki ，x ki ) The impedance of branch ki;
on the basis of node layering, the iterative process of the power distribution network forward push back power flow algorithm is as follows:
1) Initializing: given distribution feeder root node voltage V r And assign V to other node voltages (0) ，n＝0；
2) Forward calculation: calculating voltage drop to a father node according to given voltage and power of a child node from the last layer, and then calculating power distribution of each branch by using formulas (18) and (19);
3) Back generation calculation, namely, starting from a root node, starting from the root node, performing layer-by-layer back pushing calculation to child nodes according to the load power of a father node by using formulas (20) and (21), and solving node voltage distribution V (n+1) ；
Network loss:
S i ＝U i ×I i (22)
in U i And I i Respectively node voltage phasors U i And node injection current phasor I i Is a conjugate of (c).
Preferably, in step 2.5, the iterative optimization step is performed as follows: the calculated pbest is put into a set gpest;
pbest＝N'-C' DG (23)
after each evolution of all individuals, selecting one of the most excellent individuals, namely gbest; in multi-objective, non-dominant individuals, i.e., individuals not being dominant by any other individual, must be the most excellent in the current population, whereas non-dominant individuals are typically more than one; therefore, firstly picking out all non-dominant individuals and putting the non-dominant individuals into a set gbest;
in order to better control the optimizing capability of the algorithm, the patent introduces a dynamic weight factor omega (t), wherein omega (t) describes the influence of the previous generation speed on the current generation speed, and the larger the omega (t) value is, the wider the optimizing range of the algorithm is, the smaller the omega (t) value is, and the stronger the local optimizing capability of the algorithm is; the particle velocity v and the position x are updated according to the improved iteration formula. The improved iteration formula is expressed as:
Figure BDA0004015508240000071
Figure BDA0004015508240000072
/>
Figure BDA0004015508240000073
preferably, in step 2.6, the adaptation value is recalculated, and the inferior solution with small adaptation degree in the new population is deleted, so that the number of individuals of the new population is ensured not to exceed the maximum capacity of the new population; according to the result, using a selection mechanism of the niche, eliminating particles with low individual fitness in different habitats, and ensuring that the current Pareto front solution is optimal; checking whether the maximum iteration times are reached, and if not, returning to the step 2.5 to continue calculation;
the distance between particles can be expressed as:
Figure BDA0004015508240000081
wherein d ij Is the distance between particle i and particle j; x is x i 、x j The ith and jth particles, respectively; n is the total particle number in the niche;
the niche radius can be expressed as:
Figure BDA0004015508240000082
wherein d i The minimum Euclidean distance for particle i; m is the number of particles in the population; c is an initial value constant, when the inter-particle distance is smaller than the niche radius, i.e. d ij ＜r ch In this case, the particle i is stored in the niche group Xp.
Particle current fitness S i Can be expressed as:
Figure BDA0004015508240000083
in step 2.7, the fault duration and the fault severity are considered while the toughness of the power distribution network is evaluated, and the lost load caused by power failure is reflected by the lost area of the fault and the load curve under normal conditions respectively in the typhoon passing process; the percentage of the guaranteed load supply was used as a toughness evaluation index, and the results were as follows:
Figure BDA0004015508240000084
wherein AR represents a toughness evaluation index under typhoon action, T 0 The duration time of the power distribution network affected by typhoons comprises typhoons duration time and power supply recovery time; TL (t) is a desired load curve during normal operation of the power distribution system; l (t) is the actual fault operation of the power distribution system under the action of typhoonsA load curve; RES (representational state) n The area between the desired load curve and the actual load curve, i.e. the actual power loss situation, is indicated.
The following beneficial effects can be achieved in this patent:
aiming at the problem of distributed power supply site selection optimization in power distribution network planning, the invention provides a distributed power supply site selection planning model for maximizing the power supply load and minimizing the installation cost of the distributed power supply by analyzing the influence of the failure rate of system elements on the distributed power supply site selection under typhoon background in the planning stage. Aiming at different typical scenes which possibly occur, the distributed power supply site selection position meeting various constraints and maximizing the elasticity of the power grid is obtained by using the proposed method; in addition, the distributed power supply location and volume planning model is optimized and solved through an improved multi-target particle swarm algorithm. And the verification results: the distributed power supply site selection lifting measure based on the improved multi-target particle swarm algorithm can greatly improve the toughness of the power distribution network,
drawings
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIG. 1 is a schematic diagram of an improved IEEE-33 node power distribution system in accordance with embodiment 1 of the present invention;
FIG. 2 is a Pareto chart of the distributed power model in embodiment 1 of the invention;
FIG. 3 is a non-split set of the distributed power model in embodiment 1 of the present invention;
fig. 4 is a gbest optimal solution set obtained in example 1 of the present invention.
Detailed Description
The preferable scheme is as shown in fig. 1 to fig. 4, and the method for improving the elasticity of the power grid based on the improved particle swarm algorithm comprises the following steps:
step 1: analyzing the influence condition of typhoons on the meteorological load of the line by considering the line fault model under the influence of typhoons, and calculating the line fault probability by combining the load capacity which can be born by the line actually; then, a fault scene is selected by utilizing the system information entropy and is used as a typical scene of a distributed power supply site selection model; the decomposition steps are as follows:
step 1.1: determining the wind speed and the wind direction of each point in the influence range according to the wind field model; the expression is:
Figure BDA0004015508240000091
wherein x and y are actual coordinates of the section of transmission line; mu (mu) x (t) and mu y (t) is the actual coordinates of the typhoon center at time t; a is that 1 And A 2 Respectively two maximum wind speed coefficients, sigma 1 Sum sigma 2 For the corresponding attenuation coefficient, the two parameters satisfy A 1 >A 2 ，σ 1 >σ 2 The method comprises the steps of carrying out a first treatment on the surface of the Beta (t) is the included angle between the power transmission line and the wind direction.
Step 1.2: establishing a relational expression of the outage rate of the power transmission line and the effective wind speed;
the relation between the outage rate of the power transmission line and the effective wind speed is expressed by adopting the following exponential function model:
Figure BDA0004015508240000092
wherein: v (V) d The wind speed is designed for the power transmission line; lambda (lambda) p (t) is the unit length outage rate of the power transmission line, and the unit is 1/(50 km.h); model parameters a and b can be obtained from statistical analysis of historical data.
Step 1.3: segmenting the power transmission line, and establishing an outage rate expression of a certain section of power transmission line with the length of L;
the span of the transmission line in space is large, the wind speeds of all sections are different, the outage rates of unit lengths of different positions are also different, after the transmission line is segmented, the meteorological conditions on each section are assumed to be the same, and the outage rate expression of a section of the transmission line with the length L is as follows:
λ(t)＝λ p (t)L (3)
step 1.4: obtaining a system entropy value under a scene according to the probability of unreliable operation of the line;
Figure BDA0004015508240000101
wherein Ω B Representing a distribution line set; p is p i,t The failure rate of the element i at the time t; z i,t Indicating whether element i fails at time t; omega i Representing element value weights; and selecting a scene with the system entropy value in a proper range as a typical scene of the distributed power supply site selection model to perform optimization solution.
Step 2: establishing and optimally solving a distributed power supply site selection model considering the line fault rate; the decomposition steps are as follows:
step 2.1: establishing a distributed power supply site selection model objective function considering element failure rate; the objective function is expressed as:
Figure BDA0004015508240000102
wherein y is i Represents a 0-1 decision variable, represents whether node i builds a distributed power supply, and if so, y i Taking 1, otherwise taking 0; t is the considered period length; s, N is a scene set and a node set, respectively; omega i The weight coefficient of the load i;
Figure BDA0004015508240000103
active load power to restore power to node i in the presence s;
Figure BDA0004015508240000104
wherein: r is the discount rate; k is the service life of the equipment; c (C) T 、C Y Respectively representing investment cost and operation cost; x is x i Active capacity for accessing distributed power; n (N) b The number of branches in the system; line G b Representing the line b impedance; u (U) i 、U j 、δ ij Representing the actual voltage amplitude and phase angle difference at nodes i, j.
Step 2.2: establishing a constraint condition of a distributed power supply site selection model considering element failure rate;
the constraint conditions include:
constraint 1): a distributed power supply number constraint, the formula of which is:
Figure BDA0004015508240000111
wherein N represents a set of all distributed power supply candidate nodes; p represents the maximum number of distributed power supplies that can be built;
constraint 2): the tidal current constraint comprises the following formula:
Figure BDA0004015508240000112
Figure BDA0004015508240000113
p in the formula i 、Q i Representing the active and reactive power injected into node i, respectively; p (P) DGi 、Q DGi Injecting active power and reactive power of a node i into a distributed power supply; p (P) Li 、Q Li Active power and reactive power of the node i are flown out for the load; v (V) i 、V j Node voltages respectively representing nodes i and j; g ij And B ij The real part and the imaginary part of the node admittance matrix respectively; θ ij The voltage phase difference between the node i and the node j is obtained;
constraint 3): the active and reactive power output constraint of the distributed power supply is as follows:
P DGmin ≤P DGi(t) ≤P DGmax (10)
Q DGmin ≤Q DGi(t) ≤Q DGmax (11)
p in the formula DGi(t) Active power of node i at time t for distributed power supply, P DGmax And P DGmin Respectively distributed power supplyUpper and lower limits of active power are set; q (Q) DGmax 、Q DGmin The upper limit and the lower limit of active power are respectively output for DG;
constraint 4): node voltage constraint, its formula is:
V imin ≤V i(t) ≤V imax (12)
wherein the node voltage constraint represents all node voltages V i(t) Must be maintained within a specific range, the node voltage amplitude is taken to be [0.90,1.10 ]]Between them;
constraint 5): the radial topological constraint of the power distribution system is as follows:
(Q N ) T Q N ＝(Q L ) T Q L +Q island (13)
in which Q island Representing the island number in a power distribution system, Q N ＝[q n (1),…,q n (n)]、Q L ＝[q l (1),…,q l (n)]Represents an n-dimensional recovery decision vector, q n And q l When 1 is taken, the node is changed and the feeder line is recovered;
constraint 6): the power reserve constraint is as follows:
Figure BDA0004015508240000121
Figure BDA0004015508240000122
in omega island Representing the number of nodes contained in the island;
Figure BDA0004015508240000123
and->
Figure BDA0004015508240000124
Respectively representing the upper limits of active and reactive output of the distributed power supply; c (C) a And C r The standby ratio of active power and reactive power is respectively represented; p (P) D (i) And Q D (i) Watch (watch)Showing the load active and reactive power.
Step 2.3: considering the situation that wind and photoelectricity cannot be used as a standby power supply to be added into a power grid under typhoon disaster conditions, taking an energy storage system as a power generation source to provide electric energy for reconstruction of a post-disaster power distribution network;
under typhoon disaster conditions, wind and photoelectricity cannot be used as a standby power supply to be added into a power grid, and an energy storage system is used as a power generation source to provide electric energy for reconstruction of a post-disaster power distribution network. The energy storage system is in t epsilon [0, T ]]Active force P ge (i, t) and active load P ue (i, t) should satisfy:
0≤P ge (i,t)≤P ge (i) (16)
0≤P ue (i,t)≤P ue (i) (17)
wherein P is ge (i) And P ue (i) The rated power generation and charging power of the energy storage system are shown.
Step 2.4: optimizing and solving a distributed power supply site selection model by adopting a multi-target particle swarm algorithm based on an improved population updating and fitness strategy;
optimizing and solving a distributed power supply site selection model by adopting a multi-target particle swarm algorithm based on an improved population updating and fitness strategy; taking a distributed power supply installation node as a position of a particle, randomly generating an initial position and a speed of the particle with the dimension of 90×4 and the value interval of [0, 33] in a constraint condition range, and setting the particle population size pop=90 and the maximum iteration number gen=100; calculating network loss by adopting a forward push back substitution tide calculation method, and calculating a current particle adaptation value;
the iterative formula of the n+1 step of the power distribution network power flow forward push back substitution power flow algorithm is as follows:
Figure BDA0004015508240000131
the forward calculation formula of the node i is as follows:
Figure BDA0004015508240000132
wherein n is the iteration number; r is (r) ki The impedance of branch ki;
Figure BDA0004015508240000133
and->
Figure BDA0004015508240000134
For branch k i Power loss; />
Figure BDA0004015508240000135
And
Figure BDA0004015508240000136
for flowing through branch k i Is set, is provided. P (P) Di And Q Di A load of a node i which is not considered to be a load voltage characteristic;
the calculation formula of the back-push of the voltage of the node i is as follows:
Figure BDA0004015508240000137
Figure BDA0004015508240000138
in the middle of
Figure BDA0004015508240000139
Is the branch ki current; />
Figure BDA00040155082400001310
Is the conjugate of the complex voltage of node k; (r) ki ，x ki ) The impedance of branch ki;
on the basis of node layering, the iterative process of the power distribution network forward push back power flow algorithm is as follows:
1) Initializing: given distribution feeder root node voltage V r And assign V to other node voltages (0) ，n＝0；
2) Forward calculation: calculating voltage drop to a father node according to given voltage and power of a child node from the last layer, and then calculating power distribution of each branch by using formulas (18) and (19);
3) Back generation calculation, namely, starting from a root node, starting from the root node, performing layer-by-layer back pushing calculation to child nodes according to the load power of a father node by using formulas (20) and (21), and solving node voltage distribution V (n+1) ；
Network loss:
S i ＝U i ×I i (22)
in U i And I i Respectively node voltage phasors U i And node injection current phasor I i Is a conjugate of (c).
Step 2.5: iterative optimization is carried out:
the calculated pbest is put into a set gpest;
pbest＝N'-C' DG (23)
after each evolution of all individuals, selecting one of the most excellent individuals, namely gbest; in multi-objective, non-dominant individuals, i.e., individuals not being dominant by any other individual, must be the most excellent in the current population, whereas non-dominant individuals are typically more than one; therefore, firstly picking out all non-dominant individuals and putting the non-dominant individuals into a set gbest;
in order to better control the optimizing capability of the algorithm, the patent introduces a dynamic weight factor omega (t), wherein omega (t) describes the influence of the previous generation speed on the current generation speed, and the larger the omega (t) value is, the wider the optimizing range of the algorithm is, the smaller the omega (t) value is, and the stronger the local optimizing capability of the algorithm is; the particle velocity v and the position x are updated according to the improved iteration formula. The improved iteration formula is expressed as:
Figure BDA0004015508240000141
Figure BDA0004015508240000142
/>
Figure BDA0004015508240000143
step 2.6: recalculating the adaptation value, deleting the inferior solution with small adaptation degree in the new population, and ensuring that the number of individuals of the new population does not exceed the maximum capacity of the new population;
in the step 2.6, the adaptation value is recalculated, and the inferior solution with small adaptation degree in the new population is deleted, so that the number of individuals of the new population is ensured not to exceed the maximum capacity of the new population; according to the result, using a selection mechanism of the niche, eliminating particles with low individual fitness in different habitats, and ensuring that the current Pareto front solution is optimal; checking whether the maximum iteration times are reached, and if not, returning to the step 2.5 to continue calculation;
the niche technology is derived from the concept of a niche in nature, and means that in a certain specific region, a group of identical or similar species exist, communication and competition relationship exists among the species, and species with weak adaptability are eliminated through a survival mechanism of 'superior and inferior elimination', and species with strong survivability are reserved, so that the species are evolved.
The distance between particles can be expressed as:
Figure BDA0004015508240000151
wherein d ij Is the distance between particle i and particle j; x is x i 、x j The ith and jth particles, respectively; n is the total particle number in the niche;
the niche radius can be expressed as:
Figure BDA0004015508240000152
wherein d i The minimum Euclidean distance for particle i; m is the number of particles in the population; c is an initial value constant, when the inter-particle distance is smaller than the niche radius, i.e. d ij ＜r ch In this case, particle i is stored in niche group Xp。
Particle current fitness S i Can be expressed as:
Figure BDA0004015508240000153
step 2.7: and establishing a functional expression between a toughness evaluation index under the action of typhoons, duration time of the power distribution network influenced by typhoons, an expected load curve of the power distribution system during normal operation, an actual load curve of the power distribution system during fault operation under the action of typhoons and an actual power failure condition.
The method is characterized in that the fault duration and the fault severity are considered while the toughness of the power distribution network is evaluated, and the lost load caused by power failure is reflected by the lost area of a load curve under the fault and normal condition respectively in the typhoon passing process; the percentage of the guaranteed load supply was used as a toughness evaluation index, and the results were as follows:
Figure BDA0004015508240000154
/>
wherein AR represents a toughness evaluation index under typhoon action, T 0 The duration time of the power distribution network affected by typhoons comprises typhoons duration time and power supply recovery time; TL (t) is a desired load curve during normal operation of the power distribution system; l (t) is an actual load curve of power distribution system fault operation under the action of typhoons; RES (representational state) n The area between the desired load curve and the actual load curve, i.e. the actual power loss situation, is indicated.
Example 1:
1. the present invention employs an example of an improved IEEE-33 node system, as shown in fig. 1, where the geographical orientation of each feeder line is consistent with what is shown en route. Wherein the feeder and load parameters of the node system are as follows.
Table 1 improved IEEE-33 node test System load parameters
Figure BDA0004015508240000161
2. The starting time is typhoon login time. It is seen from fig. 2 that the number of failure weights of the system is in the interval [3,6], and therefore, the selection of the typical failure scenario will also be set in the interval.
3. Taking the selected scene as a basic example, modeling and solving the example by applying the distributed power supply locating and sizing model provided herein to obtain a Pareto solution set diagram of the distributed power supply locating and sizing model, as shown in fig. 3. The distributed power parameter is set to c r ＝20％；c a =10%; the diesel generator rated capacity is 1000kVA.
4. After the optimal solution set is obtained, in order to select a group of compromise solutions which can simultaneously consider 2 objective functions, the invention adopts fuzzy membership to represent objective satisfaction corresponding to Pareto solutions, and determines a final compromise solution according to the value of the satisfaction. The fuzzy membership function is expressed as follows:
Figure BDA0004015508240000171
wherein: mu (mu) i Representing the fuzzy membership degree corresponding to the ith objective function; f (f) imin And f imax Representing the lower and upper limits of the ith objective function, respectively.
5. Describing fault recovery process comparison in each scene:
scene 1: the fault recovery process of the distributed power distribution network is not included, and the recovery process of the fault element is selected according to the minimized load loss, namely, the fault line is repaired according to the sequence of the line 9, the line 19, the line 30, the line 14 and the line 16.
Scene 2: and (3) considering the recovery process of the distribution network with the distributed power supply under the line fault rate, wherein the access nodes of the distributed power supply are 6, 13, 18, 19 and 33, so that the power supply of the load is ensured.
Scene 3: and based on the recovery process of the distributed power distribution network of the improved multi-target particle swarm algorithm, the access nodes of the distributed power supply are 2, 6, 15, 22 and 30, and the power supply of the load is ensured.
Results
Table 2 describes statistics of recovery schemes in each scenario:
table 2 recovery scheme statistics
Figure BDA0004015508240000172
As can be seen from table 2, in these 3 scenarios, scenario 2 and 3 recover more power consumption load than scenario 1, after the power distribution network suffers from disaster, the downstream power grid and the upstream power grid lose connection, most of the power consumption load loses power supply, therefore, the distributed power supply can supply power to the power loss load, and the power grid elasticity is effectively improved. Compared with the scene 2, the scene 3 has the advantages that the difference between the total power consumption recovery and the power generation of the distributed power supply is not large, the calculation speed of the algorithm is improved, the algorithm is prevented from entering local optimum, and the convergence speed of the improved particle swarm algorithm is improved as shown in fig. 4.
Table 3 evaluation results of toughness of distribution network
Figure BDA0004015508240000181
As can be seen from the data in table 3, for the original distribution network, the load supply during extreme weather effects was only 57.2% of the normal level. The traditional toughness improvement mode, the distributed power source site selection mode of the line fault rate and the distributed power source site selection improvement measure based on the improved multi-target particle swarm algorithm can effectively improve the toughness of the power distribution network, the AR value of load supply is 58.9%, 62.1% and 77.5% of the original power grid respectively, and the toughness improvement effect of the added distributed power source is best.
The above embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and the scope of the present invention should be defined by the claims, including the equivalents of the technical features in the claims. I.e., equivalent replacement modifications within the scope of this invention are also within the scope of the invention.

Claims (10)

1. The power grid elasticity improving method based on the improved particle swarm algorithm is characterized by comprising the following steps of:
step 1: analyzing the influence condition of typhoons on the meteorological load of the line by considering the line fault model under the influence of typhoons, and calculating the line fault probability by combining the load capacity which can be born by the line actually; then, a fault scene is selected by utilizing the system information entropy and is used as a typical scene of a distributed power supply site selection model; the decomposition steps are as follows:
step 1.1: determining the wind speed and the wind direction of each point in the influence range according to the wind field model;
step 1.2: establishing a relational expression of the outage rate of the power transmission line and the effective wind speed;
step 1.3: segmenting the power transmission line, and establishing an outage rate expression of a certain section of power transmission line with the length of L;
step 1.4: obtaining a system entropy value under a scene according to the probability of unreliable operation of the line;
step 2: establishing and optimally solving a distributed power supply site selection model considering the line fault rate; the decomposition steps are as follows:
step 2.1: establishing a distributed power supply site selection model objective function considering element failure rate;
step 2.2: establishing a constraint condition of a distributed power supply site selection model considering element failure rate;
step 2.3: considering the situation that wind and photoelectricity cannot be used as a standby power supply to be added into a power grid under typhoon disaster conditions, taking an energy storage system as a power generation source to provide electric energy for reconstruction of a post-disaster power distribution network;
step 2.4: optimizing and solving a distributed power supply site selection model by adopting a multi-target particle swarm algorithm based on an improved population updating and fitness strategy;
step 2.5: performing iterative optimization;
step 2.6: recalculating the adaptation value, deleting the inferior solution with small adaptation degree in the new population, and ensuring that the number of individuals of the new population does not exceed the maximum capacity of the new population;
step 2.7: and establishing a functional expression between a toughness evaluation index under the action of typhoons, duration time of the power distribution network influenced by typhoons, an expected load curve of the power distribution system during normal operation, an actual load curve of the power distribution system during fault operation under the action of typhoons and an actual power failure condition.
2. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 1, wherein the method comprises the following steps: in step 1.1, determining the wind speed and the wind direction of each point in the influence range according to a wind field model, wherein the expression is as follows:
Figure FDA0004015508230000021
wherein x and y are actual coordinates of the section of transmission line; mu (mu) x (t) and mu y (t) is the actual coordinates of the typhoon center at time t; a is that 1 And A 2 Respectively two maximum wind speed coefficients, sigma 1 Sum sigma 2 For the corresponding attenuation coefficient, the two parameters satisfy A 1 >A 2 ，σ 1 >σ 2 The method comprises the steps of carrying out a first treatment on the surface of the Beta (t) is the included angle between the power transmission line and the wind direction.
3. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 2, wherein the method comprises the following steps: in step 1.2, the relationship between the outage rate of the transmission line and the effective wind speed is represented by the following exponential function model:
Figure FDA0004015508230000022
wherein: v (V) d The wind speed is designed for the power transmission line; lambda (lambda) p (t) is the unit length outage rate of the power transmission line, and the unit is 1/(50 km.h); model parameters a and b can be obtained from statistical analysis of historical data.
4. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 3, wherein the method comprises the following steps: in step 1.3, the outage rate expression of a section of power transmission line with a length of L is:
λ(t)＝λ p (t)L (3)
in step 1.4: obtaining a system entropy value under a scene according to the probability of unreliable operation of the line:
Figure FDA0004015508230000023
wherein Ω B Representing a distribution line set; p is p i,t The failure rate of the element i at the time t; z i,t Indicating whether element i fails at time t; omega i Representing element value weights; and selecting a scene with the system entropy value in a proper range as a typical scene of the distributed power supply site selection model to perform optimization solution.
5. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 4, wherein the method comprises the following steps: in step 2.1, the distributed power source site selection model objective function considering the component failure rate is expressed as:
Figure FDA0004015508230000024
wherein y is i Represents a 0-1 decision variable, represents whether node i builds a distributed power supply, and if so, y i Taking 1, otherwise taking 0; t is the considered period length; s, N is a scene set and a node set, respectively; omega i The weight coefficient of the load i;
Figure FDA0004015508230000025
active load power to restore power to node i in the presence s;
Figure FDA0004015508230000031
wherein: r is the discount rate; k is the service life of the equipment; c (C) T 、C Y Respectively representing investment cost and operation cost; x is x i Active capacity for accessing distributed power; n (N) b The number of branches in the system; line G b Representing the line b impedance; u (U) i 、U j 、δ ij Representing the actual voltage amplitude and phase angle difference at nodes i, j.
6. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 5, wherein the method comprises the following steps: in step 2.2, the constraints include:
constraint 1): a distributed power supply number constraint, the formula of which is:
Figure FDA0004015508230000032
wherein N represents a set of all distributed power supply candidate nodes; p represents the maximum number of distributed power supplies that can be built;
constraint 2): the tidal current constraint comprises the following formula:
Figure FDA0004015508230000033
Figure FDA0004015508230000034
p in the formula i 、Q i Representing the active and reactive power injected into node i, respectively; p (P) DGi 、Q DGi Injecting active power and reactive power of a node i into a distributed power supply; p (P) Li 、Q Li Active power and reactive power of the node i are flown out for the load; v (V) i 、V j Node voltages respectively representing nodes i and j; g ij And B ij The real part and the imaginary part of the node admittance matrix respectively; θ ij For node i and nodej voltage phase difference;
constraint 3): the active and reactive power output constraint of the distributed power supply is as follows:
P DGmin ≤P DGi(t) ≤P DGmax (10)
Q DGmin ≤Q DGi(t) ≤Q DGmax (11)
p in the formula DGi(t) Active power of node i at time t for distributed power supply, P DGmax And P DGmin The upper limit and the lower limit of active power are respectively output by the distributed power supply; q (Q) DGmax 、Q DGmin The upper limit and the lower limit of active power are respectively output for DG;
constraint 4): node voltage constraint, its formula is:
V imin ≤V i(t) ≤V imax (12)
wherein the node voltage constraint represents all node voltages V i(t) Must be maintained within a specific range, the node voltage amplitude is taken to be [0.90,1.10 ]]Between them;
constraint 5): the radial topological constraint of the power distribution system is as follows:
(Q N ) T Q N ＝(Q L ) T Q L +Q island (13)
in which Q island Representing the island number in a power distribution system, Q N ＝[q n (1),…,q n (n)]、Q L ＝[q l (1),…,q l (n)]Represents an n-dimensional recovery decision vector, q n And q l When 1 is taken, the node is changed and the feeder line is recovered;
constraint 6): the power reserve constraint is as follows:
Figure FDA0004015508230000041
Figure FDA0004015508230000042
in omega island Representing the number of nodes contained in the island;
Figure FDA0004015508230000043
and->
Figure FDA0004015508230000044
Respectively representing the upper limits of active and reactive output of the distributed power supply; c (C) a And C r The standby ratio of active power and reactive power is respectively represented; p (P) D (i) And Q D (i) Representing the load active and reactive power.
7. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 6, wherein the method comprises the following steps: in step 2.3, the energy storage system is operated at t.epsilon.0, T]Active force P ge (i, t) and active load P ue (i, t) should satisfy:
0≤P ge (i,t)≤P ge (i) (16)
0≤P ue (i,t)≤P ue (i) (17)
wherein P is ge (i) And P ue (i) The rated power generation and charging power of the energy storage system are shown.
8. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 7, wherein the method comprises the steps of: in step 2.4, optimizing and solving a distributed power supply site selection model by adopting a multi-target particle swarm algorithm based on an improved population updating and fitness strategy; taking a distributed power supply installation node as a position of a particle, randomly generating an initial position and a speed of the particle with the dimension of 90×4 and the value interval of [0, 33] in a constraint condition range, and setting the particle population size pop=90 and the maximum iteration number gen=100; calculating network loss by adopting a forward push back substitution tide calculation method, and calculating a current particle adaptation value;
the iterative formula of the n+1 step of the power distribution network power flow forward push back substitution power flow algorithm is as follows:
Figure FDA0004015508230000051
the forward calculation formula of the node i is as follows:
Figure FDA0004015508230000052
/>
wherein n is the iteration number; r is (r) ki The impedance of branch ki;
Figure FDA0004015508230000053
and->
Figure FDA0004015508230000054
For branch k i Power loss; />
Figure FDA0004015508230000055
And->
Figure FDA0004015508230000056
For flowing through branch k i Is set, is provided. P (P) Di And Q Di A load of a node i which is not considered to be a load voltage characteristic;
the calculation formula of the back-push of the voltage of the node i is as follows:
Figure FDA0004015508230000057
Figure FDA0004015508230000058
in the middle of
Figure FDA0004015508230000059
Is the branch ki current; />
Figure FDA00040155082300000510
Is the conjugate of the complex voltage of node k; (r) ki ，x ki ) The impedance of branch ki;
on the basis of node layering, the iterative process of the power distribution network forward push back power flow algorithm is as follows:
1) Initializing: given distribution feeder root node voltage V r And assign V to other node voltages (0) ，n＝0；
2) Forward calculation: calculating voltage drop to a father node according to given voltage and power of a child node from the last layer, and then calculating power distribution of each branch by using formulas (18) and (19);
3) Back generation calculation, namely, starting from a root node, starting from the root node, performing layer-by-layer back pushing calculation to child nodes according to the load power of a father node by using formulas (20) and (21), and solving node voltage distribution V (n+1) ；
Network loss:
S i ＝U i ×I i (22)
in U i And I i Respectively node voltage phasors U i And node injection current phasor I i Is a conjugate of (c).
9. The improved particle swarm algorithm-based power grid elasticity improvement method according to claim 8, wherein the method comprises the steps of: in step 2.5, the iterative optimization is performed as follows: the calculated pbest is put into a set gpest;
pbest＝N'-C' DG (23)
after each evolution of all individuals, selecting one of the most excellent individuals, namely gbest; in multi-objective, non-dominant individuals, i.e., individuals not being dominant by any other individual, must be the most excellent in the current population, whereas non-dominant individuals are typically more than one; therefore, firstly picking out all non-dominant individuals and putting the non-dominant individuals into a set gbest;
in order to better control the optimizing capability of the algorithm, the patent introduces a dynamic weight factor omega (t), wherein omega (t) describes the influence of the previous generation speed on the current generation speed, and the larger the omega (t) value is, the wider the optimizing range of the algorithm is, the smaller the omega (t) value is, and the stronger the local optimizing capability of the algorithm is; the particle velocity v and the position x are updated according to the improved iteration formula. The improved iteration formula is expressed as:
Figure FDA0004015508230000061
Figure FDA0004015508230000062
Figure FDA0004015508230000063
10. the improved particle swarm algorithm-based power grid elasticity improvement method according to claim 9, wherein the method comprises the steps of: in the step 2.6, the adaptation value is recalculated, and the inferior solution with small adaptation degree in the new population is deleted, so that the number of individuals of the new population is ensured not to exceed the maximum capacity of the new population; according to the result, using a selection mechanism of the niche, eliminating particles with low individual fitness in different habitats, and ensuring that the current Pareto front solution is optimal; checking whether the maximum iteration times are reached, and if not, returning to the step 2.5 to continue calculation;
the distance between particles can be expressed as:
Figure FDA0004015508230000064
wherein d ij Is the distance between particle i and particle j; x is x i 、x j The ith and jth particles, respectively; n is the total particle number in the niche;
the niche radius can be expressed as:
Figure FDA0004015508230000071
wherein d i The minimum Euclidean distance for particle i; m is the number of particles in the population; c is an initial value constant, when the inter-particle distance is smaller than the niche radius, i.e. d ij ＜r ch In this case, the particle i is stored in the niche group Xp.
Particle current fitness S i Can be expressed as:
Figure FDA0004015508230000072
in step 2.7, the fault duration and the fault severity are considered while the toughness of the power distribution network is evaluated, and the lost load caused by power failure is reflected by the lost area of the fault and the load curve under normal conditions respectively in the typhoon passing process; the percentage of the guaranteed load supply was used as a toughness evaluation index, and the results were as follows:
Figure FDA0004015508230000073
wherein AR represents a toughness evaluation index under typhoon action, T 0 The duration time of the power distribution network affected by typhoons comprises typhoons duration time and power supply recovery time; TL (t) is a desired load curve during normal operation of the power distribution system; l (t) is an actual load curve of power distribution system fault operation under the action of typhoons; RES (representational state) n The area between the desired load curve and the actual load curve, i.e. the actual power loss situation, is indicated.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117154727A (en) * 2023-11-01 2023-12-01 浙江优能电力设计有限公司 Reliability control method and system for electric power system
CN117526387A (en) * 2023-12-29 2024-02-06 太原理工大学 Optimal power distribution network energy storage locating and sizing method considering energy storage capacity attenuation

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117154727A (en) * 2023-11-01 2023-12-01 浙江优能电力设计有限公司 Reliability control method and system for electric power system
CN117154727B (en) * 2023-11-01 2024-01-16 浙江优能电力设计有限公司 Reliability control method and system for electric power system
CN117526387A (en) * 2023-12-29 2024-02-06 太原理工大学 Optimal power distribution network energy storage locating and sizing method considering energy storage capacity attenuation
CN117526387B (en) * 2023-12-29 2024-03-22 太原理工大学 Optimal power distribution network energy storage locating and sizing method considering energy storage capacity attenuation

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