CN111641205A - Active power distribution network fault management method based on random optimization - Google Patents

Active power distribution network fault management method based on random optimization Download PDF

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CN111641205A
CN111641205A CN202010390846.6A CN202010390846A CN111641205A CN 111641205 A CN111641205 A CN 111641205A CN 202010390846 A CN202010390846 A CN 202010390846A CN 111641205 A CN111641205 A CN 111641205A
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fault
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CN111641205B (en
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张有兵
胡成鹏
王国烽
徐崇博
杨宇
徐登辉
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Zhejiang University of Technology ZJUT
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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
    • 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
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • 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
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • 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
    • H02J3/004—Generation forecast, e.g. methods or systems for forecasting future energy generation
    • 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
    • H02J3/007—Arrangements for selectively connecting the load or loads to one or several among a plurality of power lines or power sources
    • H02J3/0075—Arrangements for selectively connecting the load or loads to one or several among a plurality of power lines or power sources for providing alternative feeding paths between load and source according to economic or energy efficiency considerations, e.g. economic dispatch
    • 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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • 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
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously

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Abstract

An active power distribution network fault management method based on random optimization comprises the steps of firstly, constructing an uncertainty model, initializing a system and obtaining initial data, and further simulating scene data including load requirements, renewable energy output and fault duration through a Monte Carlo method; and then establishing a power optimization and power flow optimization two-stage model, and simultaneously allocating a risk management scheme to ensure that the obtained scheduling strategy can keep good applicability when facing extreme scenes. In the solving process, decoupling calculation of power optimization and power flow optimization is carried out, iteration is carried out alternately, and the difference value of the network loss values calculated twice is used as a convergence criterion; and finally, taking the calculation result in the final convergence as a day-ahead optimization scheduling strategy. The method can effectively improve the economic benefit of the active power distribution network during normal operation and obviously reduce the load reduction cost under the fault condition.

Description

Active power distribution network fault management method based on random optimization
Technical Field
The invention relates to a fault management method for an active power distribution network based on random optimization.
Background
With the large-scale use of fossil fuels, global climate is warmed, the probability of occurrence of extreme natural disasters such as tsunami and earthquake is remarkably improved, and the large-scale power failure accident caused by the extreme natural disasters causes great economic loss to a power grid. The solution of the problems of environmental pollution, resource shortage and the like becomes reluctant, and Renewable Energy (RES) mainly including Wind Turbine WT and Photovoltaic array PV, which are clean energy, gradually becomes a research hotspot and the permeability of the Renewable energy in the power distribution network is continuously improved. However, the output of the fan at night is often more than that of the fan at daytime, the variation trend is opposite to the load demand, and the fan has the characteristic of peak inversion, while the output of the photovoltaic power generation is mainly concentrated in the daytime, and the output at night can be generally ignored. Due to the randomness and intermittency, the wind turbine and the photovoltaic are connected to the power system to have influence on the power system. The key point of the problem is to find a solution, so that the traditional power distribution network can fully utilize the RES on the basis of improving the safety.
Compared with the traditional power distribution network, the active power distribution network is taken as an advanced expression form of the smart power grid, and the specific advantages of the active power distribution network are embodied in all aspects, particularly in multi-source system coordination scheduling. The active power distribution network simultaneously focuses on autonomous control and global optimal scheduling of local areas, and is an open system compatible with multi-energy integration technology. An active power distribution network includes Distributed Generators (DG), RES and Energy Storage Systems (ESS), and when the RES output exceeds the load demand, excess power can be stored in the ESS or sold to a large power grid through a public connection point. This mode of operation both effectively consumes RES and can take advantage of the islanding characteristics after the introduction of DG to cope with unknown fault events.
The transition of the active distribution grid to the islanding mode may be initiated by a planned or unplanned event. The present invention focuses on unplanned islanding events. The unplanned island is mainly characterized in that when an unknown fault is encountered, particularly an extreme natural disaster occurs, at the moment, the large power grid cannot continue to supply power to the load in the power distribution network, and the part losing the support of the large power grid can avoid important load outage by scheduling local resources. In practice, the unplanned islanding time, i.e., the fault duration, is uncertain and cannot be accurately predicted. This poses a serious challenge to the scheduling strategy of the distribution network for fault situations, which becomes more complex when considering the intermittency and volatility of renewable energy sources and the uncertainty of load demand, and which must be solved by a suitable stochastic approach.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a two-stage random optimization method for solving the problem of optimal resource scheduling of an active power distribution network considering the fault condition. The method simultaneously considers the uncertainty problems of fault duration, load demand and RES output. In order to make the obtained scheduling strategy have good applicability in all scenes and make the power distribution network operator obtain effective balance between expected operation cost and risk measurement. A risk management scheme is provided in the proposed framework. And in the upper layer stage, the lowest expected operation cost of the active power distribution network is taken as an objective function without considering the network loss. And in the lower-layer stage, optimal power flow calculation is performed, the network loss value is fed back to the power balance constraint condition in the upper-layer model, and finally a scheduling scheme is obtained through alternate iteration, so that the calculation difficulty is reduced, and the calculation efficiency is improved.
In order to achieve the purpose, the technical scheme of the invention is as follows:
an active power distribution network fault management method based on random optimization comprises the following steps:
s1: establishing an uncertainty model, initializing the system and acquiring initial values required by optimization, including initial data of fan, photovoltaic and load requirements;
s2: establishing a scene probability model and simultaneously allocating a risk management scheme to a random optimization method;
s3: establishing an upper-layer active power distribution network power optimization model, solving an optimal power scheduling strategy by taking the lowest operation cost in each scene as a target, and reserving and substituting the strategy into a lower-layer optimization model;
s4: establishing a lower active power distribution network power flow optimization model, solving an optimal power flow scheduling strategy by taking a power scheduling strategy in an upper power optimization model as a known condition and taking the lowest network loss value in each scene as a target, and reserving and substituting the network loss value into the next iterative computation;
s5: when the variation of the network loss values of the two optimization results reaches a convergence condition and the internal scheduling strategy is not updated any more, outputting the scheduling strategy at the moment as the day-ahead optimization result of the active power distribution network;
s6: if the variation of the network loss value in the two times cannot reach the convergence condition, the procedure returns to step S2 to perform the optimization again according to the updated status information.
In the invention, the two-stage optimization of the active power distribution network is shown as follows: in the upper layer power optimization stage, when the iteration is performed for the first time, the grid loss value on the right side of the power balance equation is set to be 0, and on the basis, the output power of the DG in each time period, the charge and discharge power of the ESS in each time period and the interactive power between the ESS and the large power grid are determined. And in the lower-layer power flow optimization stage, substituting the power value calculated in the power optimization stage as a fixed value to perform optimal power flow calculation, substituting the calculated network loss value into the power optimization stage, alternately iterating until the variation of the two network loss values meets the convergence condition, and judging that iteration is finished.
Further, in step S1, the uncertainty modeling includes the following processes:
s1-1, scene generation: a series of scenes are generated by adopting a Monte Carlo method to simulate the uncertainty of the load demand and the RES output. In order to generate a relevant scene, initial values of load demand and RES output are firstly acquired, the initial values are used as mean values of Gaussian distribution, variance is added, a large number of scenes are generated, and on the basis that the sum of the probabilities of all the scenes is 1, the same probability is given to all the initial scenes;
s1-2, because a large number of scenes are difficult to solve in the proposed random optimization method, the scenes are reduced to a proper number by using a backward reduction method, in each iteration of the algorithm, the Euclidean distance between every two scenes is calculated, the scene with lower probability in the two scenes with the lowest distance is removed, and the probability of the scene is transferred to the other scene;
s1-3, power system research shows that the fault duration cannot be accurately predicted through a mathematical formula, the only solution is to perform Monte Carlo simulation, simulation analysis shows that the fault duration of an actual power system has a bell-shaped distribution, and the shape of a probability distribution depends on the standard deviation of the relevant recovery time to a large extent, so the invention adopts a normal distribution to express the uncertainty of the fault duration, wherein the average value is 5 hours, and the standard deviation is 1 hour.
Still further, in step S2, the scene probability model is established as follows:
s2-1, two uncertainty problems are considered in the stochastic optimization problem, in the solving process, probability models of the two uncertainty problems are integrated, and if the total number of the RES force-related scenes is S and the probability of the fault duration is psi about the load demand, the probability of the S × psi is considered in the proposed stochastic optimization framework, wherein P issRepresenting the probability of occurrence of the scene S, DψIndicating the probability that the fault lasts for a time ψ, then scene S ψ means when the S-th scene experiences DψHas a probability of PS×Dψ；
S2-2, in the stochastic optimization process, the resulting optimization is expected to produce the lowest expected value of running cost in all scenarios, however, due to the large difference between the scenes, the scheduling scheme generates very high cost in some scenes with low probability, to control the risk of such adverse consequences, the stochastic optimization problem is equipped with a risk management scheme, using a risk value (VaR) and a conditional risk value (CVaR) as measures of risk level, where VaR represents the maximum loss value at a given confidence, η, however, VaR represents the value of only one probability point, the loss situation corresponding to the scene after the probability point is not reflected, while the CVaR represents the expectation of the running cost under all scenes exceeding the VaR, the tail risk is well avoided, the CVaR is used for measuring the risk level,
Figure BDA0002485698360000041
Figure BDA0002485698360000042
Figure BDA0002485698360000043
in the formula: fCVaRRepresenting risk index, η representing confidence, S, S, PSRespectively representing the total number of scenes, the current optimized scene and the probability corresponding to the scene; TD, psi, DψRespectively representing the number of types of fault duration, the currently optimized fault duration and the probability corresponding to the fault duration; thetas,τλ is an auxiliary variable introduced to calculate CVaR, and its value is determined by equations (2) (3);
Figure BDA0002485698360000044
representing the power cost of the S-th scenario.
Still further, in step S3, the active distribution network power optimization model establishing process is as follows:
s3-1. Power optimization profit model
In the power optimization stage, the risk management is simultaneously equipped by taking the lowest operation cost as an objective function:
min(1-α)Fpower+αFCVaR(4)
Fpower＝(1-β)(FDG+FRES+FPU+FESS)+βFLOAD(5)
in the formula: fpower、FCVaRα respectively represent power running cost and risk indexAnd a weight value for risk management; fDG、FRES、FPU、FESS、FLOADβ respectively representing DG cost, RES cost, interaction power cost of the system and a large power grid, ESS cost, load reduction cost and weight values of economic indexes and fault indexes;
s3-2 distributed generator model
The DG cost is composed of the DG start-stop switch cost and the operation cost;
Figure BDA0002485698360000045
Figure BDA0002485698360000046
Figure BDA0002485698360000051
Figure BDA0002485698360000052
Figure BDA0002485698360000053
Figure BDA0002485698360000054
in the formula: t, t denotes the total optimization duration and the current optimization period, respectively; ND represents the total number of DG; SU, SD represent start and stop costs, respectively; a isd、bdA cost coefficient representing the d-th DG; j. the design is a squared,tRepresents the switching state quantity of the d-th DG at the time t; Δ t represents the optimization interval;
Figure BDA0002485698360000055
representing the output power of the d-th DG at time t in the S-scenario psi fault duration, the switching state quantity of the DG should be the same in all scenarios, except in the corresponding fieldThe output power of the scene is determined,
Figure BDA0002485698360000056
respectively representing the minimum and maximum output power of the d-th DG; URd、DRdRespectively representing the climbing efficiency of the d-th DG; CUd,t、CDd,tRespectively representing the starting cost coefficient and the stopping cost coefficient of the d-th DG;
s3-3 energy storage system model
Figure BDA0002485698360000057
Figure BDA0002485698360000058
Figure BDA0002485698360000059
Figure BDA00024856983600000510
Figure BDA00024856983600000511
Figure BDA00024856983600000512
Ee,0＝Ee,T(18)
In the formula: NE represents the total number of ESS;
Figure BDA00024856983600000513
respectively representing the charging power and the discharging power of the e-th ESS at the time t in the S scene psi fault duration;
Figure BDA00024856983600000514
respectively representing the charging efficiency and the discharging efficiency of the ESS; ceRepresents a charge-discharge cost coefficient;
Figure BDA00024856983600000515
represents the SOC of the ESS after the fault is over; veRepresenting the corresponding cost factor;
Figure BDA0002485698360000061
respectively represent the maximum power of charging and discharging of the e-th ESS at the moment t in the S scene psi fault duration.
Figure BDA0002485698360000062
Respectively representing charge and discharge indication amounts of the e-th ESS,
Figure BDA0002485698360000063
respectively representing the minimum capacity and the maximum capacity of the e-th ESS, wherein the constraint (16) represents that the ESS can not be charged and discharged simultaneously, and the constraint (17) represents that the initial capacity and the capacity at the end of the optimization period of the e-th ESS are the same;
s3-4 distributed energy model
Figure BDA0002485698360000064
Figure BDA0002485698360000065
In the formula: NW and NP respectively represent the number of the fan and the photovoltaic;
Figure BDA0002485698360000066
respectively representing the output power of the w-th fan and the p-th photovoltaic at the t moment in the S scene; crA cost coefficient representing RES;
Figure BDA0002485698360000067
Curespectively representing the interactive power and the real-time electricity price between the time t and a large power grid in the S scene psi fault duration;
s3-5. load model
Figure BDA0002485698360000068
Figure BDA0002485698360000069
In the formula: td represents a failure start time;
Figure BDA00024856983600000610
representing the load demand at time t in the S scenario;
Figure BDA00024856983600000611
VOLL respectively represents the load reduction amount and the load reduction cost coefficient at the time t in the S scene psi fault duration, and the situation of load reduction only occurs in the fault time period is explained here;
s3-6. Power balance model
Figure BDA00024856983600000612
Figure BDA00024856983600000613
Equation (23) represents the power balance constraint under normal conditions, where
Figure BDA00024856983600000614
Representing the grid loss value at time t in the S scenario psi fault duration, the constraint (24) representing the power balance constraint in the case of a fault, h representing the optimization period in the case of a fault, as previously described, during the first iteration,
Figure BDA0002485698360000071
should be set to 0.
Still further, in step S4, the process of establishing the active power distribution network power flow optimization model is as follows:
s4-1. flow optimization profit model
Figure BDA0002485698360000072
In the formula: omegabRepresents a collection of all nodes; r isijRepresents the resistance of branch ij; i iss,t,ijRepresenting the magnitude of the current flowing from node i to node j at time t during the fault duration of scene psi; clossRepresenting a network loss cost coefficient;
s4-2. flow constraint model
Figure BDA0002485698360000073
Figure BDA0002485698360000074
Figure BDA0002485698360000075
Figure BDA0002485698360000076
Figure BDA0002485698360000077
Figure BDA0002485698360000078
Figure BDA0002485698360000079
In the formula: ps,t,ij、Qs,t,ijRespectively representing active power and reactive power flowing to a node i at a time t in the S scene psi fault duration; ps,t,i、Qs,t,iRespectively representing the sum of injected active power and the sum of reactive power of a node i at the time t in the S scene psi fault duration; x is the number ofjiRepresents the electricity of branch ij;
Figure BDA00024856983600000710
respectively representing active power of distributed power supply injection, photovoltaic injection, fan injection, energy storage injection and load consumption on a node i at the time t in the S scene psi fault duration;
Figure BDA00024856983600000711
respectively representing reactive power injected by the distributed power supply and consumed by the load on a node i at a time t in the S scene psi fault duration; u shapemin、UmaxRespectively representing the upper and lower bounds of the allowable node voltage of the system;
s4-3. second order cone model transformation
Because the model in the power flow optimization stage contains a nonlinear term, belongs to a mixed integer nonlinear programming problem, and has higher solving difficulty, a second-order cone relaxation technology is adopted to convert the problem into a mixed integer second-order cone problem so as to be solved by a mature mathematical solving tool;
first, a new variable V is constructeds,t,iAnd Ls,t,iSubstituting the square terms of voltage and current in the original model
Figure BDA0002485698360000081
And
Figure BDA0002485698360000082
corresponding nonlinear expressions (25) and expressions (26) to (29) are converted into
Figure BDA0002485698360000083
Figure BDA0002485698360000084
Figure BDA0002485698360000085
Figure BDA0002485698360000086
Figure BDA0002485698360000087
After replacing the variables, it is found that the objective function and all constraints have become linear expressions except for the nonlinear expression of equation (37), which is further obtained by relaxing the second-order cone constraint of equation (37):
Figure BDA0002485698360000088
through the steps, the random optimization model is converted from a nonlinear model problem which is difficult to solve into a linear model problem.
In step S5, the convergence condition is realized as follows:
and the process of solving the model is carried out alternately and iteratively, the convergence condition is set to indicate that the algorithm is converged when the variation between the network loss values calculated for the Nth time and the (N + 1) th time is less than 1xe-10, the current scheduling strategy set is output as the day-ahead optimization result of the active power distribution network, otherwise, the step S6 is carried out, and the step S2 is carried out again for optimization.
The invention has the beneficial effects that:
1. the optimal scheduling of the active power distribution network considering the fault condition is completed, the optimal scheduling of the active power distribution network considering economic cost and fault loss is realized, the consumption of renewable energy sources is promoted, and the reliability of the power grid is enhanced.
2. The two-stage optimization model of the active power distribution network is considered, power optimization and power flow optimization are decoupled and calculated, meanwhile, a nonlinear model which is difficult to solve is linearized through a second-order cone conversion method, the calculation difficulty is greatly reduced, and the calculation efficiency is remarkably improved. .
3. Scene generation and scene reduction are carried out through a Monte Carlo method, and load requirements, renewable energy output and uncertainty of fault duration are comprehensively considered, so that the solution can still keep good performability under the condition of facing various unknowns. Due to the probability characteristic of the random optimization problem, the risk management scheme is provided for the optimization model, and the cost of extreme scenes is comprehensively considered, so that the solution has good economy and applicability in actual scheduling.
Drawings
Fig. 1 is a scene probability analysis diagram.
Fig. 2 is a system configuration diagram.
Fig. 3 is a flowchart of an active power distribution network fault management method based on stochastic optimization.
FIG. 4 is a graph of data prediction.
Fig. 5 is a scene graph.
Fig. 6 is a SOC map for each case.
FIG. 7 is a graph of implementation costs for different fault durations.
Detailed description of the invention
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 7, an active power distribution network fault management method based on random optimization includes the following steps:
s1: establishing an uncertainty model, initializing the system and acquiring initial values required by optimization, including initial data of fan, photovoltaic and load requirements;
s2: establishing a scene probability model and simultaneously allocating a risk management scheme to a random optimization method;
s3: establishing an upper-layer active power distribution network power optimization model, solving an optimal power scheduling strategy by taking the lowest operation cost in each scene as a target, and reserving and substituting the strategy into a lower-layer optimization model;
s4: establishing a lower active power distribution network power flow optimization model, solving an optimal power flow scheduling strategy by taking a power scheduling strategy in an upper power optimization model as a known condition and taking the lowest network loss value in each scene as a target, and reserving and substituting the network loss value into the next iterative computation;
s5: when the variation of the network loss values of the two optimization results reaches a convergence condition and the internal scheduling strategy is not updated any more, outputting the scheduling strategy at the moment as the day-ahead optimization result of the active power distribution network;
s6: if the variation of the network loss value in the two times cannot reach the convergence condition, the procedure returns to step S2 to perform the optimization again according to the updated status information.
Further, in step S1, the uncertainty modeling includes the following components:
s1-1, scene generation: a series of scenes are generated by adopting a Monte Carlo method to simulate the uncertainty of the load demand and the RES output. In order to generate a relevant scene, initial values of load demand and RES output are firstly acquired, the initial values are used as mean values of Gaussian distribution, variance is added, a large number of scenes are generated, and on the basis that the sum of the probabilities of all the scenes is 1, the same probability is given to all the initial scenes;
s1-2, because a large number of scenes are difficult to solve in the proposed random optimization method, the scenes are reduced to a set number by using a backward reduction method, in each iteration of the algorithm, the Euclidean distance between every two scenes is calculated, the scene with lower probability in the two scenes with the lowest distance is removed, and the probability of the scene is transferred to the other scene;
s1-3. power system studies show that the fault duration cannot be accurately predicted by mathematical formulas, the only solution is to perform monte carlo simulations, and simulation analysis shows that the fault duration of an actual power system has a bell-shaped distribution. Moreover, the shape of the probability distribution depends largely on the standard deviation of the associated recovery time, so a normal distribution is used to represent the uncertainty of the fault duration, with a mean value of 5 hours and a standard deviation of 1 hour.
Still further, in step S2, the scene probability model is established as follows:
s2-1. two uncertainty problems are considered in the stochastic optimization problem, and in the process of solving, probability models of the two uncertainty problems are integrated, and assuming that the total number of the RES force-related scenes is S and the probability of the fault duration is psi with respect to the load demand, the probability of S × psi should be considered in the proposed stochastic optimization framework, as shown in FIG. 1, wherein P is PsRepresenting the probability of occurrence of the scene S, DψIndicating the probability that the fault lasts for a time ψ, then scene S ψ means when the S-th scene experiences DψHas a probability of PS×Dψ；
S2-2, in the process of random optimization, the obtained optimization scheme is expected to produce the lowest expected value of the running cost in all scenes, however, due to the large difference existing among a plurality of scenes, the scheduling scheme can produce very high cost in some scenes with low probability, in order to control the risk of such adverse results, the random optimization problem is equipped with a risk management scheme, and the risk level is measured by using a risk value (VaR) and a conditional risk value (CVaR), wherein the VaR represents the maximum loss value under a given confidence eta, however, the VaR represents the value of only one probability point, the loss condition corresponding to the scene after the probability point is not reflected, and the CVaR represents the expected running cost in all scenes exceeding the VaR, the tail risk can be well avoided, the CVaR is used for measuring the risk level,
Figure BDA0002485698360000111
Figure BDA0002485698360000112
Figure BDA0002485698360000113
in the formula: fCVaRRepresenting risk index, η representing confidence, S, S, PSRespectively representing the total number of scenes, the current optimized scene and the probability corresponding to the scene; TD, psi, DψRespectively representing the number of types of fault duration, the currently optimized fault duration and the probability corresponding to the fault duration; thetas,τλ is an auxiliary variable introduced to calculate CVaR, and its value is determined by equations (2) (3);
Figure BDA0002485698360000114
representing the power cost of the S-th scenario.
Still further, in step S3, the active distribution network power optimization model building process is as follows:
s3-1. Power optimization profit model
In the power optimization stage, the risk management is simultaneously equipped by taking the lowest operation cost as an objective function:
min(1-α)Fpower+αFCVaR(4)
Fpower＝(1-β)(FDG+FRES+FPU+FESS)+βFLOAD(5)
in the formula: fpower、FCVaRα respectively representing the running cost of power, risk index and weight value of risk management, FDG、FRES、FPU、FESS、FLOADβ respectively representing DG cost, RES cost, interaction power cost of the system and a large power grid, ESS cost, load reduction cost and weight values of economic indexes and fault indexes;
s3-2 distributed generator model
The DG cost is composed of the DG start-stop switch cost and the operation cost;
Figure BDA0002485698360000121
Figure BDA0002485698360000122
Figure BDA0002485698360000123
Figure BDA0002485698360000124
Figure BDA0002485698360000125
Figure BDA0002485698360000126
in the formula: t, t denotes the total optimization duration and the current optimization period, respectively; ND represents the total number of DG; SU, SD represent start and stop costs, respectively; a isd、bdA cost coefficient representing the d-th DG; j. the design is a squared,tRepresents the switching state quantity of the d-th DG at the time t; Δ t represents the optimization interval;
Figure BDA0002485698360000127
indicating the output power of the d-th DG at time t in the S scenario ψ fault duration. It is to be noted that the switching state quantity of DG should be the same in all scenarios, differing only in the output power in the corresponding scenario,
Figure BDA0002485698360000128
respectively representing the minimum and maximum output power of the d-th DG; URd、DRdRespectively representing the climbing efficiency of the d-th DG; CUd,t、CDd,tRespectively representing the starting cost coefficient and the stopping cost coefficient of the d-th DG;
s3-3 energy storage system model
Figure BDA0002485698360000129
Figure BDA00024856983600001210
Figure BDA00024856983600001211
Figure BDA00024856983600001212
Figure BDA00024856983600001213
Figure BDA00024856983600001214
Ee,0＝Ee,T(18)
In the formula: NE represents the total number of ESS;
Figure BDA00024856983600001215
respectively representing the charging power and the discharging power of the e-th ESS at the time t in the S scene psi fault duration;
Figure BDA0002485698360000131
respectively representing the charging efficiency and the discharging efficiency of the ESS; ceRepresents a charge-discharge cost coefficient;
Figure BDA0002485698360000132
represents the SOC of the ESS after the fault is over; veRepresenting the corresponding cost factor;
Figure BDA0002485698360000133
respectively represent the maximum power of charging and discharging of the e-th ESS at the moment t in the S scene psi fault duration,
Figure BDA0002485698360000134
respectively representing charge and discharge indication amounts of the e-th ESS,
Figure BDA0002485698360000135
respectively representing the minimum capacity and the maximum capacity of the e-th ESS, wherein the constraint (16) represents that the ESS can not be charged and discharged simultaneously, and the constraint (17) represents that the initial capacity and the capacity at the end of the optimization period of the e-th ESS are the same;
s3-4 distributed energy model
Figure BDA0002485698360000136
Figure BDA0002485698360000137
In the formula: NW and NP respectively represent the number of the fan and the photovoltaic;
Figure BDA0002485698360000138
respectively representing the output power of the w-th fan and the p-th photovoltaic at the t moment in the S scene; crA cost coefficient representing RES;
Figure BDA0002485698360000139
Curespectively representing the interactive power and the real-time electricity price between the time t and a large power grid in the S scene psi fault duration;
s3-5. load model
Figure BDA00024856983600001310
Figure BDA00024856983600001311
In the formula: td represents a failure start time;
Figure BDA00024856983600001312
representing the load demand at time t in the S scenario;
Figure BDA00024856983600001313
VOLL represents the curtailed load amount and curtailed load cost coefficient, respectively, at time t in the S scene ψ fault duration. It is explained here that the case of load shedding occurs only during the failure period;
s3-6. Power balance model
Figure BDA00024856983600001314
Figure BDA0002485698360000141
Equation (23) represents the power balance constraint under normal conditions,wherein
Figure BDA0002485698360000142
Representing the grid loss value at time t in the S scenario psi fault duration, the constraint (24) representing the power balance constraint in the case of a fault, h representing the optimization period in the case of a fault, as previously described, during the first iteration,
Figure BDA0002485698360000143
should be set to 0.
Still further, in step S4, the process of establishing the active power distribution network power flow optimization model is as follows:
s4-1. flow optimization profit model
Figure BDA0002485698360000144
In the formula: omegabRepresents a collection of all nodes; r isijRepresents the resistance of branch ij; i iss,t,ijRepresenting the magnitude of the current flowing from node i to node j at time t during the fault duration of scene psi; clossRepresenting a network loss cost coefficient;
s4-2. flow constraint model
Figure BDA0002485698360000145
Figure BDA0002485698360000146
Figure BDA0002485698360000147
Figure BDA0002485698360000148
Figure BDA0002485698360000149
Figure BDA00024856983600001410
Figure BDA00024856983600001411
In the formula: ps,t,ij、Qs,t,ijRespectively representing active power and reactive power flowing to a node i at a time t in the S scene psi fault duration; ps,t,i、Qs,t,iRespectively representing the sum of injected active power and the sum of reactive power of a node i at the time t in the S scene psi fault duration; x is the number ofjiRepresents the electricity of branch ij;
Figure BDA00024856983600001412
respectively representing active power of distributed power supply injection, photovoltaic injection, fan injection, energy storage injection and load consumption on a node i at the time t in the S scene psi fault duration;
Figure BDA0002485698360000151
respectively representing reactive power injected by the distributed power supply and consumed by the load on a node i at a time t in the S scene psi fault duration; u shapemin、UmaxRespectively representing the upper and lower bounds of the allowable node voltage of the system;
s4-3. second order cone model transformation
Because the model in the power flow optimization stage contains a nonlinear term, belongs to a mixed integer nonlinear programming problem, and has higher solving difficulty, a second-order cone relaxation technology is adopted to convert the problem into a mixed integer second-order cone problem so as to be solved by a mature mathematical solving tool;
first, a new variable V is constructeds,t,iAnd Ls,t,iSubstituting the square terms of voltage and current in the original model
Figure BDA0002485698360000152
And
Figure BDA0002485698360000153
corresponding nonlinear expressions (25) and expressions (26) to (29) are converted into
Figure BDA0002485698360000154
Figure BDA0002485698360000155
Figure BDA0002485698360000156
Figure BDA0002485698360000157
Figure BDA0002485698360000158
After replacing the variables, it is found that the objective function and all constraints have become linear expressions except for the nonlinear expression of equation (37), which is further obtained by relaxing the second-order cone constraint of equation (37):
Figure BDA0002485698360000159
through the steps, the random optimization model is converted from a nonlinear model problem which is difficult to solve into a linear model problem.
In step S5, the convergence condition is realized as follows:
and the process of solving the model is carried out alternately and iteratively, the convergence condition is set to indicate that the algorithm is converged when the variation between the network loss values calculated for the Nth time and the (N + 1) th time is less than 1xe-10, the current scheduling strategy set is output as the day-ahead optimization result of the active power distribution network, otherwise, the step S6 is carried out, and the step S2 is carried out again for optimization.
To enable those skilled in the art to better understand the benefits of the present invention, applicants have adopted a modified IEEE33 node power distribution network system as the test object, with DG, RES and ESS devices added at respective nodes, as shown in fig. 2. Three different cases were considered to analyze the validity of the verification uncertainty model and the stochastic optimization scheme. Three cases are considered, wherein the occurrence time of the fault is assumed to be 8 o' clock earlier, and the situation of extreme fault is considered to cause the disconnection of the node 1 and the node 2, and all the downstream nodes lose the support of the large power grid.
Case 1: and (4) considering 15 scenes, namely 7 fault durations, and performing optimized scheduling by using a random optimization strategy without considering risk management.
Case 2: consistent with case 1, only the worst case, i.e. a fault duration of 8 hours, is considered.
Case 3: in line with case 1, risk management is deployed.
In order to implement the random optimization method proposed in the present invention, the initial value of the data should be obtained first. For this reason, a day of august is randomly selected, and the load demand, the photovoltaic, the power generation amount of the fan per hour and the real-time electricity price data of the day are plotted at intervals of one point every 1 hour as shown in fig. 4. When the load flow optimization is carried out, the load data of each node can be obtained by proportionally distributing the obtained total load per hour according to the load data proportion in the IEEE33 node system. In the invention, the error variances of the load demand and the photovoltaic output power of the fan are respectively set as: the load demand is set to 3% of the initial value, the fan output is set to 10% of the initial value, and the photovoltaic output is set to 5% of the initial value. 2500 scenes with the same probability are generated by using a Monte Carlo method, and are finally cut down into 15 scenes by using a backward cutting method, wherein a scene graph is shown in FIG. 5, and a fault duration probability table is shown in Table 1;
Figure BDA0002485698360000161
TABLE 1
Two schedulable DGs are respectively connected to 16 nodes and 30 nodes of the system, wherein MT and DU respectively represent a diesel engine and a micro turbine, and specific parameters are shown in Table 2.
Figure BDA0002485698360000162
TABLE 2
The photovoltaic generator set and the wind turbine are respectively connected to a 9 node and a 21 node of the system, and the output power of the photovoltaic generator set and the wind turbine is uncontrollable. Wherein the cost coefficient C of the photovoltaic and the fanrAre all set to be 105 yuan/MW, the ESS is accessed to the 4 nodes, the specific parameters are shown in the table 3, wherein the energy storage charge-discharge cost coefficient CeA confidence level η is set to be 49 yuan/MW, a risk weight value is set to be 0.95, a weight value β of an economic indicator and a fault indicator is set to be 0.9, a load reduction cost coefficient VOLL is set to be 7000 yuan/MW, and an SOC cost coefficient V when the ESS is re-networkedeSet to 350 yuan/MW, network loss cost ClossSet as upper and lower limits U of 560 yuan/MW, per unit value of system voltagemaxAnd Umin1.05 and 0.95, respectively.
Figure BDA0002485698360000171
TABLE 3
The ESS scheduling strategy in three cases, which assume a failure occurrence time at 8 am, is shown in fig. 6, and until that time, the scheduling strategies in the three cases are consistent, i.e., the ESS is charged such that the SOC reaches a higher level. After the fault occurs, the node 1 is disconnected from the node 2, the power grid cannot supply power to the downstream nodes, and in order to avoid the reduction of important loads, the ESS discharges to ensure the support of the important loads. Due to limitations on the storage capacity and output power of the ESS, during a failure period, normal operation of all loads in the system cannot be supported, and some loads have to be curtailed to ensure stable operation of the system.
As can be seen from table 1, the probability that the failure duration exceeds 6 hours is very low, so in case one that is not equipped with the risk management scheme, the ESS is selected to be almost completely discharged to 13 points, which can ensure that the reduction of the load is minimal in the case where the failure duration is only 6 hours. At 14 and 15, the scheduling strategy of case one begins charging the ESS to cope with the peak load that would occur at 17. This is because in the random optimization strategy not equipped with the risk management scheme, the scheduling strategy is completely made according to the probability of occurrence of the event, in other words, in the scheduling strategy of case one, the duration of the failure is considered to be only within 6 hours, and the low-probability event with the duration exceeding 6 hours is considered to be ignored.
And when the fault uncertainty is not considered, only the worst fault situation is considered, namely the fault duration is 8 hours, and the discharge strategy of the ESS needs to take account of the fault duration of 8 hours. Therefore, the discharge rate of the ESS in case two is slow to ensure that enough electric power is discharged at 14 to 15 points to support the load. Such scheduling strategies inherently take into account the occurrence of low probability events, which are too conservative and often result in unnecessarily high costs.
In case three, which is equipped with a risk management scheme, it can be seen that the scheduling policy within 6 hours of the failure duration is substantially similar to that in case one, and in case of a low probability exceeding 6 hours, case three does not charge the ESS either. Therefore, case three can solve the high probability event preferentially, and also can consider the occurrence of the low probability event. Table 4 shows the results of the optimization of the three schemes.
Case1 Case2 Case3
Expected running cost (Yuan/Tian) 6719 10763 6923
CVaR (Yuan/Tian) 14439 11396 9089
TABLE 4
The results in the three cases are shown in table 4, from which it can be seen that the operation cost is the highest in case two, in which only the failure lasting 8 hours is considered. As mentioned earlier, the scheduling strategy of case two is too conservative, causing unnecessary economic loss. Comparing the first case with the third case can find that the lowest operation cost of the three cases can be obtained in the first case which ensures the maximum income of the high probability event and neglects the low probability event as much as possible, but correspondingly, the risk metric CVaR of the first case is also the highest of the three cases. In the third counter-observation case, the CVaR value is greatly reduced at the cost of increasing a little operation cost, so that the obtained scheduling strategy can show good applicability even in the face of low-probability events.
In the above analysis, assuming that the fault duration is uncertain, the resulting operational cost value can be understood as the expected cost value in all scenarios. To further analyze the effectiveness of the proposed method, after obtaining the optimization strategies for each case, the optimization strategies are applied to a series of scenarios respectively, in which the duration of the failure is determined and the cost consumed during the failure period is referred to as the implementation cost, as shown in fig. 7. As can be seen from fig. 7, case two, as an optimization strategy formulated in consideration of the worst case, can exhibit lower implementation cost only in case of a failure duration of exactly 8 hours, and can exhibit very close implementation cost in case of a failure duration within 6 hours, but upon occurrence of a low probability event with a duration exceeding 6 hours, case one can significantly increase the reduction load amount due to its charging behavior to the ESS, so that the implementation cost significantly increases. With the help of the risk management scheme, case three can well inhibit high risk results brought by low probability events, the implementation cost is still lower than that of case two under the condition that the fault duration is 7 hours, and is slightly higher than that of case two only under the condition that the fault duration is 8 hours, so that the optimization strategy of case three has a better implementation effect compared with other two cases.
The method provides a fault management method for an active power distribution network to solve various uncertain problems. The economic benefit of the system during the normal operation period is improved while the system is prevented from suffering huge loss during the fault. The method considers the economic cost under the normal operation condition and the load loss cost under the fault condition, establishes an uncertainty model comprising the load demand, the RES output and the fault duration and a random optimization model comprising DG, RES and ESS and simultaneously prepares a risk management scheme. The scheduling strategy can keep good applicability in all scenes, and an original complex nonlinear model is converted into a linear model through a second-order cone conversion and two-stage model solving method, so that the solving difficulty is reduced, and the solving efficiency is obviously improved. The example analysis shows that the random optimization scheduling strategy can well deal with various uncertain factors, effectively improve the economic benefit of the active power distribution network during normal operation and obviously reduce the load reduction cost under the fault condition. .
In the description of the present specification, case comparison and analysis, random scene analysis, and the like are used to describe specific features, structures, and benefits of the present invention. In this specification, the schematic representations of the invention are not necessarily directed to the same embodiments or examples, and those skilled in the art may combine and combine various embodiments or examples described in this specification. In addition, the embodiments described in this specification are merely illustrative of implementation forms of the inventive concept, and the scope of the present invention should not be construed as being limited to the specific forms set forth in the implementation examples, but also includes equivalent technical means which can be conceived by those skilled in the art according to the inventive concept.

Claims (6)

1. An active power distribution network fault management method based on random optimization is characterized by comprising the following steps:
s1: establishing an uncertainty model, initializing the system and acquiring initial values required by optimization, including initial data of fan, photovoltaic and load requirements;
s2: establishing a scene probability model and simultaneously allocating a risk management scheme to a random optimization method;
s3: establishing an upper-layer active power distribution network power optimization model, solving an optimal power scheduling strategy by taking the lowest operation cost in each scene as a target, and reserving and substituting the strategy into a lower-layer optimization model;
s4: establishing a lower active power distribution network power flow optimization model, solving an optimal power flow scheduling strategy by taking a power scheduling strategy in an upper power optimization model as a known condition and taking the lowest network loss value in each scene as a target, and reserving and substituting the network loss value into the next iterative computation;
s5: when the variation of the network loss values of the two optimization results reaches a convergence condition and the internal scheduling strategy is not updated any more, outputting the scheduling strategy at the moment as the day-ahead optimization result of the active power distribution network;
s6: if the variation of the network loss value in the two times cannot reach the convergence condition, the procedure returns to step S2 to perform the optimization again according to the updated status information.
2. The active power distribution network fault management method based on stochastic optimization of claim 1, wherein in the step S1, the uncertainty modeling comprises the following processes:
s1-1, scene generation: generating a series of scenes by adopting a Monte Carlo method to simulate the uncertainty of load demand and RES output; in order to generate a relevant scene, initial values of load demand and RES output are firstly acquired, the initial values are used as mean values of Gaussian distribution, variance is added, a large number of scenes are generated, and on the basis that the sum of the probabilities of all the scenes is 1, the same probability is given to all the initial scenes;
s1-2, reducing the scenes to a set number by using a backward reduction method, calculating Euclidean distance between every two scenes in each iteration, removing the scene with lower probability in the two scenes with the lowest distance, and transferring the probability to the other scene;
s1-3, the uncertainty in the fault duration is represented using a normal distribution with a mean of 5 hours and a standard deviation of 1 hour.
3. The active power distribution network fault management method based on stochastic optimization of claim 2, wherein in step S2, the scenario probability model is established as follows:
s2-1, two uncertainty problems are considered in the stochastic optimization problem, in the process of solving, probability models of the two uncertainty problems are integrated, and if the total number of the scenes related to the load demand by RES force is S and the probability of the fault duration is psi, the probability of S × psi, P should be considered in the proposed stochastic optimization frameworksRepresenting the probability of occurrence of the scene S, DψIndicating the probability that the fault lasts for a time ψ, then scene S ψ means when the S-th scene experiences DψHas a probability of PS×Dψ；
S2-2, in the process of random optimization, the obtained optimization scheme is that the expected value of the running cost is expected to be the lowest in all the scenes, however, due to the large difference existing among a plurality of scenes, the scheduling scheme can generate very high cost in some scenes with low probability, in order to control the risk of such adverse results, the random optimization problem is provided with a risk management scheme, and the risk level is measured by adopting a risk value VaR and a conditional risk value CVaR, wherein VaR represents the maximum loss value under a given confidence coefficient eta, however, VaR represents the value of only one probability point, the loss condition corresponding to the scene after the probability point is not reflected, and CVaR represents the expected value of the running cost under all the scenes exceeding VaR, tail risk can be well avoided, and CVaR is used for measuring the risk level,
Figure FDA0002485698350000021
Figure FDA0002485698350000022
Figure FDA0002485698350000023
in the formula: fCVaRRepresenting risk index, η representing confidence, S, S, PSRespectively representing the total number of scenes, the current optimized scene and the probability corresponding to the scene; TD, psi, DψRespectively representing the number of types of fault duration, the currently optimized fault duration and the probability corresponding to the fault duration; thetasτλ is an auxiliary variable introduced to calculate CVaR, and its value is determined by equations (2) (3);
Figure FDA0002485698350000024
representing the power cost of the S-th scenario.
4. The active distribution network fault management method based on stochastic optimization of claim 3, wherein in step S3, the active distribution network power optimization model is established as follows:
s3-1. Power optimization profit model
In the power optimization stage, the risk management is simultaneously equipped by taking the lowest operation cost as an objective function:
min(1-α)Fpower+αFCVaR(4)
Fpower＝(1-β)(FDG+FRES+FPU+FESS)+βFLOAD(5)
in the formula: fpower、FCVaRα denote power operation respectivelyCost, risk index and weight value of risk management; fDG、FRES、FPU、FESS、FLOADβ respectively representing DG cost, RES cost, interaction power cost of the system and a large power grid, ESS cost, load reduction cost and weight values of economic indexes and fault indexes;
s3-2 distributed generator model
The DG cost is composed of the DG start-stop switch cost and the operation cost;
Figure FDA0002485698350000031
Figure FDA0002485698350000032
Figure FDA0002485698350000033
Figure FDA0002485698350000034
Figure FDA0002485698350000035
Figure FDA0002485698350000036
in the formula: t, t denotes the total optimization duration and the current optimization period, respectively; ND represents the total number of DG; SU, SD represent start and stop costs, respectively; a isd、bdA cost coefficient representing the d-th DG; j. the design is a squared,tRepresents the switching state quantity of the d-th DG at the time t; Δ t represents the optimization interval;
Figure FDA0002485698350000037
denotes the output power of the d-th DG at time t in the S scene psi fault durationThe switching state quantity of DG should be the same in all scenarios, differing only in the output power in the corresponding scenario,
Figure FDA0002485698350000038
respectively representing the minimum and maximum output power of the d-th DG; URd、DRdRespectively representing the climbing efficiency of the d-th DG; CUd,t、CDd,tRespectively representing the starting cost coefficient and the stopping cost coefficient of the d-th DG;
s3-3 energy storage system model
Figure FDA0002485698350000039
Figure FDA00024856983500000310
Figure FDA00024856983500000311
Figure FDA0002485698350000041
Figure FDA0002485698350000042
Figure FDA0002485698350000043
Ee,0＝Ee,T(18)
In the formula: NE represents the total number of ESS;
Figure FDA0002485698350000044
respectively representing the charging power and the discharging power of the e-th ESS at the time t in the S scene psi fault duration;
Figure FDA0002485698350000045
respectively representing the charging efficiency and the discharging efficiency of the ESS; ceRepresents a charge-discharge cost coefficient;
Figure FDA0002485698350000046
represents the SOC of the ESS after the fault is over; veRepresenting the corresponding cost factor;
Figure FDA0002485698350000047
respectively represent the maximum power of charging and discharging of the e-th ESS at the moment t in the S scene psi fault duration,
Figure FDA0002485698350000048
respectively representing charge and discharge indication amounts of the e-th ESS,
Figure FDA0002485698350000049
respectively representing the minimum capacity and the maximum capacity of the e-th ESS, wherein the constraint (16) represents that the ESS can not be charged and discharged simultaneously, and the constraint (17) represents that the initial capacity and the capacity at the end of the optimization period of the e-th ESS are the same;
s3-4 distributed energy model
Figure FDA00024856983500000410
Figure FDA00024856983500000411
In the formula: NW and NP respectively represent the number of the fan and the photovoltaic;
Figure FDA00024856983500000412
respectively representing the output power of the w-th fan and the p-th photovoltaic at the t moment in the S scene; crA cost coefficient representing RES;
Figure FDA00024856983500000413
Curespectively representing the interactive power and the real-time electricity price between the time t and a large power grid in the S scene psi fault duration;
s3-5. load model
Figure FDA00024856983500000414
Figure FDA00024856983500000415
In the formula: td represents a failure start time;
Figure FDA0002485698350000051
representing the load demand at time t in the S scenario;
Figure FDA0002485698350000052
VOLL respectively represents the load reduction quantity and the load reduction cost coefficient at the time t in the S scene psi fault duration;
s3-6. Power balance model
Figure FDA0002485698350000053
Figure FDA0002485698350000054
Equation (23) represents the power balance constraint under normal conditions, where
Figure FDA0002485698350000055
Representing the grid loss value at time t in the S scenario psi fault duration, constraint (24) representing the power balance constraint in case of a fault, h representing the optimization period in case of a fault, during the first iteration,
Figure FDA0002485698350000056
should be set toIs 0.
5. The active power distribution network fault management method based on stochastic optimization of claim 4, wherein in step S4, the active power distribution network power flow optimization model is established as follows:
s4-1. flow optimization profit model
Figure FDA0002485698350000057
In the formula: omegabRepresents a collection of all nodes; r isijRepresents the resistance of branch ij; i iss,t,ijRepresenting the magnitude of the current flowing from node i to node j at time t during the fault duration of scene psi; clossRepresenting a network loss cost coefficient;
s4-2. flow constraint model
Figure FDA0002485698350000058
Figure FDA0002485698350000059
Figure FDA00024856983500000510
Figure FDA00024856983500000511
Figure FDA00024856983500000512
Figure FDA00024856983500000513
Figure FDA0002485698350000061
In the formula: ps,t,ij、Qs,t,ijRespectively representing active power and reactive power flowing to a node i at a time t in the S scene psi fault duration; ps,t,i、Qs,t,iRespectively representing the sum of injected active power and the sum of reactive power of a node i at the time t in the S scene psi fault duration; x is the number ofjiRepresents the electricity of branch ij;
Figure FDA0002485698350000062
respectively representing active power of distributed power supply injection, photovoltaic injection, fan injection, energy storage injection and load consumption on a node i at the time t in the S scene psi fault duration;
Figure FDA0002485698350000063
respectively representing reactive power injected by the distributed power supply and consumed by the load on a node i at a time t in the S scene psi fault duration; u shapemin、UmaxRespectively representing the upper and lower bounds of the allowable node voltage of the system;
s4-3. second order cone model transformation
Converting the problem into a mixed integer second order cone problem by adopting a second order cone relaxation technology so as to be solved by a mature mathematical solving tool;
first, a new variable V is constructeds,t,iAnd Ls,t,iSubstituting the square terms of voltage and current in the original model
Figure FDA0002485698350000064
And
Figure FDA0002485698350000065
corresponding nonlinear expressions (25) and expressions (26) to (29) are converted into
Figure FDA0002485698350000066
Figure FDA0002485698350000067
Figure FDA0002485698350000068
Figure FDA0002485698350000069
Figure FDA00024856983500000610
After replacing the variables, it is found that the objective function and all constraints have become linear expressions except for the nonlinear expression of equation (37), which is further obtained by relaxing the second-order cone constraint of equation (37):
Figure FDA00024856983500000611
through the steps, the random optimization model is converted from a nonlinear model problem which is difficult to solve into a linear model problem.
6. The active power distribution network fault management method based on random optimization as claimed in claim 5, wherein in step S5, the convergence condition is implemented as follows:
and the process of solving the model is carried out alternately and iteratively, the convergence condition is set to indicate that the algorithm is converged when the variation between the network loss values calculated for the Nth time and the (N + 1) th time is less than 1xe-10, the current scheduling strategy set is output as the day-ahead optimization result of the active power distribution network, otherwise, the step S6 is carried out, and the step S2 is carried out again for optimization.
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