WO2020237847A1 - 一种基于混合整数线性规划的配电网可靠性指标计算方法 - Google Patents

一种基于混合整数线性规划的配电网可靠性指标计算方法 Download PDF

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WO2020237847A1
WO2020237847A1 PCT/CN2019/101429 CN2019101429W WO2020237847A1 WO 2020237847 A1 WO2020237847 A1 WO 2020237847A1 CN 2019101429 W CN2019101429 W CN 2019101429W WO 2020237847 A1 WO2020237847 A1 WO 2020237847A1
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branch
node
fails
circuit breaker
fault
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PCT/CN2019/101429
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English (en)
French (fr)
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吴文传
张伯明
栗子豪
孙宏斌
王彬
郭庆来
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清华大学
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Publication of WO2020237847A1 publication Critical patent/WO2020237847A1/zh
Priority to US17/500,539 priority Critical patent/US20220037883A1/en

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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
    • H02J3/001—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
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • H02J3/0012—Contingency detection
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Energy or water supply
    • 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]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • 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
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
    • Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security

Definitions

  • the invention belongs to the technical field of power system planning and evaluation, and particularly relates to a method for calculating the reliability index of a distribution network based on mixed integer linear programming.
  • reliability refers to the ability of the power system to continuously meet the quantity and quality of end users' power needs.
  • the reliability of the distribution network mainly includes the following indicators: customer interruption frequency (CIF), customer interruption duration (CID), system average interruption frequency index( SAIFI)), system average interruption duration index (SAIDI) and expected energy not supplied (EENS)).
  • CIF customer interruption frequency
  • CID customer interruption duration
  • SAIFI system average interruption frequency index
  • SAIDI system average interruption duration index
  • EENS expected energy not supplied
  • these reliability indicators are usually calculated by simulation-based methods, namely stochastic production simulation.
  • the calculation method first generates numerous Monte Carlo samples based on equipment failures and failure rates, calculates the power supply status of the distribution network in this sample, and stores and counts them; finally, the reliability index is calculated from the statistical results.
  • This method takes a long time and requires a large storage space; and cannot consider the load recovery operation after a failure, which may cause the reliability index to be underestimated.
  • the purpose of the present invention is to overcome the shortcomings of the prior art and propose a method for calculating the reliability index of the distribution network based on mixed integer linear programming.
  • This method builds a distribution network reliability evaluation optimization model based on mixed integer linear programming, instead of calculating reliability indicators by sampling, it directly obtains reliability indicators by solving the model, which improves the efficiency of distribution network reliability evaluation.
  • the present invention proposes a method for calculating reliability index of distribution network based on mixed integer linear programming, which is characterized in that it includes the following steps:
  • the circuit breaker closest to the faulty branch upstream of the branch enters the circuit breaker action stage, and first acts to open the circuit breaker and interrupt the fault current.
  • the downstream node of the circuit breaker is powered off; after that, it enters the switching action.
  • fault isolation is carried out to isolate the faulty branch; at the same time, network reconstruction is carried out through the action of switches and circuit breakers, and the load of the power-off node is restored, assuming that the full load or zero load is restored; then, the faulty branch is repaired, and the switch is activated after the repair Restore the original power supply network structure with circuit breakers;
  • the objective function of this model is to minimize the system's annual average interruption duration index SAIDI, as shown in equation (75):
  • the superscript xy represents the scene under the failure of branch xy, Represents the load of the i-node when the branch xy fails, Represents the power flowing from node j to node i on branch xy when branch xy fails, ⁇ i represents the set of branches directly connected to node i, ⁇ LN represents the set of load nodes, and ⁇ represents the set of all branches, Represents all branch failure scenarios;
  • M is a positive number, Indicates the state of the switch close to node i on branch ij when branch xy fails, Means the switch is closed, Means the switch is on, Represents the state of the switch close to node j on branch ij when branch xy fails, Means the switch is closed, Means the switch is on, Indicates the rated transmission capacity of branch ij;
  • ⁇ F represents the set of all transformer nodes
  • the superscript B represents the action stage of the circuit breaker
  • the superscript NO indicates normal operation status, Is the state of the switch close to node i on branch ij under normal operation, Means the switch is closed, Means the switch is on, Is the state of the switch close to node j on branch ij under normal operation, Means the switch is closed, Indicates that the switch is open;
  • Is the failure influence flag of node i when branch xy fails Indicates that node i is affected by the fault when the branch xy fails, Indicates that node i is not affected by the fault when branch xy fails;
  • the superscript PF represents the switching stage
  • branch ij is affected by the maintenance of the faulty branch and is in a power-off state during the switching operation stage. It means that after branch xy fails, branch ij is not affected by the maintenance of the faulty branch and is in normal operation during the switching operation stage.
  • Is the maintenance influence flag of node i in the switching action stage after the failure of branch xy It means that after branch xy fails, node i is affected by the maintenance of the faulty branch and is in a power-off state, It means that after branch xy fails, node i is not affected by the maintenance of the faulty branch and is in normal operation;
  • the power supply flag of node i after the switching action is completed after the branch xy fails Indicates that the node i is normally powered after the switching action is completed after the branch xy fails, Indicates that the node i is in the power-off state after the switching action is completed after the branch xy fails;
  • CID i represents the user interruption duration of the i-node
  • ⁇ xy represents the annual failure rate of branch xy
  • CIF i represents the user interruption frequency of the i-node
  • NC i is the number of users of a given i-node
  • SAIFI is the system's annual average interruption duration index
  • ASAI is the system average power supply index
  • B is the collection of all load levels
  • ⁇ h is the annual duration of load level h
  • ⁇ h ⁇ 1 is the peak load ratio of load level h
  • Li represents the peak load of node i;
  • the invention models the calculation of the reliability index of the distribution network as a mixed integer linear programming problem, and directly obtains the value of the reliability index by solving the model, avoiding a large number of sampling calculations in the reliability evaluation of the traditional distribution network.
  • This method can accurately describe the installation positions of circuit breakers and switches, and consider the restoration of part of the load affected by the fault by network reconstruction after a fault, obtain more accurate index calculation results, and improve the efficiency of distribution network reliability evaluation.
  • the method for calculating reliability index of distribution network based on mixed integer linear programming proposed by the present invention includes the following steps:
  • the circuit breaker closest to the faulty branch upstream of the branch first acts to open and interrupt the fault current (circuit breaker action stage), and then the downstream node of the circuit breaker is powered off; after that, the switch action (switch action) Stage), perform fault isolation and isolate the faulty branch; at the same time, perform network reconstruction through switch and circuit breaker actions to maximize the restoration of the load of the power-off node (assuming that only full load or zero load can be restored); then, repair the faulty branch , After repairing, restore the original power supply network structure through action switches and circuit breakers.
  • both ends of each branch can be installed with circuit breakers (breakable fault current) and switches (including section switches and tie switches, non-breakable fault current), and it is assumed that the circuit breakers and switches are in normal operation
  • circuit breakers breakable fault current
  • switches including section switches and tie switches, non-breakable fault current
  • the objective function of this model is to minimize the system's annual average interruption duration index SAIDI, as shown in equation (75):
  • the superscript xy represents the scenario when the branch xy fails. Represents the load of the i-node when the branch xy fails, Represents the power flowing from node j to node i on branch xy when branch xy fails, ⁇ i represents the set of branches directly connected to node i, ⁇ LN represents the set of load nodes, and ⁇ represents the set of all branches, Represents all branch fault scenarios.
  • M is a given arbitrary larger number (it needs to be greater than the maximum capacity of all lines in the distribution network
  • the value of 1000000 in this example) Represents the state of the switch close to node i on branch ij when branch xy fails ( Means the switch is closed, Means the switch is on), Represents the state of the switch close to node j on branch ij when branch xy fails ( Means the switch is closed, Means the switch is on), Indicates the rated transmission capacity of branch ij.
  • ⁇ F represents the set of all transformer nodes.
  • Is the failure effect flag of node i when the branch xy fails Indicates that node i is affected by the fault when the branch xy fails, Indicates that node i is not affected by the fault when branch xy fails).
  • branch ij is not affected by the maintenance of the faulty branch and is in normal operation during the switching operation stage), where It is the maintenance influence flag of node i in the switching action stage after the failure of branch xy ( It means that after branch xy fails, node i is affected by the maintenance of the faulty branch and is in a power-off state, It means that after branch xy fails, node i is not affected by the maintenance of the faulty branch and is in normal operation).
  • the power supply flag of node i Indicates that after the branch xy fails (after the switching action), the node i is normally powered, It means that the node i (after switching action) is in the power-off state after the branch xy fails).
  • CID i represents the user interruption duration of the i-node
  • Represents the interruption time of the fault switch action of the branch xy (if xy tr f , f ⁇ ⁇ F , it means the transformer f) (specifically the time from the occurrence of the fault to the switch action of the fault branch)
  • CIF i represents the user interruption frequency of i-node
  • NC i is the number of users of a given i-node
  • SAIFI is the system's average annual outage duration index
  • ASAI is the system's average power supply index
  • EENS is the expected loss of load energy
  • B is the set of all load levels
  • ⁇ h is the load level h
  • the number of hours per year, ⁇ h ⁇ 1 is the peak load ratio of load level h, and Li represents the peak load of node i.
  • the optimization model is solved by the optimization software CPLEX or gurobi, and the obtained CID i , CIF i , SAIDI, SAIFI, ASAI, EENS are the requirements Reliability evaluation index.
  • distribution network managers can accurately assess the reliability of the distribution network, perform system reliability index analysis, user node reliability analysis, and feeder reliability analysis, and perform bad index analysis. Based on the analysis results, according to the actual reliability requirements of the distribution network, carry out the analysis of the weak links of the power supply to improve the distribution network.

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Abstract

一种基于混合整数线性规划的配电网可靠性指标计算方法，属于电力系统规划与评估技术领域。该方法首先定义器件安装状态和支路故障后故障隔离、负荷转供和故障恢复动作原则，然后构建基于混合整数线性规划模型的配电网可靠性指标优化模型，通过求解该模型，直接得到可靠性指标的值。该方法考虑了配电网中常见的两种故障：变压器故障和线路故障，并考虑了故障后网络重构对可靠性指标的影响。该方法避免了传统配电网可靠性评估中的大量抽样计算，且可以考虑故障后网络重构对部分受故障影响负荷的恢复，计算效率高且精确。

Description

一种基于混合整数线性规划的配电网可靠性指标计算方法
相关申请的交叉引用
本申请要求清华大学于2019年05月24日提交的、发明名称为“一种基于混合整数线性规划的配电网可靠性指标计算方法”的、中国专利申请号“201910439195.2”的优先权。
技术领域
本发明属于电力系统规划与评估技术领域，特别涉及一种基于混合整数线性规划的配电网可靠性指标计算方法。
背景技术
在电力领域，可靠性是指电力系统持续满足终端用户电力需求数量和质量的能力。配电网可靠性主要包括以下几个指标：用户中断频率(customer interruption frequency(CIF))、用户中断持续时间(customer interruption duration(CID))、系统年平均中断频率指数(system average interruption frequency index(SAIFI))、系统年平均中断持续时间指数(system average interruption duration index(SAIDI))和期望失负荷能量(expected energy not supplied(EENS))。依据现行的国家标准《DL/T 1563-2016中压配电网可靠性评估导则》，上述可靠性指标是评估配电网可靠性的必需指标。
在目前应用的配电网可靠性评估方法中，这些可靠性指标通常采用基于仿真的方法计算，即随机生产模拟。该计算方法首先根据设备故障和故障率生成众多的蒙特卡罗样本，计算该样本中配电网供电情况，并对其进行存储、统计；最终由统计结果计算出可靠性指标。这种方法耗时较长，需要较大的存储空间；且无法考虑故障后负荷恢复操作，可能导致可靠性指标被低估。
发明内容
本发明的目的是为克服已有技术的不足之处，提出一种基于混合整数线性规划的配电网可靠性指标计算方法。该方法通过构建基于混合整数线性规划的配电网可靠性评估优化模型，不通过抽样计算可靠性指标，而直接通过求解该模型得到可靠性指标，提升配电网可靠性评估效率。
本发明提出一种基于混合整数线性规划的配电网可靠性指标计算方法，其特征在于，包括以下步骤：
1)定义器件安装状态和支路故障后故障隔离、负荷转供和故障恢复动作原则，具体如下：
在支路故障发生后，首先支路上游最靠近故障支路的断路器进入断路器动作阶段，先动作打开断路器、开断故障电流，此时断路器下游节点断电；之后，进入开关动作阶段，进行故障隔离，隔离故障支路；同时，通过开关和断路器动作进行网络重构，恢复断电节点负荷，假设恢复全部负荷或零负荷；而后，修复故障支路，修复后通过动作开关和断路器恢复原供电网络结构；
2)构建基于混合整数线性规划模型的配电网可靠性指标优化模型，该模型由目标函数和约束条件构成；具体如下：
2-1)确定模型的目标函数；
该模型的目标函数为最小化系统年平均中断持续时间指数SAIDI，如式(75)所示：
Minimize:SAIDI(1)
2-2)确定模型的约束条件；具体如下：
2-2-1)配电网功率平衡约束，如式(76)-(77)所示：
Figure PCTCN2019101429-appb-000001
Figure PCTCN2019101429-appb-000002
其中，上标xy表示在支路xy发生故障下的场景，
Figure PCTCN2019101429-appb-000003
表示在支路xy发生故障时i节点的负荷，
Figure PCTCN2019101429-appb-000004
表示在支路xy发生故障时支路ij上由j节点流向i节点的功率，Ψ i表示与i节点直接相连的支路集合，Ψ LN表示负荷节点集合，Υ表示所有支路的集合，
Figure PCTCN2019101429-appb-000005
代表所有支路故障场景；
2-2-2)支路功率约束，如式(78)-(80)所示：
Figure PCTCN2019101429-appb-000006
Figure PCTCN2019101429-appb-000007
Figure PCTCN2019101429-appb-000008
其中，M为正数，
Figure PCTCN2019101429-appb-000009
表示在支路xy发生故障时支路ij上靠近节点i开关的状态，
Figure PCTCN2019101429-appb-000010
表示开关闭合，
Figure PCTCN2019101429-appb-000011
表示开关打开，
Figure PCTCN2019101429-appb-000012
表示在支路xy发生故障时支路ij上靠近节点j开关的状，
Figure PCTCN2019101429-appb-000013
表示开关闭合，
Figure PCTCN2019101429-appb-000014
表示开关打开，
Figure PCTCN2019101429-appb-000015
表示支路ij额定传输容量；
2-2-3)变压器功率约束，如式(81)-(82)所示：
Figure PCTCN2019101429-appb-000016
Figure PCTCN2019101429-appb-000017
其中，
Figure PCTCN2019101429-appb-000018
为在支路xy发生故障时变压器f的功率，
Figure PCTCN2019101429-appb-000019
为在支路xy发生故障时连接变压器f的支路tr f由变压器节点流向下游节点的功率，Ψ F表示所有变压器节点的集合；
2-2-4)断路器动作约束，如式(83)-(94)所示：
Figure PCTCN2019101429-appb-000020
Figure PCTCN2019101429-appb-000021
Figure PCTCN2019101429-appb-000022
Figure PCTCN2019101429-appb-000023
Figure PCTCN2019101429-appb-000024
Figure PCTCN2019101429-appb-000025
Figure PCTCN2019101429-appb-000026
Figure PCTCN2019101429-appb-000027
Figure PCTCN2019101429-appb-000028
Figure PCTCN2019101429-appb-000029
Figure PCTCN2019101429-appb-000030
Figure PCTCN2019101429-appb-000031
Figure PCTCN2019101429-appb-000032
其中，上标B表示断路器动作阶段，
Figure PCTCN2019101429-appb-000033
为在支路xy发生故障时在断路器动作阶段支路ij的故障波及标志，
Figure PCTCN2019101429-appb-000034
表示支路xy发生故障时在断路器动作阶段支路ij受故障波及而处于断电状态，
Figure PCTCN2019101429-appb-000035
表示支路xy发生故障时在断路器动作阶段支路ij处于正常运行状态，
Figure PCTCN2019101429-appb-000036
为在支路xy发生故障时在断路器动作阶段节点i的故障波及标志，
Figure PCTCN2019101429-appb-000037
表示支路xy发生故障时在断路器动作阶段节点i受故障波及而处于断电状态，
Figure PCTCN2019101429-appb-000038
表示支路xy发生故障时在断路器动作阶段节点i处于正常运行状态；
上标NO表示正常运行状态，
Figure PCTCN2019101429-appb-000039
为在正常运行状态下支路ij上靠近节点i开关的状态，
Figure PCTCN2019101429-appb-000040
表示开关闭合，
Figure PCTCN2019101429-appb-000041
表示开关打开，
Figure PCTCN2019101429-appb-000042
为在正常运行状态下支路ij上靠近节点j开关的状态，
Figure PCTCN2019101429-appb-000043
表示开关闭合，
Figure PCTCN2019101429-appb-000044
表示开关打开；
Figure PCTCN2019101429-appb-000045
为在支路xy发生故障时支路ij上靠近节点i断路器的状态，
Figure PCTCN2019101429-appb-000046
表示断路器闭合，
Figure PCTCN2019101429-appb-000047
表示断路器打开，
Figure PCTCN2019101429-appb-000048
为在支路xy发生故障时支路ij上靠近节点j断路器的状态，
Figure PCTCN2019101429-appb-000049
表示断路器闭合，
Figure PCTCN2019101429-appb-000050
表示断路器打开，
Figure PCTCN2019101429-appb-000051
为在正常运行状态下支路ij上靠近节点i断路器的状态，
Figure PCTCN2019101429-appb-000052
表示断路器闭合，
Figure PCTCN2019101429-appb-000053
表示断路器打开，
Figure PCTCN2019101429-appb-000054
为在正常运行状态下支路ij上靠近节点j断路器的状态，
Figure PCTCN2019101429-appb-000055
表示断路器闭合，
Figure PCTCN2019101429-appb-000056
表示断路器打开；
Figure PCTCN2019101429-appb-000057
为在支路xy发生故障时节点i的故障影响标志，
Figure PCTCN2019101429-appb-000058
表示支路xy发生故障时节点i受故障影响，
Figure PCTCN2019101429-appb-000059
表示支路xy发生故障时节点i不受故障影响；
2-2-5)开关动作约束，如式(95)-(105)所示：
Figure PCTCN2019101429-appb-000060
Figure PCTCN2019101429-appb-000061
Figure PCTCN2019101429-appb-000062
Figure PCTCN2019101429-appb-000063
Figure PCTCN2019101429-appb-000064
Figure PCTCN2019101429-appb-000065
Figure PCTCN2019101429-appb-000066
Figure PCTCN2019101429-appb-000067
Figure PCTCN2019101429-appb-000068
Figure PCTCN2019101429-appb-000069
Figure PCTCN2019101429-appb-000070
Figure PCTCN2019101429-appb-000071
其中，上标PF表示开关动作阶段，
Figure PCTCN2019101429-appb-000072
为在支路xy发生故障后在开关动作阶段支路ij的维修影响标志，
Figure PCTCN2019101429-appb-000073
表示支路xy发生故障后在开关动作阶段支路ij受故障支路维修影响而处于断电状态，
Figure PCTCN2019101429-appb-000074
表示支路xy发生故障后在开关动作阶段支路ij不受故障支路维修影响而处于正常运行状态，
Figure PCTCN2019101429-appb-000075
为在支路xy发生故障后在开关动作阶段节点i的维修影响标志，
Figure PCTCN2019101429-appb-000076
表示支路xy发生故障后节点i受故障支路维修影响而处于断电状态，
Figure PCTCN2019101429-appb-000077
表示支路xy发生故障后节点i不受故障支路维修影响而处于正常运行状态；
Figure PCTCN2019101429-appb-000078
在支路xy发生故障后完成开关动作后节点i的供电标志，
Figure PCTCN2019101429-appb-000079
表示支路xy发生故 障后完成开关动作后节点i正常供电，
Figure PCTCN2019101429-appb-000080
表示支路xy发生故障后完成开关动作后节点i处于断电状态；
2-2-6)可靠性指标计算约束，如式(106)-(111)所示：
Figure PCTCN2019101429-appb-000081
Figure PCTCN2019101429-appb-000082
Figure PCTCN2019101429-appb-000083
Figure PCTCN2019101429-appb-000084
Figure PCTCN2019101429-appb-000085
Figure PCTCN2019101429-appb-000086
其中，CID i表示i节点的用户中断持续时间，λ xy表示支路xy的年故障率，
Figure PCTCN2019101429-appb-000087
表示支路xy的故障开关动作中断时间，
Figure PCTCN2019101429-appb-000088
表示支路xy的故障修复中断时间，CIF i表示i节点的用户中断频率，NC i为给定的i节点的用户数量，SAIFI为系统年平均中断持续时间指数，ASAI为系统平均供电指数，EENS为期望失负荷能量，B为所有负荷水平的集合，Δ h为负荷水平h的年持续小时数，μ h≤1为负荷水平h的峰值负荷比，L i表示i节点的峰值负荷；
3)根据目标函数(75)和约束条件(76)-(111)，求解该优化模型，得到的CID i、CIF i、SAIDI、SAIFI、ASAI、EENS即为所求的可靠性评估指标。
本发明的特点及有益效果在于：
本发明将计算配电网可靠性指标建模为一混合整数线性规划问题，通过求解该模型直接得到可靠性指标的值，避免了传统配电网可靠性评估中的大量抽样计算。该方法可以精确描述断路器和开关的安装位置，且考虑故障后网络重构对部分受故障影响负荷的恢复，得到更为准确的指标计算结果，提升配电网可靠性评估效率。
具体实施方式
本发明提出的一种基于混合整数线性规划的配电网可靠性指标计算方法，下面结合具体实施例进一步详细说明如下。
本发明提出的一种基于混合整数线性规划的配电网可靠性指标计算方法，包括以下步骤：
1)定义器件安装状态和支路故障后故障隔离、负荷转供和故障恢复动作原则，具体如下：
在支路故障发生后，首先支路上游最靠近故障支路的断路器先动作打开、开断故障电流(断路器动作阶段)，此时断路器下游节点断电；之后，开关动作(开关动作阶段)，进行故障隔离，隔离故障支路；同时，通过开关和断路器动作进行网络重构，最大限度恢复断电节点负荷(假设仅可恢复全部负荷或零负荷)；而后，修复故障支路，修复后通过动作开关和断路器恢复原供电网络结构。
其中，每条支路的两端都可安装有断路器(可开断故障电流)和开关(包括分段开关和联络开关，不可开断故障电流)，并假设正常运行状态下断路器和开关的状态已知；
2)构建基于混合整数线性规划模型的配电网可靠性指标优化模型，该模型由目标函数和约束条件构成；具体如下：
2-1)确定模型的目标函数；
该模型的目标函数为最小化系统年平均中断持续时间指数SAIDI，如式(75)所示：
Minimize:SAIDI(38)
2-2)确定模型的约束条件；具体如下：
2-2-1)配电网功率平衡约束，如式(76)-(77)所示：
Figure PCTCN2019101429-appb-000089
Figure PCTCN2019101429-appb-000090
其中，上标xy表示在支路xy发生故障下的场景。
Figure PCTCN2019101429-appb-000091
表示在支路xy发生故障时i节点的负荷，
Figure PCTCN2019101429-appb-000092
表示在支路xy发生故障时支路ij上由j节点流向i节点的功率，Ψ i表示与i节点直接相连的支路集合，Ψ LN表示负荷节点集合，Υ表示所有支路的集合，
Figure PCTCN2019101429-appb-000093
代表所有支路故障场景。
2-2-2)支路功率约束，如式(78)-(80)所示：
Figure PCTCN2019101429-appb-000094
Figure PCTCN2019101429-appb-000095
Figure PCTCN2019101429-appb-000096
其中，M为给定任意取值较大的数(需要大于配电网所有线路中最大容量
Figure PCTCN2019101429-appb-000097
的值，本实例中取为1000000)，
Figure PCTCN2019101429-appb-000098
表示在支路xy发生故障时支路ij上靠近节点i开关的状态(
Figure PCTCN2019101429-appb-000099
表示开关闭合，
Figure PCTCN2019101429-appb-000100
表示开关打开)，
Figure PCTCN2019101429-appb-000101
表示在支路xy发生故障时支路ij上靠近节点j开关的状态(
Figure PCTCN2019101429-appb-000102
表示开关闭合，
Figure PCTCN2019101429-appb-000103
表示开关打开)，
Figure PCTCN2019101429-appb-000104
表示支路ij额定传输容量。
2-2-3)变压器功率约束，如式(81)-(82)所示：
Figure PCTCN2019101429-appb-000105
Figure PCTCN2019101429-appb-000106
其中，
Figure PCTCN2019101429-appb-000107
为在支路xy发生故障时变压器f的功率，
Figure PCTCN2019101429-appb-000108
为在支路xy发生故障时连接变压器f的支路tr f由变压器节点流向下游节点的功率，Ψ F表示所有变压器节点的集合。
2-2-4)断路器动作约束，如式(83)-(94)所示：
Figure PCTCN2019101429-appb-000109
Figure PCTCN2019101429-appb-000110
Figure PCTCN2019101429-appb-000111
Figure PCTCN2019101429-appb-000112
Figure PCTCN2019101429-appb-000113
Figure PCTCN2019101429-appb-000114
Figure PCTCN2019101429-appb-000115
Figure PCTCN2019101429-appb-000116
Figure PCTCN2019101429-appb-000117
Figure PCTCN2019101429-appb-000118
Figure PCTCN2019101429-appb-000119
Figure PCTCN2019101429-appb-000120
Figure PCTCN2019101429-appb-000121
其中
Figure PCTCN2019101429-appb-000122
为在支路xy发生故障时在断路器动作阶段(上标B表示断路器动作阶段)支路ij的故障波及标志(
Figure PCTCN2019101429-appb-000123
表示支路xy发生故障时在断路器动作阶段支路ij受故障波及而处于断电状态，
Figure PCTCN2019101429-appb-000124
表示支路xy发生故障时在断路器动作阶段支路ij处于正常运 行状态)，
Figure PCTCN2019101429-appb-000125
为在支路xy发生故障时在断路器动作阶段节点i的故障波及标志(
Figure PCTCN2019101429-appb-000126
表示支路xy发生故障时在断路器动作阶段节点i受故障波及而处于断电状态，
Figure PCTCN2019101429-appb-000127
表示支路xy发生故障时在断路器动作阶段节点i处于正常运行状态)。
Figure PCTCN2019101429-appb-000128
为在正常运行状态下(上标NO表示正常运行状态)支路ij上靠近节点i开关的状态(
Figure PCTCN2019101429-appb-000129
表示开关闭合，
Figure PCTCN2019101429-appb-000130
表示开关打开)，
Figure PCTCN2019101429-appb-000131
为在正常运行状态下支路ij上靠近节点j开关的状态(
Figure PCTCN2019101429-appb-000132
表示开关闭合，
Figure PCTCN2019101429-appb-000133
表示开关打开)。
Figure PCTCN2019101429-appb-000134
为在支路xy发生故障时支路ij上靠近节点i断路器的状态(
Figure PCTCN2019101429-appb-000135
表示断路器闭合，
Figure PCTCN2019101429-appb-000136
表示断路器打开)，
Figure PCTCN2019101429-appb-000137
为在支路xy发生故障时支路ij上靠近节点j断路器的状态(
Figure PCTCN2019101429-appb-000138
表示断路器闭合，
Figure PCTCN2019101429-appb-000139
表示断路器打开)，
Figure PCTCN2019101429-appb-000140
为在正常运行状态下支路ij上靠近节点i断路器的状态(
Figure PCTCN2019101429-appb-000141
表示断路器闭合，
Figure PCTCN2019101429-appb-000142
表示断路器打开)，
Figure PCTCN2019101429-appb-000143
为在正常运行状态下支路ij上靠近节点j断路器的状态(
Figure PCTCN2019101429-appb-000144
表示断路器闭合，
Figure PCTCN2019101429-appb-000145
表示断路器打开)。
Figure PCTCN2019101429-appb-000146
为在支路xy发生故障时节点i的故障影响标志(
Figure PCTCN2019101429-appb-000147
表示支路xy发生故障时节点i受故障影响，
Figure PCTCN2019101429-appb-000148
表示支路xy发生故障时节点i不受故障影响)。
2-2-5)开关动作约束，如式(95)-(105)所示：
Figure PCTCN2019101429-appb-000149
Figure PCTCN2019101429-appb-000150
Figure PCTCN2019101429-appb-000151
Figure PCTCN2019101429-appb-000152
Figure PCTCN2019101429-appb-000153
Figure PCTCN2019101429-appb-000154
Figure PCTCN2019101429-appb-000155
Figure PCTCN2019101429-appb-000156
Figure PCTCN2019101429-appb-000157
Figure PCTCN2019101429-appb-000158
Figure PCTCN2019101429-appb-000159
Figure PCTCN2019101429-appb-000160
其中，
Figure PCTCN2019101429-appb-000161
为在支路xy发生故障后在开关动作阶段(上标PF表示开关动作阶段)支路ij的维修影响标志(
Figure PCTCN2019101429-appb-000162
表示支路xy发生故障后在开关动作阶段支路ij受故障支路维修影响而处于断电状态，
Figure PCTCN2019101429-appb-000163
表示支路xy发生故障后在开关动作阶段支路ij不受故障支路维修影响而处于正常运行状态)，其中
Figure PCTCN2019101429-appb-000164
为在支路xy发生故障后在开关动作阶段节点i的维修影响标志(
Figure PCTCN2019101429-appb-000165
表示支路xy发生故障后节点i受故障支路维修影响而处于断电状态，
Figure PCTCN2019101429-appb-000166
表示支路xy发生故障后节点i不受故障支路维修影响而处于正常运行状态)。
Figure PCTCN2019101429-appb-000167
在支路xy发生故障后(开关动作后)节点i的供电标志(
Figure PCTCN2019101429-appb-000168
表示支路xy发生故障后(开关动作后)节点i正常供电，
Figure PCTCN2019101429-appb-000169
表示支路xy发生故障后节点i(开关动作后)处于断电状态)。
2-2-6)可靠性指标计算约束，如式(106)-(111)所示：
Figure PCTCN2019101429-appb-000170
Figure PCTCN2019101429-appb-000171
Figure PCTCN2019101429-appb-000172
Figure PCTCN2019101429-appb-000173
Figure PCTCN2019101429-appb-000174
Figure PCTCN2019101429-appb-000175
其中CID i表示i节点的用户中断持续时间，λ xy表示支路xy(如果xy＝tr f,f∈Ψ F时表示变压器f)的年故障率，
Figure PCTCN2019101429-appb-000176
表示支路xy(如果xy＝tr f,f∈Ψ F时表示变压器f)的故障开关动作中断时间(具体为从故障发生后到故障支路开关动作的时间)，
Figure PCTCN2019101429-appb-000177
表示支路xy(如果xy＝tr f,f∈Ψ F时表示变压器f)的故障修复中断时间(具体为从故障发生后到故 障修复的时间)，CIF i表示i节点的用户中断频率，NC i为给定的i节点的用户数量，SAIFI为系统年平均中断持续时间指数，ASAI为系统平均供电指数，EENS为期望失负荷能量，B为所有负荷水平的集合，Δ h为负荷水平h的年持续小时数，μ h≤1为负荷水平h的峰值负荷比，L i表示i节点的峰值负荷。
3)根据目标函数(38)和约束条件(39)-(74)，通过优化软件CPLEX或gurobi求解该优化模型，得到的CID i、CIF i、SAIDI、SAIFI、ASAI、EENS即为所求的可靠性评估指标。
利用个计算得到的结果，配电网管理人员可准确评估配电网的可靠性，进行系统可靠性指标分析、用户节点可靠性分析和馈线可靠性分析，进行不良指标分析。基于分析结果，根据配电网实际可靠性需求，开展供电薄弱环节分析，对配电网进行改进。

Claims (1)

  1. 一种基于混合整数线性规划的配电网可靠性指标计算方法，其特征在于，包括以下步骤：
    1)定义器件安装状态和支路故障后故障隔离、负荷转供和故障恢复动作原则，具体如下：在支路故障发生后，首先支路上游最靠近故障支路的断路器进入断路器动作阶段，先动作打开断路器、开断故障电流，此时断路器下游节点断电；之后，进入开关动作阶段，进行故障隔离，隔离故障支路；同时，通过开关和断路器动作进行网络重构，恢复断电节点负荷，假设恢复全部负荷或零负荷；而后，修复故障支路，修复后通过动作开关和断路器恢复原供电网络结构；
    2)构建基于混合整数线性规划模型的配电网可靠性指标优化模型，该模型由目标函数和约束条件构成；具体如下：
    2-1)确定模型的目标函数；
    该模型的目标函数为最小化系统年平均中断持续时间指数SAIDI，如式(38)所示：
    Minimize:SAIDI (75)
    2-2)确定模型的约束条件；具体如下：
    2-2-1)配电网功率平衡约束，如式(39)-(40)所示：
    Figure PCTCN2019101429-appb-100001
    Figure PCTCN2019101429-appb-100002
    其中，上标xy表示在支路xy发生故障下的场景，
    Figure PCTCN2019101429-appb-100003
    表示在支路xy发生故障时i节点的负荷，
    Figure PCTCN2019101429-appb-100004
    表示在支路xy发生故障时支路ij上由j节点流向i节点的功率，Ψ i表示与i节点直接相连的支路集合，Ψ LN表示负荷节点集合，Υ表示所有支路的集合，
    Figure PCTCN2019101429-appb-100005
    代表所有支路故障场景；
    2-2-2)支路功率约束，如式(41)-(43)所示：
    Figure PCTCN2019101429-appb-100006
    Figure PCTCN2019101429-appb-100007
    Figure PCTCN2019101429-appb-100008
    其中，M为正数，
    Figure PCTCN2019101429-appb-100009
    表示在支路xy发生故障时支路ij上靠近节点i开关的状态，
    Figure PCTCN2019101429-appb-100010
    表示开关闭合，
    Figure PCTCN2019101429-appb-100011
    表示开关打开，
    Figure PCTCN2019101429-appb-100012
    表示在支路xy发生故障时支 路ij上靠近节点j开关的状，
    Figure PCTCN2019101429-appb-100013
    表示开关闭合，
    Figure PCTCN2019101429-appb-100014
    表示开关打开，
    Figure PCTCN2019101429-appb-100015
    表示支路ij额定传输容量；
    2-2-3)变压器功率约束，如式(44)-(45)所示：
    Figure PCTCN2019101429-appb-100016
    Figure PCTCN2019101429-appb-100017
    其中，
    Figure PCTCN2019101429-appb-100018
    为在支路xy发生故障时变压器f的功率，
    Figure PCTCN2019101429-appb-100019
    为在支路xy发生故障时连接变压器f的支路tr f由变压器节点流向下游节点的功率，Ψ F表示所有变压器节点的集合；
    2-2-4)断路器动作约束，如式(46)-(57)所示：
    Figure PCTCN2019101429-appb-100020
    Figure PCTCN2019101429-appb-100021
    Figure PCTCN2019101429-appb-100022
    Figure PCTCN2019101429-appb-100023
    Figure PCTCN2019101429-appb-100024
    Figure PCTCN2019101429-appb-100025
    Figure PCTCN2019101429-appb-100026
    Figure PCTCN2019101429-appb-100027
    Figure PCTCN2019101429-appb-100028
    Figure PCTCN2019101429-appb-100029
    Figure PCTCN2019101429-appb-100030
    Figure PCTCN2019101429-appb-100031
    Figure PCTCN2019101429-appb-100032
    其中，上标B表示断路器动作阶段，
    Figure PCTCN2019101429-appb-100033
    为在支路xy发生故障时在断路器动作阶段支路ij的故障波及标志，
    Figure PCTCN2019101429-appb-100034
    表示支路xy发生故障时在断路器动作阶段支路ij受故障波及而处于断电状态，
    Figure PCTCN2019101429-appb-100035
    表示支路xy发生故障时在断路器动作阶段支路ij处于正常运行状态，F i xy,B为在支路xy发生故障时在断路器动作阶段节点i的故障波及标志，F i xy,B＝0表示支路xy发生故障时在断路器动作阶段节点i受故障波及而处于断电状态，F i xy,B＝1表示支路xy发生故障时在断路器动作阶段节点i处于正常运行状态；
    上标NO表示正常运行状态，
    Figure PCTCN2019101429-appb-100036
    为在正常运行状态下支路ij上靠近节点i开关的状态，
    Figure PCTCN2019101429-appb-100037
    表示开关闭合，
    Figure PCTCN2019101429-appb-100038
    表示开关打开，
    Figure PCTCN2019101429-appb-100039
    为在正常运行状态下支路ij上靠近节点j开关的状态，
    Figure PCTCN2019101429-appb-100040
    表示开关闭合，
    Figure PCTCN2019101429-appb-100041
    表示开关打开；
    Figure PCTCN2019101429-appb-100042
    为在支路xy发生故障时支路ij上靠近节点i断路器的状态，
    Figure PCTCN2019101429-appb-100043
    表示断路器闭合，
    Figure PCTCN2019101429-appb-100044
    表示断路器打开，
    Figure PCTCN2019101429-appb-100045
    为在支路xy发生故障时支路ij上靠近节点j断路器的状态，
    Figure PCTCN2019101429-appb-100046
    表示断路器闭合，
    Figure PCTCN2019101429-appb-100047
    表示断路器打开，
    Figure PCTCN2019101429-appb-100048
    为在正常运行状态下支路ij上靠近节点i断路器的状态，
    Figure PCTCN2019101429-appb-100049
    表示断路器闭合，
    Figure PCTCN2019101429-appb-100050
    表示断路器打开，
    Figure PCTCN2019101429-appb-100051
    为在正常运行状态下支路ij上靠近节点j断路器的状态，
    Figure PCTCN2019101429-appb-100052
    表示断路器闭合，
    Figure PCTCN2019101429-appb-100053
    表示断路器打开；
    Figure PCTCN2019101429-appb-100054
    为在支路xy发生故障时节点i的故障影响标志，
    Figure PCTCN2019101429-appb-100055
    表示支路xy发生故障时节点i受故障影响，
    Figure PCTCN2019101429-appb-100056
    表示支路xy发生故障时节点i不受故障影响；
    2-2-5)开关动作约束，如式(58)-(68)所示：
    Figure PCTCN2019101429-appb-100057
    Figure PCTCN2019101429-appb-100058
    Figure PCTCN2019101429-appb-100059
    Figure PCTCN2019101429-appb-100060
    Figure PCTCN2019101429-appb-100061
    Figure PCTCN2019101429-appb-100062
    Figure PCTCN2019101429-appb-100063
    Figure PCTCN2019101429-appb-100064
    Figure PCTCN2019101429-appb-100065
    Figure PCTCN2019101429-appb-100066
    Figure PCTCN2019101429-appb-100067
    Figure PCTCN2019101429-appb-100068
    其中，上标PF表示开关动作阶段，
    Figure PCTCN2019101429-appb-100069
    为在支路xy发生故障后在开关动作阶段支路ij的维修影响标志，
    Figure PCTCN2019101429-appb-100070
    表示支路xy发生故障后在开关动作阶段支路ij受故障支路维修影响而处于断电状态，
    Figure PCTCN2019101429-appb-100071
    表示支路xy发生故障后在开关动作阶段支路ij不受故障 支路维修影响而处于正常运行状态，F i xy,PF为在支路xy发生故障后在开关动作阶段节点i的维修影响标志，F i xy,PF＝0表示支路xy发生故障后节点i受故障支路维修影响而处于断电状态，F i xy,PF＝1表示支路xy发生故障后节点i不受故障支路维修影响而处于正常运行状态；
    Figure PCTCN2019101429-appb-100072
    在支路xy发生故障后完成开关动作后节点i的供电标志，
    Figure PCTCN2019101429-appb-100073
    表示支路xy发生故障后完成开关动作后节点i正常供电，
    Figure PCTCN2019101429-appb-100074
    表示支路xy发生故障后完成开关动作后节点i处于断电状态；
    2-2-6)可靠性指标计算约束，如式(69)-(74)所示：
    Figure PCTCN2019101429-appb-100075
    Figure PCTCN2019101429-appb-100076
    Figure PCTCN2019101429-appb-100077
    Figure PCTCN2019101429-appb-100078
    Figure PCTCN2019101429-appb-100079
    Figure PCTCN2019101429-appb-100080
    其中，CID i表示i节点的用户中断持续时间，λ xy表示支路xy的年故障率，
    Figure PCTCN2019101429-appb-100081
    表示支路xy的故障开关动作中断时间，
    Figure PCTCN2019101429-appb-100082
    表示支路xy的故障修复中断时间，CIF i表示i节点的用户中断频率，NC i为给定的i节点的用户数量，SAIFI为系统年平均中断持续时间指数，ASAI为系统平均供电指数，EENS为期望失负荷能量，B为所有负荷水平的集合，Δ h为负荷水平h的年持续小时数，μ h≤1为负荷水平h的峰值负荷比，L i表示i节点的峰值负荷；
    3)根据目标函数(38)和约束条件(39)-(74)，求解该优化模型，得到的CID i、CIF i、SAIDI、SAIFI、ASAI、EENS即为所求的可靠性评估指标。
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