WO2019033820A1 - 一种电力系统静态电压稳定域边界快速搜索的优化模型 - Google Patents

一种电力系统静态电压稳定域边界快速搜索的优化模型 Download PDF

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WO2019033820A1
WO2019033820A1 PCT/CN2018/088797 CN2018088797W WO2019033820A1 WO 2019033820 A1 WO2019033820 A1 WO 2019033820A1 CN 2018088797 W CN2018088797 W CN 2018088797W WO 2019033820 A1 WO2019033820 A1 WO 2019033820A1
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power
power system
point
growth direction
voltage stability
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French (fr)
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姜涛
李雪
袁昊宇
陈厚合
李国庆
张明宇
李晓辉
张儒峰
王长江
张嵩
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东北电力大学
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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
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in 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
    • 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
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/04—Programme control other than numerical control, i.e. in sequence controllers or logic controllers
    • G05B19/042—Programme control other than numerical control, i.e. in sequence controllers or logic controllers using digital processors
    • 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
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • 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
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/26—Pc applications
    • G05B2219/2639—Energy management, use maximum of cheap power, keep peak load low
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • 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
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • 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 relates to the field of voltage stability domain boundary, in particular to a problem of accurately, quickly and efficiently searching for a static voltage stability domain of a power system based on an optimization model.
  • HVDC transmission technology has further improved the flexibility of power transmission while reducing costs, and provided conditions for large-scale renewable energy grid-connected and long-distance transmission.
  • the power system will develop rapidly in a green and intelligent direction.
  • the high-permeability renewable energy grid connection and the power system power electronics have increased the randomness of the injected power and the strong coupling of the AC-DC network, resulting in a huge change in the operating characteristics of the traditional power system, and the operating conditions are even more Complex and variable, increasing the difficulty of power system voltage stability assessment. Therefore, it is of great practical significance to study the voltage stability assessment method applicable to the background of large-scale renewable energy grid-connected and power system power electronics.
  • the volatility, randomness and uncertainty of renewable energy bring new challenges to the stable assessment of static voltage in power systems.
  • the Static Voltage Stability Region is an operating region that describes the static voltage stability of the system under the network topology and parameters. It is the analysis and evaluation of the static voltage of the power system with random and uncertain factors. An important tool for stability. However, although SVSR can comprehensively and intuitively evaluate the voltage stability of power system under the influence of multiple uncertainties and random factors, the search of SVSR boundary is the key to construct SVSR.
  • the fitting method can construct a high-precision SVSR, its calculation efficiency is low;
  • the hyperplane approximation method can improve the construction efficiency of SVSR, but the SVSR constructed by it is more conservative.
  • the boundary topology characteristics are extremely complex, and it is difficult to describe or obtain a general conclusion of accurate approximation using a unified hyperplane analytical expression. Therefore, it is necessary to study in depth the accurate, fast, efficient and universal SVSR construction method.
  • the invention provides an optimization model for fast searching of a static voltage stability domain boundary of a power system.
  • the invention not only inherits the characteristics of a high-precision search SNB (saddle-node bifurcation) point of a traditional optimal power flow (OPF) model. It also effectively reduces the time spent searching for a single SNB point, significantly improving the efficiency of the construction of the power system SVSR, as described below:
  • An optimization model for fast searching of a static voltage stability domain boundary of a power system comprising the following steps:
  • the traditional power flow is used to search the first power system saddle node bifurcation point, and map it to the two-dimensional active injection space to obtain the static voltage stability domain boundary point;
  • the step of searching for the first power system saddle node bifurcation point by using the traditional optimal power flow and mapping it to the two-dimensional active injection space is specifically as follows:
  • the first power system saddle node bifurcation point is mapped into a two-dimensional active injection space with the active injection power of the nodes i, j as the horizontal and vertical coordinate axes, respectively.
  • the power growth direction angle is specifically:
  • ⁇ is the step size of the power growth direction angle
  • the optimization model is:
  • k is the saddle node bifurcation point of the kth to-be-searched power system
  • ⁇ k-1 is the load margin corresponding to the obtained k- 1th power system saddle node bifurcation point
  • x k-1 is The vector of the system state variable corresponding to the saddle node bifurcation point of the k-1th power system
  • ⁇ k is the new state variable when searching for the saddle node bifurcation point of the kth to-be-searched power system
  • d k is the kth The direction of power growth
  • g(x k-1 ) is the power flow equation for the k-1th search.
  • the new power growth direction is:
  • d 2- [ ⁇ P 1 L ⁇ P i-1 , ⁇ P i , ⁇ P i+1 L ⁇ P j-1 , ⁇ P j , ⁇ P j+1 L ⁇ P n b, ⁇ Q 1 L ⁇ Q l ] T
  • ⁇ P 1 to ⁇ P n represent the active power components of the PV and PQ node power growth directions
  • ⁇ Q 1 to ⁇ Q l represent the reactive power components of the PQ node power growth direction
  • ⁇ P i and ⁇ P j respectively represent the corresponding directions in the power growth direction The active power component of nodes i, j.
  • the latest power growth direction angle is specifically:
  • ⁇ is the step size of the power growth direction angle
  • This method takes the SNB on the known SVSR boundary as the initial point, and uses the relevant information of the initial point as the initial value of the proposed optimization model to search for the next pending SNB point, which can realize the static power system in the two-dimensional active power injection space. Fast search of voltage stability domain boundaries;
  • the method greatly reduces the calculation time of the static voltage stability domain construction of the power system, and significantly improves the construction efficiency of the voltage stability domain of the power system. With higher precision;
  • the method can be applied to the voltage stability domain construction of the actual power system, and the sensing ability of the voltage stability state of the large power grid can be further improved compared with the existing method.
  • FIG. 1 is a schematic diagram of an optimized model search SVSR boundary of a power system static voltage stability domain boundary fast search provided by the present invention
  • FIG. 2 is a flow chart of an optimized model search SVSR boundary of a power system static voltage stability domain boundary fast search provided by the present invention
  • WECC-3 machine 9 node (Western Electricity Coordinating Council) test system diagram
  • FIG. 4 is a schematic diagram of the SVSR of the active power consumption of the load node of the 9-node system coordinate axis of the WECC-3 machine;
  • Figure 5 is a comparison of calculation errors for the SVSR boundary.
  • the embodiment of the present invention proposes an optimization model for the fast search of the static voltage stability domain boundary of the power system according to the similarity of adjacent SNB points on the SVSR boundary of the power system.
  • the optimization model can construct high-precision SVSR for the OPF model, it is necessary to search the power system on the SVSR boundary with the ground state as the initial point.
  • the SNB point has a long-term deficiency. It is proposed that the SNB on the known SVSR boundary is the initial point.
  • the initial point related information is the initial value of the proposed optimization model, and the next pending SNB point is searched, which effectively improves the search efficiency of the SNB point.
  • the static voltage stability domain of the power system is a multi-dimensional space surrounded by all saddle junctions in the system.
  • the system operates in the static voltage stability domain constructed with the saddle node bifurcation as the boundary. It is a necessary condition for maintaining voltage stability, so static
  • the search for the voltage stability domain boundary can be equivalent to the search for the power system saddle node bifurcation point.
  • An embodiment of the present invention provides an optimization model for fast boundary search of a static voltage stability domain of a power system. As shown in FIG. 1 and FIG. 2, the method includes the following steps:
  • the embodiment of the present invention searches for the saddle node bifurcation point of the next power system to be sought by using the above-mentioned steps 101-step 104 with the saddle node bifurcation point on the boundary of the known static voltage stability domain as the initial point;
  • This process not only inherits the characteristics of the traditional optimal power flow model high-precision search power system saddle node bifurcation point, but also effectively reduces the time consuming of traditional optimal power flow search for single power system saddle node bifurcation point, and significantly improves the static of power system.
  • the construction efficiency of the voltage stability domain is not only inherits the characteristics of the traditional optimal power flow model high-precision search power system saddle node bifurcation point, but also effectively reduces the time consuming of traditional optimal power flow search for single power system saddle node bifurcation point, and significantly improves the static of power system.
  • Embodiment 1 is further introduced in the following with reference to a specific calculation formula and a drawing, as described in the following:
  • step 201 includes:
  • n b +1 nodes, among which PQ (that is, active power and reactive power are known) nodes, PV (that is, active power and voltage amplitude are known) node n b -l, number 0 is the balance node, number 1 ⁇ l is the PQ node, number l+1 ⁇ n b is the PV node, and the first power growth direction d 1 is set as follows:
  • d 1 [ ⁇ P 1 L ⁇ P i-1 , ⁇ P i , ⁇ P i+1 L ⁇ P j-1 , ⁇ P j , ⁇ P j+1 L ⁇ P n b, ⁇ Q 1 L ⁇ Q l ] T (1)
  • x 1 represents the vector of the state variable corresponding to the first power system saddle node bifurcation point
  • g(x 1 ) represents the power system conventional power flow equation expression
  • ⁇ 1 is the first power system saddle node bifurcation point
  • d 1 is the first power growth direction.
  • step 202 includes:
  • step 203 includes:
  • ⁇ is the step size of the power growth direction angle
  • d 2- [ ⁇ P 1 L ⁇ P i-1 , ⁇ P i , ⁇ P i+1 L ⁇ P j-1 , ⁇ P j , ⁇ P j+1 L ⁇ P n b, ⁇ Q 1 L ⁇ Q l ] T (4)
  • step 204 includes:
  • k is the saddle node bifurcation point of the kth to-be-searched power system
  • ⁇ k-1 is the load margin corresponding to the obtained k- 1th power system saddle node bifurcation point
  • x k-1 is The vector of the system state variable corresponding to the saddle node bifurcation point of the k-1th power system
  • d k is the kth power growth direction
  • g(x k-1 ) is the power flow equation for the k-1th search
  • ⁇ k is the new state variable when searching for the saddle node bifurcation point of the kth to-be-searched power system
  • ⁇ k-1 together with the ⁇ k-1 represents the load margin ⁇ k of the saddle node bifurcation point of the kth to-be-searched power system.
  • ⁇ k-1 ⁇ k .
  • step 205 Map the new power system saddle node bifurcation point into the two-dimensional active injection space, obtain a new static voltage stability domain boundary point, perform the same steps as step 202 again, verify ⁇ , and if ⁇ is less than or equal to 0, continue Go to step 206, otherwise return to step 203;
  • step 205 includes:
  • the state variables (x k , ⁇ k ) of the saddle-junction points of the power system are mapped to the two-dimensional active injection space with the active injection power of the nodes i and j as the horizontal and vertical axes, respectively, to obtain the static voltage.
  • step 206 includes:
  • d 1 [ ⁇ P 1 L ⁇ P i-1 , ⁇ P i , ⁇ P i+1 L ⁇ P j-1 , ⁇ P j , ⁇ P j+1 L ⁇ P n b, ⁇ Q 1 L ⁇ Q l ] T (9)
  • step 207 includes:
  • ⁇ is the step size of the power growth direction angle
  • step 208 Perform the same steps as step 204 and step 202 in sequence;
  • step 208 includes:
  • step 204 1) performing the same steps as step 204, that is, using an optimization model of the power system static voltage stability domain boundary fast search to search for the saddle node bifurcation point of the power system in the new power growth direction;
  • the state variables (x k , ⁇ k ) of the saddle node bifurcation points of the power system are mapped to the two-dimensional active injection space with the active injection power of the nodes i and j as the horizontal and vertical coordinate axes, respectively, to obtain static voltage stability.
  • step 209 Verify that ⁇ ' is greater than or equal to 90°. If yes, all the obtained static voltage stability domain boundary points are sequentially connected to obtain a static voltage stability domain boundary, and the process ends; otherwise, return to step 207.
  • the foregoing steps 201-209 of the present invention not only inherit the characteristics of the high-precision search SNB of the traditional OPF model, but also effectively reduce the time-consuming of searching for a single SNB point, and significantly improve the construction efficiency of the power system SVSR.
  • This example is to verify the effectiveness of the method by searching the WEC 3 machine 9-node system SVSR boundary.
  • the WECC3 machine 9-node test system is shown in Figure 3.
  • the load nodes 5 and 7 are used as voltage stabilization key nodes, and the active power injection of nodes 5 and 7 is selected as the coordinate axis.
  • the optimized model of the method is used to search the SVSR boundary in the two-dimensional active load injection space.
  • the corresponding power growth direction angle ⁇ 5 0.7328rad
  • the search obtains the optimal solution of satisfying equation (4)
  • the above SNB point is taken as the initial point, and the relevant information is used as the initial value of the optimization model proposed by equation (7).
  • the optimization model proposed by this method is reduced along the ⁇ k in the first quadrant shown in Fig. 4. Searching for the SNB point in the small direction gives the SNB points 4, 3, 2, 1, and 0. The detailed results are shown in Table 1.
  • the method is used to search the SNB point along the ⁇ increasing direction, and the SNB points 6, 7, 8, 9, 10 are obtained until the SNB point 11, and at this time, there is ⁇ 11 > ⁇ /2, the search SNB search in the direction of increasing ⁇ is ended. So far, all the SNB points searched in the first quadrant of the two-dimensional active power injection space by the optimization model proposed by the method are shown in FIG. 4 . Connect all the SNB points in Figure 4 one by one to obtain the SVSR boundary in the first quadrant of the node 5, 7 active power injection space.
  • the accuracy of the SNB point obtained by the optimization model and the OPF search using this method is much higher than that of the SNB point obtained by CPF tracking.
  • the minimum eigenvalue is 1.3256 ⁇ 10 -4
  • the maximum value is 3.85 ⁇ 10 -2
  • the average minimum eigenvalue is 1.06 ⁇ 10 -2 .
  • the average values of the minimum eigenvalues obtained by the optimization model and OPF calculated by this method are 5.6286 ⁇ 10 -7 and 2.1656 ⁇ 10 -7 respectively .
  • the calculation accuracy of the two algorithms is approximately equal and significantly higher than CPF.
  • the model of each device is not limited unless otherwise specified, as long as the device capable of performing the above functions can be used.

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Abstract

本发明公开一种电力系统静态电压稳定域边界快速搜索的优化模型，包括：以基态潮流为起始点，采用传统最优潮流搜索第一个电力系统鞍结分岔点，将其映射至二维有功注入空间，获取静态电压稳定域边界点；重复向功率增长方向角减小的方向改变功率增长方向，通过优化模型搜索新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；若功率增长方向角小于等于0则返回第一个电力系统鞍结分岔点：重复向功率增长方向角增大的方向再次改变功率增长方向，重新搜索最新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；若最新的功率增长方向角大于等于90°，则将所有静态电压稳定域边界点顺次连接，获取静态电压稳定域边界。

Description

一种电力系统静态电压稳定域边界快速搜索的优化模型 技术领域
本发明涉及电压稳定域边界领域，尤其涉及一种基于优化模型实现电力系统静态电压稳定域的准确、快速、高效搜索的问题。
背景技术
环境问题的日益紧张，要求电力系统在提供持续、可靠、优质电能的同时，加快一次能源转型，减少对化石燃料依赖。近年来，随着大功率电力电子器件的技术革新，使得高压直流输电技术在降低成本的同时，进一步提高了电能传输的灵活性，为大规模可再生能源并网和远距离传输提供了条件，使电力系统向绿色化、智能化方向迅速发展。与此同时，高渗透率可再生能源并网、以及电力系统电力电子化加剧了注入功率的随机性和交直流网络的强耦合性，导致传统电力系统运行特性发生巨大变化，运行工况更为复杂多变，加大了电力系统电压稳定评估的难度。为此，研究适用于大规模可再生能源并网和电力系统电力电子化背景下的电压稳定评估方法具有十分重要的实际意义。可再生能源的波动性、随机性和不确定性给电力系统静态电压的稳定评估带来全新挑战。
静态电压稳定域(Static voltage stability region,SVSR)是描述确定网络拓扑结构和参数下，系统具有静态电压稳定性的运行区，是分析、评估含随机性和不确定性因素影响的电力系统静态电压稳定性的重要工具。然而SVSR虽可全面、直观评估电力系统在多重不确定性、随机性因素影响下的电压稳定性，但SVSR边界的搜索是构建SVSR的关键。
目前，SVSR边界的搜索主要为基于连续潮流(continuation power flow，CPF)的拟合法和超平面近似法：
1、拟合法虽可构建高精度的SVSR但其计算效率低；
2、超平面近似法可提高SVSR构建效率但其构建的SVSR保守性较强。此外，边界拓扑特性极为复杂，难以用统一的超平面解析式描述或获取准确近似的通用性结论。因此，有必要深入研究准确、快速、高效、通用的SVSR构建方法。
发明内容
本发明提供了一种电力系统静态电压稳定域边界快速搜索的优化模型，本发明不仅继承了传统最优潮流(optimal power flow,OPF)模型高精度搜索SNB(鞍结分岔)点的特点， 还有效降低了搜索单个SNB点的耗时，显著提高了电力系统SVSR的构建效率，详见下文描述：
一种电力系统静态电压稳定域边界快速搜索的优化模型，所述方法包括如下步骤：
以基态潮流为起始点，采用传统最优潮流搜索第一个电力系统鞍结分岔点，将其映射至二维有功注入空间，获取静态电压稳定域边界点；
重复向功率增长方向角减小的方向改变功率增长方向，通过优化模型搜索新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；若功率增长方向角小于等于0则返回第一个电力系统鞍结分岔点：
重复向功率增长方向角增大的方向再次改变功率增长方向，重新搜索最新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；
若最新的功率增长方向角大于等于90°，则将所有静态电压稳定域边界点顺次连接，获取静态电压稳定域边界。
所述采用传统最优潮流搜索第一个电力系统鞍结分岔点，将其映射至二维有功注入空间步骤具体为：
将第一个电力系统鞍结分岔点映射至分别以节点i、j的有功注入功率为横纵坐标轴的二维有功注入空间内。
其中，所述功率增长方向角具体为:
Figure PCTCN2018088797-appb-000001
式中，Δβ为功率增长方向角的步长；定义ΔP i0＝ΔP i、ΔP j0＝ΔP j分别表示上一电力系统鞍结分岔点对应的功率增长方向中对应于节点i、j的有功功率分量。
所述优化模型为：
min -η k
s.t. g(x k-1)+η kλ k-1d k＝0
式中，k为第k个待搜索电力系统鞍结分岔点；λ k-1为已求的第k-1个电力系统鞍结分岔点所对应的负荷裕度；x k-1为第k-1个电力系统鞍结分岔点所对应的系统状态变量的向量；η k为搜索第k个待搜索电力系统鞍结分岔点时的新增状态变量；d k为第k个功增长方向；g(x k-1)为进行第k-1次搜索时的潮流方程。
其中，所述新功率增长方向为：
d 2-＝[ΔP 1LΔP i-1,ΔP i,ΔP i+1LΔP j-1,ΔP j,ΔP j+1LΔP nb,ΔQ 1LΔQ l] T
Figure PCTCN2018088797-appb-000002
Figure PCTCN2018088797-appb-000003
式中，ΔP 1至ΔP n表示PV和PQ节点功率增长方向的有功功率分量；ΔQ 1至ΔQ l表示PQ节点功率增长方向的无功功率分量；ΔP i、ΔP j分别表示功率增长方向中对应于节点i、j的有功功率分量。
其中，所述最新的功率增长方向角具体为：
Figure PCTCN2018088797-appb-000004
式中，Δβ为功率增长方向角的步长；定义ΔP i0＝ΔP i、ΔP j0＝ΔP j分别表示上一电力系统鞍结分岔点对应的功率增长方向中对应于节点i、j的有功功率分量。
本发明提供的技术方案的有益效果是：
1、本方法以已知SVSR边界上SNB为初始点，将该初始点的相关信息作为所提优化模型初值，搜索下一待求SNB点，可实现二维有功功率注入空间中电力系统静态电压稳定域边界的快速搜索；
2、相比现有的基于CPF、OPF的静态电压稳定域构建方法的计算效率，本方法大幅降低了电力系统静态电压稳定域构建的计算时间，显著提高了电力系统电压稳定域的构建效率，具有更高的精度；
3、本方法可应用于实际电力系统的电压稳定域构建，相比于现有方法可进一步提高大电网电压稳定态势的感知能力。
附图说明
图1是本发明提供的一种电力系统静态电压稳定域边界快速搜索的优化模型搜索SVSR边界的示意图；
图2是本发明提供的一种电力系统静态电压稳定域边界快速搜索的优化模型搜索SVSR边界的流程图；
图3是WECC-3机9节点(Western Electricity Coordinating Council)测试系统图；
图4是WECC-3机9节点系统坐标轴为负荷节点的有功消耗的SVSR的示意图；
图5是SVSR边界的计算误差对比图。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚，下面对本发明实施方式作进一步地详 细描述。
为了实现电力系统SVSR的准确、快速、高效构建，本发明实施例依据电力系统SVSR边界上相邻SNB点存在近似性的特征，提出一种电力系统静态电压稳定域边界快速搜索的优化模型。
该优化模型针对OPF模型虽可构造高精度SVSR，但需以基态为初始点搜索SVSR边界上电力系统，SNB点存在耗时久的不足，提出以已知SVSR边界上SNB为初始点，以该初始点相关信息为所提优化模型的初值，搜索下一待求SNB点，有效提高了SNB点的搜索效率。
电力系统的静态电压稳定域是由系统中所有鞍结分岔点围成的多维空间，系统运行在以鞍结分岔点为边界构建的静态电压稳定域内是维持电压稳定的必要条件，因此静态电压稳定域边界的搜索可等效为电力系统鞍结分岔点的搜索。
实施例1
本发明实施例提供了一种电力系统静态电压稳定域边界快速搜索的优化模型，如图1、图2所示，该方法包括以下步骤：
101：以基态潮流为起始点，采用传统最优潮流搜索第一个电力系统鞍结分岔点，将其映射至二维有功注入空间，获取静态电压稳定域边界点；
102：重复向功率增长方向角减小的方向改变功率增长方向，通过优化模型搜索新功率增长方向下的电力系统鞍结分岔点；并映射至二维有功注入空间内，获取新的静态电压稳定域边界点，若功率增长方向角小于等于0则返回第一个电力系统鞍结分岔点：
103：重复向功率增长方向角增大的方向再次改变功率增长方向，重新搜索最新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；
104：若最新的功率增长方向角大于等于90°，则将所有静态电压稳定域边界点顺次连接，获取静态电压稳定域边界。
综上所述，本发明实施例通过上述步骤101-步骤104以已知静态电压稳定域边界上电力系统鞍结分岔点为初始点，搜索下一待求电力系统鞍结分岔点；通过该处理不仅继承了传统最优潮流模型高精度搜索电力系统鞍结分岔点的特点，还有效降低了传统最优潮流搜索单个电力系统鞍结分岔点的耗时，显著提高了电力系统静态电压稳定域的构建效率。
实施例2
下面结合具体的计算公式、附图对实施例1中的方案进行进一步地介绍，详见下文描述：
201：以基态潮流为起始点，采用传统最优潮流搜索第一个电力系统鞍结分岔点；
其中，该步骤201包括：
1)获取基础数据，包括：电力系统拓扑结构、支路参数和基态潮流状态变量x 0；
该获取基础数据的步骤为本领域技术人员所公知，本发明实施例对此不做赘述。
2)设电力系统共有n b+1个节点，其中，PQ(即有功功率和无功功率为已知量)节点l个，PV(即有功功率和电压幅值为已知量)节点n b-l个，编号0为平衡节点，编号1～l为PQ节点，编号l+1～n b为PV节点，设置第一个功率增长方向d 1如下：
d 1＝[ΔP 1LΔP i-1,ΔP i,ΔP i+1LΔP j-1,ΔP j,ΔP j+1LΔP nb,ΔQ 1LΔQ l] T     (1)
式中，n为PV和PQ节点的总数；ΔP 1至ΔP n表示PV和PQ节点功率增长方向的有功功率分量；ΔQ 1至ΔQ l表示PQ节点功率增长方向的无功功率分量；ΔP i、ΔP j分别表示功率增长方向中对应于节点i、j的有功功率分量；取ΔP i＝ΔP j＝1，其余节点功率增长方向的有功功率分量和无功功率分量为0。
3)采用传统最优潮流搜索第一个电力系统鞍结分岔点的模型如下：
min -λ 1           (2)
s.t. g(x 1)+λ 1d 1＝0
式中，x 1表示第一个电力系统鞍结分岔点对应的状态变量的向量；g(x 1)表示电力系统常规潮流方程表达式；λ 1为第一个电力系统鞍结分岔点对应的电力系统负荷裕度；d 1为第一个功率增长方向。
4)以基态潮流状态变量x 0为初值，带入传统最优潮流搜索第一个电力系统鞍结分岔点的模型中，计算得到(x 1,λ 1)，即第一个电力系统鞍结分岔点的状态变量信息。
202：将所得电力系统鞍结分岔点映射至二维有功注入空间内，得静态电压稳定域边界点；
其中，该步骤202包括：
1)分别以节点i、j的有功注入功率为横纵坐标轴建立二维有功注入空间；
2)将第k(搜索第一个电力系统鞍结分岔点时，k＝1)个电力系统鞍结分岔点的状态变量(x k,λ k)映射至分别以节点i、j的有功注入功率为横纵坐标轴的二维有功注入空间内，得到静态电压稳定域边界点(λ kΔP i,λ kΔP j)。
203：重复向第一功率增长方向角β减小的方向改变功率增长方向，获取改变的新功率增长方向；
其中，该步骤203包括：
1)定义第一功率增长方向角如下：
Figure PCTCN2018088797-appb-000005
式中，Δβ为功率增长方向角的步长；定义ΔP i0＝ΔP i、ΔP j0＝ΔP j分别表示上一电力系统鞍结分岔点对应的功率增长方向中对应于节点i、j的有功功率分量。
2)将功率增长方向d 1更新为向第一功率增长方向角β减小的方向改变的新功率增长方向d 2-，如下式：
d 2-＝[ΔP 1LΔP i-1,ΔP i,ΔP i+1LΔP j-1,ΔP j,ΔP j+1LΔP nb,ΔQ 1LΔQ l] T        (4)
式中，ΔP i和ΔP j的取值分别如下式：
Figure PCTCN2018088797-appb-000006
Figure PCTCN2018088797-appb-000007
204：采用电力系统静态电压稳定域边界快速搜索的优化模型搜索新功率增长方向下的电力系统鞍结分岔点；
其中，该步骤204包括：
1)电力系统静态电压稳定域边界快速搜索的优化模型如下：
min -η k          (7)
s.t. g(x k-1)+η kλ k-1d k＝0          (8)
式中，k为第k个待搜索电力系统鞍结分岔点；λ k-1为已求的第k-1个电力系统鞍结分岔点所对应的负荷裕度；x k-1为第k-1个电力系统鞍结分岔点所对应的系统状态变量的向量；d k为第k个功率增长方向；g(x k-1)为进行第k-1次搜索时的潮流方程；η k为搜索第k个待搜索电力系统鞍结分岔点时的新增状态变量，与λ k-1共同表示第k个待搜索电力系统鞍结分岔点的负荷裕度λ k＝λ k-1η k。
2)以第k-1个电力系统鞍结分岔点所对应的系统状态变量的向量x k-1为初值，带入电力系统静态电压稳定域边界快速搜索的优化模型中，计算得到(x k,λ κ-1η k)，即第k个电力系统鞍结分岔点的状态变量信息。
205：将新电力系统鞍结分岔点映射至二维有功注入空间内，获取新的静态电压稳定域边界点，再次执行与步骤202相同的步骤，校验β，若β小于等于0则继续执行步骤206，否则返回至步骤203；
其中，该步骤205包括：
1)再次执行与步骤202相同步骤，即分别以节点i、j的有功注入功率为横纵坐标轴建立二维有功注入空间；将第k(搜索第一个电力系统鞍结分岔点时，k＝1)个电力系统鞍结分岔点的状态变量(x k,λ k)映射至分别以节点i、j的有功注入功率为横纵坐标轴的二维有功注入空间内，得到静态电压稳定域边界点(λ kΔP i,λ kΔP j)；
2)校验β，若β小于等于0则继续执行步骤206，否则返回至步骤203。
206：返回第一个电力系统鞍结分岔点为起始点；
其中，该步骤206包括：
1)将功率增长方向重新设置为第一个功率增长方向d 1如下：
d 1＝[ΔP 1LΔP i-1,ΔP i,ΔP i+1LΔP j-1,ΔP j,ΔP j+1LΔP nb,ΔQ 1LΔQ l] T       (9)
式中，取ΔP i＝ΔP j＝1，其余节点功率增长方向的有功功率分量和无功功率分量为0。
2)调出第一个电力系统鞍结分岔点的信息，即(x 1,λ 1)。
207：重复向第二功率增长方向角β′增大的方向改变功率增长方向；
其中，该步骤207包括：
1)定义第二功率增长方向角如下：
Figure PCTCN2018088797-appb-000008
式中，Δβ为功率增长方向角的步长；定义ΔP i0＝ΔP i、ΔP j0＝ΔP j分别表示上一电力系统鞍结分岔点对应的功率增长方向中对应于节点i、j的有功功率分量。
2)将功率增长方向d 1更新为向第二功率增长方向角β′减小方向改变的新功率增长方向d 2-，如下式：
d 2+＝[ΔP 1LΔP i-1,ΔP i,ΔP i+1LΔP j-1,ΔP j,ΔP j+1LΔP nb,ΔQ 1LΔQ l] T    (11)
式中，ΔP i和ΔP j的取值分别如下式：
Figure PCTCN2018088797-appb-000009
Figure PCTCN2018088797-appb-000010
208：依次分别执行与步骤204、步骤202相同的步骤；
其中，该步骤208包括：
1)执行与步骤204相同步骤，即采用电力系统静态电压稳定域边界快速搜索的优化模型搜索新功率增长方向下的电力系统鞍结分岔点；
2)执行与步骤202相同步骤，即分别以节点i、j的有功注入功率为横纵坐标轴建立二维有功注入空间；将第k(搜索第一个电力系统鞍结分岔点时，k＝1)个电力系统鞍结分 岔点的状态变量(x k,λ k)映射至分别以节点i、j的有功注入功率为横纵坐标轴的二维有功注入空间内，得到静态电压稳定域边界点(λ kΔP i,λ kΔP j)；
209：校验β′是否大于等于90°，如果是，则将所有所得静态电压稳定域边界点顺次连接，得静态电压稳定域边界，流程结束；否则，返回至步骤207。
综上所述，本发明实施例通过上述步骤201-步骤209不仅继承了传统OPF模型高精度搜索SNB的特点，还有效降低了搜索单个SNB点的耗时，显著提高了电力系统SVSR构建效率。
实施例3
下面结合具体的实例对实施例1和2中的方案进行可行性验证，详见下文描述：
本实例是以搜索WECC 3机9节点系统SVSR边界为例，验证本方法的有效性，WECC3机9节点测试系统如图3所示。
以负荷节点5、7为电压稳定关键节点，选取节点5、7的有功功率注入为坐标轴，在二维有功负荷注入空间内采用本方法所提优化模型搜索SVSR边界。
设置功率增长方向角步长Δβ＝0.15rad，收敛精度为10 -8。以基态为初始点，初始功率增长方向d 5＝[ΔS d2,ΔS d3,ΔS d4,ΔS d5,ΔS d6,ΔS d7,ΔS d8,ΔS d9] T＝[0,0,0,0.6690,0,0.7433,0,0] T，对应的功率增长方向角β 5＝0.7328rad，采用式(4)所提的优化模型，沿初始功率增长方向d 5，搜索得到满足式(4)最优解的系统最大负荷裕度λ 5＝2.3233，其运行点对应图4中SNB点5，坐标为(2.3233,2.0910)。
进一步由d 5、β 5和Δβ，可得β 4＝0.5828rad，其对应的功率增长方向d 4＝[0,0,0,0.5504,0,0.8349,0,0] T。以SNB点5为初始点，(x 5,λ 5)为式(7)的初值，令η＝1，采用式(7)所提优化模型沿功率增长方向d 4搜索下一SNB点4，得到功率增长方向d 4下，满足式(7)最优解的目标值η 4＝1.0208，该方向下系统的最大负荷裕度λ 4＝η 4×λ 5＝2.3717，其在图4中SNB点4的坐标为(2.6640,1.7561)。以此类推，以上一已求SNB点为初始点，其相关信息作为式(7)所提优化模型的初值，采用本方法所提优化模型在图4所示第一象限内沿β k减小方向搜索SNB点，可得SNB点4、3、2、1、0，详细结果如表1所示。
表1 基于本方法搜索SNB点结果
Figure PCTCN2018088797-appb-000011
Figure PCTCN2018088797-appb-000012
由表1中各SNB点坐标可知：SNB点0位于图4中第一象限以外，其对应的β≤0，表明：从初始SNB点5开始在二维有功功率注入空间第一象限内沿β减小方向搜索系统的SNB点结束。此时需重新回到初始SNB点5，在有功注入空间第一象限内沿β增大方向继续搜索SNB点。类似沿β减小方向搜索SNB点的原理，采用本方法沿β增大方向搜索SNB点，得SNB点6、7、8、9、10，直至SNB点11，此时，有β 11＞π/2，结束沿β增大方向下的搜索SNB搜索。至此，采用本方法所提优化模型在二维有功功率注入空间第一象限内搜索所得的全部SNB点如图4所示。将图4中所有SNB点逐一连接即得节点5、7有功功率注入空间第一象限内的SVSR边界。
为验证本方法所提优化模型搜索SVSR边界的正确性，分别采用CPF、OPF在图4所述的二维有功注入空间内搜索相应功率增长方向下的SVSR边界点，结果如图4所示。对比图4中采用本方法所提优化模型与CPF、OPF所搜索的SVSR边界可知：同一功率增长方向下，采用本方法搜索所得SNB点与CPF、OPF搜索所得SNB点近似重合，验证了本方法搜索SVSR边界的准确性。
由SVSR边界特性可知，实际SVSR边界点处，电力系统的潮流方程雅可比矩阵奇异，因而雅可比矩阵最小特征值为0。为对比上述三种SVSR边界搜索算法所得SVSR边界点与实际SVSR边界点的误差，可通过计算和比较所得SVSR边界点处的潮流方程雅可比矩阵最小特征值来评估各算法的计算精度。图5分别给出了场景1中CPF、OPF及本方法所提优化模型所得SVSR边界点处潮流方程雅可比矩阵的最小特征值。对比图5中各SNB点最小特征值可知：采用本方法所提优化模型与OPF搜索所得SNB点的精度要远高于采用CPF追踪所得的SNB点。图中采用CPF搜索所得SNB点中，最小特征值为1.3256×10 -4，最大值3.85×10 -2，平均最小特征值为1.06×10 -2。而采用本方法所提优化模型和OPF计算所得的最小特征值平均值分别为5.6286×10 -7和2.1656×10 -7，这两种算法的计算精度近似相等，且明显高于CPF。导致上述结果的主要原因为：采用CPF搜索SNB点时，需以基态 为起始点，通过不断的预测-校正，追踪PV(有功功率-电压)曲线的“鼻尖点”，以此点作为搜索所得的SNB点。然而，受算法原理和计算效率限制，CPF搜索所得SNB点可能越过或未达到真实SNB点处，不能保证其所得任意功率增长方向下的SNB点均为实际SNB点，这使得CPF计算所得SNB点精度波动较大。即使缩短CPF计算步长，使所求得的校正点在PV曲线上的分布更为密集，也难以消除这一误差。此外，过小的计算步长会大幅度恶化CPF计算效率。而利用优化算法求解SNB点时，对准确描述SNB点的模型进行直接求解，可避免所得SNB点越过或未达到真实SNB点的情况，所得SNB点的精度取决于优化算法所设定的收敛条件。对比结果表明：在有功负荷注入空间内，本方法所提优化模型与OPF具有相同的精度，且远高于CPF，验证了本方法的可行性。
本发明实施例对各器件的型号除做特殊说明的以外，其他器件的型号不做限制，只要能完成上述功能的器件均可。
本领域技术人员可以理解附图只是一个优选实施例的示意图，上述本发明实施例序号仅仅为了描述，不代表实施例的优劣。
以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

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  1. 一种电力系统静态电压稳定域边界快速搜索的优化模型，其特征在于，所述方法包括如下步骤：
    以基态潮流为起始点，采用传统最优潮流搜索第一个电力系统鞍结分岔点，将其映射至二维有功注入空间，获取静态电压稳定域边界点；
    重复向功率增长方向角减小的方向改变功率增长方向，通过优化模型搜索新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；若功率增长方向角小于等于0则返回第一个电力系统鞍结分岔点：
    重复向功率增长方向角增大的方向再次改变功率增长方向，重新搜索最新功率增长方向下的电力系统鞍结分岔点，并映射至二维有功注入空间内，获取新的静态电压稳定域边界点；
    若最新的功率增长方向角大于等于90°，则将所有静态电压稳定域边界点顺次连接，获取静态电压稳定域边界。
  2. 根据权利要求1所述的一种电力系统静态电压稳定域边界快速搜索的优化模型，其特征在于，所述采用传统最优潮流搜索第一个电力系统鞍结分岔点，将其映射至二维有功注入空间步骤具体为：
    将第一个电力系统鞍结分岔点映射至分别以节点i、j的有功注入功率为横纵坐标轴的二维有功注入空间内。
  3. 根据权利要求1所述的一种电力系统静态电压稳定域边界快速搜索的优化模型，其特征在于，所述功率增长方向角具体为:
    Figure PCTCN2018088797-appb-100001
    式中，Δβ为功率增长方向角的步长；定义ΔP i0＝ΔP i、ΔP j0＝ΔP j分别表示上一电力系统鞍结分岔点对应的功率增长方向中对应于节点i、j的有功功率分量。
  4. 根据权利要求1所述的一种电力系统静态电压稳定域边界快速搜索的优化模型，其特征在于，所述优化模型为：
    min-η k
    s.t.g(x k-1)+η kλ k-1d k＝0
    式中，k为第k个待搜索电力系统鞍结分岔点；λ k-1为已求的第k-1个电力系统鞍结分岔点所对应的负荷裕度；x k-1为第k-1个电力系统鞍结分岔点所对应的系统状态变量的向量； k为搜索第k个待搜索电力系统鞍结分岔点时的新增状态变量；d k为第k个功率增长方向；g(x k-1)为进行第k-1次搜索时的潮流方程。
  5. 根据权利要求1所述的一种电力系统静态电压稳定域边界快速搜索的优化模型，其特征在于，所述新功率增长方向为：
    d 2-＝[ΔP 1L ΔP i-1,ΔP i,ΔP i+1L ΔP j-1,ΔP j,ΔP j+1L ΔP nb,ΔQ 1L ΔQ l] T
    Figure PCTCN2018088797-appb-100002
    Figure PCTCN2018088797-appb-100003
    式中，ΔP 1至ΔP n表示PV和PQ节点功率增长方向的有功功率分量；ΔQ 1至ΔQ l表示PQ节点功率增长方向的无功功率分量；ΔP i、ΔP j分别表示功率增长方向中对应于节点i、j的有功功率分量。
  6. 根据权利要求1所述的一种电力系统静态电压稳定域边界快速搜索的优化模型，其特征在于，所述最新的功率增长方向角具体为：
    Figure PCTCN2018088797-appb-100004
    式中，Δβ为功率增长方向角的步长；定义ΔP i0＝ΔP i、ΔP j0＝ΔP j分别表示上一电力系统鞍结分岔点对应的功率增长方向中对应于节点i、j的有功功率分量。
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