CN103093037B - Power system splitting fracture surface searching method based on principal and subordinate's problem alternative optimization - Google Patents

Abstract

The invention discloses a kind of power system splitting fracture surface searching method based on principal and subordinate's problem alternative optimization, it is principal and subordinate's problem based on figure Knapsack Theory (Connected Graph constrained Knapsack Problem, CGKP) by complete Active Splitting model conversation；The optimal balance segmentation problem of the entitled figure of examination in chief, uses CGKP technology to solve；It is scheduling problem based on optimal power flow problems from problem, uses OPF technology to solve；Coupling is realized by the regulated quantity of node load between principal and subordinate's problem.By the alternating iteration between principal and subordinate's problem, and obtain more excellent off-the-line scheme；Compared with prior art, the present invention proposes the New Policy alternately solving power system optimum Active Splitting section based on principal and subordinate's problem, also makes off-the-line scheme closer to the optimal solution of complete model simultaneously, thus has more load to realize power supply after ensureing off-the-line.

Description

Power system splitting fracture surface searching method based on principal and subordinate's problem alternative optimization

Technical field

The present invention relates to power technology, particularly relate to the splitting fracture surface searching method of a kind of power system.

Background technology

Active Splitting is as one of effective measure of reply power system collapse, the most gradually by industrial circle and academia Accreditation and attention.Optimum Active Splitting section selection problem is according to operation of power networks state and fault message, finds and makes off-the-line Rear each isolated subsystem can quick-recovery stable operation and entirety cut machine soon, cutting load is the fewest off-the-line section.Because of this plan Slightly for ensureing that electricity net safety stable ground runs continuously, machine of cutting cutting load amount after reducing system sectionalizing and there is important meaning Justice, and paid close attention to by numerous research worker.

The method solving optimum off-the-line section at present substantially can be divided three classes from the difference of the main method used:

1) off-the-line section based on graph theory search

List of references [1]-[4] propose a kind of based on ordered binary decision diagram (Ordered Binary Decision Diagram, OBDD) three stage bulk power grid off-the-line strategies, there is the theoretical basis that comparison is rigorous, but solution amount of calculation phase of still needing To bigger problem.List of references [5] proposes heuristic based on adjacent side search, though the method devises balance The explicit representation method of the connection constraint of segmentation problem, but and its optimum solution strategies unrealized.List of references [6] proposes to finish Close spectrum algorithm (Spectral Method) and the Active Splitting strategy of multistage kernel K-Means method；The method calculated Journey is simple, speed is fast, but is difficult to ensure that specific Coherent Generator Group one is scheduled on same subsystem.List of references [7], [8] then utilize The power system of simplification is divided into multiple isolated subsystem by pMETIS figure segmentation software bag, then through union operation and recovery operation Obtain corresponding off-the-line scheme.The method of list of references [6]-[8] not every height after figure is divided into k subgraph in fact Figure is all connected subgraph, is required to obtain connected subgraph by artificial recombinant, therefore inevitably reduces its figure and divide Solve the optimality of result.List of references [9] is " search+adjust " separate two based on Graph-theoretical Approach system decomposition In the stage, in succession solve, thus reduce complexity and the amount of calculation of system solution, and actual big system can be solved；But It has isolated the coupling between former problem various piece completely, and its result can only be approximate solution.

2) off-the-line strategy based on slow homology theory

List of references [10], the strategy of [11] is first with the generalized eigenvalue in " the slow people having the same aspiration and interest " theory and characteristic vector Calculating and identify potential unit oscillation mode information, and then by oscillation mode relative to the sensitivity of each node, right All load buses in network are grouped, and search out weak connection node set, and and then obtain optimal off-the-line interface. Literary composition [12] proposes the slow homology theory of a kind of combination and the improved method of graph theory searching method.The method is substantially also based on thoroughly The search thinking lifted, when the scale of network and structure comparison big and complicated time, its amount of calculation or bigger than normal.Based on slow homology theory The common drawback of off-the-line strategy be to make amount of calculation excessive because eigenvalue and characteristic vector need to be calculated.

3) additive method

First power system is divided into instability area and remaining area, so according to dispatch situation and Failure Model by list of references [13] Each isolated area is made to meet power-balance requirement by adjusting the load on this two parts zone boundary afterwards.List of references [14] Power flow tracing algorithm is utilized to realize the original allocation of non-power generator node, then by foundation mismatch power near initial section Minimum principle carries out the adjustment of load bus ownership and is only exchanged the off-the-line section that power is minimum.List of references [15] proposes The power system multi-line that a kind of algebraic method and graph theory combine cut-off in the case of power subsystem inspection policies.The method has There is the strongest theory support, though carry out the detection of subsystem just for general power system network, if actively solving with other Row searching method combines, and is expected to accelerate its search speed.

List of references:

[1] SUN Kai, ZHENG Dazhong, LU Qiang.Splitting strategies for islanding Operation of large-scale power systems using OBDD-based methods [J] .IEEE Transactions on power systems, 2003,18 (2): 912-923.

[2] ZHAO Qianchuan, SUN Kai, ZHENG Dazhong, et al.A study of system splitting strategies for island operation of power system:a two-phase method Based on OBDDs [J] .IEEE transactions on power systems, 2003,18 (4): 1556-1565.

[3] SUN Kai, ZHENG Dazhong, LU Qiang.A simulation study of OBDD-based proper splitting strategies for power systems under consideration of Transient stability [J] .IEEE transactions on power systems, 2005,20 (1): 389-399.

[4] SUN Kai, ZHENG Dazhong, LU Qiang.Searching for feasible splitting Strategies of controlled system islanding [J] .IEE Proceedings of Generation Transmission and Distribution, 2006,153 (1): 89-98.

[5] Sen A, Ghosh P, Vittal V, et al.A new min-cut problem with Application to electric power network partitioning [J] .European Transactions On Electrical Power, 2009,19 (6): 778-797.

[6] Peiravi A, Ildarabadi R.A fast Algorithm for intentional islanding Of power systems using the multilevel Kernel K-Means Approach [J] .Journal of Applied Sciences, 2009,9 (12): 2247-2255.

[7] Xu G, Vittal V.Slow coherency based cutset determination algorithm For large power systems [J] .IEEE Transactions on power systems, 2010,25 (2): 877- 844.

[8] Li J, Liu C C, Schneider K P.Controlled Partitioning of Power Network considering real and reactive power balance [J] .IEEE Transactions on Smart grid, 2010,1 (3): 261-269.

[9] Lin Jikeng, Li Shengwen, Wang Xudong, etc. power system optimum Active Splitting section search model and algorithm [J]. Electrical engineering journal, 2012,32 (13): 86-94.

[10] Qiao Ying, Shen Chen, Lu Qiang. bulk power grid separation decision space screening and method for fast searching [J]. China's motor work Journey journal, 2008,28 (22): 23-28.

[11] Najafi S, Hosseinian S H, Abedi M.Proper Splitting of Interconnected Power System [J] .IEEJ Transactions on Electrical and Electronic Engineering, 2010,5 (2): 211-220.

[12] WANG Xiaoming, Vittal Vijay.System islanding using minimal cutsets with minimum net flow[C]//Proceeding of IEEE PES Power Systems Conference and Exposition, New York, USA:IEEE, 2004:379-384.

[13] Liu Yuanqi, Liu Yutian. power system off-the-line cut set searching algorithm [J] based on scheduling subregion. power system Automatization, 2008,32 (11): 20-24.

[14] WANG C G.ZHANG B H, HAO Z G, et al.A Novel Real-Time Searching Method for Power System Splitting Boundary [J] .IEEE Transactions On Power Systems.2010,25 (4): 1902-1909.

[15] Guler T, Gross G.Detection of island formation and identification Of causal factors under multiple line outages [J] .IEEE Transactions on Power Systems.2007,22 (2): 483-491.

[16] Lin Jikeng, Wang Xudong, Li Shengwen, etc. figure dividing method based on the knapsack problem retrained containing connected graph [J]. electrical engineering journal, 2012,32 (10): 134-141.

[17] Lin Jikeng, SHIWEI encourages, Wu Naihu, etc. meter and discrete variable full Smoothing Newton Method based on Constraints Idle work optimization [J]. electrical engineering journal, 2012,32 (1): 93-100.

Summary of the invention

Based on above-mentioned technical problem, the present invention proposes a kind of power system off-the-line based on principal and subordinate's problem alternative optimization and breaks Faceted search method, based on figure Knapsack Theory (Connected Graph constrained Knapsack Problem, CGKP) It is principal and subordinate's problem by complete Active Splitting model conversation；The optimal balance segmentation problem of the entitled figure of examination in chief, uses CGKP technology to enter Row solves；It is scheduling problem based on optimal power flow problems from problem, uses OPF technology to solve；Lead between principal and subordinate's problem The regulated quantity crossing node load realizes coupling.By the alternating iteration between principal and subordinate's problem, and obtain more excellent off-the-line scheme.

The present invention proposes a kind of power system splitting fracture surface searching method based on principal and subordinate's problem alternative optimization, based on principal and subordinate Problem alternating iteration optimizes, and described power system includes s Coherent Generator Group and is decomposed into s independent particle system, the method bag Include following steps:

Step one, G are original power system diagram model, each isolated island optimal load flow result of calculation according to G ' and adjust the most former The new power system graph model obtained after system loading data, j is iterative processing parameter, and i is Coherent Generator Group in power system Sequentially, initialization operation, make G '=G, i=1, j=0, set iterative processing number of times and be limited to N；

Step 2, carry out described iterative processing, specifically include: utilize the primal problem of CGKP Algorithm for Solving correspondence G ' to be wrapped Corresponding isolated island S containing i-th Coherent Generator Group_iAnd original system is except S_iResidue isolated island S ' in addition_iOptimal load flow model, S '_iTable It is shown asEach node correspondence electromotor of described optimal load flow model and load power regulate limit value and original power system In system graph model G, the relevant parameter of corresponding node is identical.By solving corresponding isolated island S_iWith S '_iOptimal load flow model obtain Isolated island S under optimal load flow pattern_iWith S '_iThe interior cut load power of each nodeWherein m=1,2 corresponds respectively to subsystem S_i, S '_i；S_iNear middle boundary node, load excision surpasses the node of 2/3, and S '_iThe node retained by 100% near middle border, group Become set of node to merge and be assigned to V_set；

Make j=j+1；The node load value of each isolated island, generator output, and off-the-line section constitute current optimal solution Row scheme, is designated asThe total load being maintained safe power supply in the program is L_j, described total load includes S_iWith S '_iIn Load；

If j=N, iterative processing terminates, and forwards step 5 to；Otherwise, step 3 is forwarded to；

Step 3, according to the load correction of each node in network optimization result of calculation new system diagram model G ': G ' of structure For d_v=d_v-p′_v, wherein d_vFor the load of G interior joint v, p '_vFor being needed the load cut away by the node v fed back to from problem Value；

Step 4, utilize CGKP algorithm to find optimum off-the-line section in the case of current graph model, and comprise in searching In the expansion process of the extension subgraph of i-th Coherent Generator Group optimum isolated island, node set V_setIn node cannot function as extension son The end points on the extension limit of figure or the alternate node of extension subgraph；OrderForward step step 2 to；

Step 5, selection setIn be maintained power supply load total amount Lj the maximum make Optimum off-the-line scheme for i-th subsystem；Making i=i+1, if i=s, the method terminates；Otherwise, step one is gone to.

The mathematical model of described primal problem is expressed as formula (1)

$\left\{\begin{array}{c}\mathrm{Max}\underset{v\∈V}{\mathrm{\Σ}}(w_v-p_v^{\′})x_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}(d_v-p_v^{\′})x_v\≤P_{G_1}-\mathrm{\ΔP}\\ (1-x_v)(1-\underset{i\∈l_{v,h}^{\mathrm{Node}},l_{v,h}^{\mathrm{Node}}\∈L_{v,h}^{\mathrm{Node}}}{\mathrm{\Σ}}{x}_i)+\\ x_v\left(\underset{i\∈l_{v,g}^{\mathrm{Node}},l_{v,g}^{\mathrm{Node}}\∈L_{v,g}^{\mathrm{Node}}}{\mathrm{\Π}}{x}_i\right)=1,\∀v\∈V\backslash G,g\∈G_1,h\∈G_2\\ x_v\∈\left\{\mathrm{0,1}\right\},\∀v\∈V\\ x_v=1,\∀v\∈G_1\\ x_v=0,\∀v\∈G_2\\ G=G_1\∪G_2\end{array}\right.---\left(1\right)$

In above formula, G₁And G₂It it is electromotor node set contained by two Coherent Generator Groups；It is sending out of the 1st Coherent Generator Group Motor gross capability；x_vFor node state variable, if v is selected in the independent particle system comprising G1, x_v=1, otherwise, x_v=0；Represent the set of node on all chains between node v and node g,For on any bar chain between node v and node g Node set.

Described is subsystems control and regulation based on optimal load flow problem from problem, is expressed as formula (2)

$\left\{\begin{array}{c}\underset{P^{\mathrm{Gen},m},Q^{\mathrm{Gen},m},p_i^{m\′},q_i^{m\′},U^m,T^m,C^m}{\mathrm{Max}}{P}_{\mathrm{sum}}^m=\underset{m=1}{\overset{2}{\mathrm{\Σ}}}\underset{i=1}{\overset{n^m}{\mathrm{\Σ}}}(P_i^{\mathrm{Load},m}-p_i^{m\′})\\ S.T.:\\ 1.P_i^{\mathrm{Load},m}-p_i^{m\′}=\underset{j=1}{\overset{n^m}{\mathrm{\Σ}}}{U}_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}),i=\mathrm{1,2},...,n^m\\ 2.Q_i^{\mathrm{Load},m}-q_i^{m\′}=\underset{j=1}{\overset{n^m}{\mathrm{\Σ}}}{U}_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}),i=\mathrm{1,2},...,n^m\\ 3.{\underset{\‾}{U}}_i\≤U_i\≤\stackrel{\‾}{U_i},i=\mathrm{1,2},...,n^m\\ 4.{\underset{\‾}{T}}_i\≤T_i\≤{\stackrel{\‾}{T}}_i,T_i\∈T^m\\ 5.{\underset{\‾}{C}}_i\≤C_i\≤{\stackrel{\‾}{C}}_i,C_i\∈C^m\\ 6.P_{l_{i,j}}^{\mathrm{Lone}}\≤{\stackrel{\‾}{P}}_{l_{i,j}}^{\mathrm{Line}},i,j=\mathrm{1,2},...,n^m\\ 7.0\≤P_i^{\mathrm{Gen},m}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Gen},m},i=\mathrm{1,2},...,t^m\\ 8.{\underset{\‾}{Q}}_i^{\mathrm{Gen},m}\≤Q_i^{\mathrm{Gen},m}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Gen},m},i=\mathrm{1,2},...,n^m\\ 9.0\≤P_i^{\mathrm{Load},m}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Load},m},i=\mathrm{1,2},...,n^m\\ 10.0\≤Q_i^{\mathrm{Load},m}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Load},m},i=\mathrm{1,2},...,n^m\end{array}\right.---\left(2\right)$

Subscript m in formula (2) represents m-th subsystem (m=0,1), P^Gen,m, Q^Gen,m, P^Load,mAnd Q^Load,m, m is m The electromotor of individual isolated island interior nodes connection and meritorious, the reactive power set of load,^m、t^m、T^m、C^mIt is respectively this subsystem Nodes, electromotor number, adjustable transformer number, capacitor number, 1～t^mFor electromotor node； Represent subsystem respectively Meritorious and the load or burden without work that in system m, the i-th node is cut.In order to reduce calculating scale, the present invention uses active reactive in proportion Excision, i.e.Wherein k is proportionality coefficient.

Compared with prior art, the power system Active Splitting strategy of the present invention is the effective measure of reply system crash, Solving of its complete model-Large-scale mixed integer programming problem, takes to decompose approximate solution method mostly.The present invention Propose the New Policy alternately solving power system optimum Active Splitting section based on principal and subordinate's problem, also make off-the-line scheme simultaneously Closer to the optimal solution of complete model, thus more load after ensureing off-the-line, is had to realize power supply.

Accompanying drawing explanation

Boundary node after the off-the-line that Fig. 1 provides for the present invention and V_set；

The power system off-the-line section searching algorithm flow process based on principal and subordinate's problem alternative optimization that Fig. 2 provides for the present invention Figure；

The structural representation of the IEEE-118 node system that Fig. 3 provides for the present invention；

The schematic diagram of the sub-network of first Coherent Generator Group of search that Fig. 4 provides for the present invention；

During first subsystem of division that Fig. 5 provides for the present invention, each iteration can realize the signal of supply load change curve Figure；

The schematic diagram of first subsystem of division that Fig. 6 provides for the present invention；

The schematic diagram of the sub-network of second Coherent Generator Group of search that Fig. 7 provides for the present invention；

During second subsystem of division that Fig. 8 provides for the present invention, each iteration can realize the signal of supply load change curve Figure；

The schematic diagram of second subsystem of division that Fig. 9 provides for the present invention；

The optimum off-the-line section result based on " search+adjust " independent two benches solution strategies that Figure 10 provides for the present invention Schematic diagram.

Detailed description of the invention

Below in conjunction with accompanying drawing, technical scheme and detailed description of the invention are described in further detail.

Complete model for system sectionalizing, it is proposed that the optimum Active Splitting solved based on principal and subordinate's problem alternative optimization breaks Face selection strategy.The complete model of system sectionalizing is decomposed into the optimal balance segmentation of the primal problem-figure intercoupled by this strategy Problem, from problem-scheduling problem based on optimal load flow, and sets up the contact between principal and subordinate's problem by system load value.

For sake of convenience, original power system diagram model is designated as G, and system will be adjusted according to optimal load flow result in isolated island The existing system diagram model obtained after parameter is designated as G ', i=1.

Complete model for system sectionalizing, it is proposed that the optimum Active Splitting solved based on principal and subordinate's problem alternative optimization breaks Face selection strategy.The complete model of system sectionalizing is decomposed into the optimal balance segmentation of the primal problem-figure intercoupled by this strategy Problem, from problem-scheduling problem based on optimal load flow, and sets up the contact between principal and subordinate's problem by system load value.

(1) primal problem

By power system with some weighting Connected undigraph G (V, E, w, d) represent, in G demand dv of each node v and Weight w v is the load power of node v.It is being decomposed in the case of two subsystems in formula (1) with the on off state on limit as shape The mathematical model of state variable can be converted into the corresponding Optimized model with node-home as state variable, and corresponding primal problem number Learn shown in model such as formula (1).

In formula (1), G1 and G2 is electromotor node set contained by two Coherent Generator Groups.It is the 1st Coherent Generator Group Electromotor gross capability.Xv is node state variable, if v is selected in the independent particle system comprising G1, and xv=1, otherwise, xv=0.Represent the set of node on all chains between node v and node g,For on any bar chain between node v and node g Node set.In formula (1) first is constrained to knapsack constraint, or capacity-constrained；Second constraint is a connection constraint, Constraint four and constraint five on the basis of, this constraint guarantee each non-power generator node with and be only connected with a Coherent Generator Group Connect.In other words, this constraint guarantees to solve node one connected graph of composition that collected state is 1, and meanwhile, state is the node group of 0 Become a connected graph.In the case of being divided into two groups, the connection of formula (1) and coherent constraints are equal to the constraint 2,3 in formula (1), 4,5；P ' in formula (1)_vRepresenting the loading cut for node v fed back by subproblem, Δ P represents network loss estimated value.

$\left\{\begin{array}{c}\mathrm{Max}\underset{v\∈V}{\mathrm{\Σ}}(w_v-p_v^{\′})x_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}(d_v-p_v^{\′})x_v\≤P_{G_1}-\mathrm{\ΔP}\\ (1-x_v)(1-\underset{i\∈l_{v,h}^{\mathrm{Node}},l_{v,h}^{\mathrm{Node}}\∈L_{v,h}^{\mathrm{Node}}}{\mathrm{\Σ}}{x}_i)+\\ x_v\left(\underset{i\∈l_{v,g}^{\mathrm{Node}},l_{v,g}^{\mathrm{Node}}\∈L_{v,g}^{\mathrm{Node}}}{\mathrm{\Π}}{x}_i\right)=1,\∀v\∈V\backslash G,g\∈G_1,h\∈G_2\\ x_v\∈\left\{\mathrm{0,1}\right\},\∀v\∈V\\ x_v=1,\∀v\∈G_1\\ x_v=0,\∀v\∈G_2\\ G=G_1\∪G_2\end{array}\right.---\left(1\right)$

(2) from problem

It is subsystems control and regulation based on optimal load flow problem from problem, as shown in formula (2):

$\left\{\begin{array}{c}\underset{P^{\mathrm{Gen},m},Q^{\mathrm{Gen},m},p_i^{m\′},q_i^{m\′},U^m,T^m,C^m}{\mathrm{Max}}{P}_{\mathrm{sum}}^m=\underset{m=1}{\overset{2}{\mathrm{\Σ}}}\underset{i=1}{\overset{n^m}{\mathrm{\Σ}}}(P_i^{\mathrm{Load},m}-p_i^{m\′})\\ S.T.:\\ 1.P_i^{\mathrm{Load},m}-p_i^{m\′}=\underset{j=1}{\overset{n^m}{\mathrm{\Σ}}}{U}_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}),i=\mathrm{1,2},...,n^m\\ 2.Q_i^{\mathrm{Load},m}-q_i^{m\′}=\underset{j=1}{\overset{n^m}{\mathrm{\Σ}}}{U}_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}),i=\mathrm{1,2},...,n^m\\ 3.{\underset{\‾}{U}}_i\≤U_i\≤\stackrel{\‾}{U_i},i=\mathrm{1,2},...,n^m\\ 4.{\underset{\‾}{T}}_i\≤T_i\≤{\stackrel{\‾}{T}}_i,T_i\∈T^m\\ 5.{\underset{\‾}{C}}_i\≤C_i\≤{\stackrel{\‾}{C}}_i,C_i\∈C^m\\ 6.P_{l_{i,j}}^{\mathrm{Lone}}\≤{\stackrel{\‾}{P}}_{l_{i,j}}^{\mathrm{Line}},i,j=\mathrm{1,2},...,n^m\\ 7.0\≤P_i^{\mathrm{Gen},m}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Gen},m},i=\mathrm{1,2},...,t^m\\ 8.{\underset{\‾}{Q}}_i^{\mathrm{Gen},m}\≤Q_i^{\mathrm{Gen},m}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Gen},m},i=\mathrm{1,2},...,n^m\\ 9.0\≤P_i^{\mathrm{Load},m}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Load},m},i=\mathrm{1,2},...,n^m\\ 10.0\≤Q_i^{\mathrm{Load},m}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Load},m},i=\mathrm{1,2},...,n^m\end{array}\right.---\left(2\right)$

Subscript m in formula (2) represents m-th subsystem (m=0,1), P^Gen,m, Q^Gen,m, P^Load,mAnd Q^Load,mIt is that m-th is lonely The electromotor of island interior nodes connection and meritorious, the reactive power set of load, n^m、t^m、T^m、C^mIt is respectively the node of this subsystem Number, electromotor number, adjustable transformer number, capacitor number, 1～t^mFor electromotor node；Represent subsystem m respectively In the cut meritorious and load or burden without work of the i-th node.In order to reduce calculating scale, active reactive is used to excise in proportion herein, I.e.Wherein k is proportionality coefficient (can determine according to power factor (PF)).

As in figure 2 it is shown, optimize based on principal and subordinate's problem alternating iteration, include s Coherent Generator Group and be decomposed into s independently Subsystem overall DECOMPOSED OPTIMIZATION process comprise the following steps:

(1) initialize G '=G, j=0, set iterations and be limited to N；Utilize CGKP algorithm to find and comprise i-th people having the same aspiration and interest machine The optimum isolated island S of group_i, i.e. including that the network of i-th Coherent Generator Group, as a sub-network, is left all people having the same aspiration and interest including remaining The network of a group of planes is a sub-network, then utilize CGKP algorithm find meet power-balance they between optimum section；

(2) corresponding isolated island S is formed_iAnd original system is except S_iRemaining system (or residue isolated island) in addition(it is designated as S′_i) optimal load flow model, wherein, the electromotor of each node and load power regulation limit value right with original system graph model G The relevant parameter answering node is identical.By solving corresponding isolated island S_iWith S '_iOptimal load flow model obtain under optimal load flow pattern Isolated island S_iWith S '_iThe interior cut load power of each node(m=1,2 corresponds respectively to subsystem S_i, S '_i)；S_iMiddle boundary node Neighbouring load excision surpasses the node of 2/3, and S '_iThe node retained by 100% near middle border, composition set of node merging is assigned to V_set.j=j+1；The node load value of each isolated island, generator output, and off-the-line section constitute current optimum off-the-line scheme, It is designated asThe total load being maintained safe power supply in the program (includes S_iWith S '_iIn load) be L_j。

(3) if j=N, 6 are forwarded to)；Otherwise, step (4) is forwarded to；

(4) construct the load of each node in new system diagram model G ': G ' according to network optimization result of calculation and be modified to d_v= d_v-p′_v, wherein d_vFor the load of G interior joint v, p '_vFor being needed the load value cut away by the node v fed back to from problem.

(5) utilize CGKP algorithm to find the optimum off-the-line section in the case of current graph model, and comprise i-th in searching In the expansion process of the extension subgraph of Coherent Generator Group optimum isolated island, node set V_setIn node cannot function as extending subgraph The end points on extension limit or the alternate node of extension subgraph；OrderForward step (2) to.

(6) set is selectedIn be maintained load total amount L of power supply_jThe maximum is as i-th The optimum off-the-line scheme of individual subsystem.

(7) i=i+1.If i=s, calculating terminates；Otherwise, 1 is turned).

The relevant step explanation of aforesaid operations process:

Step (2): utilize the S that CGKP obtained through step (1)_iAnd S '_i, it is adjacent node in original system, and at figure point After solution, and belong to S_iAnd S '_iNode, be boundary node.As shown in Figure 1, node 1,2,3,4,5,6 represent S_iWith S′_iBorderline node.Excising more than 2/3 owing to load optimal load flow in Si of node 2 and 3 calculates afterload, node 5 exists S′_iMiddle optimal load flow calculates afterload and all retains, then node 2,3 and 5 belongs to V_set。

Step (4): this operation is that node can safe power supply Load Regulation.If at isolated island S_iOptimal load flow control and regulation During the cut sub-load of some node, then illustrate that the load of these nodes only has sub-load can be pacified in Si Full power supply.So needing before again solving primal problem the load (weights) of respective nodes is revised as remaining load after excision Value.

Step 5)-this operation is that node-home adjusts.At isolated island S_iOptimal load flow control and regulation during cut Major part (more than 2/3) load and be positioned at node near border, illustrates that these nodes can not be divided into S_iIn, therefore in step (5), when carrying out figure decomposition again in, need to get rid of in advance these nodes (set V_setMiddle respective nodes) add isolated island S_iIn, I.e. by these nodes are got rid of outside the alternate node of extension subgraph.For at isolated island S '_iOptimal load flow control and regulation During retain whole load and be positioned at the node near border, the most should not be divided into S_iIn, also need by these Node (set V_setMiddle part of nodes) get rid of in advance outside the alternate node of extension subgraph.

Convergence criterion: the criterion that principal and subordinate's problem iteration terminates has two kinds substantially: the change of the feedback information between principal and subordinate's problem Change amount is less than threshold value, and another kind is with iterations for iteration termination condition.Former is primarily adapted for use in continuous variable optimization；And Latter is suitable for mixed integer optimization problem.Owing to problem herein is mixed-integer problem, therefore select herein with iteration time Number is for terminating iterated conditional.But after iteration terminates, therefrom selecting best scheme is optimal case.

About document be correlated with CGKP algorithm amendment: the CGKP algorithm that list of references [9] relates to, in order to complete above-mentioned algorithm Step (5), the step (2) of annex algorithm need to be made corresponding amendment, i.e. change into: traversal obtains the limit adjacent with E, in satisfied expansion In the limit that exhibition requires, if having node at V_setIn, then not as extension limit.

The above-mentioned flow process such as accompanying drawing solving the optimum isolated island division comprising s Coherent Generator Group based on principal and subordinate's problem alternative optimization Shown in 2.

The effectiveness of inventive algorithm is verified as a example by IEEE-118 node system.This system wiring as shown in Figure 3, Wherein stain represents that load bus, white square represent electromotor node.This system is altogether containing 19 generating sets, and generating is total to be exported Power is 4374.9MW, and in network, total load is 4242MW, and reference capacity is 100MVA.Balance node voltage amplitude per unit value 1.035, other node voltage amplitude bounds are respectively adopted 1.1 and 0.95, and initial magnitude 1.0 phase angle is 0；Load tap changer Excursion 0.9-1.1, tap step-length is set to 0.02；Other parameters are shown in IEEE-118 node code test system data.

Coherent Generator Group packet in system is as shown in table 1:

Table 1 Coherent Generator Group is grouped

First independent particle system is with first Coherent Generator Group as power supply.With the electromotor node that wherein output is maximum The 10 initial subgraph E0 formed for root node, as shown in figure attached 4.

Wherein, solid line connection spanning tree is the subtree connecting first Coherent Generator Group；It is connected with this subtree by a dotted line Node be the island load node that will occur after respective branch.

The iterations limit value N that principal and subordinate's problem alternative optimization solves is 6.The solution that the process that iteration obtains every time is optimized and revised The load total amount of sustainable power supply in row scheme is as shown in Figure 5.

From accompanying drawing 5 it will be seen that the off-the-line scheme that obtains of the 4th iteration is optimum, therefore as the solution that this subsystem is final Row scheme.Correspondingly 8 circuit 33-37,15-19,18-19,30-38,21-20,70-69,70-75,74-75 quilts in original system Disconnect, as shown in Figure 6.From left to right, two isolated islands realize delivery and are respectively 1080.51MW and 3154.00MW, always power Amount 4234.51MW.

Second independent particle system is with second Coherent Generator Group as power supply.With the electromotor node that wherein output is maximum The 89 initial subgraph E0 formed for root node, as shown in Figure 7, in figure, solid line is identical with accompanying drawing 4 with the meaning of dotted line.

The iterations limit value that principal and subordinate's problem alternative optimization solves be 6,6 iteration obtain through the off-the-line optimized and revised The load total amount of sustainable power supply in scheme is as shown in Figure 8.

From accompanying drawing 8 it will be seen that the off-the-line scheme that obtains of the 4th iteration is optimum, obtain independence subsystem in bottom right in accompanying drawing 9 System；Correspondingly 5 circuit 82-77,96-80,97-80,100-98,100-99 in original system, be disconnected.In accompanying drawing 93 are only Vertical subsystem is the isolated island ultimately formed, and it is disconnected sets of lines accordingly, is optimum off-the-line section.Three subsystems can Realizing safe power supply amount and be respectively as follows: 1080.51MW, 902.88MW and 2235.00MW, total delivery is 4218.39MW, always cuts negative Lotus amount is 23.61MW.

And under same constraints, use " search+adjust " independent two benches method for solving, obtain the off-the-line of accompanying drawing 10 Section result, three subsystems can realize safe power supply amount and be respectively 1038.00MW, 902.55MW and 2237.89MW, always power Amount 4178.44MW, total cutting load amount is 63.56MW, and it always excises loading (23.61MW) than the method that the present invention proposes and wants many Cut away 39.95MW load many excision load proportions accordingly and reach 62.85%.Principal and subordinate the most proposed by the invention alternately solves Method can find more excellent off-the-line scheme relative to independent two benches solution strategies.

Claims (1)

1. a power system splitting fracture surface searching method based on principal and subordinate's problem alternative optimization, based on principal and subordinate's problem alternating iteration Optimizing, described power system includes s Coherent Generator Group and is decomposed into s independent particle system, it is characterised in that the method includes Following steps:

Step one, G are original power system diagram model, each isolated island optimal load flow result of calculation according to G ' and adjust corresponding original system The new power system graph model obtained after load data, j is iterative processing parameter, and i is Coherent Generator Group order in power system, Initialization operation, makes G '=G, i=1, j=0, sets iterative processing number of times and is limited to N；

Step 2, carry out described iterative processing, specifically include: utilize the primal problem of CGKP Algorithm for Solving correspondence G ' to obtain comprising The corresponding isolated island S of i Coherent Generator Group_iAnd original system is except S_iResidue isolated island S ' in addition_iOptimal load flow model, S '_iIt is expressed asEach node correspondence electromotor of described optimal load flow model and load power regulate limit value and original power system diagram In model G, the relevant parameter of corresponding node is identical；By solving corresponding isolated island S_iWith S '_iOptimal load flow model obtain at optimum Isolated island S under trend pattern_iWith S '_iThe interior cut load power of each nodeWherein m=1,2 corresponds respectively to subsystem S_i, S′_i；S_iNear middle boundary node, load excision surpasses the node of 2/3, and S '_iThe node retained by 100% near middle border, composition Set of node merging is assigned to V_set；

The optimal balance segmentation problem of the entitled figure of described examination in chief, uses CGKP technology to solve, and its mathematical model is expressed as public affairs Formula (1)

In above formula, G₁And G₂It it is electromotor node set contained by two Coherent Generator Groups；It it is the electromotor of the 1st Coherent Generator Group Gross capability；x_vFor node state variable, if v is selected in the independent particle system comprising G1, x_v=1, otherwise, x_v=0； Represent the set of node on all chains between node v and node g,For the node on any bar chain between node v and node g Set, w_vFor the load weights of node v, p '_vFor being needed the load value cut away by the node v fed back to from problem, Δ P is net Damaging approximation, h is node, and V is node set；

Make j=j+1；The node load value of each isolated island, generator output, and off-the-line section constitute current optimum off-the-line side Case, is designated asThe total load being maintained safe power supply in the program is L_j, described total load includes S_iWith S '_iIn negative Lotus；

If j=N, iterative processing terminates, and forwards step 5 to；Otherwise, step 3 is forwarded to；

Step 3, it is modified to d according to the load of each node in network optimization result of calculation new system diagram model G ': G ' of structure_v= d_v-p′_v, wherein d_vFor the load of G interior joint v, p '_vFor being needed the load value cut away by the node v fed back to from problem；

Described is subsystems control and regulation based on optimal load flow problem from problem, is expressed as formula (2)

Subscript m in formula (2) represents m-th subsystem, m=0,1, P^Gen _, ^m, Q^Gen _, ^m, P^Load,mAnd Q^Load _, ^mIt is m-th respectively The electromotor of isolated island interior nodes connection and meritorious, the reactive power set of load；n^m、t^m、T^m、C^mIt is respectively the joint of this subsystem Count, electromotor number, adjustable transformer number, capacitor number, 1～t^mFor electromotor node；Represent subsystem respectively Meritorious and the load or burden without work that in system m, the i-th node is cut；

Step 4, utilize CGKP algorithm to find optimum off-the-line section in the case of current graph model, and comprise i-th in searching In the expansion process of the extension subgraph of individual Coherent Generator Group optimum isolated island, node set V_setIn node cannot function as extend subgraph Extension limit end points or extension subgraph alternate node；OrderForward step 2 to；

Step 5, selection setIn be maintained load total amount Lj the maximum of power supply as i-th The optimum off-the-line scheme of subsystem；Making i=i+1, if i=s, the method terminates；Otherwise, step one is gone to.