CN104734162B - Node reactive voltage constrains unified complementary tidal current computing method - Google Patents

Abstract

The invention discloses node reactive voltage constrains unified complementary tidal current computing method, belong to the technical field of Power System Stability Analysis.The present invention introduces the reactive complementation equation that electromotor node voltage bound is normalized expression in power flow algorithm.The present invention has more preferable convergence；By the correction of complementary equation operative constraint reactive voltage value, with preferably anti-numerical oscillation ability；The impact of numerical oscillation is avoided by gradual correction of constraint equation, can smooth judgement generator reactive exactly in an iterative process and be exerted oneself situation；Node type identity Divergent Phenomenon is showed corresponding to Constraints equation by quantizing.

Description

Node reactive voltage constrains unified complementary tidal current computing method

Technical field

The invention discloses node reactive voltage constrains unified complementary tidal current computing method, belong to power system stability point The technical field of analysis.

Background technology

Developing rapidly for modern power systems, has gradually formed the big electricity with the characteristics of Large Copacity, remote, regional internet Net, on the other hand, Load flow calculation as the requisite instrument of Power System Analysis, need fully meter and system element characteristic with Obtain the power flow solutions of more reasonable.In large scale electric network is calculated, usually through the process of PV-PQ node types conversion logic The out-of-limit problem of generator reactive, such as document《The research of PV-PQ nodes conversion logic in Load flow calculation》(Chinese electrical engineering Report, page 54 of the 1st phase of volume 25 in 2005) provide the bi-directional logic of Load flow calculation interior joint type conversion, it is indicated that Load flow calculation Middle identity diverging is corresponding to constraint induction type collapse of voltage phenomenon.Heuristic Node type conversion logic action opportunity is to trend Convergence has a major impact, and empirical relatively strong, stability is not good enough.

Constraints are obtained as the mathematical theory that can portray non-differentiability logical relation, in power system extensively should With.Reactive voltage modulating properties are described by Mathematical Programs With Nonlinear Complementarity Constraints equation, in Load flow calculation, mainly has two categories below at present Method：

First kind method processes reactive limit value constraint such as text based on Constraints Nonlinear programming Model by optimum theory Offer《The mixing complementarity method of trend PV-PQ conversion》(Automation of Electric Systems, 2009 the 14th phase of volume 33 page 37) was introduced Complementary theory builds the Nonlinear programming Model of Load flow calculation, solves to improve lacking for heuristic logic in conjunction with Modern Interior Point Optimization Algorithm Fall into.But Load flow calculation problem is configured to optimization problem by such method, the suitability is not good.

Equations of The Second Kind method describes the idle control constraints of electromotor node, such as document by smoothing Newtion method《Smoothing is non- The node type transformation model of linear complementary constraint》(Proceedings of the CSEE, 2008 the 31st phase of volume 28 page 29) is logical Cross smoothing Constraints model to exert oneself node type transfer problem, but system equation and variable increase more.Document《A Modified Newton-Raphson Load Flow Scheme for Directly Including Generator Reactive Power Limits Using Complementarity Framework》(Electric Power Systems Research, 2014 volume 109 page 45) by Fischer-Burmeister functions build Mix Complementarity Problems calculation block Frame, can keep conventional Load Flow to calculate overall structure.But the differentiability problem of its model that is wanting in consideration, calculates still to continue to use and heuristic sentences Disconnected correcting structure, calculates effect undesirable.Such method builds complementary power flow algorithm, needs to solve differentiability and model is multiple The problem of miscellaneous degree.

When large scale system is calculated, the correctness and action opportunity of node type conversion logic may all cause trend meter Calculate failure or converge on wrong solution.Idle for electromotor node bound of exerting oneself is constrained independent table by existing complementary power flow algorithm Show, the solvability in order to ensure tide model increased the voltage equilibrium relationships of electromotor node in tide model, complicated Complementary tide model, Jacobian matrix change greatly, are unfavorable for extending in practical implementation.By Constraints the Theory Construction Complementary tide model for avoiding problem above from providing preferable resolving ideas.

Content of the invention

The technical problem to be solved is the deficiency for above-mentioned background technology, there is provided node reactive voltage is about The complementary tidal current computing method of Shu Tongyi, describes reactive voltage binding feature, energy by normalized nonlinear complementation approximating function Load flow calculation Jacobian overall structure is kept enough, is solved due to causing tide using wrong PV-PQ node types conversion logic Stream calculation failure converges on the technical problem that mistake is solved.

The present invention is adopted the following technical scheme that for achieving the above object：

Node reactive voltage constrains unified complementary tidal current computing method, comprises the steps：

A. initialization initial data forms bus admittance matrix；

B. build complementary tide model and calculate complementary tide model equation amount of mismatch, the complementary tide model includes： Each node active power equation, load bus reactive power equation, normalization represent the idle bound of exerting oneself of electromotor node Reactive complementation equation, and the convergence equation of approximating parameter；

C. when complementary tide model equation amount of mismatch reaches the convergence precision of setting, terminate Load flow calculation, otherwise, enter Next step；

D. the Jacobian matrix of the complementary tide model is calculated according to current system voltage status information；

E. the correction of solving system variable each node voltage information and approximating parameter value, return to step B are updated.

As the further prioritization scheme that the node reactive voltage constrains unified complementary tidal current computing method, step B Described in complementary tide model be shown below, the complementary tide model equation amount of mismatch Δ F includes：The active mistake of each node Dosage Δ P, the idle amount of mismatch Δ Q of load bus, reactive complementation equation amount of mismatch Δ ρ, the approximating parameter μ of electromotor node are received Hold back the amount of mismatch Δ f of equation_μ：

Wherein：Ω_G、Ω_DRespectively electromotor node set, load bus set, Δ P_iFor the active amount of mismatch of node i, P_isFor the active power injection rate of node i, V_iFor the voltage of node i, V_jIt is the voltage with the node j of node i Topology connection, G_ij For the transconductance between the node j of node i and node i Topology connection, B_ijFor node i and node i Topology connection node j it Between mutual susceptance, θ_ijFor the phase difference of voltage between the node j of node i and node i Topology connection, Δ Q_kFor load bus k's Idle amount of mismatch, Q_ksFor the reactive power injection rate of load bus k, V_kFor the voltage of load bus k, V_mIt is and load bus k The voltage of the node m of Topology connection, G_kmFor the transconductance between the node m of load bus k and load bus k Topology connections, B_kmFor the mutual susceptance between the node m of load bus k and load bus k Topology connections, θ_kmFor load bus k and load section Phase difference of voltage between the node m of point k Topology connections, Δ ρ_lFor the reactive complementation equation amount of mismatch of electromotor node l, Φ is Approximating function,Idle at respectively electromotor node l exert oneself and its bound, V_l、Respectively send out The voltage of motor node l and its setting value, α are lax norm.

Further, the node reactive voltage is constrained in unified complementary tidal current computing method, and step D is according to current system System voltage status information calculates the Jacobian matrix of the complementary tide model：

Wherein：H, N, M, L, N ', M ', L ', L ", L " ' for Jacobian matrix submatrix, S and K is diagonal matrix, and w is row Vector,ρ be each electromotor node reactive complementation equation, Q^genFor each Motor node is idle to exert oneself,For electromotor node set Ω_GIn each node voltage, Δ θ be node between voltage phase angle Difference,For each node voltage variable quantity in load bus set,For each node voltage change in electromotor node set Amount, Δ μ are approximating parameter variable quantity.

Further, the node reactive voltage constrains unified complementary tidal current computing method, and step E is using such as following table Each node voltage information and approximating parameter value is updated up to formula：

θ^(d+1)=θ^(d)-Δθ^(d)

V^(d+1)=V^(d)-ΔV^(d)*V^(d)

μ^(d+1)=μ^(d)-Δμ^(d)

Wherein：V^(d)、θ^(d)、μ^(d)The voltage magnitude of respectively the d time iterative calculation, phase angular amount and approximating parameter value, V^{(d +1)}、θ^(d+1)、μ^(d+1)The voltage magnitude of respectively the d+1 time iterative calculation, phase angular amount and approximating parameter value, Δ V^(d)、Δθ^(d)、 Δμ^(d)The voltage magnitude changing value of respectively the d time iterative calculation, phase angle amount changing value and approximating parameter changing value, V^(d)For The information of voltage of each node in d iterative calculation.

Further, the node reactive voltage constrains unified complementary tidal current computing method, and be related in step B sends out Idle at motor node l exert oneselfTried to achieve by following expression：

Wherein：For the load or burden without work value at electromotor node l, V_lFor the voltage of electromotor node l, V_nIt is and generating The voltage of the node n of machine node l Topology connections, G_lnBetween node n for electromotor node l and electromotor node l Topology connections Transconductance, B_lnFor the mutual susceptance between the node n of electromotor node l and electromotor node l Topology connections, θ_lnFor electromotor Phase difference of voltage between the node n of node l and electromotor node l Topology connections.

The present invention adopts above-mentioned technical proposal, has the advantages that：

(1) complementary tidal current computing method according to the present invention has more preferable convergence, by complementary equation operative constraint The correction of reactive voltage value, with preferably anti-numerical oscillation ability；

(2) impact for avoiding numerical oscillation is corrected by constraint equation is gradual, can smooth in an iterative process accurately Ground judges that generator reactive is exerted oneself situation；

(3) node type identity Divergent Phenomenon is showed by quantizing corresponding to Constraints equation.

Description of the drawings

Fig. 1 is that the generator reactive of IEEE300 systems contrast tide model in the embodiment of the present invention is exerted oneself iterative process；

Fig. 2 is the electromotor node voltage iterative process that IEEE300 systems contrast tide model in the embodiment of the present invention；

Fig. 3 is iterative process under IEEE118 conditional systems identity divergent cases in the embodiment of the present invention；

Fig. 4 is the flow chart of the present invention.

Specific embodiment

Technical scheme to inventing is described in detail below in conjunction with the accompanying drawings.

Node reactive voltage according to the present invention constrains unified complementary tidal current computing method, as shown in figure 4, including as follows Step.

Step A, input electric network data, carry out topological analysis, form bus admittance matrix according to grid parameter.

Step B, structure include：Each node active power equation, the idle work(of load bus shown in formula (2) shown in formula (1) Rate equation, normalization shown in formula (3) represent the reactive complementation equation of the idle bound of exerting oneself of electromotor node, and formula (4) institute Show the convergence equation of approximating function, try to achieve complementary tide model equation amount of mismatch Δ F.

Complementary tide model is：

According to current system state information (electromotor node voltage) calculate each electromotor node idle go out force value：

Formula (1) into formula (6), Ω_G、Ω_DRespectively electromotor node set, load bus set, Δ P_iFor node i Active amount of mismatch, P_isFor the active power injection rate of node i, j ∈ i represent that topology is connected between node i and node j, V_iFor section The voltage of point i, V_jIt is the voltage with the node j of node i Topology connection, G_ijFor node i and node i Topology connection node j it Between transconductance, B_ijFor the mutual susceptance between the node j of node i and node i Topology connection, θ_ij=θ_i-θ_j, expression node i, And the phase difference of voltage between the node j of node i Topology connection, Δ Q_kFor the idle amount of mismatch of load bus k, Q_ksFor load section The reactive power injection rate of point k, V_kFor the voltage of load bus k, V_mIt is the voltage with the node m of load bus k Topology connections, G_kmFor the transconductance between the node m of load bus k and load bus k Topology connections, B_kmFor load bus k and load section Mutual susceptance between the node m of point k Topology connections, θ_kmBetween node m for load bus k and load bus k Topology connections Phase difference of voltage, Δ ρ_lFor the reactive complementation equation amount of mismatch of electromotor node l, Φ is approximating function,Idle at respectively electromotor node l exert oneself and its bound, V_l、Respectively electromotor node l Voltage and its setting value, α is lax norm, can use 10,For the load or burden without work value at electromotor node l, V_lFor generating electricity The voltage of machine node l, V_nIt is the voltage with the node n of electromotor node l Topology connections, G_lnFor electromotor node l and electromotor Transconductance between the node n of node l Topology connections, B_lnFor the electromotor node l and node n of electromotor node l Topology connections Between mutual susceptance, θ_lnFor the phase difference of voltage between the node n of electromotor node l and electromotor node l Topology connections, Δ P For the active amount of mismatch of each node, idle amount of mismatch of the Δ Q for load bus, reactive complementation equations of the Δ ρ for electromotor node Amount of mismatch, Δ f_μFor the amount of mismatch that approximating parameter μ restrains equation.

The formula of approximating function Φ is：

In formula (7), μ approaches the approximating parameter of equation Φ (a, b, μ) for complementation, and initial value takes 0.001.

When step C, complementary tide model equation amount of mismatch reach convergence precision ε of setting, | Δ F |<ε, terminates trend meter Calculate, otherwise, enter next step.

Step D, complementary tide model amount of mismatch described in current system information of voltage correction obtain Jacobian matrix.

Corrected Calculation equation is：

In formula (8), the submatrix of H, N, M and L for Jacobian matrix, N ', M ', L ', the solution of L ", L " ' and N, M and L method Identical；S and K is diagonal matrix, and w is column vector, and related definition is as follows：

Formula (9) into formula (11), ρ be each electromotor node reactive complementation equation, Q^genFor each electromotor node idle go out Power,For electromotor node set Ω_GIn each node voltage, Δ θ be node between phase difference of voltage,For load section Each node voltage variable quantity in point set,For each node voltage variable quantity in electromotor node set, Δ μ is to approach ginseng Number variable quantity.

Step E, the correction of solving system variable simultaneously update each node voltage information and approximating parameter, return to step B.

θ^(d+1)=θ^(d)-Δθ^(d)(12)

V^(d+1)=V^(d)-ΔV^(d)*V^(d)(13)

μ^(d+1)=μ^(d)-Δμ^(d)(14)

Formula (12) is into formula (14)：V^(d)、θ^(d)、μ^(d)The voltage magnitude of respectively the d time iterative calculation, phase angular amount and force Nearly parameter value, V^(d+1)、θ^(d+1)、μ^(d+1)The voltage magnitude of respectively the d+1 time iterative calculation, phase angular amount and approximating parameter value, Δ V^(d)、Δθ^(d)、Δμ^(d)The change of the voltage magnitude changing value of respectively the d time iterative calculation, phase angle amount changing value and approximating parameter Value, V^(d)Information of voltage for each node in the d time iterative calculation.

Compliance test result：

For verify the inventive method effectiveness, respectively multiple ieee standard examples are tested, and with PV-PQ nodes Type conversion logic calculates the result of gained and is compared analysis.Structural environment sample calculation analysis dissipate feelings in trend identity simultaneously The numerical value form of expression of this method under shape.Wherein, using perunit value, the unification of trend convergence precision is for voltage and power deviation 0.00001, initial value μ₀0.001 is taken, Load flow calculation takes 1.0 using flat startup method, i.e. load bus voltage magnitude, all nodes Phase angle takes 0.0 degree.

The inventive method and conventional Load Flow computation model are respectively adopted to the node system of IEEE14,118,300, table 1 is provided The test result of both iterationses

The test example trend convergence result of table 1

	IEEE14	IEEE118	IEEE300
				Conventional model	3	6	Diverging
This paper models	4	6	9

From the data in table 1, it can be seen that conventional Load Flow calculating convergence when large scale system is processed is unsatisfactory, at the beginning of iterative process Phase more violent numerical oscillation is easily caused the voltage-controlled node type of node type conversion logic wrong identification.Complementation trend side of the invention Method is compared with more preferable convergence, by the correction of complementary equation operative constraint reactive voltage value, with preferably anti-numerical value Lasing capability.

Tide model is contrasted for further relative analyses and is processing the difference in reactive voltage constraint, studied in detail The out-of-limit situation of generator reactive in IEEE300 example iterative process.Conventional Load Flow method adopts PV-PQ node type conversion logics Process generator reactive out-of-limit, in iterative process, there are multiple node type frequent transitions phenomenons, locking that wherein 1 node is idle Lower limit, remaining are the upper limit.But actual power flow solutions show that the more lower limit node is idle finally due to the upper limit, and the node type is known Do not fail.Fig. 1 and Fig. 2 provide this node reactive voltage iterative information in contrast model.Understand that PV-PQ node conversion logics pass through Heuristic judge that positive lock node is idle exerts oneself and voltage magnitude, processing method is coarse and easy overcorrect.Acute in numerical oscillation When strong, possible recognition node type failure, is absorbed in type frequent transitions and causes trend not restrain.Comparatively, the inventive method The impact for avoiding numerical oscillation is corrected by constraint equation is gradual, judgement electromotor exactly can be smoothed in an iterative process Idle situation of exerting oneself.

For avoiding convergence problem caused by heuristic logic in engineering practice, often node class is repeatedly introduced afterwards in Newton iteration Type conversion logic, the method are empirical stronger and unstable.Following solution strategies are adopted for diverging example in table 1：First not Flow solution is tried to achieve in the limit value constraint of consideration generator reactive, then introduces PV-PQ node type conversion logic weights with this solution as initial value New calculating trend.The voltage magnitude maximum deviation of contrast model flow solution listed by table 2.Wherein, the inventive method and conventional Load Flow The voltage magnitude deviation of method in 0.00001 order of magnitude, verified by accuracy.

The test example trend convergence result of table 2

Numerical value modification is made to IEEE118 modular systems, 59 load of node is increased and is built for 1055.66+j502.33MVA Condition example.The calculation result and analysis of conventional Load Flow method are referring to document《In Load flow calculation, PV-PQ nodes conversion logic grinds Study carefully》(Proceedings of the CSEE, 2005 the 1st phase of volume 25 page 54), belongs to node type identity divergent cases.This Bright tide model with this understanding equally occur diverging, model equation amount of mismatch small range numerical oscillation, multiple voltage-controlled nodes without Method meets its reactive voltage Constraints.Fig. 3 provides tide model equation of the present invention and No. 66 electromotor Constraints equations lose Contrast between dosage.It can be seen that key power generator node Constraints meet the convergence that situation constrains trend, corresponding to opening Hairdo logic interior joint type frequent transitions phenomenon, the inventive method is then by corresponding to Constraints equation number value performance section Vertex type identity Divergent Phenomenon.

Claims (4)

1. node reactive voltage constrains unified complementary tidal current computing method, it is characterised in that comprise the steps：

A. initialization initial data forms bus admittance matrix；

B. build complementary tide model and calculate complementary tide model equation amount of mismatch, the complementary tide model includes：Each section Point active power equation, load bus reactive power equation, normalization represent the idle of the idle bound of exerting oneself of electromotor node Complementary equation, and the convergence equation of approximating parameter, the complementary tide model are shown below, the complementary tide model side Journey amount of mismatch Δ F includes：The active amount of mismatch Δ P of each node, the idle amount of mismatch Δ Q of load bus, the nothing of electromotor node Work(complementation equation amount of mismatch Δ ρ, approximating parameter μ restrain the amount of mismatch Δ f of equation_μ：

$\left\{\begin{array}{c}{\mathrm{MP}}_i=P_{is}-V_i\underset{j\&Element;i}{\&Sigma;}{V}_j(G_{ij}{\mathrm{cos\&theta;}}_{ij}+B_{ij}{\mathrm{sin\&theta;}}_{ij}),i\&Element;{\mathrm{\&Omega;}}_G\&cup;{\mathrm{\&Omega;}}_D\\ {\mathrm{\&Delta;Q}}_k=Q_{ks}-V_k\underset{m\&Element;k}{\&Sigma;}{V}_m(G_{km}{\mathrm{sin\&theta;}}_{km}-B_{km}{\mathrm{cos\&theta;}}_{km}),k\&Element;{\mathrm{\&Omega;}}_D\\ {\mathrm{\&Delta;\&rho;}}_l=\mathrm{\&Phi;}\left(\right(Q_l^{gen}-Q_l^{\min }),\mathrm{\&Phi;}(\left(Q_l^{\max }-Q_l^{gen}\right),-\mathrm{\&alpha;}\left(V_l-V_l^{set}\right),\mathrm{\&mu;}),\mathrm{\&mu;}),l\&Element;{\mathrm{\&Omega;}}_G\\ {\mathrm{\&Delta;f}}_{\mathrm{\&mu;}}=e^{\mathrm{\&mu;}}-1\end{array}\right.,$

Wherein：Ω_G、Ω_DRespectively electromotor node set, load bus set, Δ P_iFor the active amount of mismatch of node i, P_isFor The active power injection rate of node i, V_iFor the voltage of node i, V_jIt is the voltage with the node j of node i Topology connection, G_ijFor section Transconductance between the node j of point i and node i Topology connection, B_ijFor between the node j of node i and node i Topology connection Mutual susceptance, θ_ijFor the phase difference of voltage between the node j of node i and node i Topology connection, Δ Q_kFor the idle of load bus k Amount of mismatch, Q_ksFor the reactive power injection rate of load bus k, V_kFor the voltage of load bus k, V_mIt is and load bus k topologys The voltage of the node m of connection, G_kmFor the transconductance between the node m of load bus k and load bus k Topology connections, B_kmFor Mutual susceptance between the node m of load bus k and load bus k Topology connections, θ_kmIt is that load bus k and load bus k are opened up The phase difference of voltage that flutters between the node m of connection, Δ ρ_lFor the reactive complementation equation amount of mismatch of electromotor node l, Φ is to approach Function,Idle at respectively electromotor node l exert oneself and its bound, V_l、V_l ^setRespectively electromotor The voltage of node l and its setting value, α are lax norm；

C. when complementary tide model equation amount of mismatch reaches the convergence precision of setting, terminate Load flow calculation, otherwise, enter next Step；

D. the Jacobian matrix of the complementary tide model is calculated according to current system voltage status information；

E. the correction of solving system variable each node voltage information and approximating parameter value, return to step B are updated.

2. node reactive voltage according to claim 1 constrains unified complementary tidal current computing method, it is characterised in that step Rapid D calculates the Jacobian matrix of the complementary tide model according to current system voltage status information：

$\left[\begin{array}{c}\mathrm{\&Delta;}P\\ \mathrm{\&Delta;}Q\\ \mathrm{\&Delta;}\mathrm{\&rho;}\\ \mathrm{\&Delta;}{f}_{\mathrm{\&mu;}}\end{array}\right]=\left[\begin{array}{cccc}H& N& N^{\&prime;}& 0\\ M& L& L^{\&prime;}& 0\\ -{\mathrm{SM}}^{\&prime;}& -{\mathrm{SL}}^{\&prime;\&prime;}& K-{\mathrm{SL}}^{\&prime;\&prime;}& w\\ 0& 0& 0& e^{\mathrm{\&mu;}}\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}\mathrm{\&theta;}\\ \mathrm{\&Delta;}{V}^{{\mathrm{\&Omega;}}_D}\\ {\mathrm{\&Delta;V}}^{{\mathrm{\&Omega;}}_G}\\ \mathrm{\&Delta;}\mathrm{\&mu;}\end{array}\right]$

Wherein：H, N, M, L, N ', M ', L ', L ", L " ' for Jacobian matrix submatrix, S and K is diagonal matrix, w for row to Amount,ρ be each electromotor node reactive complementation equation, Q^genFor each generating Machine node is idle to exert oneself,For electromotor node set Ω_GIn each node voltage, Δ θ be node between phase difference of voltage,For each node voltage variable quantity in load bus set,For each node voltage variable quantity in electromotor node set, Δ μ is approximating parameter variable quantity.

3. node reactive voltage according to claim 2 constrains unified complementary tidal current computing method, it is characterised in that step Rapid E updates each node voltage information and approximating parameter value using following expression：

θ^(d+1)=θ^(d)-Δθ^(d)

V^(d+1)=V^(d)-ΔV^(d)*V^(d)

μ^(d+1)=μ^(d)-Δμ^(d)

Wherein：V^(d)、θ^(d)、μ^(d)The voltage magnitude of respectively the d time iterative calculation, phase angular amount and approximating parameter value, V^(d+1)、 θ^(d+1)、μ^(d+1)The voltage magnitude of respectively the d+1 time iterative calculation, phase angular amount and approximating parameter value, Δ V^(d)、Δθ^(d)、Δ μ^(d)The voltage magnitude changing value of respectively the d time iterative calculation, phase angle amount changing value and approximating parameter changing value, V^(d)For d The information of voltage of each node in secondary iterative calculation.

4. node reactive voltage as claimed in any of claims 2 to 3 constrains unified complementary tidal current computing method, Characterized in that, idle at the electromotor node l being related in step B exert oneselfTried to achieve by following expression：

$Q_l^{gen}=Q_l^{load}+V_l\underset{n\&Element;l}{\&Sigma;}{V}_n(G_{\ln }{\mathrm{sin\&theta;}}_{\ln }-B_{ln}{\mathrm{cos\&theta;}}_{ln}),l\&Element;{\mathrm{\&Omega;}}_G$

Wherein：For the load or burden without work value at electromotor node l, V_lFor the voltage of electromotor node l, V_nIt is and electromotor section The voltage of the node n of point l Topology connections, G_lnFor mutual between the node n of electromotor node l and electromotor node l Topology connections Conductance, B_lnFor the mutual susceptance between the node n of electromotor node l and electromotor node l Topology connections, θ_lnFor electromotor node Phase difference of voltage between the node n of l and electromotor node l Topology connections.