CN103795058B - The air extract analysis of electric power system and system failure sort method - Google Patents

Abstract

The present invention proposes a kind of air extract analysis and system failure sort method of electric power system, comprising: based on the Newton iteration method determination quiescent voltage collapse point of Optimal Multiplier; The type of voltage collapse point is judged according to the characteristic of iteration convergence; Require checking system Failure risk situation according to stability margin and provide the sequence of stable fault; By fault parameter and use iterative method provide de-stabilise fault the order of severity sequence.The present invention can provide the voltage stability margin of electric power system online more quickly, carries out effective monitoring in real time to voltage stability; Stable fault and de-stabilise fault integrated ordered can when system jam the switching of the adjustment of online direction generator and reactive-load compensation equipment, also can instruct the configuration etc. of branch parameters adjustment, circuit increase and decrease, FACTS equipment by off-line, all have important meaning to the operation of electric power system and planning.

Description

The air extract analysis of electric power system and system failure sort method

Technical field

The present invention relates to the technical field of power system monitoring, analysis and control, the air extract analysis of specifically a kind of electric power system and system failure sort method.

Background technology

The Voltage-stabilizing Problems research starting of electric power system is later than the research of frequency stabilization problem, be started in the forties in last century, until after last century the seventies, Voltage-stabilizing Problems just starts to receive publicity as a special field, along with the development of modern power systems, the development of field of power transmission may lag behind the growth of system loading growth and power generation level, under electric power networks often operates in high load capacity level, face the critical restriction of voltage stabilization, cause a series of great voltage stabilization accident.

Static voltage stability problem has many analytical methods.Utilize system PV curve, be given in the voltage stability margin of load bus on certain load growing direction, it is the static voltage stability analysis method commonly used the most, the method has clear and definite physical background, analytical effect is directly perceived, has the analytical method of the maturations such as continuous tide, as shown in Figure 1, voltage stability margin λ is defined by following formula

$\mathrm{\λ}=\frac{P_{\max c}-P_{\mathrm{initial}}}{P_{\mathrm{initial}}}$

In Fig. 1, P _maxcrefer to the active power level of system during voltage collapse point, P _initialrefer to system initial launch point active power level, P _maxIrefer to that system cloud gray model meets the maximum reactive power level of system under certain margin requirement, V _irefer to that system cloud gray model meets lowest voltage of a system level under certain margin requirement, V _crefer to voltage levvl during voltage collapse point.

The system failure such as the exiting of injection type equipment such as generator, parallel reactive compensator can produce direct impact with the Voltage Stability Level exited for system of the Branch Type such as system line, transformer equipment, the generation of generic failure all can cause the reduction of voltage stability margin λ, if when λ is greater than 0, can think that post-fault system still keeps stable, if λ is less than 0, then post-fault system will lose stable, be called unstability fault.

Voltage stability margin real-time assessment after Chinese invention patent (application number 201010140847.1) power transmission network catastrophe failure and method for optimally controlling, by judging that the solution point calculated in iterative trend step is true to separate or optimal solution carrys out the voltage stability of system after failure judgement, damped Newton method is utilized to solve, add an iterative process, recycling continuous tide solves stability margin, iterations is more, the time is longer, and does not have to realize the sequence to fault severity level.

According to simulation process information, Chinese invention patent (application number 201110368041.2) a kind of method for evaluating severity of power system fault, judges whether system there occurs merit angle, voltage, frequency unstability; The serious coefficient of this fault is had respectively according to merit angle, voltage, frequency three index calculate, aforementioned three the serious coefficients obtained are weighted combination and draw comprehensive serious coefficient, this fault severity level sort method relates to voltage stabilization and frequency stabilization, be not solve voltage stabilization contingency ranking name problem pointedly, and the foundation of contingency ranking is fail result, that fault is sorted on the impact that system produces, the complexity solving fault is not discussed, the traffic control method solving fault cannot be provided simultaneously.

Summary of the invention

The invention provides a kind of air extract analysis and system failure sort method of electric power system, the voltage stability margin of system can be provided online more quickly, effective monitoring is in real time carried out to the voltage stability of electric power system; Stable fault and de-stabilise fault integrated ordered can when system jam the switching of the adjustment of online direction generator output and reactive-load compensation equipment, also can instruct the configuration etc. of branch parameters adjustment, circuit increase and decrease, FACTS equipment by off-line, all have important meaning to the operation of electric power system and planning.

The technology used in the present invention means are as follows:

The air extract analysis of electric power system and system failure sort method, comprise the following steps:

(1) according to the monitoring result to electric power system, judge whether electric power system breaks down, if electric power system is not broken down, namely under normal operating mode, then carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for the voltage stability margin of electric power system on predetermined load growing direction and determine voltage collapse critical point, then proceeding to step 2); If electric power system is broken down, then directly enter step 3);

(2) according to Newton iteration method convergence situation analysis voltage stability margin, and voltage collapse vertex type is distinguished;

(3) if electric power system is broken down, still according to the Newton iteration method of carrying out from feasible zone outside based on Optimal Multiplier, ask for voltage stability margin and determine voltage collapse critical point, in an iterative process, the voltage collapse critical point nargin asked under selecting described step (1) normal operating mode of iteration initial point;

(4) analyze the voltage stability margin that described step (3) is asked for, if voltage stability margin is not less than 0, be then stable fault, carry out order of severity sequence according to voltage stability margin size to stable fault, voltage stability margin value is less, and fault is more serious; If voltage stability margin is less than 0, be then unstability fault, first parametrization carried out to fault, then ask for voltage collapse critical point according to the Newton iteration method based on Optimal Multiplier from feasible zone outside, in an iterative process, voltage stability margin when iteration initial point selects fault parameter to be 0;

(5) calculate the voltage collapse critical point fault parameter that described step (4) is asked for, carry out order of severity sequence according to fault parameter size to unstability fault, fault parameter is larger, and fault is more serious;

(6) two kinds of sequences of combining step (4) and step (5), according to voltage stability margin value from big to small, then fault parameter order from small to large, to unified sequence of being out of order, instructs power system operation.

In aforesaid step (1), carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for voltage stability margin and determine that the concrete grammar of voltage collapse critical point is:

The growing direction of load and generator is defined by following formula:

P _Li＝P _Li0+λb _Pi

Q _Li＝Q _Li0+λb _Qi

P _Gi＝P _Gi0+λb _Gi

Wherein, λ is voltage stability margin, P _li0, Q _li0be respectively active power and reactive power that node i injects under normal condition, P _li, Q _libe respectively active power and reactive power that node i injects under current state, P _gi0, P _gifor the active power that node i generator injects under normal condition and under current state, b _pi, b _qi, b _gibe respectively that the load of node i is meritorious exerts oneself, idlely exert oneself and the change direction vector of generator output;

Power flow equation with parameter is expressed as:

f(x,λ)＝f(x)-S＝0

S＝S ₀+λb

Wherein, S ₀, S is respectively under normal condition and current state lower node and generator injecting power vector, S ₀=(P _li0, Q _li0, P _gi0), S=(P _li, Q _li, P _gi), b is node and generator injecting power change direction vector, b=(b _pi, b _qi, b _gi), x is state variable;

Adopt the Newton iteration method of Optimal Multiplier, iteration initial point is chosen and is met the voltage stability margin value of trend outside feasible zone, obtains state variable x in trend kth time iteration ^(k)correction amount x ^(k), Δ x ^(k)=J ^(k)-1f (x ^(k)), wherein, J ^(k)for the Jacobian matrix of kth time iteration, f (x ^(k)) for kth time iteration is obtained state variable x ^(k)substitute into power flow equation group, the concrete form of Jacobian matrix is:

Correction amount x is multiplied by with a scalar multiplier β ^(k), then revise state variable x ^(k), the sub-β of its Scalar Multiplication is tried to achieve by following target function:

$\min F\left(\mathrm{\β}\right)=\frac{1}{2}\underset{i=1}{\overset{2n}{\mathrm{\Σ}}}{f}_i^2(x^{\left(k\right)}+\mathrm{\β\Δ}{x}^{\left(k\right)})$

F _i() represents i-th equation in equation group f (x, λ)=f (x)-S=0, and 2n is the number of equation, obtains scalar multiplier β by asking for F (β) extreme value, equation as shown in the formula:

$\frac{\mathrm{dF}\left(\mathrm{\β}\right)}{\mathrm{d\β}}=0;$

The state variable x that scalar multiplier β is corresponding when being 0 ^*for the least square solution of power flow equation, voltage stability margin λ when β is 0 _criticalbe the margin value that voltage collapse critical point is corresponding.

The specific implementation process of aforesaid step (2) is:

If in the iteration of step (1), occur that the situation of PV/PQ type conversion occurs certain node repeatedly, then the type of voltage collapse point is constraint induction type, and this node is voltage collapse point;

If in the iteration of step (1), occur that the situation of PV/PQ type conversion occurs certain several node repeatedly, then the type of voltage collapse point is constraint induction type, record these nodes, select 1 node i at every turn, calculate trend by described step (1), after trend convergence, according to final Jacobian matrix meter sensitivity, if meet the following conditions:

$\left\{\begin{array}{c}\frac{\mathrm{d\λ}}{d{V}_{\mathrm{Gi}}}>0\\ \frac{\mathrm{d\λ}}{d{Q}_{\mathrm{Gi}}}>0\end{array}\right.$

Then node i is voltage collapse point, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power that node i generator injects,

If in the iteration of step (1), the correction of voltage stability margin is less than default precision, then the type of voltage collapse point is saddle junction type, after then obtaining least square solution, need to revise voltage stability margin λ further, search voltage collapse point, namely search the voltage stability margin λ of corresponding voltage collapse point _critical, be specially:

Definition ∑ is have between power flow equation to separate and without the border of separating between region, node clean injecting power vector S forms a space, S ^λ, S ', S ^mthree is vector power in space, and S ' is current power vector, definition S ^mfor ∑ is at state variable x ^*point nearest apart from current power vector S ' Euclidean distance on the section at place, definition S ^λfor section and node injecting power change direction vector b intersection point, S ^λwith S ^criticaloverlap, S ^criticalrepresent the vector power that voltage collapse critical point is corresponding, the correction amount λ of definition voltage stability margin is S ' and S ^λbetween load parameter difference, then S ^λcan following formula be expressed as:

S ^λ＝S′-Δλb

$\mathrm{\Δ\λ}=\frac{{\left|\right|S^{\′}-f\left(x^{*}\right)\left|\right|}_2\cos {\mathrm{\θ}}_1}{{\left|\right|b\left|\right|}_2\cos {\mathrm{\θ}}_2}$

Wherein, θ ₁represent vector power S ^mwith the power flow equation f (x at least square solution place ^*) between angle, θ ₂represent vector power S ^mand S ^λbetween angle,

When ∑ is convex surface, the amendment type of voltage stability margin λ is:

λ ^(k+1)＝λ ^(k)-Δλ ^(k+1)

When ∑ is concave curved surface,

If Δ λ ^(k)be greater than default precision, then the amendment type of voltage stability margin λ is:

${\mathrm{\λ}}^{(k+1)}={\mathrm{\λ}}^{\left(k\right)}+\frac{\mathrm{\Δ}{\mathrm{\λ}}^{\left(k\right)}}{2}$

If θ ₁=90 ° or θ ₂=90 ° and θ ₁when ≠ 90 °, then according to the correction amount λ of following formula calculating voltage stability margin:

$\mathrm{\Δ\λ}=\frac{{\left|\right|S^{\′}-f\left(x^{*}\right)\left|\right|}_2}{{\left|\right|b\left|\right|}_2}$

The amendment type of voltage stability margin λ is: λ ^(k+1)=λ ^(k)-Δ λ ^(k+1).

Aforesaid step (5) is carried out parametrization to fault and is referred to, if reflection system failure parameters is μ, and parameter area is:

0＜μ＜1

Fault parameter μ represents that fault does not occur when being 0, represents that fault thoroughly occurs when being 1.

In aforesaid step (5), for different faults, the calculating of fault parameter μ is obtained by following parametrization power flow equation:

(1) the parametrization power flow equation that exits of single generator

$\left\{\begin{array}{c}\mathrm{\μ}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\∈I}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})-V_i^2{G}_{\mathrm{ii}}=0\\ \mathrm{\μ}{Q}_{G\min U}\≤Q_{\mathrm{Gi}}\≤\mathrm{\μ}{Q}_{G\max U}\end{array}\right.$

(2) the parametrization power flow equation that exits of single shunt capacitor or reactor

$\mathrm{\μ}{Q}_{\mathrm{Si}}-Q_{\mathrm{Di}}-V_i\underset{j\∈I}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+V_i^2{B}_{\mathrm{ii}}=0$

(3) the parametrization power flow equation that exits of single load

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-\mathrm{\μ}{P}_{\mathrm{Di}}-V_i\underset{j\∈I}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}){-V}_i^2{G}_{\mathrm{ii}}=0\\ Q_{\mathrm{Si}}-\mathrm{\μ}{Q}_{\mathrm{Di}}-V_i\underset{j\∈I}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+V_i^2{B}_{\mathrm{ii}}=0\end{array}\right.$

(4) the parametrization power flow equation that exits of single branch road

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\∈I,j\≠m}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})-V_i{V}_m(\mathrm{\μ}{G}_{\mathrm{im}}\cos {\mathrm{\θ}}_{\mathrm{im}}+\mathrm{\μ}{B}_{\mathrm{im}}\sin {\mathrm{\θ}}_{\mathrm{im}})-V_i^2{G}_{\mathrm{iinew}}=0\\ Q_{\mathrm{Ri}}-Q_{\mathrm{Di}}-V_i\underset{j\∈I}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})-V_i{V}_m(\mathrm{\μ}{G}_{\mathrm{im}}\cos {\mathrm{\θ}}_{\mathrm{im}}+\mathrm{\μ}{B}_{\mathrm{im}}\sin {\mathrm{\θ}}_{\mathrm{im}})-V_i^2{G}_{\mathrm{iinew}}+V_i^2{B}_{\mathrm{ii}}\mathrm{new}=0\end{array}\right.$

If there is multiple faults, then parametrization power flow equation is the linear superposition of each single fault parameter power flow equation in this multiple faults;

Wherein, P _dithe active power of the load absorption of node i; P _gifor the active power that node i generator injects; Q _gifor the reactive power that node i generator injects; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit that generator reactive exports; Q _rifor the capacity of reactive-load compensation capacitor after fault; V _ifor the voltage magnitude of node i; I is all node set; θ _ijfor the phase angle difference between node i, j; B _ijfor the susceptance between admittance matrix interior joint i, j; G _ijfor the conductance between admittance matrix interior joint i, j; G _iifor the self-conductance of node i; B _iifor node i from susceptance; G _iinewfor branch road i-m break down after self-conductance in system admittance matrix; B _iinewfor branch road i-m break down after in system admittance matrix from susceptance.

By adopting above-mentioned technological means, the beneficial effect that the present invention has is:

1) operation is simple, and step is clear, and the data that on-line analysis can be obtained by system SCADA or PMU carry out Direct Analysis, and off-line analysis completes easily through emulation tool;

2) calculate simply, fast, use avoiding continuous tide based on Load Flow Method with Optimal Multiplier iterative analysis method and solve voltage collapse critical point close to situation about not easily restraining during collapse point from feasible zone outside, trend iteration initial point is clear and definite, decreases iterations, affects few by system scale;

3) parametrization is carried out to system jam, utilizing does not have the fault parameter between the 0-1 of physical significance to carry out fault severity level sequence, parameter for sorting is not only the sequence to the failure effect order of severity, mostly ordering scenario being fault generating process or on-line operation and solving difficulty;

4) by fault severity level, by after fault, whether unstability is divided into two large classes, and in two steps two class steps are sorted respectively, the ranking results carried out respectively has carried out unified Ordination, unified ranking results can the operation of guidance system and planning, by preconsolidation stress and on-the-spot operation, reduce the order of severity sequence that may break down.

Accompanying drawing explanation

Fig. 1 is Continuation power flow and voltage stability margin definition schematic diagram;

Fig. 2 is the schematic diagram carried out from feasible zone based on Optimal Multiplier Newton iteration;

Fig. 3 is the iteration geometrical model schematic diagram looking for voltage collapse point from area of feasible solutions;

Fig. 4 is the unified sequence schematic diagram describing stable fault and unstability fault;

Fig. 5 is air extract analysis and the system failure sort method flow chart of electric power system of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

The present invention utilizes the Optimal Multiplier Newton iteration method of carrying out iteration from feasible zone outside, the method iterative target is for finding voltage collapse critical point, system voltage stabilizes nargin can be analyzed, this method avoid conventional continuous tide to calculate in the problem close to the convergence difficulties produced during collapse point, decrease iterations, improve solving speed, also can according to convergence characteristic identification voltage collapse type.

As shown in Figure 5, the inventive method comprises the following steps:

1, first according to the monitoring result to electric power system, judge whether electric power system breaks down, if electric power system is not broken down, namely under normal operating mode, then carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for the voltage stability margin of electric power system on predetermined load growing direction and determine voltage collapse critical point, then proceeding to step 2; If electric power system is broken down, then directly enter step 3;

Under normal operating mode,

The growing direction of load and generator can be defined by following formula:

P _Li＝P _Li0+λb _Pi

Q _Li＝Q _Li0+λb _Qi

P _Gi＝P _Gi0+λb _Gi

Wherein, λ is voltage stability margin, P _li0, Q _li0be respectively active power and reactive power that node i injects under normal condition, P _li, Q _libe respectively active power and reactive power that node i injects under current state, P _gi0, P _gifor the active power that node i generator injects under normal condition and under current state, b _pi, b _qi, b _gibe respectively that the load of node i is meritorious exerts oneself, idlely exert oneself and the change direction vector of generator output.Above node power can substitute into power flow equation,

Power flow equation with parameter can be expressed as:

f(x,λ)＝f(x)-S＝0

S＝S ₀+λb

Wherein, S ₀, S is respectively under normal condition and current state lower node and generator injecting power vector, S ₀=(P _li0, Q _li0, P _gi0), S=(P _li, Q _li, P _gi), b is node and generator injecting power change direction vector, b=(b _pi, b _qi, b _gi), x is state variable.

As shown in Figure 2, adopt the Newton iteration method of Optimal Multiplier, iteration initial point is chosen and is met the voltage stability margin value λ of trend outside feasible zone ₀, along approaching direction as shown in the figure, find the nargin λ that voltage collapse critical point is corresponding _critical;

Load Flow Method with Optimal Multiplier utilizes the characteristic that power equation under rectangular coordinate is quadratic function, obtains the correction amount x of state variable in trend kth time iteration ^(k), Δ x ^(k)=J ^(k)-1f (x ^(k)), wherein, J ^(k)for the Jacobian matrix of kth time iteration, f (x ^(k)) for kth time iteration is obtained state variable x ^(k)substitute into power flow equation group, the concrete form of Jacobian matrix is:

Correction amount x is multiplied by with a scalar multiplier β ^(k), then revise state variable x ^(k), the sub-β of its Scalar Multiplication is tried to achieve by following target function:

$\min F\left(\mathrm{\β}\right)=\frac{1}{2}\underset{i=1}{\overset{2n}{\mathrm{\Σ}}}{f}_i^2(x^{\left(k\right)}+\mathrm{\β\Δ}{x}^{\left(k\right)})$

F _i() represents i-th equation in equation group f (x, λ)=f (x)-S=0, and 2n is the number of equation, obtains scalar multiplier β by asking for F (β) extreme value, equation as shown in the formula:

$\frac{\mathrm{dF}\left(\mathrm{\β}\right)}{\mathrm{d\β}}=0$

Before finding collapse critical point, carry out with iteration, β is more and more less, until be 0, now target function maintains one on the occasion of upper, corresponding state variable x ^*for the least square solution of trend, corresponding Jacobian matrix J (x ^*) unusual.

2, according to Newton iteration method convergence situation analysis voltage stability margin, and voltage collapse vertex type is distinguished;

If in the iteration of step 1, occur that the situation of PV/PQ type conversion occurs certain node repeatedly, this node is idle, and units limits causes system generation voltage collapse active constraint, and constraint induction type voltage collapse occurs, and this node is voltage collapse point;

If in the iteration of step 1, occur that the situation of PV/PQ type conversion occurs certain several node repeatedly, its mechanism and single node are changed similar repeatedly, then record these nodes, select 1 node i at every turn, calculate trend by described step 1, after trend convergence, according to final Jacobian matrix meter sensitivity, if meet the following conditions:

$\left\{\begin{array}{c}\frac{\mathrm{d\λ}}{d{V}_{\mathrm{Gi}}}>0\\ \frac{\mathrm{d\λ}}{d{Q}_{\mathrm{Gi}}}>0\end{array}\right.$

Then node i is the node causing constraint induction type voltage collapse, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power that node i generator injects,

If in the iteration of step 1, the correction of voltage stability margin is less than default precision, default precision is depending on counting accuracy requirement, 0.001 is got in the present invention, then the type of voltage collapse point is saddle junction type, then, after obtaining least square solution, need to revise voltage stability margin λ further, search voltage collapse point, namely search the voltage stability margin λ of corresponding voltage collapse point _critical, be specially:

As shown in Figure 3, definition ∑ is have between power flow equation to separate and without the border of separating between region, the least square solution x of gained ^*meet (1) f (x ^*) be positioned on ∑, corresponding Jacobian matrix J (x ^*) unusual; (2) J (x ^*) left eigenvector ω corresponding to zero eigenvalue ^*with ∑ at f (x ^*) place is orthogonal.Node clean injecting power vector S forms a space, S ^λ, S ', S ^mthree is vector power in space, and definition S ' is current power vector, definition S ^mfor ∑ is at state variable x ^*point nearest apart from current power vector S ' Euclidean distance on the section at place, definition S ^λfor section and node injecting power change direction vector b intersection point, S ^λwith S ^criticaloverlap, S ^criticalrepresent the vector power that voltage collapse critical point is corresponding, the correction amount λ of definition voltage stability margin is S ' and S ^λbetween load parameter difference, then S ^λcan following formula be expressed as:

S ^λ＝S′-Δλb

$\mathrm{\Δ\λ}=\frac{{\left|\right|S^{\′}-f\left(x^{*}\right)\left|\right|}_2\cos {\mathrm{\θ}}_1}{{\left|\right|b\left|\right|}_2\cos {\mathrm{\θ}}_2}$

Wherein, θ ₁represent vector power S ^mwith the power flow equation f (x at least square solution place ^*) between angle, θ ₂represent vector power S ^mand S ^λbetween angle,

When ∑ is convex surface, the amendment type of voltage stability margin λ is:

λ ^(k+1)＝λ ^(k)-Δλ ^(k+1)

When ∑ is concave curved surface,

If Δ λ ^(k)be greater than default precision, then the amendment type of voltage stability margin λ is:

${\mathrm{\λ}}^{(k+1)}={\mathrm{\λ}}^{\left(k\right)}+\frac{\mathrm{\Δ}{\mathrm{\λ}}^{\left(k\right)}}{2}$

If θ ₁=90 ° or θ ₂=90 ° and θ ₁when ≠ 90 °, then according to the correction amount λ of following formula calculating voltage stability margin:

$\mathrm{\Δ\λ}=\frac{{\left|\right|S^{\′}-f\left(x^{*}\right)\left|\right|}_2}{{\left|\right|b\left|\right|}_2}$

The amendment type of voltage stability margin λ is: λ ^(k+1)=λ ^(k)-Δ λ ^(k+1).

If 3 electric power systems are broken down, still according to the Newton iteration method of carrying out from feasible zone outside based on Optimal Multiplier, ask for voltage stability margin and determine voltage collapse critical point, in an iterative process, the voltage collapse critical point nargin that iteration initial point is asked under selecting described step 1 normal operating mode, i.e. λ _critical;

4, the voltage stability margin asked for of analytical procedure 3, if voltage stability margin is not less than 0, be then stable fault, carry out order of severity sequence according to voltage stability margin size to stable fault, voltage stability margin value is less, and fault is more serious; If voltage stability margin is less than 0, is then unstability fault, first carries out parametrization to fault, if reflection system failure parameters is μ, and parameter area is: 0 < μ < 1,

Fault parameter μ represents that fault does not occur when being 0, represent that fault thoroughly occurs when being 1, for a unstability fault, thoroughly there is rear power flow equation without solution in fault, therefore passes through from feasible zone based on the Newton iteration method of Optimal Multiplier, this load flow feasible region outside from μ=0, namely in an iterative process, voltage stability margin when iteration initial point selects fault parameter to be 0, along with μ increases gradually, find voltage collapse critical point, corresponding μ value is namely as the parameter of contingency ranking.μ value is larger, and fault is more serious, the most catastrophe failure of μ=1 correspondence.

5, calculation procedure 4) the voltage collapse critical point fault parameter asked for, carry out order of severity sequence according to fault parameter size to unstability fault, fault parameter is larger, and fault is more serious; The calculating of fault parameter μ is obtained by following parametrization power flow equation:

(1) the parametrization power flow equation that exits of single generator

$\left\{\begin{array}{c}\mathrm{\&mu;}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})-V_i^2{G}_{\mathrm{ii}}=0\\ \mathrm{\&mu;}{Q}_{G\min U}\&le;Q_{\mathrm{Gi}}\&le;\mathrm{\&mu;}{Q}_{G\max U}\end{array}\right.$

(2) the parametrization power flow equation that exits of single shunt capacitor or reactor

$\mathrm{\&mu;}{Q}_{\mathrm{Si}}-Q_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})+V_i^2{B}_{\mathrm{ii}}=0$

(3) the parametrization power flow equation that exits of single load

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-\mathrm{\&mu;}{P}_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})-V_i^2{G}_{\mathrm{ii}}=0\\ Q_{\mathrm{Si}}-\mathrm{\&mu;}{Q}_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})+V_i^2{B}_{\mathrm{ii}}=0\end{array}\right.$

(4) the parametrization power flow equation that exits of single branch road

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\&Element;I,j\&NotEqual;m}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})-V_i{V}_m(\mathrm{\&mu;}{G}_{\mathrm{im}}\cos {\mathrm{\&theta;}}_{\mathrm{im}}+\mathrm{\&mu;}{B}_{\mathrm{im}}\sin {\mathrm{\&theta;}}_{\mathrm{im}})-V_i^2{G}_{\mathrm{iinew}}=0\\ Q_{\mathrm{Ri}}-Q_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})-V_i{V}_m(\mathrm{\&mu;}{G}_{\mathrm{im}}\cos {\mathrm{\&theta;}}_{\mathrm{im}}+\mathrm{\&mu;}{B}_{\mathrm{im}}\sin {\mathrm{\&theta;}}_{\mathrm{im}})-V_i^2{G}_{\mathrm{iinew}}+V_i^2{B}_{\mathrm{ii}}\mathrm{new}=0\end{array}\right.$

When there is multiple faults, the system parameters power flow equation of multiple compound contingency is the linear superposition of above several situation, only adopts a parameter μ, and multiple faults occurs with certain parameter level, and weighs,

Wherein, P _dithe active power of the load absorption of node i; P _gifor the active power that node i generator injects; Q _gifor the reactive power that node i generator injects; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit that generator reactive exports; Q _rifor the capacity of reactive-load compensation capacitor after fault; V _ifor the voltage magnitude of node i; I is all node set; θ _ijfor the phase angle difference between node i, j; B _ijfor the susceptance between admittance matrix interior joint i, j; G _ijfor the conductance between admittance matrix interior joint i, j; G _iifor the self-conductance of node i; B _iifor node i from susceptance; G _iinewfor branch road i-m break down after self-conductance in system admittance matrix; B _iinewfor branch road i-m break down after in system admittance matrix from susceptance.

6, as shown in Figure 4, two kinds of sequences of combining step 4 and step 5, according to voltage stability margin value from big to small, then fault parameter order from small to large, to unified sequence of being out of order, instructs power system operation.

Claims (5)

1. the air extract analysis of electric power system and system failure sort method, is characterized in that, comprise the following steps:

(1) according to the monitoring result to electric power system, judge whether electric power system breaks down, if electric power system is not broken down, namely under normal operating mode, then carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for the voltage stability margin of electric power system on predetermined load growing direction and determine voltage collapse critical point, then proceeding to step 2); If electric power system is broken down, then directly enter step 3);

(2) according to Newton iteration method convergence situation analysis voltage stability margin, and voltage collapse vertex type is distinguished;

(3) if electric power system is broken down, still according to the Newton iteration method of carrying out from feasible zone outside based on Optimal Multiplier, ask for voltage stability margin and determine voltage collapse critical point, in an iterative process, the voltage stability margin asked under selecting described step (1) normal operating mode of iteration initial point and voltage collapse critical point;

(4) voltage stability margin that described step (3) is asked for is analyzed, if voltage stability margin is not less than 0, is then stable fault, according to voltage stability margin size, order of severity sequence is carried out to stable fault, voltage stability margin value is less, and fault is more serious; If voltage stability margin is less than 0, be then unstability fault, first parametrization carried out to fault, then ask for voltage collapse critical point according to the Newton iteration method based on Optimal Multiplier from feasible zone outside, in an iterative process, voltage stability margin when iteration initial point selects fault parameter to be 0;

(5) calculate the voltage collapse critical point fault parameter that described step (4) is asked for, carry out order of severity sequence according to fault parameter size to unstability fault, fault parameter is larger, and fault is more serious;

(6) two kinds of sequences of combining step (4) and step (5), according to voltage stability margin value from big to small, then fault parameter order from small to large, to unified sequence of being out of order, instructs power system operation.

2. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, in described step (1), carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for voltage stability margin and determine that the concrete grammar of voltage collapse critical point is:

The growing direction of load and generator is defined by following formula:

P _Li＝P _Li0+λb _Pi

Q _Li＝Q _Li0+λb _Qi

P _Gi＝P _Gi0+λb _Gi

Wherein, λ is voltage stability margin, P _li0, Q _li0be respectively active power and reactive power that node i injects under normal condition, P _li, Q _libe respectively active power and reactive power that node i injects under current state, P _gi0, P _gifor the active power that node i generator injects under normal condition and under current state, b _pi, b _qi, b _gibe respectively that the load of node i is meritorious exerts oneself, idlely exert oneself and the change direction vector of generator output;

Power flow equation with parameter is expressed as:

f(x,λ)＝f(x)-S＝0

S＝S ₀+λb

Wherein, S ₀, S is respectively under normal condition and current state lower node and generator injecting power vector, S ₀=(P _li0, Q _li0, P _gi0), S=(P _li, Q _li, P _gi), b is node and generator injecting power change direction vector, b=(b _pi, b _qi, b _gi), x is state variable;

Adopt the Newton iteration method of Optimal Multiplier, iteration initial point is chosen and is met the voltage stability margin value of trend outside feasible zone, obtains state variable x in trend kth time iteration ^(k)correction amount x ^(k),

Δ x ^(k)=J ^(k)-1f (x ^(k)), wherein, J ^(k)for the Jacobian matrix of kth time iteration, f (x ^(k)) for kth time iteration is obtained state variable x ^(k)substitute into power flow equation group, the concrete form of Jacobian matrix is:

$J=\left[\begin{array}{cccc}\frac{\&PartialD;f_1}{\&PartialD;x_1}& \frac{\&PartialD;f_1}{\&PartialD;x_2}& ...& \frac{\&PartialD;f_1}{\&PartialD;x_n}\\ \frac{\&PartialD;f_2}{\&PartialD;x_1}& \frac{\&PartialD;f_2}{\&PartialD;x_2}& ...& \frac{\&PartialD;f_2}{\&PartialD;x_n}\\ & ...& & \\ \frac{\&PartialD;f_n}{\&PartialD;x_1}& \frac{\&PartialD;f_n}{\&PartialD;x_2}& ...& \frac{\&PartialD;f_n}{\&PartialD;x_n}\end{array}\right]$

Correction amount x is multiplied by with a scalar multiplier β ^(k), then revise state variable x ^(k), the sub-β of its Scalar Multiplication is tried to achieve by following target function:

$\min F\left(\mathrm{\&beta;}\right)=\frac{1}{2}\underset{i=1}{\overset{2n}{\mathrm{\&Sigma;}}}{f_i}^2(x^{\left(k\right)}+\mathrm{\&beta;\&Delta;}{x}^{\left(k\right)})$

F _i() represents i-th equation in equation group f (x, λ)=f (x)-S=0, and 2n is the number of equation, obtains scalar multiplier β by asking for F (β) extreme value, equation as shown in the formula:

$\frac{\mathrm{dF}\left(\mathrm{\&beta;}\right)}{\mathrm{d\&beta;}}=0;$

The state variable x that scalar multiplier β is corresponding when being 0 ^*for the least square solution of power flow equation, voltage stability margin λ when β is 0 _criticalbe the margin value that voltage collapse critical point is corresponding.

3. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, the specific implementation process of described step (2) is:

If in the iteration of step (1), occur that the situation of PV/PQ type conversion occurs certain node repeatedly, then the type of voltage collapse point is constraint induction type, and this node is voltage collapse point;

If in the iteration of step (1), occur that the situation of PV/PQ type conversion occurs certain several node repeatedly, then the type of voltage collapse point is constraint induction type, record these nodes, select 1 node i at every turn, calculate trend by described step (1), after trend convergence, according to final Jacobian matrix meter sensitivity, if meet the following conditions:

$\left\{\begin{array}{c}\frac{\mathrm{d\&lambda;}}{d{V}_{\mathrm{Gi}}}>0\\ \frac{\mathrm{d\&lambda;}}{d{Q}_{\mathrm{Gi}}}>0\end{array}\right.$

Then node i is voltage collapse point, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power that node i generator injects,

If in the iteration of step (1), the correction of voltage stability margin is less than default precision, then the type of voltage collapse point is saddle junction type, after then obtaining least square solution, need to revise voltage stability margin λ further, search voltage collapse point, namely search the voltage stability margin λ of corresponding voltage collapse point _critical, be specially:

Definition Σ has between power flow equation to separate and without the border of separating between region, node clean injecting power vector S forms a space, S ^λ, S', S ^mthree is vector power in space, and S' is current power vector, definition S ^mfor Σ is at state variable x ^*point nearest apart from current power vector S' Euclidean distance on the section at place, definition S ^λfor section and node injecting power change direction vector b intersection point, S ^λwith S ^criticaloverlap, S ^criticalrepresent the vector power that voltage collapse critical point is corresponding, the correction amount λ of definition voltage stability margin is S' and S ^λbetween load parameter difference, then S ^λcan following formula be expressed as:

S ^λ＝S'-Δλb

$\mathrm{\&Delta;\&lambda;}=\frac{{\left|\right|S^{\&prime;}-f\left(x^{*}\right)\left|\right|}_2\cos {\mathrm{\&theta;}}_1}{{\left|\right|b\left|\right|}_2\cos {\mathrm{\&theta;}}_2}$

Wherein, θ ₁represent vector power S ^mwith the power flow equation f (x at least square solution place ^*) between angle, θ ₂represent vector power S ^mand S ^λbetween angle,

When Σ is convex surface, the amendment type of voltage stability margin λ is:

λ ^(k+1)＝λ ^(k)-Δλ ^(k+1)

When Σ is concave curved surface,

If Δ λ ^(k)be greater than default precision, then the amendment type of voltage stability margin λ is:

${\mathrm{\&lambda;}}^{(k+1)}={\mathrm{\&lambda;}}^{\left(k\right)}+\frac{\mathrm{\&Delta;}{\mathrm{\&lambda;}}^{\left(k\right)}}{2}$

If θ ₁=90 ° or θ ₂=90 ° and θ ₁when ≠ 90 °, then according to the correction amount λ of following formula calculating voltage stability margin:

$\mathrm{\&Delta;\&lambda;}=\frac{{\left|\right|S^{\&prime;}-f\left(x^{*}\right)\left|\right|}_2}{{\left|\right|b\left|\right|}_2}$

The amendment type of voltage stability margin λ is: λ ^(k+1)=λ ^(k)-Δ λ ^(k+1).

4. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, described step (5) is carried out parametrization to fault and is referred to, if reflection system failure parameters is μ, and parameter area is:

0＜μ＜1

Fault parameter μ represents that fault does not occur when being 0, represents that fault thoroughly occurs when being 1.

5. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, in described step (5), for different faults, the calculating of fault parameter μ is obtained by following parametrization power flow equation:

(1) the parametrization power flow equation that exits of single generator

$\left\{\begin{array}{c}\mathrm{\&mu;}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})-{V_i}^2{G}_{\mathrm{ii}}=0\\ \mathrm{\&mu;}{Q}_{G\min U}\&le;Q_{\mathrm{Gi}}\&le;\mathrm{\&mu;}{Q}_{G\max U}\end{array}\right.$

(2) the parametrization power flow equation that exits of single shunt capacitor or reactor

$\mathrm{\&mu;}{Q}_{\mathrm{Si}}-Q_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})+{V_i}^2{B}_{\mathrm{ii}}=0$

(3) the parametrization power flow equation that exits of single load

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-\mathrm{\&mu;}{P}_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})-{V_i}^2{G}_{\mathrm{ii}}=0\\ Q_{\mathrm{Si}}-\mathrm{\&mu;}{Q}_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})+{V_i}^2{B}_{\mathrm{ii}}=0\end{array}\right.$

(4) the parametrization power flow equation that exits of single branch road

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\&Element;I,j\&NotEqual;m}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})-V_i{V}_m(\mathrm{\&mu;}{G}_{\mathrm{im}}\cos {\mathrm{\&theta;}}_{\mathrm{im}}+\mathrm{\&mu;}{B}_{\mathrm{im}}\sin {\mathrm{\&theta;}}_{\mathrm{im}})-{V_i}^2{G}_{\mathrm{iinew}}=0\\ Q_{\mathrm{Ri}}-Q_{\mathrm{Di}}-V_i\underset{j\&Element;I}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})-V_i{V}_m(\mathrm{\&mu;}{G}_{\mathrm{im}}\cos {\mathrm{\&theta;}}_{\mathrm{im}}+\mathrm{\&mu;}{B}_{\mathrm{im}}\sin {\mathrm{\&theta;}}_{\mathrm{im}})-{V_i}^2{G}_{\mathrm{iinew}}+{V_i}^2{B}_{\mathrm{ii}}\mathrm{new}=0\end{array}\right.$

If there is multiple faults, then parametrization power flow equation is the linear superposition of each single fault parameter power flow equation in this multiple faults;

Wherein, P _dithe active power of the load absorption of node i; P _gifor the active power that node i generator injects; Q _gifor the reactive power that node i generator injects; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit that generator reactive exports; Q _rifor the capacity of reactive-load compensation capacitor after fault; V _ifor the voltage magnitude of node i; I is all node set; θ _ijfor the phase angle difference between node i, j; B _ijfor the susceptance between admittance matrix interior joint i, j; G _ijfor the conductance between admittance matrix interior joint i, j; G _iifor the self-conductance of node i; B _iifor node i from susceptance; G _iinewfor branch road i-m break down after self-conductance in system admittance matrix; B _iinewfor branch road i-m break down after in system admittance matrix from susceptance.