CN103795058A - Static voltage stability margin analyzing and system fault ordering method of power system - Google Patents

Abstract

The invention provides a static voltage stability margin analyzing and system fault ordering method of a power system. The static voltage stability margin analyzing and system fault ordering method includes the following steps that the Newton iteration method based on the optimal multiplier is used for determining a static voltage collapse point; according to the characteristic of iteration convergence, the type of the voltage collapse point is judged; according to the requirement for stability margin, system fault danger conditions are checked and ordering of stability faults is performed; the faults are parameterized and the iteration method is used for giving out the order of seriousness degrees of instability faults. According to the static voltage stability margin analyzing and system fault ordering method of the power system, voltage stability margins of the power system can be rapidly given online, real-time effective monitoring is carried out on the voltage stability and the comprehensive order of the stability faults and the instability faults can be used for guiding a power generator to adjust online and switching reactive power compensation devices when the system encounters faults, can also guide sub-circuit parameter adjusting, line increasing and decreasing, configuration of an FACTS device and the like off line and have great significance in operation and planning of the power system.

Description

The static voltage stability nargin of electric power system is analyzed and system failure sort method

Technical field

The present invention relates to the technical field of power system monitoring, analysis and control, the static voltage stability nargin of specifically a kind of electric power system is analyzed 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, electric power networks often operates under high load capacity level, face the critical restriction of voltage stabilization, caused a series of great voltage stabilization accidents.

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 of commonly using the most, the method has clear and definite physical background, analytical effect is directly perceived, has the ripe analytical methods such as continuous tide, as shown in Figure 1, define voltage stability margin λ by following formula

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

In Fig. 1, P _maxcthe active power level of system while referring to voltage collapse point, P _initialrefer to system initial launch point active power level, P _maxIrefer to that system operation meets the maximum reactive power level of the lower system of certain nargin requirement, V _irefer to that system operation meets certain nargin and requires lower lowest voltage of a system level, V _cvoltage levvl while referring to voltage collapse point.

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

Voltage stability margin real-time assessment and method for optimally controlling after Chinese invention patent (application number 201010140847.1) power transmission network catastrophe failure, by judging that the solution point calculating in iterative trend step is true separates or optimal solution is carried out the voltage stability of system after failure judgement, utilize damped Newton method to solve, increase iterative process one time, recycling continuous tide solves stability margin, iterations is more, the time is longer, and there is no to realize the sequence to the fault order of severity.

A kind of method for evaluating severity of power system fault of Chinese invention patent (application number 201110368041.2), judges according to simulation process information whether system merit angle, voltage, frequency unstability have occurred; Calculate respectively the serious coefficient of this fault according to merit angle, voltage, three indexs of frequency, aforementioned three serious coefficients that obtain are weighted to combination and draw comprehensive serious coefficient, this fault order of severity sort method relates to voltage stabilization and frequency stabilization, be not to solve pointedly voltage stabilization contingency ranking name problem, and contingency ranking according to being fail result, that the impact that fault is produced system is sorted, the complexity that solves fault is not discussed, cannot be provided the traffic control method that solves fault simultaneously.

Summary of the invention

The invention provides a kind of analysis of static voltage stability nargin and system failure sort method of electric power system, can provide more quickly online the voltage stability margin of system, the voltage stability of electric power system is carried out in real time to effectively monitoring; Stable fault and de-stabilise fault integrated ordered can be in the time that system breaks down online direction generator output adjust and the switching of reactive-load compensation equipment, also can off-line instruct the configuration of branch road parameter adjustment, circuit increase and decrease, FACTS equipment etc., the operation of electric power system and planning are all had to important meaning.

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

The static voltage stability nargin of electric power system is analyzed and system failure sort method, comprises 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, under normal operating mode, carry out the Newton iteration method based on Optimal Multiplier from feasible zone, ask for voltage stability margin and the definite voltage collapse critical point of electric power system on predetermined load growing direction, then proceed to step 2); If electric power system is broken down, directly enter step 3);

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

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

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

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

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

In aforesaid step (1), carry out the Newton iteration method based on Optimal Multiplier from feasible zone, the concrete grammar of asking for voltage stability margin and definite 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 is injected under normal condition, P _li, Q _libe respectively active power and reactive power that node i is injected 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 meritorious the exerting oneself of load of node i, idle exerting 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;

The Newton iteration method that adopts 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 the k time iteration of trend ^(k)correction amount x ^(k), Δ x ^(k)=J ^(k)-1f (x ^(k)), wherein, J ^(k)be the Jacobian matrix of the k time iteration, f (x ^(k)) for the k time iteration obtained to state variable x ^(k)substitution power flow equation group, the concrete form of Jacobian matrix is:

Be multiplied by correction amount x 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 equation in equation group f (x, λ)=f (x)-S=0, the number that 2n is equation, by asking for F (β) extreme value acquisition scalar multiplier β, equation as shown in the formula:

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

Scalar multiplier β is 0 o'clock corresponding state variable x ^*for the least square solution of power flow equation, β is the voltage stability margin λ of 0 o'clock _criticalbe margin value corresponding to voltage collapse critical point.

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, the type of voltage collapse point is constraint induction type, 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, 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:

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

Node i is voltage collapse point, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power of node i generator injection,

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

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

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 ^mpower flow equation f (x with 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, 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 ₁≠ 90 ° time, 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, establishing reflection system failure parameter is μ, and parameter area is:

0＜μ＜1

Fault parameter μ represents that fault does not occur at 0 o'clock, is to represent that fault thoroughly occurs at 1 o'clock.

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 single generator exits

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

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

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

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

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

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

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

If there is multiple faults, 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 of node i generator injection; Q _gifor the reactive power of node i generator injection; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit of generator reactive output; 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 node i, j in admittance matrix; G _ijfor the electricity between node i, j in admittance matrix is led; 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 obtain by system SCADA or PMU are carried out Direct Analysis, and off-line analysis is easy to complete by emulation tool;

2) calculating is simple, quick, use has avoided continuous tide to solve the situation that voltage collapse critical point is difficult for convergence in the time approaching collapse point from feasible zone based on Load Flow Method with Optimal Multiplier iterative analysis method, trend iteration initial point is clear and definite, has reduced iterations, affected by system scale few;

3) system is broken down and carries out parametrization, utilization does not have the fault parameter between the 0-1 of physical significance to carry out the sequence of the fault order of severity, be not only the sequence to the failure effect order of severity for the parameter sorting, is mostly sequence situations that fault generating process or on-line operation solve difficulty;

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

Accompanying drawing explanation

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

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

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

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

Fig. 5 is the analysis of static voltage stability nargin 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.

Utilization of the present invention is carried out the Optimal Multiplier Newton iteration method of iteration from feasible zone, the method iterative target is for finding voltage collapse critical point, can analyze system voltage stability margin, the method has avoided conventional continuous tide to calculate the problem of the convergence difficulties producing in the time approaching collapse point, reduce iterations, improve the speed of solving, also can identify voltage collapse type according to convergence characteristic.

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, under normal operating mode, carry out the Newton iteration method based on Optimal Multiplier from feasible zone, ask for voltage stability margin and the definite voltage collapse critical point of electric power system on predetermined load growing direction, then proceed to step 2; If electric power system is broken down, 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 is injected under normal condition, P _li, Q _libe respectively active power and reactive power that node i is injected 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 meritorious the exerting oneself of load of node i, idle exerting oneself and the change direction vector of generator output.Above node power can substitution 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 as shown in the figure direction, find nargin λ corresponding to voltage collapse critical point _critical;

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

Be multiplied by correction amount x 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 equation in equation group f (x, λ)=f (x)-S=0, the number that 2n is equation, by asking for F (β) extreme value acquisition scalar multiplier β, 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 distinguish voltage collapse vertex type;

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 is to cause system generation voltage collapse active constraint, and constraint induction type voltage collapse occurs, 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, 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:

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

Node i is the node that causes constraint induction type voltage collapse, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power of node i generator injection,

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, in the present invention, get 0.001, the type of voltage collapse point is saddle junction type, obtains after least square solution, needs further to revise voltage stability margin λ, search voltage collapse point, search the voltage stability margin λ of corresponding voltage collapse point _critical, be specially:

As shown in Figure 3, definition ∑ is to have and separate and without the border of separating between region, the least square solution x of gained between power flow equation ^*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 ^*) locate orthogonal.A space of the clean injecting power vector of node S composition, 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 ^*on the section at place, apart from the nearest point of current power vector S ' Euclidean distance, define S ^λfor the intersection point of section and node injecting power change direction vector b, S ^λwith S ^criticaloverlap, S ^criticalrepresent vector power corresponding to voltage collapse critical point, the correction amount λ of definition voltage stability margin is S ' and S ^λbetween load parameter difference, S ^λcan be expressed as following formula:

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 ^mpower flow equation f (x with 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, 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 ₁≠ 90 ° time, 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 carrying out the Newton iteration method based on Optimal Multiplier from feasible zone, ask for voltage stability margin and definite voltage collapse critical point, in iterative process, iteration initial point is selected the voltage collapse critical point nargin of asking under described step 1 normal operating mode, i.e. λ _critical;

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

Fault parameter μ represents that fault does not occur at 0 o'clock, be to represent that fault thoroughly occurs at 1 o'clock, for a unstability fault, after fault thoroughly occurs, power flow equation is without solution, therefore by the Newton iteration method based on Optimal Multiplier from feasible zone, this trend feasible zone from μ=0, in iterative process, iteration initial point selection fault parameter is the voltage stability margin of 0 o'clock, along with μ increases gradually, find voltage collapse critical point, corresponding μ value is as the parameter of contingency ranking.μ value is larger, and fault is more serious, the catastrophe failure of μ=1 correspondence.

5, calculation procedure 4) the voltage collapse critical point fault parameter asked for, according to fault parameter size, unstability fault is carried out to order of severity sequence, 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 single generator exits

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

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

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

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

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

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

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

In the time there is multiple faults, the system parameters power flow equation of multiple complex fault is the linear superposition of above several situations, 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 of node i generator injection; Q _gifor the reactive power of node i generator injection; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit of generator reactive output; 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 node i, j in admittance matrix; G _ijfor the electricity between node i, j in admittance matrix is led; 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 comprehensive step 4 and step 5, according to voltage stability margin value from big to small, then fault parameter order from small to large, gives the unified sequence of being out of order, and instructs power system operation.

Claims (5)

1. the static voltage stability nargin of electric power system is analyzed and system failure sort method, it is characterized in that, comprises 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, under normal operating mode, carry out the Newton iteration method based on Optimal Multiplier from feasible zone, ask for voltage stability margin and the definite voltage collapse critical point of electric power system on predetermined load growing direction, then proceed to step 2); If electric power system is broken down, directly enter step 3);

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

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

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

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

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

2. the static voltage stability nargin of electric power system according to claim 1 is analyzed 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, the concrete grammar of asking for voltage stability margin and definite 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 is injected under normal condition, P _li, Q _libe respectively active power and reactive power that node i is injected 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 meritorious the exerting oneself of load of node i, idle exerting 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;

The Newton iteration method that adopts 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 the k time iteration of trend ^(k)correction amount x ^(k), Δ x ^(k)=J ^(k)-1f (x ^(k)), wherein, J ^(k)be the Jacobian matrix of the k time iteration, f (x ^(k)) for the k time iteration obtained to state variable x ^(k)substitution power flow equation group, the concrete form of Jacobian matrix is:

Be multiplied by correction amount x 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 equation in equation group f (x, λ)=f (x)-S=0, the number that 2n is equation, by asking for F (β) extreme value acquisition scalar multiplier β, equation as shown in the formula:

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

Scalar multiplier β is 0 o'clock corresponding state variable x ^*for the least square solution of power flow equation, β is the voltage stability margin λ of 0 o'clock _criticalbe margin value corresponding to voltage collapse critical point.

3. the static voltage stability nargin of electric power system according to claim 1 is analyzed 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, the type of voltage collapse point is constraint induction type, 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, 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:

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

Node i is voltage collapse point, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power of node i generator injection,

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

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

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 ^mpower flow equation f (x with 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, 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 ₁≠ 90 ° time, 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 static voltage stability nargin of electric power system according to claim 1 is analyzed and system failure sort method, it is characterized in that, described step (5) is carried out parametrization to fault and referred to, establishing reflection system failure parameter is μ, and parameter area is:

0＜μ＜1

Fault parameter μ represents that fault does not occur at 0 o'clock, is to represent that fault thoroughly occurs at 1 o'clock.

5. the static voltage stability nargin of electric power system according to claim 1 is analyzed 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 single generator exits

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

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

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

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

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

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

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

If there is multiple faults, 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 of node i generator injection; Q _gifor the reactive power of node i generator injection; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit of generator reactive output; 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 node i, j in admittance matrix; G _ijfor the electricity between node i, j in admittance matrix is led; 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.

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