CN103972881A - Multi-FACTS (flexible alternating-current transmission system) structure based chain structure high-voltage grid security control method - Google Patents

Abstract

The invention discloses a multi-FACTS (flexible alternating-current transmission system) structure based chain structure high-voltage grid security control method. The chain structure high-voltage grid security control method mainly comprises establishing a power system model and a dynamic element model on the basis of transient stability; establishing a coordinated optimization model considering coordination among multiple FACTS for the chain structure high-voltage grid on the basis of the power system model and the dynamic element model; and solving the optimal solution of the coordinated optimization model. The multi-FACTS structure based chain structure high-voltage grid security control method can overcome the defects of low reliability, poor coordination and stability and the like in the prior art and has the advantages of high reliability, good coordination and stability.

Description

Chain structure high-voltage fence method of controlling security based on many FACTS structure

Technical field

The present invention relates to the generator scheduling controlling technical field in electric power system, particularly, relate to the chain structure high-voltage fence method of controlling security based on many FACTS structure.

Background technology

Electric power system is the Dynamic Large-Scale Systems of non-linear, a high dimension, multiple target, layer distributed, keeps its safe and stable operation to be significant to national economy, electric power enterprise and user.Along with the continuous expansion of Power System Interconnection scale, and significantly improving of requiring of the fast development of electricity market and user's side quality of power supply, the running environment of electric power system and dynamic characteristic more sophisticated, have higher requirement to the safe and stable operation of electrical network.

In order to improve power system transient stability, dynamic stability and voltage stability, avoid the generation of the accident of having a power failure on a large scale, ensure that electric power is reliable and secure, high-quality is supplied economically, the effect of security and stability control measurement is further important.As the important means of security and stability control measurement, Survey of Flexible AC Transmission System Technology (FACTS) is more and more extensive in the application of electric power system, and the effect of performance is more and more significant.FACTS element is based on high-power electric and electronic technology, control in real time voltage, electric current, reactance and the phase angle of transmission system, can improve the ability to transmit electricity of transmission channel and the voltage support ability of system, strengthen fail safe and the flexibility of system, improve the stability of system.Therefore, in Xinjiang and 750 kilovolts of second channel engineerings of northwest major network networking, FACTS element is widely applied, for system stability after improving networking has played important function.

Xinjiang and 750 kilovolts of second channel engineerings of northwest major network networking, that State Grid Corporation of China implements energy intensive development, the important engineering of construction of energy electric power major path, after Xinjiang, Tibet and the networking of northwest major network, further strengthen the another major project that 750 kilovolts of northwests main grid structure is built, also be the key project of " boundary electricity is sent outside ", after building up, the important Transmission Corridor of Jiuquan, Hami, Qaidam area wind energy and solar power generation will be become, form typical chain structure high voltage network, promote effectively Xinjiang power exploitation to send outside.Meanwhile, Qinghai Power Grid short of electricity situation be will effectively alleviate, the power supply capacity of recycling economy trial zone, Qaidam and the reliability to Tibet direct current transportation improved.The dynamic passive compensation of sending outside for meeting the large electrical network of chain structure high pressure and new forms of energy, this project has been equipped with many FACTS system, this system comprises station, husky state 66kV side 360Mvar SVC, the magnet controlled bus high resistance of fish card station 750kV side 330MVar (magnetically controlled reactor, be called for short MCR), the valve-regulated high resistance of shark circuit 4*390Mvar (valve-controlled reactors, be called for short VCR).

Many FACTS system provides good supporting role for the safe and stable operation of Xinjiang and northwest networked system, but, the installation of so extensive, eurypalynous FACTS equipment has also brought series of problems to system safety, wherein that multiple FACTS interelements disperse independent control the most significantly, do not consider that the control that the reciprocation of multiple FACTS elements may cause is inharmonious, cause operational effect to weaken even system unstability.

Realizing in process of the present invention, the defect such as inventor finds at least to exist in prior art that reliability is low, inaccurate coordination and poor stability.

Summary of the invention

The object of the invention is to, for the problems referred to above, propose the chain structure high-voltage fence method of controlling security based on many FACTS structure, to realize, reliability is high, harmony good and the advantage of good stability.

For achieving the above object, the technical solution used in the present invention is: the chain structure high-voltage fence method of controlling security based on many FACTS structure, mainly comprises:

A, electric power system model and the dynamic element model of foundation based on transient stability;

B, based on electric power system model and dynamic element model, for chain structure high-voltage fence, set up the Coordination and Optimization Model of considering cooperation between many FACTS;

C, utilize Genetic Algorithms, solve the optimal solution of Coordination and Optimization Model.

Further, described step b, specifically comprises:

By transient stability is analyzed, set up the mathematical description form of electric power system transient stability, in conjunction with the model of dynamic element, set up Coordination and Optimization Model and its constraints.

Further, described step c, specifically comprises:

In the situation that there is different disturbance, by solving-optimizing model, how determine according to the order of severity of disturbance and demand for control, optimize the controlled quentity controlled variable of different FACTS equipment, to meet systematic steady state and transient voltage requirement, guarantee system angle stability and voltage stabilization simultaneously, putting before this, make the control Least-cost of paying.

Further, the operation of described solving-optimizing model, specifically comprises:

The establishment of target function; The foundation of various constraintss; Solve by Genetic Algorithms.

Further, the operation of the establishment of described target function, is specially:

min F(x,y,u)

$s.t.\left\{\begin{array}{cc}{G}_i(x,y,u)=0& i=\mathrm{1,2,3},...,N_{\mathrm{eq}}\\ H_j(x,y,u)<0& j=\mathrm{1,2,3},...N_{\mathrm{ueq}}\\ u_{\min }<u_k<u_{\max }& k=\mathrm{1,2,3},...,N_u\\ \mathrm{\&eta;}(u^1,u^2,...,u^{\mathrm{Nu}})>\mathrm{\&epsiv;}& \end{array}\right.$

Wherein F(x, y, u) be target function, G _iand H _ifor equation and static inequality constraints, η is merit angle, voltage stability margin constraint; X is state variable; Y representation algebra variable; U is control variables; u _max, u _minit is respectively the upper and lower limit of control variables; N _eq, N _ueqand N _ube respectively the sum of equality constraint, inequality constraints and control variables.

Further, the described operation solving by Genetic Algorithms, specifically comprises:

1) coding adopts and has easily convergence under large aberration rate, processes comparatively effectively real coding of function optimization problem;

2) initialization population: adopt Small section method, first the span of each parameter to be optimized is divided into the total several minizones of colony, then generate randomly respectively an initial individuality in each minizone;

3) choosing of target function: the target function using exponential type target function as parameter identification;

4) selection strategy: adopt random system of selection uniformly;

5) crossover and mutation: cross method is selected Heuristic, variation method is selected Adaptive feasible.

Further, in step a, described electric power system model and dynamic element model based on transient stability, is specially:

Power system transient stability refers to that can electric power system is being subjected to after large disturbance, be transitioned into ability new or that return to original steady operational status; The stability of electric power system under large disturbance, is generally divided into three phases system transient process, they respectively:

System before fault:

$\begin{array}{c}\stackrel{.}{x}=f_0(x,y,\mathrm{\&alpha;})\\ 0=g_0(x,y,\mathrm{\&alpha;})\end{array}t\&le;0^{-};$

System in fault:

$\begin{array}{c}\stackrel{.}{x}=f_{F,1}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,1}(x,y,\mathrm{\&alpha;})\end{array}{0}^{+}\&le;t\&le;t_{\mathrm{cl},1}^{-}$

$\begin{array}{c}\stackrel{.}{x}=f_{F,2}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,2}(x,y,\mathrm{\&alpha;})\end{array}{t}_{\mathrm{cl},1}^{+}\&le;t\&le;t_{\mathrm{cl},2}^{-}$

…

$\begin{array}{c}\stackrel{.}{x}=f_{F,k}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,k}(x,y,\mathrm{\&alpha;})\end{array}{t}_{\mathrm{cl},(k-1)}^{+}\&le;t\&le;t_F^{-};$

System after fault:

$\begin{array}{c}\stackrel{.}{x}=f_{\mathrm{PF}}(x,y,\mathrm{\&alpha;})\\ 0=g_{\mathrm{PF}}(x,y,\mathrm{\&alpha;})\end{array}{t}_F^{+}\&le;t;$

X ∈ R ⁿthe state variable of system to Time Continuous; Y ∈ R ^lit is the algebraically variable that can undergo mutation; α ∈ R ^mthat the parameter that dispatcher can regulate and control is called adjustable parameter; Matrix the hypothesis of full rank can ensure that electric power system can be described as the form of ordinary differential equation.

The chain structure high-voltage fence method of controlling security based on many FACTS structure of various embodiments of the present invention, owing to mainly comprising: set up electric power system model and dynamic element model based on transient stability; Based on electric power system model and dynamic element model, for chain structure high-voltage fence, set up the Coordination and Optimization Model of considering cooperation between many FACTS; Utilize Genetic Algorithms, solve the optimal solution of Coordination and Optimization Model; The coordination application of large-scale F ACTS equipment be can be used for instructing, safety and stability, the high-efficiency and economic operation of extensive interconnected network guaranteed; Thereby can overcome that reliability in prior art is low, the defect of inaccurate coordination and poor stability, to realize, reliability is high, harmony good and the advantage of good stability.

Other features and advantages of the present invention will be set forth in the following description, and, partly from specification, become apparent, or understand by implementing the present invention.

Below by embodiment, technical scheme of the present invention is described in further detail.

Embodiment

Describe below in conjunction with the preferred embodiments of the present invention, should be appreciated that preferred embodiment described herein, only for description and interpretation the present invention, is not intended to limit the present invention.

For chain structure high-voltage fence, according to the embodiment of the present invention, chain structure high-voltage fence based on many FACTS structure method of controlling security is provided, has related in particular to one for chain structure high-voltage fence, considered the method for controlling security of cooperation between many FACTS.Be somebody's turn to do the chain structure high-voltage fence method of controlling security based on many FACTS structure; the method of controlling security of considering cooperation between many FACTS not only has important directive significance to the coordination application of large-scale F ACTS equipment; and safety and stability to extensive interconnected network, high-efficiency and economic operation have important value; for instructing the coordination application of large-scale F ACTS equipment, guarantee safety and stability, the high-efficiency and economic operation of extensive interconnected network.

The chain structure high-voltage fence method of controlling security based on many FACTS structure of above-described embodiment, mainly comprises:

Step 1: set up the electric power system transient stability model based on element and the detailed dynamic model of control device;

In step 1, the electric power system transient stability model based on element and the detailed dynamic model of control device is:

Power system transient stability refers to that can electric power system is being subjected to after large disturbance, be transitioned into ability new or that return to original steady operational status.Electric power system for this class disturbance show as generator trend, relatively merit angle, node voltage and other state variable be with respect to the extensive skew of nominal situation.The transient state process of electric power system that large disturbance causes is very complicated, and particularly, under multiple faults, the structure and parameter of system all changes during disturbance.If in the power system stability territory of the Trajectory of the state variable that disturbance causes after fault, system is transient stability so.The stability of research electric power system under large disturbance, is generally divided into three phases system transient process, they respectively:

System before fault:

$\begin{array}{c}\stackrel{.}{x}=f_0(x,y,\mathrm{\&alpha;})\\ 0=g_0(x,y,\mathrm{\&alpha;})\end{array}t\&le;0^{-};$

System in fault:

$\begin{array}{c}\stackrel{.}{x}=f_{F,1}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,1}(x,y,\mathrm{\&alpha;})\end{array}{0}^{+}\&le;t\&le;t_{\mathrm{cl},1}^{-}$

$\begin{array}{c}\stackrel{.}{x}=f_{F,2}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,2}(x,y,\mathrm{\&alpha;})\end{array}{t}_{\mathrm{cl},1}^{+}\&le;t\&le;t_{\mathrm{cl},2}^{-}$

…

$\begin{array}{c}\stackrel{.}{x}=f_{F,2}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,2}(x,y,\mathrm{\&alpha;})\end{array}{t}_{\mathrm{cl},1}^{+}\&le;t\&le;t_{\mathrm{cl},2}^{-}$

System after fault:

$\begin{array}{c}\stackrel{.}{x}=f_{\mathrm{PF}}(x,y,\mathrm{\&alpha;})\\ 0=g_{\mathrm{PF}}(x,y,\mathrm{\&alpha;})\end{array}{t}_F^{+}\&le;t;$

X ∈ R ⁿthe state variable of system to Time Continuous; Y ∈ R ^lit is the algebraically variable that can undergo mutation; α ∈ R ^mthat parameter that dispatcher can regulate and control is called adjustable parameter (transient stability that usually, this parameter can unique decision electric power system).Be noted that matrix the hypothesis of full rank can ensure that electric power system can be described as the form of ordinary differential equation.

(1) generator model and simulator:

In transient stability, equation of rotor motion and the electromagnetic conversion equation of being described by Faraday law etc. etc. dynamically described for Newton second law of generator, its electromagnetic conversion equation mathematics is described below:

Stator voltage equation (being obtained by Park conversion)

$u_d={\stackrel{.}{\mathrm{\&psi;}}}_d-{\mathrm{\&psi;}}_q\mathrm{\&omega;}-R_a{i}_d$

$u_q={\stackrel{.}{\mathrm{\&psi;}}}_d+{\mathrm{\&psi;}}_d\mathrm{\&omega;}-R_a{i}_q$

$u_0={\stackrel{.}{\mathrm{\&psi;}}}_0-R_a{i}_0;$

ψ in above formula _d(i _d), ψ _q(i _q), ψ ₀(i ₀), be respectively d axle and q axle magnetic linkage and electric current; ω is rotating speed, u _d(u _q) be d(q) electromotive force of axle, R _ait is the every phase resistance of armature.

(ii) the each winding voltage equation of rotor:

$e_{\mathrm{fd}}={\stackrel{.}{\mathrm{\&psi;}}}_{\mathrm{fd}}+R_{\mathrm{fd}}{i}_{\mathrm{fd}}$

$0={\stackrel{.}{\mathrm{\&psi;}}}_{1d}+R_{1d}{i}_{1d}$

$0={\stackrel{.}{\mathrm{\&psi;}}}_{1q}+R_{1q}{i}_{1q}$

$0={\stackrel{.}{\mathrm{\&psi;}}}_{2q}+R_{2q}{i}_{2q}$

ψ in above formula _fd, ψ _1d, ψ _1q, ψ _2qbe respectively excitation winding f, the equivalent damping winding D of d axle, the equivalent damping winding q of q axle ₁and q ₂magnetic linkage, R _fd, R _1d, R _1q, R _2qand i _fd, i _1d, i _1q, i _2qfor substitutional resistance and the electric current of above-mentioned four windings, e _fdfor the electromotive force of excitation winding f.

(iii) stator magnetic linkage equation:

ψ _d=-(L _ad+L _l)i _d+L _adi _fd+L _adi _1d

ψ _q=-(L _aq+L _l)i _q+L _aqi _1q+L _aqi _2q

ψ ₀=-L ₀i ₀；

L in above formula _ad(L _aq), L _lmutual inductance and the leakage inductance of difference stator and rotor d axle (q axle).(iv) air gap torque:

T _e=ψ _di _q-ψ _qi _d；

Its equation of rotor motion is:

$\stackrel{.}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_0{\mathrm{\&Delta;\&omega;}}_r;$

${\mathrm{\&Delta;}\stackrel{.}{\mathrm{\&omega;}}}_r=\frac{1}{2H}(T_m-T_e-K_D{\mathrm{\&Delta;\&omega;}}_r);$

Wherein, δ and Δ ω _rrespectively rotor angle and the rotor velocity of generator under synchronous rotating frame, T _mmechanical force moment, T _eit is the electromagnetic torque of definition.

(2) excitation system model:

The equipment of exciting current is provided for synchronous generator specially,, with the foundation of synchronous generator rotor voltage, adjusts and make if desired the relevant equipment of its disappearance, become excitation system.Excitation system is mainly made up of field regulator and exciting power unit.Exciting power unit provides DC excitation electric current to the excitation winding of synchronous generator; Excitation regulation device AER, according to the output of the change in voltage control exciting power unit of extreme voltage, thereby reaches the object that regulates exciting current.

(i) exciting power unit

Do the used time ignoring amplitude limit link (saturation element), typically, the corresponding excitation system of exciter (exciting power unit) can be with basic differential equation:

$T_e{\stackrel{\&CenterDot;}{E}}_{\mathrm{fd}}=-\mathrm{Efd}+K_e{U}_R,$

(ii) field regulator model

Power generator electrode terminal voltage U _tthrough measurement links and given reference voltage U _refmake comparisons, its deviation enters voltage regulator amplify after, output voltage U _ras the exciting voltage of exciter _,to control the output voltage of exciter, machine generator excitation voltage E _fd.For how the stable operation of excitation system improves its dynamic quality _,introduce excitation system negative feedback links, i.e. excitation system stabilizer, it is generally soft feedback element.U _sfor the additional control signal of magnetizing exciter, the often output of power system stabilizer.

Measurement links is T by a time constant _rinertial element represent, due to T _rminimum, (being generally 0～0.02s) is therefore be often left in the basket.Voltage regulator has a lead-lag link and an inertia amplifying element to represent conventionally.Lead-lag link has reflected the phase characteristic of adjuster, due to T _band T _cgenerally very little, can be ignored.It is K that inertia amplifying element amplifies speed _a, time constant is T _a.

Its third-order system model is:

$\begin{array}{c}{T}_e{\stackrel{\&CenterDot;}{E}}_{\mathrm{fd}}=-(K_L+S_E)E_{\mathrm{fd}}+U_r\\ T_f{\stackrel{\&CenterDot;}{U}}_F=-U_F+K_F/T_L(U_R-(K_L+S_E)E_{\mathrm{fd}})\\ T_A{\stackrel{\&CenterDot;}{U}}_R=-U_R+K_A(U_{\mathrm{ref}}-U_t+U_s-U_F)\end{array};$

(3) prime mover and governing system model:

The device that mechanical output and mechanical energy are provided to generator in electric power system, as steam turbine, the hydraulic turbine etc. are referred to as prime mover.In order to control the mechanical output of prime mover to generator output, and keep electrical network about normal running frequency, and between generator arranged side by side separately reasonable distribution load.The system that completes above-mentioned task, is called as governing system.Governing system generally realizes power and frequency adjustment by controlling the porthole aperture of steam turbine or the guide vane aperture of the hydraulic turbine.Adjust parameter and the set-point (general given speed or given power) holded up to obtain the generator power-frequency characteristic needing by change.

(i) steam turbine

Steam turbine is the vane type engine using the steam of uniform temperature and pressure as working medium, on mathematics, represents with first order inertial loop, is write as differential equation form and is:

$T_m{\stackrel{\&CenterDot;}{P}}_m=-P_m+\mathrm{\&mu;};$

In formula, μ is porthole aperture, P _mfor the mechanical output of steam turbine, T _mfor the time constant of reflection vapor volume effect.

(ii) the hydraulic turbine

The hydraulic turbine is the vane type engine taking the water of certain pressure as working medium, and that the model of the hydraulic turbine is described is water wheels aperture μ and output mechanical power P _mbetween dynamic relationship.If ignore the elasticity of conduit pipe, rigidity conduit pipe water hammer effect can be simplified as follows:

$\frac{{\mathrm{\&Delta;P}}_m}{\mathrm{\&Delta;\&mu;}}=\frac{1-T_{w}s}{1+0.5T_{w}s};$

The wherein negative sign of molecule, shows that system is non minimum phase system, has embodied water hammer effect.

(iii) governing system model

The hydrogovernor of simplifying, in the time not considering the links such as amplitude limit, can be write as:

$\begin{array}{c}{T}_s\stackrel{\&CenterDot;}{\mathrm{\&mu;}=K_{\mathrm{\&delta;}}}({\mathrm{\&omega;}}_{\mathrm{ref}}-\mathrm{\&omega;})-K_i(\mathrm{\&mu;}-{\mathrm{\&mu;}}_0)-{\mathrm{\&xi;}}_1\\ {\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_1=-{\mathrm{\&xi;}}_1/T_i+K_{\mathrm{\&beta;}}\stackrel{\&CenterDot;}{\mathrm{\&mu;}}\\ =-(K_{\mathrm{\&beta;}}/T_s+/T_i){\mathrm{\&xi;}}_1-K_{\mathrm{\&beta;}}[K_{\mathrm{\&delta;}}(\mathrm{\&omega;}-{\mathrm{\&omega;}}_{\mathrm{ref}})+K_i(\mathrm{\&mu;}-{\mathrm{\&mu;}}_0)]/T_s\end{array};$

(4) load model:

(i) static load model

Static load model has reacted load meritorious and idle slowly to be changed and the rule of variation in system frequency and voltage, and available algebraic equation or curve represent.The static load that depends on voltage is often expressed as the exponential function form shown in following formula:

$P=P_0{\left(\stackrel{\&OverBar;}{V}\right)}^a$

$Q=Q_0{\left(\stackrel{\&OverBar;}{V}\right)}^b;$

Wherein, P and Q are the meritorious and idle of load; V is the voltage magnitude of busbar voltage that load connects; p ₀, Q ₀and V ₀the active power of load while being respectively datum mark operation, reactive power and load busbar voltage amplitude.

(ii) dynamic load model

In the time that system voltage and frequency change fast, should consider the dynamic characteristic of load, and represent with the differential equation, be referred to as dynamic load model.General Electrical Power System Dynamic load, approximately having 60-70% to be load is motor.The present invention adopts the induction motor model of considering electromechanical transient process.Specific as follows:

Under synchronous coordinate, motor stator winding equation is:

U _x=E′ _x+X′I _y-r _aI _x

U _y=E′ _y-X ^′I _y-r _aI _y；

Wherein X '=X _s+ X _mx _r/ (X _m+ X _r) be the reactance of asynchronous motor transient state.

Above formula can be write as:

U=E′+(r _s+jX′)I

The voltage dynamical equation of rotor:

$\begin{array}{c}{T}_{d0}^{\&prime;}{\stackrel{\&CenterDot;}{E}}_x^{\&prime;}=-E_x^{\&prime;}+(X-X\&prime;)I_y+s{T}_{d0}^{\&prime;}2\mathrm{\&pi;}{f}_0{E}_y^{\&prime;}\\ T_{d0}^{\&prime;}{\stackrel{\&CenterDot;}{E}}_y^{\&prime;}=-E_y^{\&prime;}-(X-X\&prime;)I_x+s{T}_{d0}^{\&prime;}2\mathrm{\&pi;}{f}_0{E}_x^{\&prime;}\end{array};$

Above formula can be write as:

$T_{d0}^{\&prime;}\stackrel{\&CenterDot;}{E}\&prime;=-E\&prime;-j(X-X\&prime;)I-\mathrm{js}{T}_{d0}^{\&prime;}2\mathrm{\&pi;}{f}_{0}E\&prime;;$

Equation of rotor motion is:

$J\stackrel{\&CenterDot;}{s}=T_m-T_e;$

T _e=Re(E′I ^*) ；

(5) FACTS model:

Flexible AC transmission technology (Flexible AC Transmission System, be called for short FACTS) thus the device that mainly utilizes high-power electric and electronic element to form controls or regulates the operational factor/network parameter of AC electric power systems to optimize the running status of electric power system, improves the ability of the technology of transmission of electricity of electric power system.

(i) static reacance generator (Static Var Compensator is called for short SVC)

1. TCR part

2. TSC part

3. overall fundametal compoment analysis:

$Q_{\mathrm{SVC}}=(\mathrm{\&omega;C}-\frac{2\mathrm{\&beta;}-\sin 2\mathrm{\&beta;}}{\mathrm{\&pi;\&omega;L}})V^2;$

(ii) STATCOM STATCOM

STATCOM also claims static reacance generator (Advanced Static Var Generator is called for short ASVG).

The fundamental voltage amplitude of AC output is:

$V_{\mathrm{ASVG}}={\mathrm{KV}}_C\sin \frac{\mathrm{\&theta;}}{2};$

Suppose contravarianter voltage V _aSVGlagging behind system voltage angle is δ, and reactance is y ∠ α, and the active power that inverter absorbs from system is: $P=V_s{V}_{\mathrm{ASVG}}y\sin (\mathrm{\&delta;}+\mathrm{\&alpha;})-V_{\mathrm{ASVG}}^{2}y\sin \mathrm{\&alpha;};$

The reactive power that STATCOM sends into system is:

$Q_{\mathrm{ASVG}}=V_s{V}_{\mathrm{ASVG}}y\cos (\mathrm{\&delta;}+\mathrm{\&alpha;})-V_{\mathrm{ASVG}}^{2}y\cos \mathrm{\&alpha;};$

Under stable situation, inverter neither absorbs and does not also send active power.Therefore it is zero known making P:

$V_{\mathrm{ASVG}}=V_s\frac{\sin (\mathrm{\&delta;}+\mathrm{\&alpha;})}{\sin \mathrm{\&alpha;}};$

Therefore have:

$Q_{\mathrm{ASVG}}=\frac{V_s^2}{2r}\sin 2\mathrm{\&delta;},V_C=\frac{V_s\sin (\mathrm{\&delta;}+\mathrm{\&alpha;})}{K\sin \mathrm{\&alpha;}\sin (\mathrm{\&theta;}/2)};$

Above formula shows, can change if keep constant of pulsewidth θ to adjust phase angle δ the reactive power that STATCOM injects to system, and capacitance voltage also changes thereupon simultaneously.If adjusting pulsewidth θ and whole phase angle δ can make capacitance voltage keep constant and only adjust reactive power simultaneously.

(iii) the series capacitance TCSC of thyristor control:

X _TCSC=K _βX _C；

X _C=1/ωC ；

$K_{\mathrm{\&beta;}}=1+\frac{2{\mathrm{\&lambda;}}^2}{\mathrm{\&pi;}({\mathrm{\&lambda;}}^2-1)}[\frac{{2\cos }^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2-1}(\mathrm{\&lambda;}\tan \mathrm{\&lambda;\&beta;}-\tan \mathrm{\&beta;})-\mathrm{\&beta;}-\frac{\sin 2\mathrm{\&beta;}}{2}];$

Conventionally, consider economic factor, in TCSC, get ω L<1/ ω C, and make λ ²be 7 left and right.When β ∈ [0, pi/2 λ], TCSC is capacitive, and when β ∈ (pi/2 λ, pi/2), TCSC is perceptual.

(6) network model---power flow equation:

For the AC electric power systems of a N node, the power flow equation under its polar coordinate system is as follows:

$P_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(V_i{V}_j{B}_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}+V_i+V_j{G}_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})=0$

$Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(V_i{V}_j{G}_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}+V_i+V_j{B}_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})=0;$

Wherein, P _gi, Q _gi, P _li, Q _lirespectively the generated power in node i, generate electricity idle, load meritorious and reactive load, G _ij, B _ijthat electricity between node i and node j is led, susceptance; θ _ij=θ _i-θ _jpoor for node i and node j voltage phase angle; V _ithe voltage magnitude of representation node i.

Step 2: set up the chain structure high-voltage fence security control Optimized model to control cooperation between Least-cost, taking into account system Transient Stability Constraints and many FACTS;

In step 2, to control the chain structure high-voltage fence security control Optimized model of cooperation between Least-cost, taking into account system Transient Stability Constraints and many FACTS:

Polymorphic type, large capacity FACTS are coordinated to risk and the economy of control measure and carry out comprehensive assessment and optimize research, coordinate control measure to obtain optimum mixing.Control range and controlled quentity controlled variable under responsive serious disturbance are larger, alternative is larger, control law is more complicated, for same disturbance, may there be more feasible control measure, need to carry out complex optimum research to these control measure and control object, propose risk and economy comprehensive optimization method, to obtain the more feasible and less coordination control measure of control cost.

Many FACTS coordinate to control optimization problem and can be described as: in the situation that there is different disturbance, how according to the order of severity of disturbance and demand for control, optimize the controlled quentity controlled variable of different FACTS equipment, to meet systematic steady state and transient voltage requirement, guarantee system angle stability and voltage stabilization simultaneously, putting before this, making the control Least-cost of paying.Its model can be described as:

min F(x,y,u)

$s.t.\left\{\begin{array}{cc}{G}_i(x,y,u)=0& i=\mathrm{1,2,3},...,N_{\mathrm{eq}}\\ H_j(x,y,u)<0& j=\mathrm{1,2,3},...N_{\mathrm{ueq}}\\ u_{\min }<u_k<u_{\max }& k=\mathrm{1,2,3},...,N_u\\ \mathrm{\&eta;}(u^1,u^2,...,u^{\mathrm{Nu}})>\mathrm{\&epsiv;}& \end{array}\right.$

Wherein F(x, y, u) be target function, G _iand H _ifor equation and static inequality constraints, η is merit angle, voltage stability margin constraint; X is state variable, as fast dynamic variable, the trend variable etc. of generator and excitation system; Y representation algebra variable, as node voltage, phase angle etc.; U is control variables, chooses the controlled quentity controlled variable of conventional string benefit, reactive power compensation and FACTS equipment here, the reactance of for example reactive-load compensation equipment in parallel, the condensance of controlled series compensation, the reactance of controlled high resistance, the reactance of SVC, the reactance of the controlled high resistance of magnet controlled bus etc.; u _max, u _minit is respectively the upper and lower limit of control variables; N _eq, N _ueqand N _ube respectively the sum of equality constraint, inequality constraints and control variables.Introduce in detail one by one target function and constraints below.

1) target function

The actuating quantity cost that the target function that optimization problem is controlled in many FACTS coordinations is chosen each control variables is minimum, that is:

min L(u)=u ^TRu ；

L(u in formula) be cost function, u is dominant vector, comprises the reactance of reactive-load compensation equipment in parallel, the condensance of controlled series compensation, the reactance of controlled high resistance, the reactance of SVC, the reactance of the controlled high resistance of magnet controlled bus etc.; Control variables u had both comprised continuous variable, as the condensance of string benefit and the reactance of SVC, had also comprised discrete variable, as the inductive reactance of shunt reactor.R is diagonal angle Cost matrix, the sequencing that this diagonal matrix can optimal control variable be implemented, such as switching Shunt Capacitor Unit, regulate serial compensation capacitance capacity, regulate the cost coefficient of SVC reactive power compensation amount to be made as respectively 5,4 and 3, just explanation in the middle of whole control variables implementation process, regulate SVC reactive power compensation amount be lowermost level other, pay the utmost attention to enforcement, and opening-closing capacitor bank is the just permission enforcement in the time meeting specified conditions of highest level.

In sum, the target function that optimization is controlled in many FACTS coordinations is a coordination optimization problem that blendes together that comprises discrete control variables and continuous control variable.

2) equality constraint

The equality constraint that many FACTS coordinate to control optimization problem, except comprising conventional system load flow constraint, also comprises short-term dynamic Constraints of Equilibrium and network constraint, and its expression formula is:

f(x,y,u)=0

g(x,y,u)=0

h(x,y,u)=0；

Wherein x is differential state variable, as generator excited system dynamic variable and load dynamic variable; Y representation algebra variable, as node voltage, phase angle etc.; U is control variables, chooses the controlled quentity controlled variable of conventional string benefit, reactive power compensation and FACTS equipment here; F represents the equation that short-term dynamic is relevant, comprise generator dynamically and excitation system dynamically; G represents system load flow equation, specifically comprises:

1. generator node

$\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_{\mathrm{Gi}}=P_{\mathrm{Gi}}-U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})\\ {\mathrm{\&Delta;Q}}_{\mathrm{Gi}}=Q_{\mathrm{Gi}}-U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})\end{array}\right.;$

Wherein P _gi, Q _girepresent that respectively generator injects active power and the reactive power of node i, the two can give cancellation by simultaneous solution generator node algebraic equation.

2. load bus:

$\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_{\mathrm{Li}}=P_{\mathrm{Li}}-U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})\\ {\mathrm{\&Delta;Q}}_{\mathrm{Li}}=Q_{\mathrm{Li}}-U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})\end{array}\right.;$

Wherein P _li, Q _lirepresent that respectively load injects active power and the reactive power of node i, loading algebraic equation by simultaneous solution can these two amount of cancellation.

3. noenergy is injected node:

$\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_i=U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})\\ {\mathrm{\&Delta;Q}}_i=U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})\end{array}\right.;$

3) static inequality constraints

Static inequality constraints mainly comprises the upper and lower limit constraint that adjustable generated power is exerted oneself, the upper and lower limit constraint that adjustable generator reactive is exerted oneself, the upper and lower limit constraint of adjustable generator terminal voltage amplitude, the upper and lower limit constraint of OLTC tap, the upper and lower limit constraint of nodal frequency and the upper limit of branch road through-put power:

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}^{\min <P_{\mathrm{Gi}}<P_{\mathrm{Gi}}^{\max }}& i\&Element;S_G\\ Q_{\mathrm{Gi}}^{\min }<Q_{\mathrm{Gi}}{Q}_{\mathrm{Gi}}^{\max }& i\&Element;S_G\\ V_i^{\min }<V_i<V_i^{\max }& i\&Element;S_N\\ T_i^{\min }<T_i{T}_i^{\max }& i\&Element;S_O\\ f_i^{\min }<f_i<f_i^{\max }& i\&Element;S_F\\ S_{\mathrm{ij}}<S_{\mathrm{ij}}^{\max }& i\&Element;S_L\end{array}\right.;$

Wherein for the meritorious upper and lower limit of exerting oneself of adjustable generator i; for the idle upper and lower limit of exerting oneself of adjustable generator i; for the upper and lower limit of adjustable generator i set end voltage amplitude; it is the upper and lower limit of the each OLTC tap of i; for the upper and lower limit of node i frequency; for the upper limit of branch road ij through-put power.

4) transient state merit inequality constraint

Get the inertia center C OI of system as a reference, the relative angle of oscillation limit of each generator amature is:

$|{\mathrm{\&delta;}}_i\left(t_f\right)-{\mathrm{\&delta;}}_{\mathrm{COI}}\left(t_f\right)|\&le;{\mathrm{\&delta;}}_{\max };$

Corresponding transient rotor angle stability nargin is:

$\mathrm{\&eta;}=1-\frac{|{\mathrm{\&delta;}}_i\left(t_f\right)-{\mathrm{\&delta;}}_{\mathrm{COI}}\left(t_f\right)|}{{\mathrm{\&delta;}}_{\max }}\&GreaterEqual;0$

In formula, δ _i(t _f) be that synchronous generator i is at t _fthe merit angle in moment, δ _cOI(t _f) be that electric power generator group is at the center of inertia in tf moment angle, δ _maxfor the relative angle of oscillation upper limit of generator amature.

${\mathrm{\&delta;}}_{\mathrm{COI}}\left(t_f\right)=\underset{j=S_G}{\mathrm{\&Sigma;}}{\mathrm{\&delta;}}_i\left(t_f\right)M_j/\underset{j=S_G}{\mathrm{\&Sigma;}}{M}_j;$

In formula, SG is system generator number, M _jit is the moment of inertia of j platform generator.

5) transient voltage inequality constraints

System voltage is stable directly related with steady load, thereby can adopt the integrated form of load bus voltage deviation as the performance index of voltage stabilization, and its expression formula is:

$J\left(u\right)={\&Integral;}_{t_0}^{t_f}\mathrm{\&psi;}(y,u,t)\mathrm{dt}\&le;M.$

ψ in formula (y, u, t)=[y (t)-y _r(t)] ^tq[y (t)-y _r(t)].Q is diagonal angle weight matrix, y(t) be the voltage vector in load bus t moment, y _r(t) be the reference vector in load bus t moment, M is the desired value of performance index, and expression is wherein V _dfor time interval t _f-t ₀in y(t) target average load node voltage deviation, N _yy(t) inner load bus number.This inequality has ensured that controlled system can have the dynamic behaviour feature of expectation.Because the time interval of emergency control analogue system track is 10s left and right, thereby conventionally adopt 10s, i.e. t _f-t ₀=10s.

Step 3: set up and utilize Genetic Algorithms to solve Coordination and Optimization Model.

In step 3, set up Coordination and Optimization Model, solve target function and use GA genetic algorithm, concrete steps are as follows:

1) coding adopts and has easily convergence under large aberration rate, processes comparatively effectively real coding of function optimization problem.

2) initialization population: adopt Small section method, first the span of each parameter to be optimized is divided into the total several minizones of colony, in each minizone, generate randomly respectively a more initial individuality, this has ensured the range that initial population distributes at Feasible Solution Region to a certain extent, and amount of calculation is also little simultaneously.

3) choosing of target function: the target function using exponential type target function as parameter identification.

4) selection strategy: adopt random system of selection uniformly.

5) crossover and mutation: cross method is selected Heuristic, variation method is selected Adaptive feasible.

The present invention is directed to chain structure high-voltage fence; consider that between many FACTS, cooperation has proposed rational method of controlling security; not only the coordination application of large-scale F ACTS equipment is had to important directive significance, and safety and stability, high-efficiency and economic operation to extensive interconnected network has important value.

below in conjunction with Xinjiang, northwest interconnected network, technical scheme of the present invention is elaborated.Should be emphasized that,under it is only exemplary stating bright, instead of in order to limit the scope of the invention and to apply.

The chain structure high-voltage fence control method implementation step of considering many FACTS cooperation is as follows:

Genetic algorithmic steps:

1) coding adopts and has easily convergence under large aberration rate, processes comparatively effectively real coding of function optimization problem.

2) initialization population: adopt Small section method, first the span of each parameter to be optimized is divided into the total several minizones of colony, in each minizone, generate randomly respectively a more initial individuality, this has ensured the range that initial population distributes at Feasible Solution Region to a certain extent, and amount of calculation is also little simultaneously.

3) choosing of target function: using the optimal load flow model of loss minimization as target function.

4) selection strategy: adopt random system of selection uniformly.

5) crossover and mutation: cross method is selected Heuristic, variation method is selected Adaptive feasible.

The optimized individual number of GA is set to 120, and genetic algebra is set to 25.

For Xinjiang and 750 kilovolts of second channel engineerings of northwest major network networking with chain structure, in Sha Zhouzhan He in fish card station, tuning controller is set respectively, to control the coordination of the inner FACTS equipment of our station.Control strategy and checking situation after optimizing are as follows.

(1) steady state output fluctuation control strategy checking

Utilize Xinjiang, northwest in 2013 networking large mode of summer to carry out control strategy check.Before and after optimizing, the reactive power compensation configuration of the networking each transformer station of passage is as shown in table 1 below.Perception is "+", and capacitive is "-".

table 1: the reactive power compensation configuration of the networking each transformer station of passage

Can find out according to the reactive power compensation input amount before and after optimizing, adopt aforementioned FACTS system coordination control strategy can greatly reduce required reactive-load compensation equipment input amount.Can meet the requirement of system safety stable operation in disturbance situation for further illustrating the reactive power compensation configuration adopting after optimizing, consider that wind-powered electricity generation evenly fluctuates to 4000MW from 2400MW, every 300MW one-level, consider the pressure regulation effect of following of SVC, the controlled high resistance of magnet controlled bus, the change in voltage that the controlled high resistance in husky state, the controlled high resistance single movement of fish card one-level cause is as shown in following table 2,3.The change in voltage of transformer station's medium voltage side is within 2.5%, and change in voltage is reasonable.

the husky state of large mode of table 2:2013 summer controlled high resistance single movement one-level change in voltage situation

the controlled high resistance single movement of table 3:2013 summer large mode fish card one-level change in voltage situation

Can find out according to above calculating conclusion, based on aforementioned FACTS system coordination control strategy, the wind-powered electricity generation fluctuation of exerting oneself, near region busbar voltage is not out-of-limit, in the reasonable scope, control strategy is effective and feasible for the change in voltage that the controlled high resistance in husky state, the controlled high resistance single movement of fish card one-level cause simultaneously.

(2) in the extensive off-grid situation of new forms of energy, control strategy is checked

Research is based on large operational mode of winter in 2013, i.e. Hami direct current 4000MW that puts into operation, the unestablished weak mode of supporting power supply, the situation of the extensive off-grid of simulation new forms of energy.Consider to be limited to N-2 steady limit operational mode temporarily, now Dunhuang and Jiuquan wind-powered electricity generation access 4200MW altogether, wherein Dunhuang wind-powered electricity generation access 3200MW, and Jiuquan wind-powered electricity generation counts 1000MW.

Under large limit mode of winter in 2013, initial mode SVC capacity is 0, and the controlled high resistance in four groups of both sides of husky state～fish card circuit all drops into the controlled capacity 117Mvar of capacity 156Mvar(fixed capacity 39Mvar+1 level).Jiuquan wind energy turbine set is set and collects side Yumen～the Jiayu Pass three N-1 fault forever, 4200MW wind-powered electricity generation whole off-grids in Gansu after simulated failure.After wind-powered electricity generation off-grid, consider that SVC follows pressure regulation effect, Sha Zhou and fish card ceiling voltage still reach on 830kV, start FACTS system coordination control strategy, and the two groups of controlled high resistances of circuit in Sha Zhouzhan and fish card station are all thrown to heap(ed) capacity 390Mvar.After controlled high resistance action, voltage can return in zone of reasonableness, and husky state voltage returns to 790kV, and fish card voltage returns to 790kV.After the off-grid fault causing after dynamic passive compensation device action, each station change in voltage is as shown in table 4 below.

under table large limit mode of 4:2013 winter, after the wind-powered electricity generation off-grid of Gansu, dynamic passive compensation device action causes each station change in voltage table

Can be found out by above result of calculation, the large originating party formula of networking passage near region wind-powered electricity generation, once there is the chain off-grid accident of wind-powered electricity generation, more than near region 750kV bus steady state voltage reaches as high as 840kV, serious threat device security and power grid operation, even if consider SVC auto-action, fish card, station, Qaidam 750kV busbar voltage still reach 835kV, and voltage is seriously out-of-limit; Adopt this project emergency control policy, ceiling voltage is controlled at 800kV, meets power network safety operation requirement, and it is effective and feasible that control strategy is carried by institute.

In sum, the chain structure high-voltage fence method of controlling security based on many FACTS structure of the various embodiments described above of the present invention, for chain structure high-voltage fence, considers the method for controlling security of cooperation between many FACTS; The method comprises transient stability model and the each dynamic element model by analyzing electric power system, sets up Coordination and Optimization Model; And by GA genetic algorithm, Coordination and Optimization Model is solved and how determined according to the order of severity of disturbance and demand for control, optimize the controlled quentity controlled variable of different FACTS equipment, to meet systematic steady state and transient voltage requirement, guarantee system angle stability and voltage stabilization simultaneously, and putting before this, make the control Least-cost of paying.

Finally it should be noted that: the foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, although the present invention is had been described in detail with reference to previous embodiment, for a person skilled in the art, its technical scheme that still can record aforementioned each embodiment is modified, or part technical characterictic is wherein equal to replacement.Within the spirit and principles in the present invention all, any amendment of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (7)

1. the chain structure high-voltage fence method of controlling security based on many FACTS structure, is characterized in that, mainly comprises:

A, electric power system model and the dynamic element model of foundation based on transient stability;

B, based on electric power system model and dynamic element model, for chain structure high-voltage fence, set up the Coordination and Optimization Model of considering cooperation between many FACTS;

C, utilize Genetic Algorithms, solve the optimal solution of Coordination and Optimization Model.

2. the chain structure high-voltage fence method of controlling security based on many FACTS structure according to claim 1, is characterized in that, described step b, specifically comprises:

By transient stability is analyzed, set up the mathematical description form of electric power system transient stability, in conjunction with the model of dynamic element, set up Coordination and Optimization Model and its constraints.

3. the chain structure high-voltage fence method of controlling security based on many FACTS structure according to claim 1, is characterized in that, described step c, specifically comprises:

In the situation that there is different disturbance, by solving-optimizing model, how determine according to the order of severity of disturbance and demand for control, optimize the controlled quentity controlled variable of different FACTS equipment, to meet systematic steady state and transient voltage requirement, guarantee system angle stability and voltage stabilization simultaneously, putting before this, make the control Least-cost of paying.

4. the chain structure high-voltage fence method of controlling security based on many FACTS structure according to claim 3, is characterized in that, the operation of described solving-optimizing model, specifically comprises:

The establishment of target function; The foundation of various constraintss; Solve by Genetic Algorithms.

5. the chain structure high-voltage fence method of controlling security based on many FACTS structure according to claim 4, is characterized in that, the operation of the establishment of described target function, is specially:

min F(x,y,u)

$s.t.\left\{\begin{array}{cc}{G}_i(x,y,u)=0& i=\mathrm{1,2,3},...,N_{\mathrm{eq}}\\ H_j(x,y,u)<0& j=\mathrm{1,2,3},...N_{\mathrm{ueq}}\\ u_{\min }<u_k<u_{\max }& k=\mathrm{1,2,3},...,N_u\\ \mathrm{\&eta;}(u^1,u^2,...,u^{\mathrm{Nu}})>\mathrm{\&epsiv;}& \end{array}\right.$

Wherein F(x, y, u) be target function, G _iand H _ifor equation and static inequality constraints, η is merit angle, voltage stability margin constraint; X is state variable; Y representation algebra variable; U is control variables; u _max, u _minit is respectively the upper and lower limit of control variables; N _eq, N _ueqand N _ube respectively the sum of equality constraint, inequality constraints and control variables.

6. the chain structure high-voltage fence method of controlling security based on many FACTS structure according to claim 4, is characterized in that, the described operation solving by Genetic Algorithms, specifically comprises:

1) coding adopts and has easily convergence under large aberration rate, processes comparatively effectively real coding of function optimization problem;

2) initialization population: adopt Small section method, first the span of each parameter to be optimized is divided into the total several minizones of colony, then generate randomly respectively an initial individuality in each minizone;

3) choosing of target function: the target function using exponential type target function as parameter identification;

4) selection strategy: adopt random system of selection uniformly;

5) crossover and mutation: cross method is selected Heuristic, variation method is selected Adaptive feasible.

7. according to the chain structure high-voltage fence method of controlling security based on many FACTS structure described in any one in claim 1-6, it is characterized in that, in step a, described electric power system model and dynamic element model based on transient stability, is specially:

Power system transient stability refers to that can electric power system is being subjected to after large disturbance, be transitioned into ability new or that return to original steady operational status; The stability of electric power system under large disturbance, is generally divided into three phases system transient process, they respectively:

System before fault:

$\begin{array}{c}\stackrel{.}{x}=f_0(x,y,\mathrm{\&alpha;})\\ 0=g_0(x,y,\mathrm{\&alpha;})\end{array}t\&le;0^{-};$

System in fault:

$\begin{array}{c}\stackrel{.}{x}=f_{F,1}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,1}(x,y,\mathrm{\&alpha;})\end{array}{0}^{+}\&le;t\&le;t_{\mathrm{cl},1}^{-}$

$\begin{array}{c}\stackrel{.}{x}=f_{F,2}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,2}(x,y,\mathrm{\&alpha;})\end{array}{t}_{\mathrm{cl},1}^{+}\&le;t\&le;t_{\mathrm{cl},2}^{-}$

…

$\begin{array}{c}\stackrel{.}{x}=f_{F,k}(x,y,\mathrm{\&alpha;})\\ 0=g_{F,k}(x,y,\mathrm{\&alpha;})\end{array}{t}_{\mathrm{cl},(k-1)}^{+}\&le;t\&le;t_F^{-};$

System after fault:

$\begin{array}{c}\stackrel{.}{x}=f_{\mathrm{PF}}(x,y,\mathrm{\&alpha;})\\ 0=g_{\mathrm{PF}}(x,y,\mathrm{\&alpha;})\end{array}{t}_F^{+}\&le;t;$

X ∈ R ⁿthe state variable of system to Time Continuous; Y ∈ R ^lit is the algebraically variable that can undergo mutation; α ∈ R ^mthat the parameter that dispatcher can regulate and control is called adjustable parameter; Matrix the hypothesis of full rank can ensure that electric power system can be described as the form of ordinary differential equation.