CN105978003A - Power system additional wide-area damping controller design method giving consideration to time lag - Google Patents

Abstract

The invention discloses a power system additional wide-area damping controller design method giving consideration to time lag, and the method comprises the steps: (1), enabling an oscillation mode with the weakest damping of a power system to serve as a target control mode, determining the optimal installation positions of AVR and FACTS equipment, further building a power system mode and a WADC model which comprise the AVR and FACTS equipment and do not give consideration to time lag; (2), introducing a time lag link on the basis of the power system mode and the WADC model which comprise the AVR and FACTS equipment and do not give consideration to time lag, and further building a closed loop time lag power system model giving consideration to a time lag factor; (3), building a WADC parameter-optimization mathematic model according to the closed loop time lag power system model; (4), employing a PSO algorithm, and solving the optimal parameters of WADC at step (3). The method gives consideration to the time lag factor in each iteration optimization process, employs the SOD algorithm to solve the key characteristic value of the right side of a closed loop time lag power system, so as to achieve a big purpose that the damping of the key characteristic value is the biggest.

Description

A kind of power system additional wide area damping control method for designing considering time lag

Technical field

The present invention relates to a kind of power system additional wide area damping control method for designing considering time lag.

Background technology

Mechanism that extensive interconnected network is complicated and severe service condition so that it is overall dynamic behaviour be difficult to analyze and Control.The low-frequency oscillation repeatedly occurred in interconnected electric power system, threatens the safe and stable operation of electrical network, restricts region The ability to transmit electricity on some major transmission line road interior and interval so that the initial target that trans-regional electric energy dispatches this Power System Interconnection is difficult To complete.

Along with WAMS (Wide Area Measurement System, WAMS) technology development with become Ripe, WAMS is used for extensive interconnected electric power system and forms closed loop control, be one of the direction of power system development.WAMS can There is provided the information such as through-put power of generator's power and angle, rotating speed and interregional interconnection in real time, for design wide area damping control With suppression system inter-area oscillations, it is provided that new data platform.Wide area signal based on WAMS, fully reflection system local oscillation With the modal information of inter-area oscillations, provide it to damping controller and constitute closed loop control, it is possible to obtain superior control performance.

But, application Wide-area Measurement Information brings new problem also can to the control of system.Modern digital communication network is The transmission of WAMS information provides strong physical support, although communication for information is convenient and swift, but, it is contemplated that transmission range is relatively Far, Wide-area Measurement Information is transmitted in a communication network and be there is inevitable communication delay.When time lag is bigger, may result in damping Controller action effect is deteriorated, even induction power system unstability.

At present, it is considered to the wide area stability contorting of time-delay can be largely classified into wide area robust PSS and controls and wide area damp Control two big classes.Wide area robust PSS controls to primarily focus on robust control theory to be applied to power system, by means of robust control Workbox processed can complete the design of single damping controller, the most existing sensitive based on loop molding, gain scheduling and mixing The Wide-area Time-delay damping controller method for designing of the technology such as degree.But in the design process, it is respectively provided with not due to system and time lag Definitiveness, needs system model and Time Delay are carried out depression of order and approximate processing.Model reduction and the error of approximation link, directly Connect the performance affecting robust controller.

For the design of wide area damping control (Wide Area Damping Controller, WADC), mainly pin To the power system stabilizer, PSS (Power System Stabilizer, PSS) in electrical network, automatic voltage regulator (Automatic Voltage Regular, AVR) and typical flexible AC transmitting system (Flexible Alternative Current Transmission Systems, FACTS) additional damping controller of equipment (SVC, TCSC etc.) is optimized and sets Meter.Current research is mostly based on single, the power system of fixed time lag, system exists multiple, stochastic Time-Delay situation and grinds Study carefully the most less.These researchs are the most all to use Method of Pole Placement design parameter, time lag factor is introduced Optimized model, or sets Count suitable time lag compensation link, to improve robustness and the damping of controller, and have no special with power system key Value indicative is calculated as the WADC on basis and optimizes the achievement in research designed.Calculate additionally, existing based on WAMS and Modified particle swarm optimization The SVC additional damping controller Optimization Design of method, obtains the relevant information of oscillation mode by Prony analytical tool, should By modified particle swarm optiziation optimal control parameter, but the method does not accounts for the time delay of Wide-area Measurement Information to controlling effect Impact.

Summary of the invention

In order to solve the shortcoming of prior art, the present invention provides a kind of power system additional wide area damp control considering time lag Device method for designing processed.When the method calculates the stability of the critical eigenvalue of real system and judgement system, take into full account communication The time lag impact on system damping performance, can be greatly improved the damping of inter-area oscillation mode, strengthens the stability of time lag system.

For achieving the above object, the present invention is by the following technical solutions:

A kind of power system additional wide area damping control method for designing considering time lag, comprises the following steps:

Step (1): using oscillation mode the most weak for power system damping as target control pattern, determines that AVR and FACTS sets Standby best position, further foundation do not consider time lag factor the electric power system model comprising AVR and FACTS equipment and WADC model；

Step (2): do not considering the electric power system model comprising AVR and FACTS equipment and the WADC model of time lag factor On the basis of, introduce Time Delay, and then set up the model of the closed loop time-lag power system considering time lag factor；

Step (3): according to the model of closed loop time-lag power system, build the mathematical model of WADC parameter optimization；

Step (4): use particle group optimizing (Particle Swarm Optimization, PSO) algorithm, solution procedure (3) optimized parameter of WADC in；

In each iterative optimization procedure, it is considered to time lag factor, use SOD Algorithm for Solving closed loop time-lag power system The critical eigenvalue on right side, to reach the damping of critical eigenvalue this target maximum.

In described step (1), use associating geometric measures method based on controllability and observability, determine AVR and FACTS equipment Best position.

In described step (1), use associating geometric measures method based on controllability and observability, determine AVR and FACTS equipment The detailed process of best position, including:

Step (1.1): the parameter of given AVR and FACTS equipment, sets some node of power system as AVR and FACTS Standby alternative installation site；

Step (1.2): calculate containing installing the system load flow equation of AVR and FACTS equipment and the initial of state variable Value, forms system linearity coefficient matrix；According to linearisation coefficient matrix, calculate the critical eigenvalue of power system and right The left and right characteristic vector answered, and set the oscillation mode to be investigated of power system；

Step (1.3): under the oscillation mode set, with the reference value of AVR and FACTS equipment for input, with different Feedback signal is output, calculates the associating geometric measures of the controllability and observability of AVR and FACTS equipment；

Step (1.4): compare the modulus value size of the associating geometric measures of controllability and observability, filter out associating geometric measures The node of modulus value maximum is defined as the best position of AVR and FACTS equipment, using the control signal of its correspondence as additional The feedback signal of WADC, input WADC constitutes closed loop control, thus increases the damping capacity of system.

In step (1.4), the address installed according to AVR and the FACTS equipment selected and feedback signal, set up following system System linearized state-space model:

$\left\{\begin{array}{c}\mathrm{\Δ}\stackrel{\·}{x}=A\mathrm{\Δ}x+B\mathrm{\Δ}u\\ \mathrm{\Δ}y=C\mathrm{\Δ}x+D\mathrm{\Δ}u\end{array}\right.$

In formula: x is the state vector of system, u and y is respectively input vector and output vector；A, B, C, D are respectively system State matrix, input matrix, output matrix and straight-through matrix.If the eigenvalue of matrix A is λ_i(i=1 ..., n), accordingly Left and right eigenvectors matrix is: U=[u₁,u₂,…,u_n], V=[v₁,v₂,…,v_n].Wherein, u_iAnd v_iIt is respectively ith feature The left and right characteristic vector of value.After standardization processing, U and V meets U^HV=V^HU=I_n, I_nFor n rank unit matrix.

System i-th oscillation mode λ_iControllability geometric measures m_ciWith controllability geometric measures m_oiCan be calculated by following formula:

$\left\{\begin{array}{c}{m}_{ci}\left(k\right)=cos\left(\mathrm{\α}\left(u_i,b_k\right)\right)=\frac{\left|b_k^T{u}_i\right|}{\left|\right|u_i\left|\right|\left|\right|b_k\left|\right|}\\ m_{oi}\left(l\right)=cos\left(\mathrm{\θ}\left(c_l^T,v_i\right)\right)=\frac{\left|c_l{v}_i\right|}{\left|\right|v_i\left|\right|\left|\right|c_l\left|\right|}\end{array}\right.$

In formula: b_kKth for input matrix B arranges；c_lL row for output matrix C；α(u_i,b_k) it is input vector b_kAnd a left side Characteristic vector u_iAngle；θ(c_l ^T,v_i) it is output vector c_lWith right characteristic vector v_iAngle；| | and | | | | represent respectively Delivery value and European norm.

For oscillation mode λ_i, can control/the associating geometric measures of controllability is:

m_coi(k, l)=m_ci(k)m_oi(l)

In step (1.4), according to (1.3) calculated can the associating geometric measures of control/controllability determine AVR with The best position of FACTS equipment.If m_coi(k, l) ≠ 0, then explanation can pass through u_kAnd y_lControl model λ_i。m_coi(k l) takes U during maximum_kAnd y_lIt is maximally effective；Work as m_coi(k, when l) taking maximum, if u_kAnd y_lSignal take from the same area, shake Swing pattern λ_iCan be controlled by this locality damping；Otherwise, if u_kAnd y_lSignal take from different regions, then need with wide-area control come Damp corresponding oscillation mode.

In described step (1), the structure of additional WADC is similar to tradition PSS.It is made up of lead-lag link, belongs to dynamic Compensator.Apply it to form closed loop control, the damping capacity of power system can be promoted.

In described step (2), time-lag power system model is as follows:

In formula: Δ x is the state variable of system.τ=[τ₁,…,τ_i,…,τ_m]^T, τ_i> 0 it is the transmission of i-th wide area signal Time lag, i=1,2 ..., m, maximum of which time lag is expressed as τ_max。It is the state matrix of system, for dense matrix；It is the hangover state matrix of system, for sparse matrix.Δ x (t) is the increment of t system state variables, Δx(t-τ_i) it is t-τ_iThe increment of moment system state variables,Increment for t system state variables derivative.Δx (0) it is the initial value (i.e. initial condition) of system state variables, and is abbreviated asThe feature of the time-lag power system that above formula represents Equation is:

$({\tilde{A}}_0+\underset{i=1}{\overset{m}{\Σ}}{\tilde{A}}_i{e}^{-{\mathrm{\λ\τ}}_i})v=\mathrm{\λ}v$

In formula: λ is characterized value, v is characterized the right characteristic vector that value is corresponding.

In described step (3), additional WADC Parametric optimization problem mathematical model is expressed as:

Max J, J=min{ ζ_i, i ∈ electromechanic oscillation mode set }

$s.t.\left\{\begin{array}{c}{K}_d^{\min }\≤K_d\≤K_d^{\max }\\ K_a^{\min }\≤K_a\≤K_a^{\max }\\ T_1^{min}\≤T_1\≤T_1^{max}\\ T_2^{\min }\≤T_2\≤T_2^{\max }\\ T_3^{\min }\≤T_3\≤T_3^{\max }\\ T_4^{\min }\≤T_4\≤T_4^{\max }\end{array}\right.$

In formula: ζ_iFor the damping ratio of system i-th oscillation mode, cost function J is expressed as system whole electromechanical oscillations mould Damping ratio minimum in formula, K_dFor the amplification of the Control of Voltage link of AVR and FACTS equipment, K_aFor additional damping controller Amplification, T₁～T₄Time constant for lead-lag link；WithIt is respectively amplification K_dHigher limit and Lower limit；WithIt is respectively amplification K_aHigher limit and lower limit；WithWhen being respectively Between constant T₁～T₄Higher limit and lower limit.

In described step (4), use PSO algorithm, before the WADC optimized parameter in solution procedure (3), also include: arrange Population number and maximum iteration time also initialize population.

In described step (4), according to spectral mapping theorem, the eigenvalue being positioned at left half complex plane of closed loop time-lag power system Being mapped to Solution operator and be positioned at the unit circle of z-plane, the eigenvalue being positioned at right half complex plane is mapped in outside unit circle.

In described step (4), use equally spaced linear multistep method (Linear Multi-Step, LMS) that Solution operator is entered Row processes, and according to eigenvalue λ and eigenvalue (composing) the μ corresponding relation of Solution operator of time-lag power system, tries to achieve time lag power train The critical eigenvalue of system.

Solution operator T (h): X → X is defined as the initial condition (state) in the θ moment in space XBeing mapped to the h+ θ moment is The linear operator of system state ψ.

In formula: h is transfer step-length, 0≤h≤τ_max；x_tThe part solution of etching system when=x (t+ θ) is t >=0.Mapped by spectrum Theorem understands, and has following relation between spectrum μ and the eigenvalue λ of time lag system of Solution operator T (h):

$\mathrm{\λ}=\frac{1}{h}ln\mathrm{\μ},\mathrm{\μ}\∈\mathrm{\σ}\left(T\right(h\left)\right)\backslash \left\{0\right\}$

In formula: σ () represents spectrum, represent eliminating.

By semigroup of operators theory, the Solution operator in Banach space is infinite dimensional.In order to calculate Solution operator Eigenvalue, needs T (h) is carried out discretization.After discretization, obtain corresponding with Solution operator, a finite dimensional approximate matrix, The critical eigenvalue of former time lag system is can be obtained by by calculating the eigenvalue of approximate matrix.

Based in SOD Algorithm for Solving time-lag power system critical eigenvalue in described step (4), use equally spaced LMS Method carries out approximate processing to differential equations with delay (Delay Differential Equations, DDE) relevant Solution operator, can Former problem is converted into the eigenvalue problem solving a canonical matrix.

Assume h≤τ_max, Solution operator can be expressed as form:

In above formula, the first row of right-hand side expression is initial-value problem, and LMS method can be used to solve.

Use equally spaced some θ_j=jh, j=-N ..., 0, Solution operator is carried out discretization, N is more than or equal to τ_max/h Smallest positive integral, i.e.

The expression formula of LMS method is:

$\underset{j=0}{\overset{k}{\Σ}}{\mathrm{\α}}_j{\mathrm{\ψ}}_{n+j}=h\underset{j=0}{\overset{k}{\Σ}}{\mathrm{\β}}_j{f}_{n+j}$

At mesh point, with ψ_jApproximation replaces ψ (θ_j), withApproximation replacesThen ψ_jWithMathematical relationship express Formula:

In formula: T_NDiscretization matrix for Solution operator T (h), it may be assumed that

T_NLast block row Γ be the coefficient matrix of polynomial eigenvalue problem, be specifically represented by:

$\mathrm{\Γ}=R^{-1}\underset{i=0}{\overset{m}{\Σ}}{w}_i\⊗{\tilde{A}}_i$

Especially, when system contains only a time lag and N=τ/h is integer, Γ can explicitly be expressed as follows:

Γ=[Γ₀,0_n×n(N-k-1),Γ₁]

In each iterative process of PSO algorithm of described step (4), the search information of the most more new particle:

$\left\{\begin{array}{c}{x}_{i,d}^{k+1}=x_{i,d}^k+v_{i,d}^{k+1}\\ v_{i,d}^{k+1}={\mathrm{\ωv}}_{i,d}^k+c_{1}rand(\·)({\mathrm{pbest}}_d-x_{i,d}^k)+c_{2}Rand(\·)({\mathrm{gbest}}_d-x_{i,d}^k)\end{array}\right.$

In formula: k is the number of times that current iteration calculates,D for particle i search speed ties up component, WithRepresent the upper and lower bound of search speed respectively,The d projecting to search volume for i-th particle ties up component； pbest_dOptimum position for i-th particle up till now projects to the d dimension component of search volume；gbest_dFor current all grains The optimum position of son search projects to the d of search volume and ties up component；c₁And c₂For aceleration pulse；Rand () and Rand () It is the random number between two 0 to 1；ω is weight coefficient.

For improving convergence rate, linear narrowing weight coefficient in each iterative process of PSO algorithm of step (4).

$\mathrm{\ω}={\mathrm{\ω}}_{max}-\frac{{\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min }}{K}k$

In formula: k is current iteration number of times；K is as ω=ω_minTime algorithm iterations；ω_maxAnd ω_minAt the beginning of Fen Bieweiing The weight coefficient maximum arranged during beginningization algorithm and minima.

The invention have the benefit that

(1) the method for the present invention is for designing the additional WADC of AVR and FACTS equipment, interval can be greatly improved and shake Swing the damping of pattern, strengthen the stability of time lag system；Calculating the critical eigenvalue of real system and stablizing of judgement system During property, take into full account the communication delay impact on system damping performance；

(2) method of the present invention combines SOD and PSO both algorithms, and designed additional wide area damping control is same Original local PSS is mutually coordinated, the most there is not the reciprocal action being unfavorable for system damping performance；

(3) method of the present invention is with critical eigenvalue for the additional wide area damping control of design, it is to avoid traditional Wide area power system regulator based on POLE PLACEMENT USING and Robust Damping controller design method need to drop system model Rank and time lag carries out the deficiency of approximate processing, purposiveness is strong, control device is direct, action effect is obvious, and the most any Conservative.

Accompanying drawing explanation

Fig. 1 is time-lag power system schematic diagram；

Fig. 2 is the SVC stability analysis model considering additional wide-area damping control；

Fig. 3 is the TCSC stability analysis model installing additional wide-area damping control；

Fig. 4 is the calculation process of the controlled/ornamental associating geometric measures of target pattern；

Fig. 5 is additional WADC design flow diagram based on PSO algorithm；

Fig. 6 is time-lag power system based on the SOD algorithm additional WADC method for designing flow chart of the present invention.

Detailed description of the invention

The present invention will be further described with embodiment below in conjunction with the accompanying drawings:

As shown in Figure 1: in the modeling process of actual large-scale electrical power system, introduce Time Delay.Time-lag power system bag Exporting time lag four part containing without time-lag power system, wide area Feedback Delays, additional WADC and wide area, the connection between each several part is closed System is as shown in the figure.In FIG, y_fFor the output without time-lag power system, y_dfFor the wide area feedback signal after consideration Feedback Delays And as the input of damping controller, y_cFor the output of wide area damping control, y_dcWide area damp delayed during for considering to export The output of controller, also serves as inputting without the control of time-lag power system simultaneously.

Time lag system is positioned at the eigenvalue of left half complex plane and is mapped to Solution operator and is positioned at the unit circle of z-plane, and time lag System is positioned at the eigenvalue of right half complex plane and is mapped in outside unit circle.Therefore, the eigenvalue of Solution operator is utilized, it is possible to solve Corresponding time lag system critical eigenvalue.

As shown in Figures 2 and 3, the structure of additional WADC is similar with PSS, is made up of lead-lag link and belongs to dynamically benefit Repay device.The state-space expression of additional WADC can be written as:

$\frac{{\mathrm{d\Δx}}_c}{dt}=A_c{\mathrm{\Δx}}_c+B_c{y}_f$

$\frac{{\mathrm{d\Δx}}_S}{dt}=A_S{\mathrm{\Δx}}_S+B_S{\mathrm{\ΔV}}_{SVC}+\frac{K_{SVC}}{T_{SVC}}{\mathrm{\ΔV}}_{IS}$

In formula: Δ x_c=[Δ V₁ ΔV₂ ΔV₃ ΔV_IS]^T；

$A_c=\left[\begin{array}{cccc}-\frac{1}{T_R}& & & \\ -\frac{1}{T_R}& -\frac{1}{T_W}& & \\ -\frac{T_1}{T_2{T}_R}& \frac{T_W-T_1}{T_W}& -\frac{1}{T_2}& \\ -\frac{T_1{T}_3}{T_2{T}_4{T}_R}& \frac{T_2(T_W-T_1)}{T_2{T}_4{T}_W}& -\frac{T_2-T_3}{T_2{T}_4}& -\frac{1}{T_4}\end{array}\right],B_c=\left[\begin{array}{c}\frac{K_R}{T_R}\\ \frac{K_R}{T_R}\\ \frac{K_R{T}_1}{T_R{T}_2}\\ \frac{K_R{T}_1{T}_3}{T_R{T}_2{T}_4}\end{array}\right].$

In formula: Δ V₁、ΔV₂、ΔV₃For the intermediate variable of WADC links, Δ V_ISOutput variable for WADC, it is provided that Constituting feedback control to FACTS equipment, K is amplification, and T is time constant.

As shown in Figure 4, use associating geometric measures method based on controllability and observability, determine that AVR and FACTS equipment is The detailed process of good installation site, including:

Step (1.1): the parameter of given AVR and FACTS equipment, sets some node of power system as AVR and FACTS Standby alternative installation site；

Step (1.2): calculate containing installing the system load flow equation of AVR and FACTS equipment and the initial of state variable Value, forms system linearity coefficient matrix；According to linearisation coefficient matrix, calculate the critical eigenvalue of power system and right The left and right characteristic vector answered, and set the oscillation mode to be investigated of power system；

Step (1.3): under the oscillation mode set, with the reference value of AVR and FACTS equipment for input, with different Feedback signal is output, calculates the associating geometric measures of the controllability and observability of AVR and FACTS equipment；

Step (1.4): compare the modulus value size of the associating geometric measures of controllability and observability, filter out associating geometric measures The node of modulus value maximum is defined as the best position of AVR and FACTS equipment, using the control signal of its correspondence as additional The feedback signal of WADC, input WADC constitutes closed loop control, thus increases the damping capacity of system.

As Fig. 5 shows, additional WADC based on PSO algorithm designs and specifically includes following steps:

Step (4.1): population number and maximum iteration time are set, and initialize population

Step (4.2): Dynamic simulation model；

Step (4.3): consider time lag factor, calculates the rightmost side critical eigenvalue of time-lag power system based on SOD algorithm And damping ratio, design controller parameter；

Step (4.4): Population Regeneration, it may be judged whether reach the iterations upper limit or meet required precision, if it is not, Then return step (4.2) to recalculate, if it is, output parameters optimization.

In described step (4.4), additional WADC Parametric optimization problem mathematical model is expressed as:

Max J, J=min{ ζ_i, i ∈ electromechanic oscillation mode set }

$s.t.\left\{\begin{array}{c}{K}_d^{\min }\≤K_d\≤K_d^{\max }\\ K_a^{\min }\≤K_a\≤K_a^{\max }\\ T_1^{min}\≤T_1\≤T_1^{max}\\ T_2^{\min }\≤T_2\≤T_2^{\max }\\ T_3^{\min }\≤T_3\≤T_3^{\max }\\ T_4^{\min }\≤T_4\≤T_4^{\max }\end{array}\right.$

In formula: ζ_iFor the damping ratio of system i-th oscillation mode, cost function J is expressed as system whole electromechanical oscillations mould Damping ratio minimum in formula, K_dFor the amplification of the Control of Voltage link of AVR and FACTS equipment, K_aFor additional damping controller Amplification, T₁～T₄Time constant for lead-lag link；WithIt is respectively amplification K_dHigher limit and Lower limit；WithIt is respectively amplification K_aHigher limit and lower limit；WithWhen being respectively Between constant T₁～T₄Higher limit and lower limit.

In described step (4.4), in each iterative process of PSO algorithm, the search information of the most more new particle:

$\left\{\begin{array}{c}{x}_{i,d}^{k+1}=x_{i,d}^k+v_{i,d}^{k+1}\\ v_{i,d}^{k+1}={\mathrm{\ωv}}_{i,d}^k+c_{1}rand(\·)({\mathrm{pbest}}_d-x_{i,d}^k)+c_{2}Rand(\·)({\mathrm{gbest}}_d-x_{i,d}^k)\end{array}\right.$

In formula: k is the number of times that current iteration calculates,D for particle i search speed ties up component, WithRepresent the upper and lower bound of search speed respectively,The d projecting to search volume for i-th particle ties up component； pbest_dOptimum position for i-th particle up till now projects to the d dimension component of search volume；gbest_dFor current all grains The optimum position of son search projects to the d of search volume and ties up component；c₁And c₂For aceleration pulse；Rand () and Rand () It is the random number between two 0 to 1；ω is weight coefficient.

For improving convergence rate, linear narrowing weight coefficient in each iterative process of PSO algorithm of step (4).

$\mathrm{\ω}={\mathrm{\ω}}_{max}-\frac{{\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min }}{K}k$

In formula: k is current iteration number of times；K is as ω=ω_minTime algorithm iterations；ω_maxAnd ω_minAt the beginning of Fen Bieweiing The weight coefficient maximum arranged during beginningization algorithm and minima.

As shown in Figure 6, a kind of power system additional wide area damping control method for designing considering time lag of the present invention, bag Include following steps:

Step (1): using oscillation mode the most weak for power system damping as target control pattern, determines that AVR and FACTS sets Standby best position, further foundation do not consider time lag factor the electric power system model comprising AVR and FACTS equipment and WADC model；

Step (2): do not considering the electric power system model comprising AVR and FACTS equipment and the WADC model of time lag factor On the basis of, introduce Time Delay, and then set up the model of the closed loop time-lag power system considering time lag factor；

Step (3): according to the model of closed loop time-lag power system, build the mathematical model of WADC parameter optimization；

Step (4): use PSO algorithm, the optimized parameter of WADC in solution procedure (3).At each iterative optimization procedure In, it is considered to time lag factor, use the critical eigenvalue of the SOD Algorithm for Solving closed loop time-lag power system rightmost side, to reach crucial The damping of eigenvalue this target maximum.

In specific implementation process, in step (1), use controllability and observability associating geometric measures method, determine AVR and The best position of FACTS equipment.

The address installed according to AVR and the FACTS equipment selected and feedback signal, set up following system linearization state empty Between model:

$\left\{\begin{array}{c}\mathrm{\Δ}\stackrel{\·}{x}=A\mathrm{\Δ}x+B\mathrm{\Δ}u\\ \mathrm{\Δ}y=C\mathrm{\Δ}x+D\mathrm{\Δ}u\end{array}\right.$

In formula: x is the state vector of system, u and y is respectively input vector and output vector；A, B, C, D are respectively system State matrix, input matrix, output matrix and straight-through matrix.If the eigenvalue of matrix A is λ_i(i=1 ..., n), accordingly Left and right eigenvectors matrix is: U=[u₁,u₂,…,u_n], V=[v₁,v₂,…,v_n].Wherein, u_iAnd v_iIt is respectively ith feature The left and right characteristic vector of value.After standardization processing, U and V meets U^HV=V^HU=I_n, I_nFor n rank unit matrix.

System i-th oscillation mode λ_iControllability geometric measures m_ciWith controllability geometric measures m_oiCan be calculated by following formula:

$\left\{\begin{array}{c}{m}_{ci}\left(k\right)=cos\left(\mathrm{\α}\left(u_i,b_k\right)\right)=\frac{\left|b_k^T{u}_i\right|}{\left|\right|u_i\left|\right|\left|\right|b_k\left|\right|}\\ m_{oi}\left(l\right)=cos\left(\mathrm{\θ}\left(c_l^T,v_i\right)\right)=\frac{\left|c_l{v}_i\right|}{\left|\right|v_i\left|\right|\left|\right|c_l\left|\right|}\end{array}\right.$

In formula: b_kKth for input matrix B arranges；c_lL row for output matrix C；α(u_i,b_k) it is input vector b_kAnd a left side Characteristic vector u_iAngle；θ(c_l ^T,v_i) it is output vector c_lWith right characteristic vector v_iAngle；| | and | | | | represent respectively Delivery value and European norm.

For oscillation mode λ_i, can control/the associating geometric measures of controllability is:

m_coi(k, l)=m_ci(k)m_oi(l)

If m_coi(k, l) ≠ 0, then explanation can pass through u_kAnd y_lControl model λ_i。m_coi(k l) takes u during maximum_kAnd y_lIt is Maximally effective；Work as m_coi(k, when l) taking maximum, if u_kAnd y_lSignal take from the same area, oscillation mode λ_iCan be by this locality Damping controls；Otherwise, if u_kAnd y_lSignal take from different regions, then need to damp corresponding oscillation mode with wide-area control.

Although the detailed description of the invention of the present invention is described by the above-mentioned accompanying drawing that combines, but not the present invention is protected model The restriction enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme, and those skilled in the art are not Need to pay various amendments or deformation that creative work can make still within protection scope of the present invention.

Claims (10)

1. the power system additional wide area damping control method for designing considering time lag, it is characterised in that include following step Rapid:

Step (1): using oscillation mode the most weak for power system damping as target control pattern, determine AVR and FACTS equipment Best position, further foundation does not consider the electric power system model comprising AVR and FACTS equipment and the WADC of time lag factor Model；

Step (2): do not considering the electric power system model comprising AVR and FACTS equipment and the base of WADC model of time lag factor On plinth, introduce Time Delay, and then set up the model of the closed loop time-lag power system considering time lag factor；

Step (3): according to the model of closed loop time-lag power system, build the mathematical model of WADC parameter optimization；

Step (4): using PSO algorithm, in solution procedure (3), the optimized parameter of WADC, in each iterative optimization procedure, examines Consider time lag factor, use the critical eigenvalue of the SOD Algorithm for Solving closed loop time-lag power system rightmost side, to reach critical eigenvalue Damping this target maximum.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 1, it is special Levy and be, in described step (1), use the associating geometric measures method of controllability and observability, determine that AVR and FACTS equipment is The Optimal Feedback signal of good installation site and additional wide area damping control.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 2, it is special Levy and be, in described step (1), determine the detailed process of the best position of AVR and FACTS equipment, including:

Step (1.1): the parameter of given AVR and FACTS equipment, using some node of power system as AVR and FACTS equipment Alternative installation site；

Step (1.2): calculate containing system load flow equation and the initial value of state variable, the shape installing AVR and FACTS equipment Become system linearity coefficient matrix；According to linearisation coefficient matrix, calculate the critical eigenvalue of power system and correspondence thereof Left and right characteristic vector, and set the oscillation mode to be investigated of power system；

Step (1.3): under the oscillation mode set, with the reference value of AVR and FACTS equipment for input, with different feedbacks Signal is output, calculates the associating geometric measures of the controllability and observability of AVR and FACTS equipment；

Step (1.4): compare the modulus value size of the associating geometric measures of controllability and observability, filter out the modulus value of associating geometric measures Maximum node is defined as the best position of AVR and FACTS equipment, using the control signal of its correspondence as additional WADC's Feedback signal, input WADC constitutes closed loop control, thus increases the damping capacity of system.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 1, it is special Levying and be, additional wide area damping control is made up of lead-lag link, belongs to dynamic compensator.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 1, it is special Levying and be, according to spectral mapping theorem, the eigenvalue being positioned at left half complex plane of closed loop time-lag power system is mapped to Solution operator position In the unit circle of z-plane, the eigenvalue being positioned at right half complex plane is mapped in outside unit circle.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 5, it is special Levy and be, utilize the eigenvalue of Solution operator, solve corresponding closed loop time-lag power system critical eigenvalue.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 1, it is special Levy and be, in described step (4), use PSO intelligent algorithm, before the WADC optimized parameter in solution procedure (3), also include: Population number and maximum iteration time are set and initialize population.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 6, it is special Levy and be, in described step (4), use equally spaced LMS that Solution operator is processed, according to the eigenvalue of time-lag power system With the eigenvalue corresponding relation of Solution operator, try to achieve the critical eigenvalue of time-lag power system.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 1, it is special Levy and be, in each iterative process of PSO algorithm of described step (4), the search information of the most more new particle:

$\left\{\begin{array}{c}{x}_{i,d}^{k+1}=x_{i,d}^k+v_{i,d}^{k+1}\\ v_{i,d}^{k+1}={\mathrm{\ωv}}_{i,d}^k+c_{1}rand(\·)({\mathrm{pbest}}_d-x_{i,d}^k)+c_{2}Rand(\·)({\mathrm{gbest}}_d-x_{i,d}^k)\end{array}\right.$

In formula: k is the number of times that current iteration calculates,D for particle i search speed ties up component, WithRepresent the upper and lower bound of search speed respectively；The d projecting to search volume for i-th particle ties up component；pbest_d Optimum position for i-th particle up till now projects to the d dimension component of search volume；gbest_dFor current all particle search Optimum position project to search volume d tie up component；c₁And c₂For aceleration pulse；Rand () and Rand () is two Random number between individual 0 to 1；ω is weight coefficient.

A kind of power system additional wide area damping control method for designing considering time lag the most as claimed in claim 1, it is special Levy and be, for improving convergence rate, linear narrowing weight coefficient in each iterative process of PSO algorithm of step (4).