CN105977986A - Electric power system excitation voltage decoupling control method based on wide-area information - Google Patents

Abstract

The present invention relates to an electric power system excitation voltage decoupling control method based on wide-area information. The method comprises the following steps: realizing the decoupling control of the excitation voltage and frequency based on the system equivalent simplified model of the wide-area information; compensating wide-area control time delay by employing a second-order Pade approximation method, and obtaining an excitation voltage decoupling control model including the time delay compensation; and converting the excitation voltage decoupling control problem to a linear quadratic type optimal control problem, and obtaining an excitation voltage control strategy. Through adoption of the wide-area information, the present invention provides an electric power system excitation voltage decoupling control method, and therefore the decoupling control of the excitation voltage and frequency of a generator is realized, the complex non-linear excitation voltage control problem is converted to a simple linear quadratic type optimal control problem, the method of rapidly obtaining an effective excitation voltage control strategy is realized, and the electric power system excitation voltage decoupling control method has good application values and popularization prospects.

Description

A kind of power system excitation voltage decoupling control method based on Wide-area Measurement Information

Technical field

The present invention relates to a kind of dynamically excitation voltage control method, especially relate to a kind of power train based on Wide-area Measurement Information System excitation voltage decoupling control method

Background technology

Power system voltage is one of key factor supporting power network safety operation.In modern power network is run, base The Power system security control technology combined in simplification, experience and employing local information is difficult to fully meet the reliable and stable operation of electrical network Requirement.Set up the voltage control method based on system dynamic model, to improve system Fast dynamic voltage response characteristic, To ensureing that power network safety operation is significant.

Both at home and abroad, Control of Voltage problem is roughly divided into quiescent voltage control and dynamic electric voltage control.Wherein the most dynamically Voltage-controlled Main Means is generator excitation voltage control.Existing excitation voltage control method mainly have feedback linearization, Nonlinear Control etc..These methods mostly design excitation voltage control strategy from the local angle of electromotor, and method for designing is multiple Miscellaneous, it is difficult to adapt to the real-time change of operation of power networks state completely, there is certain risk.Along with electrical power system wide-area measures system The development of system (Wide Area Measurement System, WAMS), by phasor measurement unit (Phasor Measurements Units, PMUs) high-precision real-time synchronization data can be obtained, data acquisition cycle is 20 milliseconds or 10 millis Second, will control, for electrical network wide area excitation voltage, the technological approaches that offer is new.

Summary of the invention

In art methods, electric system generator excitation voltage and frequency control for coupling so that dynamically excitation electricity Pressure control strategy design is complex.The present invention proposes a kind of power system excitation voltage decoupling based on Wide-area Measurement Information and controls Method, it is achieved excitation voltage and the uneoupled control of frequency, simplifies the design of dynamic excitation voltage control strategy.

In order to solve above-mentioned technical problem, the present invention adopts the following technical scheme that:

A kind of power system excitation voltage decoupling control method based on Wide-area Measurement Information, it is characterised in that based on multiple moulds Type, wherein,

Model one, based on a meter and the dynamic model of power system excitation voltage characteristic:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_s=A_s{x}_s+B_s{u}_s+E_s{W}_s\\ y={\mathrm{Zx}}_s-r\end{array}\right.$ Formula one

In formula: x_s、u_sAnd W_sBeing respectively system mode vector, dominant vector and perturbation vector, it is expressed as

x_s=[Δ E '_q1..., Δ E '_qi..., Δ E '_qm]^T, u_s=[Δ E_f1..., E_fi..., Δ E_fm]^T, W_s=[w₁..., w_i..., w_m]^T,

w_i=V_gicosδ_i-V_gi0cosδ_i0,

Matrix A_s、B_sAnd E_sIt is expressed as

$A_s=diag(-\frac{X_{d1}}{T_{d01}^{\′}{X}_{d1}^{\′}},...,-\frac{X_{di}}{T_{d0i}^{\′}{X}_{di}^{\′}},...,-\frac{X_{dm}}{T_{d0m}^{\′}{X}_{dm}^{\′}}),$

$B_s=diag\left(\frac{1}{T_{d01}^{\′}},\mathrm{...},\frac{1}{T_{d0i}^{\′}},\mathrm{...},\frac{1}{T_{d0m}^{\′}}\right),E_s=diag\[\frac{X_{d1}-X_{d1}^{\′}}{T_{d01}^{\′}{X}_{d1}^{\′}},\mathrm{...},\frac{X_{di}-X_{di}^{\′}}{T_{d0i}^{\′}{X}_{di}^{\′}},\mathrm{...},\frac{X_{dm}-X_{dm}^{\′}}{T_{d0m}^{\′}{X}_{dm}^{\′}}\]$

Wherein: T '_d0i、E_fi、E′_qi、X_di、X′_di、δ_iAnd V_giIt is respectively the d axle open circuit time constant of electromotor, excitation electricity Pressure, q axle transient potential, d axle reactance, d axle transient state reactance, merit angle and set end voltage；δ_i0And V_gi0It is respectively variable δ_iAnd V_giAt the beginning of Initial value；ΔE_fiWith Δ E '_qiIt is respectively dependent variable relative to the deviation of initial value；M is electromotor number.

Y represents load bus voltage deviation amount, and i.e. system output, is represented by

Y=[Δ V_l1,…,ΔV_li,…,ΔV_ln]^T

Wherein: Δ V_liFor i-th load bus voltage deviation.Z_sTieing up time-varying matrix for n × m, r is that n ties up time-varying vector；n For load number.

Model two: the excitation voltage uneoupled control model containing delay compensation:

$\min J=\frac{1}{2}{\∫}_{t_0}^{\mathrm{\∞}}(y^{T}Qy+v^{T}Rv)dt$

Formula two

$st:\left\{\begin{array}{c}\stackrel{\·}{x}=Ax+Bv+E{W}_s\\ y=Cx-r\\ v_{\min }\≤v\≤v_{max}\end{array}\right.$

In formula: J is object function, t₀The moment is there is for disturbance；Matrix Q and R is respectively voltage deviation weighting matrix and control Cost weighting matrix processed, they are diagonal matrix；.v_max、v_minBound for controlled quentity controlled variable v.

The concrete grammar of excitation voltage control strategy design is: excitation voltage uneoupled control problem is converted into linear quadratic Type optimal control problem., the most do not consider the inequality constraints condition in formula two, excitation voltage uneoupled control problem be converted into Linear-Quadratic Problem tracking control problem.That is, formula two is found a Feedback Control Law:

V=Kx+G formula three

Make object function J minimum.

In formula three: K is STATE FEEDBACK CONTROL matrix, K ∈ R^m×3m；G is feedback control vector, G ∈ R^m。

Definition any time, formula two meets following two conditions.

Condition one:: (A, B) is to control；

Condition two: (A, C) is to see；

Then can be theoretical according to Quadratic Optimal Control, the solution of feedback control matrix K and G is

$\left\{\begin{array}{c}K=-R^{-1}{B}^{T}P\\ G=R^{-1}{B}^T\mathrm{\ϵ}\end{array}\right.$ Formula four

Wherein: matrix P and ε is the solution of formula five, and P ∈ R^3m×3m, ε ∈ R^3m。

$\left\{\begin{array}{c}0=-PA-A^{T}P+PB{R}^{-1}{B}^{T}P-C^{T}QC\\ 0=({\mathrm{PBR}}^{-1}{B}^T-A^T)\mathrm{\ϵ}+{\mathrm{PEW}}_s-C^{T}Qr\end{array}\right.$ Formula five

Then, the controlled quentity controlled variable inequality constraints in formula two is embedded in control law formula three, obtains excitation voltage control Strategy.Its detailed construction is as shown in Figure 2.

Compared with prior art, the invention have the advantages that and beneficial effect: 1, from the angle of electrical network wide area, it is proposed that A kind of power system excitation voltage control method, it is achieved that excitation voltage and the uneoupled control of frequency；And utilize second order Pad é near Wide-area control delay problem is compensated like method.2, the non-linear exciter Control of Voltage problem that tradition is complicated is converted into better simply line Property quadratic optimal control problem, can quickly obtain a kind of simple and effective excitation voltage control strategy, have good popularization Using value and prospect.3, realize the uneoupled control of excitation voltage and frequency, have not been reported.

Accompanying drawing explanation

Fig. 1 is the workflow diagram of the inventive method.

Fig. 2 is excitation voltage control strategy based on Wide-area Measurement Information.

Fig. 3 is the power system schematic diagram of certain actual band electrolytic aluminium load.

Fig. 4 is that the excitation voltage only with local information feedback controls load bus voltage change curve.

Fig. 5 is that the excitation voltage only with local information feedback controls generator excitation voltage change curve.

Fig. 6 is that the excitation voltage only with local information feedback controls generator reactive power change curve.

Fig. 7 is that excitation voltage based on Wide-area Measurement Information controls load bus voltage change curve.

Fig. 8 is that excitation voltage based on Wide-area Measurement Information controls generator excitation voltage change curve.

Fig. 9 is that excitation voltage based on Wide-area Measurement Information controls generator reactive power change curve.

Detailed description of the invention

It is the non-linear of complexity that the present invention mainly solves electric system generator excitation voltage and frequency in prior art Coupling control problem.In order to improve system dynamics voltage response characteristic and maintenance level, needs design one is simple and effective encourages Magnetic voltage control strategy.The present invention proposes a kind of based on Wide-area Measurement Information, more effective power system excitation Control of Voltage side Method, the method achieves the uneoupled control of generator excitation voltage and frequency, it is possible to obtain a kind of simple and effective excitation voltage Control strategy, has good application value and prospect.

Below in conjunction with accompanying drawing be embodied as that the invention will be further described.

First, the present invention proposes a kind of system equivalent simplified model based on Wide-area Measurement Information, as follows:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_s=A_s{x}_s+B_s{u}_s+E_s{W}_s\\ y={\mathrm{Zx}}_s-r\end{array}\right.$ (9)

In formula: x_s、u_sAnd W_sBeing respectively system mode vector, dominant vector and perturbation vector, it is expressed as x_s=[Δ E′_q1,…,ΔE′_qi,…,ΔE′_qm]^T, u_s=[Δ E_f1,…,E_fi,…,ΔE_fm]^T, W_s=[w₁,…,w_i,…,w_m]^T,

w_i=V_gicosδ_i-V_gi0cosδ_i0, i=1 ..., m, x_s,u_s,W_s∈R^m

Matrix A_s、B_sAnd E_sIt is expressed as

$A_s=diag(-\frac{X_{d1}}{T_{d01}^{\′}{X}_{d1}^{\′}},...,-\frac{X_{di}}{T_{d0i}^{\′}{X}_{di}^{\′}},...,-\frac{X_{dm}}{T_{d0m}^{\′}{X}_{dm}^{\′}}),$

$B_s=diag\left(\frac{1}{T_{d01}^{\′}},\mathrm{...},\frac{1}{T_{d0i}^{\′}},\mathrm{...},\frac{1}{T_{d0m}^{\′}}\right),E_s=diag\[\frac{X_{d1}-X_{d1}^{\′}}{T_{d01}^{\′}{X}_{d1}^{\′}},\mathrm{...},\frac{X_{di}-X_{di}^{\′}}{T_{d0i}^{\′}{X}_{di}^{\′}},\mathrm{...},\frac{X_{dm}-X_{dm}^{\′}}{T_{d0m}^{\′}{X}_{dm}^{\′}}\]$

Wherein: T '_d0i、E_fi、E′_qi、X_di、X′_di、δ_iAnd V_giIt is respectively the d axle open circuit time constant of electromotor, excitation electricity Pressure, q axle transient potential, d axle reactance, d axle transient state reactance, merit angle and set end voltage；δ_i0And V_gi0It is respectively variable δ_iAnd V_giAt the beginning of Initial value；ΔE_fiWith Δ E '_qiIt is respectively dependent variable relative to the deviation of initial value；M is electromotor number.

Y represents load bus voltage deviation amount, and i.e. system output, is represented by

Y=[Δ V_l1,…,ΔV_li,…,ΔV_ln]^T

Wherein: Δ V_liFor i-th load bus voltage deviation.Z_sTieing up time-varying matrix for n × m, r is that n ties up time-varying vector；n For load number.

System equivalent simplified model derivation based on Wide-area Measurement Information is as follows.

PMUs is provided that high-precision real-time synchronization data, including: meritorious and reactive power, node voltage, electromotor merit The information such as angle.After power system carries out PMU optimal allocation, it is possible to ensure system-wide observability.On the one hand, send out from synchronization Motor side PMU obtains generator's power and angle δ in real time_i, angular frequency_i, active-power P_gi, set end voltage V_giAnd phase angle theta_giAfter information, Q axle transient potential E ' can be tried to achieve by formula (10) and formula (11)_qi。

$P_{gi}=\frac{E_{qi}^{\′}{V}_{gi}}{X_{di}^{\′}}\sin \left({\mathrm{\δ}}_i-{\mathrm{\θ}}_{gi}\right)+\frac{X_{di}^{\′}-X_{qi}}{2X_{di}^{\′}{X}_{qi}}{V}_{gi}^2\sin 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_{gi}\right)---\left(10\right)$

$E_{qi}^{\′}=\[P_{gi}-\frac{X_{di}^{\′}-X_{qi}}{2X_{di}^{\′}{X}_{qi}}{V}_{gi}^2\sin 2\left({\mathrm{\δ}}_i-{\mathrm{\θ}}_{gi}\right)\]X_{di}^{\′}/V_{gi}\sin \left({\mathrm{\δ}}_i-{\mathrm{\θ}}_{gi}\right)---\left(11\right)$

Meanwhile, electromotor d, q shaft current i_diAnd i_qiCan be obtained by formula (12).

$\left\{\begin{array}{c}{i}_{di}=(E_{qi}^{\′}-V_{gi}{\mathrm{cos\δ}}_i)/X_{di}^{\′}\\ i_{qi}=V_{gi}{\mathrm{sin\δ}}_i/X_{qi}\end{array}\right.---\left(12\right)$

Electromotor electromagnetic torque T_eiCan be obtained by formula (13), i.e.

T_ei=E '_qii_qi-(X′_di-X_qi)i_dii_qi (13)

And the synchronous generator 3 order mode type that tradition considers dynamic excitation voltage characteristic is represented by

$T_{d0i}^{\′}{\stackrel{\·}{E}}_{qi}^{\′}=E_{fi}-E_{qi}^{\′}-(X_{di}-X_{di}^{\′})i_{di}---\left(14\right)$

$T_{ji}{\stackrel{\·}{\mathrm{\ω}}}_i=T_{mi}-T_{ei}-D_i({\mathrm{\ω}}_i-1)---\left(15\right)$

${\stackrel{\·}{\mathrm{\δ}}}_i={\mathrm{\ω}}_0({\mathrm{\ω}}_i-1)---\left(16\right)$

Wherein: formula (14) represents that generator excitation voltage dynamic characteristic equation, formula (15)-formula (16) represent generator mechanical Dynamic characteristic equation.i_di、T_ji、ω₀、D_iAnd T_miDo not represent the d shaft current of electromotor, electromotor inertia time constant, specified angle Frequency, merit angle, damped coefficient and machine torque.

Can be obtained by formula (14)-formula (16), conventional electric generators excitation voltage and frequency control for coupling.Utilization utilizes wide area to believe After breath, quantity of state and electric parameters in equation (15) and (16) all become known quantity.For excitation voltage control, available wide area The instantaneous value that information obtains replaces dynamical equation (15) and (16).So, equation can be eliminated from the dynamical equation of electromotor 3 rank (15) and (16), thus only retain generator excitation dynamical equation (14).After above-mentioned equivalent-simplification, electromotor is by 3 order modes Type is reduced to 1 order mode type, it is achieved generator excitation voltage and the uneoupled control of frequency.

Further formula (12) is substituted into formula (14) can obtain

${\stackrel{\·}{E}}_{qi}^{\′}=-\frac{X_{di}}{T_{d0i}^{\′}{X}_{di}^{\′}}{E}_{qi}^{\′}+\frac{1}{T_{d0i}^{\′}}{E}_{fi}+\frac{X_{di}-X_{di}^{\′}}{T_{d0i}^{\′}{X}_{di}^{\′}}{V}_{gi}{\mathrm{cos\δ}}_i---\left(17\right)$

Take Δ E '_qi=E '_qi-E′_qi0(E′_qi0For variable E '_qiInitial value), formula (17) is represented by

$\mathrm{\Δ}{\stackrel{\·}{E}}_{qi}^{\′}=-\frac{X_{di}}{T_{d0i}^{\′}{X}_{di}^{\′}}{\mathrm{\ΔE}}_{qi}^{\′}+\frac{1}{T_{d0i}^{\′}}{\mathrm{\ΔE}}_{fi}+\frac{\left(X_{di}-X_{di}^{\′}\right)}{T_{d0i}^{\′}{X}_{di}^{\′}}\left(V_{gi}{\mathrm{cos\δ}}_i-V_{gi0}{\mathrm{cos\δ}}_{i0}\right)---\left(18\right)$

To the power system containing m electromotor, its dynamical equation is represented by

${\stackrel{\·}{x}}_s=A_s{x}_s+B_s{u}_s+E_s{W}_s---\left(19\right)$

On the other hand, load side node voltage V is obtained in real time from WAMS system_liAnd phase angle theta_liAfter, set up load bus electricity Pressure bias vector Δ V_L(ΔV_L=V_L-V_L0, V_LAnd V_L0Be respectively load bus voltage vector and load bus Initial Voltage Value to Amount) and system state amount x_sRelation.Detailed process is as follows:

After the contact knots removal in electric power networks equation, comprise only the network equation of electromotor node and load bus It is represented by

$\left[\begin{array}{c}{I}_G\\ I_L\end{array}\right]=\left[\begin{array}{cc}{Y}_{GG}& Y_{GL}\\ Y_{LG}& Y_{LL}\end{array}\right]\left[\begin{array}{c}{V}_G\\ V_L\end{array}\right]---\left(20\right)$

Wherein: I_GAnd V_GFor electromotor injection current vector sum voltage vector, I_LAnd V_LFor load injection current vector sum electricity The amount of pressing to, I_G,V_G∈R^2m, I_L, V_L∈R²ⁿ；Y_GGFor network power machine node self-admittance matrix, Y_LLFor network load node self-conductance Receive matrix, Y_GL、Y_LGTransadmittance matrix for electromotor node and load bus.

Meanwhile, electromotor network interface equation is

$\left[\begin{array}{c}{I}_{gxi}\\ I_{gyi}\end{array}\right]=\left[\begin{array}{cc}{G}_{gxi}& -B_{gxi}\\ B_{gyi}& G_{gyi}\end{array}\right]\left[\begin{array}{c}{E}_{qi}^{\′}{\mathrm{cos\δ}}_i-V_{gxi}\\ E_{qi}^{\′}{\mathrm{sin\δ}}_i-V_{gyi}\end{array}\right]=\left[\begin{array}{c}{a}_{xi}{E}_{qi}^{\′}\\ a_{yi}{E}_{qi}^{\′}\end{array}\right]-Y_{gi}\left[\begin{array}{c}{V}_{gxi}\\ V_{gyi}\end{array}\right]---\left(21\right)$

Wherein: $\left[\begin{array}{c}{I}_{gxi}\\ I_{gyi}\end{array}\right],\left[\begin{array}{c}{V}_{gxi}\\ V_{gyi}\end{array}\right]$ It is respectively vector I_GAnd V_GThe 2i and 2i+1 element； $y_{gi}=\left[\begin{array}{cc}{G}_{gxi}& -B_{gxi}\\ B_{gyi}& G_{gyi}\end{array}\right],$ Variable G_gxi、B_gxi、B_gyiAnd G_gyiIt is respectively

$G_{gxi}=\frac{-(X_{di}^{\′}-X_{qi})sin2{\mathrm{\δ}}_i}{2X_{di}^{\′}{X}_{qi}}$

$B_{gxi}=-\frac{1}{X_{di}^{\′}{X}_{qi}}(X_{di}^{\′}{\cos }^2{\mathrm{\δ}}_i+X_{qi}{\sin }^2{\mathrm{\δ}}_i)$

$B_{gyi}=-\frac{1}{X_{di}^{\′}{X}_{qi}}(X_{di}^{\′}{\sin }^2{\mathrm{\δ}}_i+X_{qi}{\cos }^2{\mathrm{\δ}}_i)$

G_gyi=-G_gxi

a_xi、a_yiIt is respectively a_xi=G_gxicosδ_i-B_gxisinδ_i, a_yi=B_gyicosδ_i+G_gyisinδ_i。

Present invention is generally directed to voltage sensitivity load, i.e. load power and depend primarily on system voltage change.Such is born Lotus model is represented by

$\left\{\begin{array}{c}{P}_{li}=P_{li0}{(V_{li}/V_{li0})}^{K_{pv}}\\ Q_{li}=Q_{li0}{(V_{li}/V_{li0})}^{K_{qv}}\end{array}\right.---\left(22\right)$

Wherein: P_li、Q_li、V_liIt is respectively the active power of load, reactive power, node voltage；P_li0、Q_li0、V_li0Respectively For the initial value to dependent variable；K_pvFor active power about the coefficient of voltage；K_qvFor reactive power about the coefficient of voltage.

So, loaded network interface equation is

$\left[\begin{array}{c}{I}_{lxi}\\ I_{lyi}\end{array}\right]=-\frac{1}{V_{li0}^2}\left[\begin{array}{cc}{P}_{li0}{V}_{li}^{\left(K_{pv}-2\right)}& Q_{li0}{V}_{li}^{\left(K_{qv}-2\right)}\\ -Q_{li0}{V}_{li}^{\left(K_{qv}-2\right)}& P_{li0}{V}_{li}^{\left(K_{pv}-2\right)}\end{array}\right]\left[\begin{array}{c}{V}_{lxi}\\ V_{lyi}\end{array}\right]=-Y_{li}\left[\begin{array}{c}{V}_{lxi}\\ V_{lyi}\end{array}\right]---\left(23\right)$

Wherein: $\left[\begin{array}{c}{I}_{lxi}\\ I_{lyi}\end{array}\right],\left[\begin{array}{c}{V}_{lxi}\\ V_{lyi}\end{array}\right]$ Not Wei vector I_LAnd V_LThe 2i and 2i+1 element.Matrix Y_liIt is expressed as

$y_{li}=\frac{1}{V_{li0}^2}\left[\begin{array}{cc}{P}_{li0}{V}_{li}^{(K_{pv}-2)}& Q_{li0}{V}_{li}^{(K_{qv}-2)}\\ -Q_{li0}{V}_{li}^{(K_{qv}-2)}& P_{li0}{V}_{li}^{(K_{pv}-2)}\end{array}\right]$

Formula (21) and formula (23) are substituted into formula (20) can obtain

$V_L=-{(Y_{NLL}-Y_{LG}{Y}_{NGG}^{-1}{Y}_{GL})}^{-1}{Y}_{LG}{Y}_{NGG}^{-1}{I}_{NG}=Z_N{I}_{NG}---\left(24\right)$

Wherein: vector I_NGThe 2i and 2i+1 element be $\left[\begin{array}{c}{a}_{xi}{E}_{qi}^{\′}\\ a_{yi}{E}_{qi}^{\′}\end{array}\right],$ I_NG∈R^2m；Matrix Y_NLL、Y_NGGAnd Z_NIt is respectively

Y_NLL=Y_LL+diag(Y_l1,…Y_li,…Y_ln)

Y_NGG=Y_GG+diag(Y_g1,…Y_gi,…Y_gm)

$Z_N=-{(Y_{NLL}-Y_{LG}{Y}_{NGG}^{-1}{Y}_{GL})}^{-1}{Y}_{LG}{Y}_{NGG}^{-1},Z_N\∈R^{2n\×2m}$

Note matrix Z_NI-th behavior Z_Ni=[z_i1,…,z_ij,…,z_i,2m].Based on formula (24), set up load bus voltage V_li And x_sRelation, as follows:

V_li=Z_i·(x_s+E′_q0)=Z_ix_s+r_li (25)

Wherein:

$Z_i=\frac{1}{{\mathrm{cos\θ}}_{li}}\[z_{2i,1}{a}_{x1}+z_{2i,2}{a}_{y1},...,z_{2i,2m-1}{a}_{xm}+z_{2i,2m}{a}_{ym}\],$ Z_i∈R^1×m；Work as θ_li=(2k+1) pi/2, k During for integer, $Z_i=\frac{1}{{\mathrm{sin\θ}}_{li}}\[z_{2i+1,1}{a}_{x1}+z_{2i+1,2}{a}_{y1},...,z_{2i+1,2m-1}{a}_{xm}+z_{2i+1,2m}{a}_{ym}\].$ r_li=Z_iE′_q0, E '_q0For initially Value E '_qi0The vector of composition.

The vectorial Δ V that all for system load bus voltage deviations are formed_LAs output, and it is designated as y, then has

Y=Δ V_L=Zx_s+r_l-V_L0=Zx_s-r (26)

Wherein: the i-th behavior Z of matrix Z_i, Z ∈ R^n×m；Vector r_lThe i-th behavior r_li, r_l∈Rⁿ；R=V_l0-r_l。

As generator's power and angle δ_i, load bus voltage V_liAnd phase angle theta_liAfter known, matrix Z and r in formula (26) is The amount of knowing.

Association type (19) and formula (26) can obtain, system Simplified equivalent model based on Wide-area Measurement Information, i.e. formula (9).

Then, operate according to the following steps:

Step 1: utilize second order Pad é method of approximation to compensate wide-area control time delay, obtain the control system containing delay compensation.

Assuming that wide-area control time delay value is τ, second order Pad é method of approximation compensates the state space description of wide-area control time delay and is

${\stackrel{\·}{x}}_{pi}=A_{pi}{x}_{pi}+B_{pi}{v}_i$

(27)

u_si=C_pix_pi+D_piv_i

Wherein: x_piFor the state variable of second order Pad é approximation, x_pi∈R²；v_iFor the control variable of second order Pad é approximation, v_i ∈R；u_siIt is vector u_sI-th element.Matrix A_pi、B_pi、C_piAnd D_piIt is expressed as

$A_{pi}=\left[\begin{array}{cc}0& 1\\ -12/{\mathrm{\τ}}^2& -6/\mathrm{\τ}\end{array}\right],B_{pi}=\left[\begin{array}{c}0\\ 1\end{array}\right]$

C_pi=[0-12/ τ], D_pi=1

Formula (27) is substituted into formula (19) and obtains the control system of delay compensation, as follows:

$\stackrel{\·}{x}=\left[\begin{array}{cc}{A}_s& B_s{C}_p\\ \mathrm{\θ}& A_p\end{array}\right]x+\left[\begin{array}{c}{B}_s{D}_p\\ B_p\end{array}\right]v+\left[\begin{array}{c}{E}_s\\ 0\end{array}\right]W_s=Ax+Bv+{\mathrm{EW}}_s---\left(28\right)$

Wherein: x is the state vector containing delay compensation control system, x ∈ R^3m；V is the dominant vector after delay compensation, v ∈R^m；

Vector x, v are expressed as

X=[x_s；x_p], x_p=[x_p1,…,x_pi,…,x_pm]^T

V=[v₁…；v_i,…,v_m]^T

Matrix A_pi、B_pi、C_piAnd D_piIt is expressed as

A_p=diag (A_p1,…,A_pi,…,A_pm), B_p=diag (B_p1,…,B_pi,…B_pm)

C_p=diag (C_p1,…,C_pi,…,C_pm), D_p=diag (D_p1,…,D_pi,…,D_pm)

Matrix A, B, E are expressed as

$A=\left[\begin{array}{cc}{A}_s& B_s{C}_p\\ 0& A_p\end{array}\right],B=\left[\begin{array}{c}{B}_s{D}_p\\ B_p\end{array}\right],E=\left[\begin{array}{c}{E}_s\\ 0\end{array}\right]$

A∈R^3m×3m, B ∈ R^3m×m, E ∈ R^3m×m

Meanwhile, the output containing delay compensation control system is

Y=[Z, 0] x-r=Cx-r, C ∈ R^n×3m (29)

So, association type (28) and formula (29) can contain the control system of delay compensation.

Step 2: form the excitation voltage uneoupled control model containing delay compensation.

Based on formula (28) and formula (29), with load bus voltage deviation and the minimum target of quadratic performance of control cost Function, sets up the excitation voltage uneoupled control model containing delay compensation, as follows:

$\min J=\frac{1}{2}{\∫}_{t_0}^{\mathrm{\∞}}(y^{T}Qy+v^{T}Rv)dt$

(30)

$st:\left\{\begin{array}{c}\stackrel{\·}{x}=Ax+Bv+E{W}_s\\ y=Cx-r\\ v_{\min }\≤v\≤v_{max}\end{array}\right.$

In formula: J is object function, t₀The moment is there is for disturbance；Matrix Q and R is respectively voltage deviation weighting matrix and control Cost weighting matrix processed, they are diagonal matrix；.v_max、v_minBound for controlled quentity controlled variable v.

Step 3: ask for excitation voltage control strategy.

The most do not consider the inequality constraints condition in formula (30), excitation voltage uneoupled control problem is converted into linear two Secondary type optimal control problem.That is, formula (30) is found a Feedback Control Law:

V=Kx+G (31)

Make object function J minimum.

In formula (31): K is STATE FEEDBACK CONTROL matrix, K ∈ R^m×3m；G is feedback control vector, G ∈ R^m。

Assume that any time, formula (5) meet following two conditions.1): (A, B) is to control；2): (A, C) is to see. Then can be theoretical according to Quadratic Optimal Control, the solution of feedback control matrix K and G is

$\left\{\begin{array}{c}K=-R^{-1}{B}^{T}P\\ G=R^{-1}{B}^T\mathrm{\ϵ}\end{array}\right.---\left(32\right)$

Wherein: matrix P and ε is the solution of formula (33), and P ∈ R^3m×3m, ε ∈ R^3m。

$\left\{\begin{array}{c}0=-PA-A^{T}P+PB{R}^{-1}{B}^{T}P-C^{T}QC\\ 0=({\mathrm{PBR}}^{-1}{B}^T-A^T)\mathrm{\ϵ}+{\mathrm{PEW}}_s-C^{T}Qr\end{array}\right.---\left(33\right)$

Then, the controlled quentity controlled variable inequality constraints in formula (30) is embedded in control law formula (31), obtains excitation voltage Control strategy, its detailed construction is as shown in Figure 2.

Hereinafter will further illustrate advantages of the present invention and beneficial effect with certain application for example.

Fig. 3 is the power system of certain actual band electrolytic aluminium load, and it mainly includes that 8 fired power generating unit and 3 electrolytic aluminiums are born Lotus.System thermoelectricity total installation of generating capacity be 1800MW (G1～G2:2 × 100MW, G3～G4:2 × 150MW, G5～G6:2 × 300MW, G7～G8:2 × 350MW), load aggregate demand capacity is 1638MW (aluminum load 1:330MW, aluminum load 2:420MW, aluminum Load 3:640MW, thermic load and station-service load: 248MW).In this system, electrolytic aluminium load belongs to exemplary voltages sensitivity and bears Lotus.For meeting the normal production of electrolytic aluminium, it is desirable to system voltage deviation is not more than the 5% of normal value, i.e. allow maximum voltage inclined Difference is 0.05p.u..Currently, this system is configured with the PMU of abundance, it is ensured that the observability of system.And wide-area control time delay value τ is 0.5s.

Fault is assumed: in Fig. 3, aluminum load 2 does not initially have access system；As t=3.5s, aluminum load 2 input coefficient, always Power is 420+j*254.8MVA.

The generator excitation voltage fed back only with local information is controlled, is designated as strategy 1；Use the present invention carried based on The generator excitation voltage of Wide-area Measurement Information controls, and is designated as strategy 2.

Use the aluminum load bus voltage of strategy 1, generator excitation voltage and reactive power change respectively such as Fig. 4, Fig. 5 and Shown in Fig. 6.Can be obtained by Fig. 4, before fault the voltage of aluminum load 1,2 and 3 be respectively 0.9962p.u., 1.0121p.u. and 0.9923p.u..After fault, system voltage is along with the input of aluminum load 2 and rapid decrease；After using strategy 1, aluminum load 1,2 and The voltage of 3 remains 0.9430p.u., 0.9292p.u. and 0.9220p.u. respectively.Load bus voltage deviation is all higher than 0.05p.u.。

Use the aluminum load bus voltage of strategy 2, generator excitation voltage and reactive power change respectively such as Fig. 7, Fig. 8 and Shown in Fig. 9.Can be obtained by Fig. 7, after using strategy 2, load voltage recovers rapidly.When t is more than 20s, the electricity of aluminum load 1,2 and 3 Pressure returns to 1.0044p.u., 0.9960p.u. and 0.9852p.u. respectively, and keeps stable.So, at fast dynamic processes In, system voltage quickly recovers to normal operating level, without affecting actual production and the system stable operation of electrolytic aluminium.

Can be obtained by Fig. 5 and Fig. 6, Fig. 8 and Fig. 9, each generating under above two excitation voltage control strategy, after system stability Machine excitation voltage and reactive power are as shown in table 1.Can be obtained by table 1, under the effect of strategy 2, the excitation voltage of each electromotor is equal Result higher than strategy 1；The result being all higher than strategy 1 without work output of electromotor, particularly electromotor G6's and G5 is idle Output is much larger than the result of strategy 1.Therefore, strategy 2 can more preferably keep system voltage level than strategy 1, improves system dynamics Voltage response characteristic.

Each generator excitation voltage and reactive power after table 1 system stability

In the present embodiment, can use and a kind of implement a kind of power system excitation voltage decoupling control based on Wide-area Measurement Information The device of method processed realizes the method step of the present invention, and it includes that the power system equivalent simplified model being sequentially connected with is set up single Unit, wide-area control delay compensation unit and control strategy ask for feedback unit.

Specific embodiment described herein is only to present invention spirit explanation for example.Technology neck belonging to the present invention Described specific embodiment can be made various amendment or supplements or use similar mode to replace by the technical staff in territory Generation, but without departing from the spirit of the present invention or surmount scope defined in appended claims.

Claims (1)

1. a power system excitation voltage decoupling control method based on Wide-area Measurement Information, it is characterised in that based on multiple models, Wherein,

Model one, based on a meter and the dynamic model of power system excitation voltage characteristic:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_s=A_s{x}_s+B_s{u}_s+E_s{W}_s\\ y={\mathrm{Zx}}_s-r\end{array}\right.$ Formula one

In formula: x_s、u_sAnd W_sBeing respectively system mode vector, dominant vector and perturbation vector, it is expressed as

x_s=[Δ E '_q1,…,ΔE′_qi,…,ΔE′_qm]^T, u_s=[Δ E_f1,…,E_fi,…,ΔE_fm]^T, W_s=[w₁,…,w_i,…, w_m]^T,

w_i=V_gicosδ_i-V_gi0cosδ_i0,

Matrix A_s、B_sAnd E_sIt is expressed as

$A_s=diag(-\frac{X_{d1}}{T_{d01}^{\′}{X}_{d1}^{\′}},\mathrm{...},-\frac{X_{di}}{T_{d0i}^{\′}{X}_{di}^{\′}},\mathrm{...},-\frac{X_{dm}}{T_{d0m}^{\′}{X}_{dm}^{\′}}),$

$B_s=diag(\frac{1}{T_{d01}^{\′}},\mathrm{...},\frac{1}{T_{d0i}^{\′}},\mathrm{...},\frac{1}{T_{d0m}^{\′}}),E_s=diag\[\frac{X_{d1}-X_{d1}^{\′}}{T_{d01}^{\′}{X}_{d1}^{\′}},\mathrm{...},\frac{X_{di}-X_{di}^{\′}}{T_{d0i}^{\′}{X}_{di}^{\′}},\mathrm{...},\frac{X_{dm}-X_{dm}^{\′}}{T_{d0m}^{\′}{X}_{dm}^{\′}}\]$

Wherein: T '_d0i、E_fi、E′_qi、X_di、X′_di、δ_iAnd V_giIt is respectively the d axle open circuit time constant of electromotor, excitation voltage, q axle Transient potential, d axle reactance, d axle transient state reactance, merit angle and set end voltage；δ_i0And V_gi0It is respectively variable δ_iAnd V_giInitial value； ΔE_fiWith Δ E '_qiIt is respectively dependent variable relative to the deviation of initial value；M is electromotor number；

Y represents load bus voltage deviation amount, and i.e. system output, is represented by

Y=[Δ V_l1,…,ΔV_li,…,ΔV_ln]^T

Wherein: Δ V_liFor i-th load bus voltage deviation；Z_sTieing up time-varying matrix for n × m, r is that n ties up time-varying vector；N is negative Lotus number；

Model two: the excitation voltage uneoupled control model containing delay compensation:

$\min J=\frac{1}{2}{\∫}_{t_0}^{\mathrm{\∞}}(y^{T}Qy+v^{T}Rv)dt$

$st:\left\{\begin{array}{c}\stackrel{\·}{x}=Ax+Bv+{\mathrm{EW}}_s\\ y=Cx-r\\ v_{\min }\≤v\≤v_{max}\end{array}\right.$ Formula two

In formula: J is object function, t₀The moment is there is for disturbance；Matrix Q and R is respectively voltage deviation weighting matrix and controls cost Weighting matrix, they are diagonal matrix；；v_max、v_minBound for controlled quentity controlled variable v；

The concrete grammar of excitation voltage control strategy design is: excitation voltage uneoupled control problem is converted into Linear-Quadratic Problem Excellent control problem；The most do not consider the inequality constraints condition in formula two, excitation voltage uneoupled control problem is converted into linearly Quadratic form tracking control problem；That is, formula two is found a Feedback Control Law:

V=Kx+G formula three

Make object function J minimum；

In formula three: K is STATE FEEDBACK CONTROL matrix, K ∈ R^m×3m；G is feedback control vector, G ∈ R^m；

Definition any time, formula two meets following two conditions；

Condition one:: (A, B) is to control；

Condition two: (A, C) is to see；

Then can be theoretical according to Quadratic Optimal Control, the solution of feedback control matrix K and G is

$\left\{\begin{array}{c}K=-R^{-1}{B}^{T}P\\ G=R^{-1}{B}^T\mathrm{\ϵ}\end{array}\right.$ Formula four

Wherein: matrix P and ε is the solution of formula five, and P ∈ R^3m×3m, ε ∈ R^3m；

$\left\{\begin{array}{c}0=-PA-A^{T}P+{\mathrm{PBR}}^{-1}{B}^{T}P-C^{T}QC\\ 0=({\mathrm{PBR}}^{-1}{B}^T-A^T)\mathrm{\ϵ}+{\mathrm{PEW}}_s-C^{T}Qr\end{array}\right.$ Formula five

Then, the controlled quentity controlled variable inequality constraints in formula two is embedded in control law formula three, obtains excitation voltage control strategy.