CN101915203A - Damping injection control method for improving power angle oscillation of water turbine generator set - Google Patents

Abstract

The invention relates to a damping injection control method for improving power angle oscillation of a water turbine generator set. An autocorrelation factor of the unit power angle is increased based on the structural analysis of a Hamilton model damping matrix of the water turbine generator set, namely the power angle damping is injected based on a dynamical mechanism associated inside the system, and the structural change is equivalent by designing a corresponding control law. Due to the applicability analysis of the equivalent control law, a variable structure control strategy by combining the algorithm and a traditional PID control algorithm is provided so as to control the machine set, and corresponding solutions are provided for the control of output phase step and other problems. The simulation proves that: the provided control algorithm can effectively improve the oscillating characteristics of the power angle of the machine set, even can keep the stability of the machine set under lower damping.

Description

Improve the damping injection control method of power-angle oscillation of hydroelectric generating set

Technical field

The present invention relates to hydraulic generator unit control technique field, be specifically related to a kind of damping injection control method that improves power-angle oscillation of hydroelectric generating set.

Background technique

The Large Hydroelectric Set underdamping problem that exists of networking at a distance is the key factor that influences the stabilization of power grids.Although the research of PSS and grid side FACTS equipment and be applied as to address this problem valid approach is provided.But because all there are some difficulties in the complexity of grid side in theory analysis and practical application.Therefore, adopt an effective measure in the unit side, to improve the stability of underdamping electric power system, be the hot issue of research always.

From unit parametric oscillation feature, its machinery and property to oscillation of electric aspect can be reflected in the merit angle of generator, therefore, is that the stability that unit is studied in representative is appropriate with the power-angle oscillation characteristic.

Traditional controlling Design method mainly is based on the Differential Equation Model of generator set, uses various control algorithms and improves control performance.The broad sense hamiltonian system theory that development in recent years is got up, because system capacity stream is provided, and dynamics details such as internal system parameter association mechanism, thereby in generator set and electric power system, obtained application.It mainly comprises two kinds of application modes: one is based on unit Hamilton model, improves its control performance in conjunction with other control theories, promptly utilizes the differential equation information of Hamilton's row formula; Two are based on the various application of energy reforming, promptly utilize the energy function of Hamilton's model fully to portray the characteristic of differential equation system.Yet do not make full use of the Inter parameter relation mechanism that Hamilton's model provides in the research.Main cause is to inject damping by control, and the controlling Design of improving systematic function all is in the starting stage on theoretical and method, and present some are used only can handle the following single system in three rank.

Summary of the invention

The object of the present invention is to provide a kind of damping injection control method that improves power-angle oscillation of hydroelectric generating set, promptly based on broad sense Hamilton theory, adopt the damping method for implanting to increase merit angle damping, improve the underdamping problem that the networking of hydraulic generator unit exists, to improve the stability of electric power system.

The technical solution adopted in the present invention is: the merit angle auto correlation factor of revising damping matrix in the hydraulic generator unit Hamilton model, thought is injected in damping based on broad sense Hamilton theory, propose a kind of simplified design method and be used for the modification that design control law is come equivalent this structure, obtained the applicable elements of this controlling method according to theory analysis.Secondly applicable elements and the traditional PID control according to this controlling method constitutes change structure control strategy, and the deficiency that exists in the specific implementation is revised, and to improve power-angle oscillation characteristic and stability, it is characterized in that comprising following steps:

Step 1: the merit angular correlation factor R of revising generator set Hamilton model damping matrix _δ, design equivalent control rule β ₁(x) and β ₂(x), specifically be calculated as follows:

${\mathrm{\β}}_1\left(x\right)=-\frac{T_y{C}_1{A}_{s1}}{r_{*}{C}_y}\frac{\∂H}{{\∂x}_3}\left(x_{*}\right)-R_{\mathrm{\δ}}{\mathrm{\Δx}}_3$

${\mathrm{\β}}_2\left(x\right)=\frac{X_{\mathrm{ad}}^2}{X_f}\frac{\∂H}{{\∂x}_5}\left(x_{*}\right)$

According to its applicability and traditional speed governing and excitation PID control formation change structure control strategy.

Step 2: the merit angular correlation factor R that is calculated as follows damping matrix according to the unit characteristic parameter _δValue restriction: 0＜R _δ＜0.25

Step 3: utilize unit characteristic parameter initialization controller, adopt following formula calculated equilibrium point x _*And control corresponding:

$\left\{\begin{array}{c}0=[J\left(x\right)-R\left(x\right)]\frac{\∂H}{\∂x}+g\left(x\right)v_{*}\\ p_{e^{*}}=\frac{U_s\sin x_{3^{*}}}{{X_{\mathrm{d\Σ}}}^{\′}}{x}_{5^{*}}+\frac{1}{2}{U}_s^2\sin {2x}_{3^{*}}(\frac{1}{X_{\mathrm{q\Σ}}}-\frac{1}{X_{d{\mathrm{\Σ}}^{\′}}})\\ Q_{e^{*}}=\frac{U_s\cos x_{3^{*}}}{{X_{\mathrm{d\Σ}}}^{\′}}{x}_{5^{*}}-\frac{1}{2}{U}_s^2(\frac{1}{X_{\mathrm{q\Σ}}}+\frac{1}{{X_{\mathrm{d\Σ}}}^{\′}})+\frac{1}{2}{U}_s^2\cos {2x}_{3^{*}}(\frac{1}{X_{\mathrm{q\Σ}}}-\frac{1}{{X_{\mathrm{d\Σ}}}^{\′}})\end{array}\right.$

In the formula:

Be respectively equinoctial point active power (pu) and wattless power (pu); U _sBe Infinite bus system voltage (pu); X _{The d ∑}=X _d+ X _T+ X _LX _dBe the reactance of generator d axle; X _TBe the transformer equivalent reactance; X _LBe the circuit equivalent reactance; X _{The q ∑}=X _q+ X _T+ X _LX _qBe the reactance of generator q axle; X _{The d ∑}'=X _d'+X _T+ X _LX _d' be generator d axle subtranient reactance; X _fBe the exciting winding reactance; X _AdBe d armature axis reaction reactance, each reactance is per unit value (pu); x _3*, x _5*Be respectively merit angle δ and q axle transient internal voltage E _q' (pu).

Step 4: control algorithm design

It exports the problem that step influences transient performance at different equinoctial points in the calm control, proposes to adopt the simple index way of output to improve the parameter response characteristic.The control of dissipation Hamilton model is converted into the output control of actual speed regulator and field regulator.The control algorithm that has derived the actual set controller through arrangement is as follows:

Speed regulator output is controlled to be:

$u={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">u</figure-callout>}}_0+(u_1-u_0)(1-e^{-T_{\mathrm{tout}}t})-R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3$

Equinoctial point control is wherein calculated by following formula:

$u_0={[-\frac{T_y^2(r_{{*}_0}^2+C_{T^{*}}^2)}{r_{*}}{p}_{e^{*}}+\frac{A_t{x}_{1^{*}}^3}{p_{m^{*}}{x}_{2^{*}}}]}_{x=x_{{*}_0}}$

$u_1={[-\frac{T_y^2(r_{{*}_0}^2+C_{T^{*}}^2)}{r_{*}}{p}_{e^{*}}+\frac{A_t{x}_{1^{*}}^3}{p_{m^{*}}{x}_{2^{*}}}]}_{x=x_{{*}_1}}$

Excitation output is controlled to be:

$E_f={\mathrm{<figure-callout\; id="0"\; label="E\; f"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">E</figure-callout>}}_f+(E_{f1}-E_{f0})(1-e^{-T_{\mathrm{Efout}}t})$

In the formula: the parameter of subscript " 0 ", " 1 " initial operating mode of expression and new equinoctial point; T _Tout, T _EfoutParameter decay time of representing speed governing, excitation output step signal respectively; T _yBe main servomotor time constant (second); r _*With

Be the value of matrix variables at equinoctial point; A _tBe the water turbine gain; U is speed regulator control; E _fBe excitation control output;

Be equinoctial point water turbine output mechanical power (pu); Variable x ₁, x ₂Be respectively flow and guide vane opening (pu).

Switch to controlling method of the present invention after set grid-connection band 10% rated load, traditional PID control is adopted in other operating mode such as unit starting and stopping, zero load.

The present invention has following advantage and effect:

1, control thought is different with traditional approach, from the dynamical mechanism CONTROLLER DESIGN of unit parameter internal correlation, can utilize the dynamics intrinsic propesties of unit operation control more fully.

2, control algorithm of the present invention is made up of the additional control of calm control under the given output and merit angle two-part.Calm control is control target with the equinoctial point, has reduced the coupling between unit and the electric power system, more helps set steady; In fact the additional control in merit angle be equivalent to the damping that has increased the angular motion of unit merit, improved the power-angle oscillation characteristic.

3, damping injection control method of the present invention is the control strategy of unit side, promptly improves the stable of electric power system with stablizing of unit itself, has avoided the influence of the complexity of electric power system to the generator set controller design, is easy to realize.

4, the control algorithm of being invented is the control method for coordinating about excitation and debugging.

5, emulation shows, control algorithm of the present invention still can be kept the operation stability of unit preferably under lower damping, has actual using value for solving the intrinsic underdamping problem of the remote networking of large-scale unit.

Description of drawings

Fig. 1 is simulation calculation result of the present invention, D=2, the merit angular response during meritorious the adjusting;

Fig. 2 is simulation calculation result of the present invention, D=-2, different R _δInfluence to the power-angle oscillation characteristic;

Fig. 3 is simulation calculation result of the present invention, D=4, the merit angular response during idle adjusting.

Embodiment

Below in conjunction with embodiment the present invention is described further.

Step 1: revise the merit angular correlation factor of generator set Hamilton model damping matrix, design equivalent control rule β ₁(x) and β ₂(x), constitute and according to its applicability and traditional speed governing and excitation PID control and to become the structure control strategy.

In order to increase the damping at unit merit angle, in the damping matrix of hydraulic generator unit Hamilton model, increase the auto correlation factor at merit angle among the present invention, come the change of equivalent this structure then by design control law.For determining the applicable elements of controlling method of the present invention, analyze by following three aspects:

1, revises the association factor R of damping matrix _δ

Hydraulic generator unit Hamilton model is:

$\stackrel{\&CenterDot;}{x}=[J\left(x\right)-R\left(x\right)]\frac{\&PartialD;H}{\&PartialD;x}\left(x_{*}\right)+g\left(x\right)v\left(x\right)---\left(1\right)$

$J\left(x\right)=\left[\begin{array}{ccccc}0& C_T& 0& 0& 0\\ -C_T& 0& 0& \frac{C_y}{2}& 0\\ 0& 0& 0& C_1& 0\\ 0& -\frac{C_y}{2}& -C_1& 0& 0\\ 0& 0& 0& 0& 0\end{array}\right],$ $R\left(x\right)=\left[\begin{array}{ccccc}\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">r</figure-callout>}& 0& 0& 0& 0\\ 0& r& 0& \frac{C_y}{2}& 0\\ 0& 0& 0& 0& 0\\ 0& \frac{C_y}{2}& 0& C_D& 0\\ 0& 0& 0& 0& C_G\end{array}\right],$ $g\left(x\right)=\left[\begin{array}{cc}0& 0\\ \frac{1}{T_y}& 0\\ 0& 0\\ 0& 0\\ 0& \frac{{\mathrm{\&omega;}}_B}{{T_{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">d</figure-callout>}0}}^{\&prime;}}\end{array}\right],$ $v\left(x\right)=\left[\begin{array}{c}{u}_p\left(x\right)\\ E_f\left(x\right)\end{array}\right]$

Hamiltonian function is:

$H\left(x\right)=T_y{A}_t\frac{{x_1}^2}{x_2}(x_1-q_{n1})+\frac{1}{2}{T}_j^{*}{(x_4-1)}^2+\frac{1}{2}{U_s}^2{\cos }^2{x}_3(\frac{1}{X_{\mathrm{d\&Sigma;}}}-\frac{1}{X_{\mathrm{q\&Sigma;}}})+\frac{1}{2}\frac{1}{X_{\mathrm{q\&Sigma;}}}{U_s}^2+$ (2)

$+\frac{1}{2}\frac{1}{X_{\mathrm{d\&Sigma;}}{X_{\mathrm{d\&Sigma;}}}^{\&prime;}{X}_f}{(X_{\mathrm{ad}}{U}_s\cos x_3-X_{\mathrm{d\&Sigma;}}\frac{X_f}{X_{\mathrm{ad}}}{x}_5)}^2$

Wherein: x=[x ₁x ₂x ₃x ₄x ₅] ^T=[q y δ ω E _q'] ^T

$f_1\left(x\right)=\frac{1}{T_w}(1-f_p{x_1}^2-\frac{{x_1}^2}{{x_2}^2});$

$f_2\left(x\right)=\frac{1}{T_y}(y_0-x_2);$

$r\left(x\right)=\{-f_2\left(x\right)\frac{\&PartialD;H}{{\&PartialD;x}_2}\left(x\right)+A_t\frac{x_1^3}{x_2}\}/\{{\left[\frac{\&PartialD;H}{{\&PartialD;x}_2}\right]}^2+{\left[\frac{\&PartialD;H}{{\&PartialD;x}_1}\left(x\right)\right]}^2\};$

$C_T\left(x\right)=[f_1\left(x\right)+\frac{\&PartialD;H}{{\&PartialD;x}_1}\left(x\right)r\left(x\right)]/\frac{\&PartialD;H}{{\&PartialD;x}_2}\left(x\right);$

$C_G=\frac{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="B\; T\; d"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">B</figure-callout>}}}{{T_d}^{}}\frac{X_{\mathrm{ad}}^2}{X_f};$

$C_1=\frac{1}{T_j};$

$C_D=\frac{D}{T_j^2{\mathrm{\&omega;}}_B};$

$C_y=\frac{1}{T_j{T}_y};$

In the formula, q is hydraulic turbine discharge (pu); q _NlBe no load discharge (pu); Y is guide vane opening (pu); y ₀Be guide vane opening initial value (pu); T _wBe current inertia time constant (second); f _pBe the loss of head coefficient; T _yBe main servomotor time constant (second); A _tBe the water turbine gain; u _pBe speed regulator control loop output signal; δ is unit merit angle (rad); ω is unit angular velocity (pu); E _q' be q axle transient internal voltage (pu); T _jBe unit set inertia time constant (second); ω _B=314 (rad/s); U _sBe Infinite bus system voltage (pu); D is a unit equivalent damping coefficient; X _{The d ∑}=X _d+ X _T+ X _LX _dBe the reactance of generator d axle; X _TBe the transformer equivalent reactance; X _LBe the circuit equivalent reactance; X _{The q ∑}=X _q+ X _T+ X _LX _qBe the reactance of generator q axle; X _{The d ∑}'=X _d'+X _T+ X _LX _d' be generator d axle subtranient reactance; X _fBe the exciting winding reactance; X _AdBe d armature axis reaction reactance, each reactance is per unit value (pu); T _D0' be d axle open circuit transient state time constant (second); E _fBe excitation control output.

Because it is among the damping matrix R (x) of generator set Hamilton model, related with merit angle δ without any parameter.According to the physical interpretation of damping matrix, the kinetic damping that shows δ this moment on system port is zero.Increase the auto correlation item R of δ for this reason _δ＞0, promptly increase the kinetic damping of merit angle δ, to being revised as of damping matrix:

$R_a\left(x\right)=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& R_{\mathrm{\&delta;}}& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\end{array}\right]---\left(3\right)$

Revised sytem matrix is:

J _d(x)-R _d(x)＝J(x)-[R(x)+R _a(x)] (4)

2, design equivalent control rule

In the design of equivalent control rule, a kind of simplified design method of broad sense Hamilton's interconnect architecture Correction and Control design has been proposed.The equivalent control rule of using this method design is:

${\mathrm{\&beta;}}_1\left(x\right)=-\frac{T_y{C}_1{A}_{s1}}{r_{*}{C}_y}\frac{\&PartialD;H}{{\&PartialD;x}_3}\left(x_{*}\right)-R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3---\left(5\right)$

${\mathrm{\&beta;}}_2\left(x\right)=\frac{X_{\mathrm{ad}}^2}{X_f}\frac{\&PartialD;H}{{\&PartialD;x}_5}\left(x_{*}\right)---\left(6\right)$

Wherein:

β ₁(x) be the control output of speed regulator, u _p=β ₁(x); β ₂(x) be excitation system output, E _f(x)=β ₂(x), A _S2=R _δC _DC _G+ C ₁ ²C _G, subscript " * " expression variable is at given equinoctial point x _*Value.

3, determine association factor R _δThe value restrictive condition

Utilization obtains R based on the Lyapunov functional based method _δRestrictive condition:

Directly calculate and know [J _d(x)-R _d(x)] reversible, the function below then defining:

$K\left(x\right)-{[J_d\left(x\right)-R_d\left(x\right)]}^{-1}[J_a\left(x\right)-R_a\left(x\right)]\frac{\&PartialD;H}{\&PartialD;x}+{[J_d\left(x\right)-R_d\left(x\right)]}^{-1}g\left(x\right)\mathrm{\&beta;}\left(x\right)---\left(7\right)$

Controlling type (5) and (6) substitution following formula can be calculated K (x).

According to the form of K (x), the present invention proposes a kind of approximate processing method, H _a(x) approximate being chosen as:

$H_a\left(x\right)=T_y{p}_{e^{*}}(\frac{C_{T*}}{r_{*}}{x}_1+x_2)+C_D{b}_2[b_4\cos 2x_3+\frac{U_s\cos x_3}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}}{x}_5]-b_3[\frac{1}{2}{C}_1{\left({\mathrm{\&Delta;x}}_3\right)}^2+R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3{\mathrm{\&Delta;x}}_4]-$

$-p_{e^{*}}(b_1{\mathrm{\&Delta;x}}_3-C_1{b}_2{\mathrm{\&Delta;x}}_4)+C_1{b}_2[2b_4\sin {2x}_3+\frac{U_s\sin x_3}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}}{x}_5]{\mathrm{\&Delta;x}}_4-[{\mathrm{<figure-callout\; id="5"\; label="b"\; filenames="HSA00000218931000011.png,HSA00000218931000013.png"\; state="\{\{state\}\}">b</figure-callout>}}_5+b_1\frac{\&PartialD;H}{{\&PartialD;x}_5}\left(x_{*}\right)]x_5$

(8)

Wherein:

b ₅=C _Db ₂a ₂x _5*

Meritorious (pu) for equinoctial point.

Selected H _a(x) near equinoctial point, satisfy, and satisfy following formula at equinoctial point:

$\frac{{\&PartialD;H}_a}{\&PartialD;x}\left(x\right)=K\left(x\right)---\left(9\right)$

Utilize H _a(x) Hamiltonian function can be modified to:

H _d(x)＝H(x)+H _a(x) (10)

Under input control v (x)=β (x) effect, utilize formula (7) and (9) system (1) can turn to following autonomous system

$\stackrel{\&CenterDot;}{x}=[J_d\left(x\right)-R_d\left(x\right)]\frac{{\&PartialD;H}_d}{\&PartialD;x}\left(x\right)---\left(11\right)$

Notice that generator set control model satisfies following relation at equinoctial point:

f ₁＝0， $\frac{\&PartialD;H}{{\&PartialD;x}_3}\left(x_{*}\right)=-\frac{1}{T_y}\frac{\&PartialD;H}{{\&PartialD;x}_2}\left(x_{*}\right),$ $C_{T*}\frac{\&PartialD;H}{{\&PartialD;x}_2}\left(x_{*}\right)=r_{*}\frac{\&PartialD;H}{{\&PartialD;x}_1}\left(x_{*}\right).$

Because x _*Be the equinoctial point of system (1), so x _*Also be the equinoctial point of (11) formula, that is:

$\frac{{\&PartialD;H}_d}{\&PartialD;x}\left(x_{*}\right)=0---\left(12\right)$

The extra large gloomy matrix of closed-loop system is:

$\frac{{\&PartialD;}^2{H}_d}{{\&PartialD;x}^2}=\frac{{\&PartialD;}^{2}H}{{\&PartialD;x}^2}+\frac{{\&PartialD;}^2{H}_a}{{\&PartialD;x}^2}=\frac{{\&PartialD;}^{2}H}{{\&PartialD;x}^2}-\frac{\&PartialD;K}{\&PartialD;x}---\left(13\right)$

And if only if the gloomy matrix in above-mentioned sea is at equinoctial point x _*Be positive definite matrix, that is:

$\frac{{\&PartialD;}^2{H}_d}{{\&PartialD;x}^2}\left(x_{*}\right)>0---\left(14\right)$

H then _d(x) at x _*Minimalization, H _d(x) be a Lyapunov function, and system is can controlled β (x) calm, makes that output is progressive to be stable at given equinoctial point.

Directly calculate each rank order principal minor of extra large gloomy matrix, can derive its positive fixed condition and be:

$\left\{\begin{array}{c}{R}_{\mathrm{\&delta;}}<0.25\\ x_1>\frac{4}{3}{q}_{\mathrm{nl}}\end{array}\right.---\left(15\right)$

Set grid-connection operation and institute's on-load can satisfy above-mentioned second positive fixed condition greater than 10% rated load.And R _δDirectly value can satisfy in control is set.

Thus, can draw working control device structural scheme and be: according to the calm condition of the gloomy matrix in sea, have only when set grid-connection on-load＞10% rated load, could satisfy the calm condition of extra large gloomy matrix; Because this restriction of stability controller can not be handled unit starting, shutdown and no-load running operating mode; Therefore, need combine, constitute change structure control strategy with traditional speed governing and excitation PID control strategy; Switch to calm control after set grid-connection band 10% rated load, operating modes such as other operating mode such as unit starting and stopping, zero load adopt the traditional PID control strategy.

Step 2: select merit angular correlation factor R _δValue

Adopt emulation mode to determine R _δValue, to obtain transient characterisitics preferably.

According to the unit characteristic parameter, adopt formula (15) to calculate R _δBehind simulation analysis, select R _δ=0.1 has the better dynamic response.

Step 3: utilize unit characteristic parameter initialization controller, calculate the equinoctial point parameter under the given output, adopt following formula calculated equilibrium point x _*And control corresponding:

$\left\{\begin{array}{c}0=[J\left(x\right)-R\left(x\right)]\frac{\&PartialD;H}{\&PartialD;x}+g\left(x\right)v_{*}\\ p_{e^{*}}=\frac{U_s\sin x_{3^{*}}}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}}{x}_{5^{*}}+\frac{1}{2}{U}_s^2\sin {2x}_{3^{*}}(\frac{1}{X_{\mathrm{q\&Sigma;}}}-\frac{1}{X_{d{\mathrm{\&Sigma;}}^{\&prime;}}})\\ Q_{e^{*}}=\frac{U_s\cos x_{3^{*}}}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}}{x}_{5^{*}}-\frac{1}{2}{U}_s^2(\frac{1}{X_{\mathrm{q\&Sigma;}}}+\frac{1}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}})+\frac{1}{2}{U}_s^2\cos {2x}_{3^{*}}(\frac{1}{X_{\mathrm{q\&Sigma;}}}-\frac{1}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}})\end{array}\right.---\left(16\right)$

Step 4: control algorithm design

The speed regulator part is owing to adopt feedback dissipative implementation method, the control signal u of its dissipation model _pThere is conversion relation with the input signal u of original hydraulic turbine model.Hamilton's dissipation model control law (5), (6) are converted into speed governing and excitation control algorithm form is:

$\left\{\begin{array}{c}u=u_p-{u_p}^{\&prime;}={u_p}^{\&prime;\&prime;}-{u_p}^{\&prime;}-R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3\\ E_f={\mathrm{\&beta;}}_2\left(x\right)=\frac{X_{\mathrm{ad}}^2}{X_f}\frac{\&PartialD;H}{{\&PartialD;x}_5}\left(x_{*}\right)\end{array}\right.---\left(17\right)$

In the following formula,

Be dissipate feedback factor in realizing of water turbine Hamilton,, can be written as at equinoctial point:

Be control β ₁(x) in first, this is the calm control of equinoctial point.

For improving the step problem of calm control output, adopt the simple index way of output to improve the parameter response characteristic.

Speed regulator output is controlled to be:

$u={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">u</figure-callout>}}_0+(u_1-u_0)(1-e^{-T_{\mathrm{tout}}t})-R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3---\left(18\right)$

Equinoctial point control is wherein calculated by following formula:

${\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">u</figure-callout>}}_0={[-\frac{T_y^2(r_{{*}_0}^2+C_{T^{*}}^2)}{r_{*}}{p}_{e^{*}}+\frac{A_t{x}_{1^{*}}^3}{p_{m^{*}}{x}_{2^{*}}}]}_{x=x_{{*}_0}}---\left(19\right)$

$u_1={[-\frac{T_y^2(r_{{*}_0}^2+C_{T^{*}}^2)}{r_{*}}{p}_{e^{*}}+\frac{A_t{x}_{1^{*}}^3}{p_{m^{*}}{x}_{2^{*}}}]}_{x=x_{{*}_1}}---\left(20\right)$

Excitation output is controlled to be:

$E_f={\mathrm{<figure-callout\; id="0"\; label="E\; f"\; filenames="HSA00000218931000011.png,HSA00000218931000012.png"\; state="\{\{state\}\}">E</figure-callout>}}_f+(E_{f1}-E_{f0})(1-e^{-T_{\mathrm{Efout}}t})---\left(21\right)$

Wherein: the parameter of subscript " 0 ", " 1 " initial operating mode of expression and new equinoctial point; T _Tout, T _EfoutRepresent parameter decay time of speed governing, excitation output step signal respectively, determine according to actual set quick-action and transient process quality requirements.

Detect unit parameter in real time and change, corresponding control is calculated and exported in employing formula (18)-(21).

The simulation calculation example

Present embodiment is the simulation example to certain water power plant hydraulic generator unit control.

Power station unit characteristic parameter: A _t=1.127; T _w=2.242s; q _Nl=0.1265; T _y=0.5s; T _j=8.999s; T _D0'=5.4s; X _d=1.07; X _d'=0.34; X _q=0.66; X _f=1.29; X _Ad=0.97; These parameters are set in the controller as controller basic calculating parameter.

Select a kind of typical unit control structure to carry out the emulation contrast, speed regulator partly adopts typical PID control in parallel, K _p=5.0; K _I=1.7; K _D=1.3; Excitation system adopts PI, K _Pe=1.0; K _Ie=1.5.Speed regulator works in the power adjustments pattern, and field regulator works in permanent idle mode.Adopt emulation mode, determine controller parameter: T _Tout=0.5s; T _Efout=0.5s.

(1) the meritorious example of regulating

Initial operating mode: meritorious p _e=0.5 (pu), idle Q _e=0.3 (pu).

The unit adjusting of gaining merit meritoriously is increased to 0.9 (pu) from 0.5 (pu), and getting the equivalent damping coefficient is D=2.

Step 1: unit is initially meritorious greater than 10% rated load, and controller switches to control strategy of the present invention and controls.

Step 2: get R _δ=0.1

Step 3: utilize unit characteristic parameter initialization controller, calculate the equinoctial point parameter under the given output

Utilize set of equation (16) to calculate new and old equinoctial point parameter to be:

Initial balance point is:

Calm control initial value:

New equinoctial point is:

New the calm of equinoctial point is controlled to be:

Step 4: control algorithm design

Utilize formula (19), (20) to calculate new and old equinoctial point controlled quentity controlled variable:

u ₀＝0，u ₁＝0.3725。

Adopting formula (18) to calculate speed regulator output is controlled to be:

u＝0.3725(1-e ^-0.5t)-0.1Δx ₃

Adopting formula (21) to calculate excitation control is output as:

E _f＝1.5803+0.3101(1-e ^-0.5t)

The generator's power and angle response curve as shown in Figure 1.

In the accompanying drawing 1, solid line is calm Control Parameter response curve, and dotted line is the pid control parameter response curve.As seen from the figure, the selected stability controller system that can calm make that system is asymptotic to be stable at given equinoctial point, and governing speed is fast, has parameter interference rejection capability preferably.

In order to analyze the effect of the merit angular correlation factor, under the situation of other parameter constants, get unit equivalent damping coefficient D=-2, when unit carried out same adjustment, generator's power and angle responded as shown in Figure 2.

By accompanying drawing 2 as seen, because R _δAdditional damping is provided,, has suitably adjusted R even unit is under the negative damping situation _δThe stability that still can keep unit to regulate preferably.

(2) idle adjusting example

Initial operating mode: the unit p that gains merit _e=0.9 (pu), Q _e=0.3 (pu).

Unit carries out idle adjusting, idlely is increased to 0.5 (pu) from 0.3 (pu), and getting the equivalent damping coefficient is D=4;

Step 1: unit is initially meritorious greater than 10% rated load, and controller switches to control strategy of the present invention and controls.

Step 2: get R _δ=0.1

Step 3: utilize unit characteristic parameter initialization controller, calculate the equinoctial point parameter under the given output

Utilize set of equation (16) to calculate new and old equinoctial point parameter to be:

Initial balance point is:

Calm control initial value:

New equinoctial point is:

New the calm of equinoctial point is controlled to be:

Step 4: control algorithm design

Utilize formula (19), (20) to calculate new and old equinoctial point controlled quentity controlled variable:

u ₀＝0，u ₁＝0。

Adopting formula (18) to calculate speed regulator output is controlled to be:

u＝-0.1Δx ₃

Adopting formula (21) to calculate excitation control is output as:

E _f＝1.8904+0.2222(1-e ^-0.5t)

Each parameter response curve as shown in Figure 3.In the accompanying drawing 3, solid line is calm Control Parameter response curve, and dotted line is the pid control parameter response curve.As seen from the figure, the selected stability controller system that can calm make that system is asymptotic to be stable at given equinoctial point, and governing speed is fast, has parameter interference rejection capability preferably.

Claims (1)

1. damping injection control method that improves power-angle oscillation of hydroelectric generating set, it is characterized in that: based on hydraulic generator unit Hamilton model, adopt the damping of Hamilton's interconnect architecture correction to inject the controlling Design method, the control law of design set speed adjustment and excitation system, concrete steps are as follows:

Step 1: the merit angular correlation factor R of revising generator set Hamilton model damping matrix _δ, design equivalent control rule β ₁(x) and β ₂(x), specifically be calculated as follows:

${\mathrm{\&beta;}}_1\left(x\right)=-\frac{T_y{C}_1{A}_{s1}}{r_{*}{C}_y}\frac{\&PartialD;H}{{\&PartialD;x}_3}\left(x_{*}\right)-R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3$

${\mathrm{\&beta;}}_2\left(x\right)=\frac{X_{\mathrm{ad}}^2}{X_f}\frac{\&PartialD;H}{{\&PartialD;x}_5}\left(x_{*}\right)$

Step 2: the merit angular correlation factor R that is calculated as follows damping matrix according to the unit characteristic parameter _δValue restriction: 0＜R _δ＜0.25

Step 3: utilize unit characteristic parameter initialization controller, adopt following formula calculated equilibrium point x _*And control corresponding:

$\left\{\begin{array}{c}0=[J\left(x\right)-R\left(x\right)]\frac{\&PartialD;H}{\&PartialD;x}+g\left(x\right)v_{*}\\ p_{e^{*}}=\frac{U_s\sin x_{3^{*}}}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}}{x}_{5^{*}}+\frac{1}{2}{U}_s^2\sin {2x}_{3^{*}}(\frac{1}{X_{\mathrm{q\&Sigma;}}}-\frac{1}{X_{d{\mathrm{\&Sigma;}}^{\&prime;}}})\\ Q_{e^{*}}=\frac{U_s\cos x_{3^{*}}}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}}{x}_{5^{*}}-\frac{1}{2}{U}_s^2(\frac{1}{X_{\mathrm{q\&Sigma;}}}+\frac{1}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}})+\frac{1}{2}{U}_s^2\cos {2x}_{3^{*}}(\frac{1}{X_{\mathrm{q\&Sigma;}}}-\frac{1}{{X_{\mathrm{d\&Sigma;}}}^{\&prime;}})\end{array}\right.$

In the formula:

Be respectively equinoctial point active power (pu) and wattless power (pu); U _sBe Infinite bus system voltage (pu); X _{The d ∑}=X _d+ X _T+ X _LX _dBe the reactance of generator d axle; X _TBe the transformer equivalent reactance; X _LBe the circuit equivalent reactance; X _{The q ∑}=X _q+ X _T+ X _LX _qBe the reactance of generator q axle; X _{The d ∑}'=X _d'+X _T+ X _LX _d' be generator d axle subtranient reactance; X _fBe the exciting winding reactance; X _AdBe d armature axis reaction reactance, each reactance is per unit value (pu); x _3*, x _5*Be respectively merit angle δ and q axle transient internal voltage E _q' (pu).

Step 4: control algorithm design: control algorithm adopts following formula to calculate:

Speed regulator output is controlled to be:

$u=u_0+(u_1-u_0)(1-e^{-T_{\mathrm{tout}}t})-R_{\mathrm{\&delta;}}{\mathrm{\&Delta;x}}_3$

Equinoctial point control is wherein calculated by following formula:

$u_0={[-\frac{T_y^2(r_{{*}_0}^2+C_{T^{*}}^2)}{r_{*}}{p}_{e^{*}}+\frac{A_t{x}_{1^{*}}^3}{p_{m^{*}}{x}_{2^{*}}}]}_{x=x_{{*}_0}}$

$u_1={[-\frac{T_y^2(r_{{*}_0}^2+C_{T^{*}}^2)}{r_{*}}{p}_{e^{*}}+\frac{A_t{x}_{1^{*}}^3}{p_{m^{*}}{x}_{2^{*}}}]}_{x=x_{{*}_1}}$

Excitation output is controlled to be:

$E_f=E_{f0}+(E_{f1}-E_{f0})(1-e^{-T_{\mathrm{Efout}}t})$

In the formula: the parameter of subscript " 0 ", " 1 " initial operating mode of expression and new equinoctial point; T _Tout, T _EfoutParameter decay time of representing speed governing, excitation output step signal respectively; T _yBe main servomotor time constant (second); r _*With

Be the value of matrix variables at equinoctial point; A _tBe the water turbine gain; U is speed regulator control; E _fBe excitation control output; Be equinoctial point water turbine output mechanical power (pu); Variable x ₁, x ₂Be respectively flow and guide vane opening (pu).

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