CN104063584A - Control parameter setting method for steam turbine speed governing system - Google Patents

Abstract

The invention relates to a control parameter setting method for a steam turbine speed governing system. The control parameter setting method comprises the following steps: (1) building a mathematical model and a transfer function of the steam turbine speed governing system provided with a stand-alone infinitely great system in a power network model; (2) when the control parameters Ki and Kp change within the range of 0-10, unceasingly working out the numerical solutions of the characteristic roots of the transfer function of the system under the given parameters, and the expression of the characteristic root is s=A+Bj; (3) working out the value of the characteristic parameter Xi of each group of the characteristic roots, and obtaining the minimum value of Xi; (4) drawing the tendency chart of the minimum value of the characteristic parameter Xi of each group varying along with the control parameters Ki and Kp; (5) judging whether the system is stabilized on the basis of the positive or negative values of the characteristic parameter Xi, acquiring the value range of the control parameters that stabilize the system, and conducting fine adjustment by adopting the cut-and-try method to set up the optimal control parameter that is veritably practical to a machine set. The control parameter setting method has significance on further normalizing the parameter arrangement of a steam turbine control system and reducing the low-frequency oscillation of the system.

Description

A kind of turbine regulating system is controlled parameter tuning method

Technical field

The invention belongs to the control method of steam turbine speed control and power network safety operation, particularly in order to improve power system dynamic stability, to prevent the method to turbine controller parameter tuning in electricity grid oscillating field.

Background technology

In recent years, along with Electricity Demand increases year by year, the scale of electric system is increasing, the power of carrying on main force's transmission line of electricity also constantly increases, it is day by day severe that the service condition of whole electric system becomes, low-frequency oscillation happens occasionally, and has become one of key factor of restriction interconnection power delivery and interconnected network safe and stable operation.Due to several low-frequency oscillation accidents that caused by mains side in recent years, make mains side low-frequency oscillation research obtain gradually people's attention.Many experts, by several oscillation of power events of south electric network are analyzed, show low-frequency oscillation and the unstable correlativity that exists of steam turbine side governing system.

By the analysis to steam turbine acting principle, in conjunction with the resonance mechanism of low-frequency oscillation, analyzed the possible cause of steam turbine side initiation forced power oscillation, show the pressure fluctuation of steam turbine, and regulate hunting of valve all may cause the low-frequency oscillation that forces of electrical network.Although forced power oscillation mechanism can be explained some low-frequency oscillations, in the middle of research in the past, for simulation Forced disturbance source, be all often directly in system link, artificially to have added one-period disturbance, this does not conform to actual conditions.There are some researches show if mains side some control parameter and arrange improperly, can provide a negative damping torque to system, thereby reduce system damping, cause the negative damping vibration of electrical network.Some experts utilize the model of the governing system of having simplified, analyzed the impact of major parameter on electrical network damping characteristic, point out in controller that scale-up factor arranges improper, produce effect of negative damping after can causing Primary Frequency Modulation Loop to drop into, thereby produce electricity grid oscillating.But which kind of impact controller parameter variation meeting produces to system stability, and how based on stability of power system, analysis provides the zone of reasonableness of controller parameter, still lacks at present research.

Summary of the invention

For solving the zone of reasonableness of the reasonable setting about controller parameter recited above, the invention provides a kind of turbine regulating system and control parameter tuning method, object be the setting of further standard steam turbine control system parameter, the generation of minimizing system low frequency oscillation, safeguards the stable of electric system.

To achieve these goals, the present invention's step realization as follows:

Step 1: the mathematical model of setting up the turbine regulating system of the one machine infinity bus system while having comprised electric network model, utilize in existing working condition system corresponding object model identification module to obtain mathematical model and the various parameter of controlled device, the transport function of the mathematical model of the transport function between each major parameter that is the turbine regulating system while comprising electric network model, is shown below:

$-\mathrm{\Δ}{P}_m=(\frac{1}{(1+T_{1}s)\mathrm{\δ}}(1+G_{\mathrm{pid}})+\frac{1}{s}{G}_1{G}_{\mathrm{pid}})G_e{G}_t\mathrm{\Δ\ω};$

$(\mathrm{\Δ}{P}_m-\mathrm{\Δ}{P}_e)\frac{1}{T_{\mathrm{\σ}}s}=\mathrm{\Δ\ω};$

$\mathrm{\Δ}{P}_e=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A})\mathrm{\Δ\δ};$

$\⇒\frac{\mathrm{\Δ}{P}_m}{\mathrm{\Δ}{\mathrm{\ω}}_r}=\frac{G_2(1+G_{\mathrm{pid}})G_e{G}_t}{1+G_3{G}_4};$

K in above-mentioned formula ₁, K ₂, K ₃, K ₄, K ₅, K ₆be respectively scale-up factor, K _afor exciter scale-up factor, s is the differentiating operator after Laplace transformation, the difference coefficient that δ is rotating speed, and Δ w is rotating speed angular velocity deviator, Δ w _rfor rotating speed disturbed value, Δ δ is generator's power and angle deviation, Δ P _mfor mechanical output increment, Δ P _efor electromagnetic power increment, T ₁represent rotating speed transducer time constant, T ₃for energized circuit time constant, T _rfor voltage sensor time constant, T _σfor the time constant of turbine rotor, the transport function that G1 is one machine infinity bus system, G2 is the one order inertia transport function of the rotating speed transducer in control system, G _efor the transport function of electrohydraulic servomechanism, G _tfor the transport function of tandem compound, single reheat steam turbine, G _pidfor the transport function of controller, G3 is turbine regulating system ground transport function, G ₄there is no a corresponding physical meaning for what reduced form was set up.Wherein G1, G2, G3, G4 are defined as:

$G_1=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A});$

$G_2=\frac{1}{(1+T_{1}s)};$

$G_3=(\frac{1}{(1+T_{1}s)\mathrm{\δ}}(1+G_{\mathrm{pid}})+\frac{1}{s}{G}_1{G}_{\mathrm{pid}})G_e{G}_t;$

$G_4=\frac{1}{T_{\mathrm{\σ}}s+G_1\frac{1}{s}};$

Step 2: to control system model transport function in governing system control parameter K p the different arrays of many groups be set in 0～10 scope with Ki, obtain respectively the characteristic root of respectively organizing the transport function of controlled device under array parameter, by asking for numerical method, ask for the numerical solution of characteristic root, and then ask for the span of the control parameter of governing system, K in formula _ifor governing system integration control parameter, K _pfor proportional control parameter, K _dfor differential, control parameter, s is differentiating operator;

Analyze the transport function of controlled device, obtain non-zero root and conjugate complex that the characteristic root of controlled device transport function can be on real axis several, with following formula, represent:

s＝A+Bj，

In formula, A and B are respectively real part and the imaginary part of characteristic root;

For order Oscillating link, its characteristic root is that a pair of conjugate complex is several, and expression formula is as follows:

$s_{\mathrm{1,2}}=-\mathrm{\ξ}{\mathrm{\ω}}_n\±j{\mathrm{\ω}}_n\sqrt{1-{\mathrm{\ξ}}^2},$

Wherein characteristic parameter ξ is damping ratio, ω _nfor undamped oscillation frequency.

Step 3: obtain the size of the characteristic parameter ξ of every stack features root, and obtain the ξ of its intermediate value minimum, as shown from the above formula,

A＝-ξω _n，

$B=\±j{\mathrm{\ω}}_n\sqrt{1-{\mathrm{\ξ}}^2},$

A, B in above-mentioned equation are used as known, simultaneous equations are tried to achieve damping ratio

$\mathrm{\ξ}=\frac{-A}{\sqrt{A^2+B^2},}$

While knowing that by above formula ξ is less than zero, system features root real part is not for negative, and second-order system is unstable, and the damping ratio of second-order system can reflect whether stablizing of second-order system, when whether the turbine regulating system of analyzing consideration electric network model is stablized, each characteristic root is asked for to its characteristic parameter ξ;

Step 4: draw characteristic parameter ξ with the parameter K of speed regulator according to the minimal characteristic parameter ξ that respectively organizes parameter characteristic of correspondence root in the governing system of trying to achieve in step 3 _p, K _ithe curve changing, when this characteristic root is Conjugate complex roots, ξ is the damping ratio of its second order link; When this characteristic root is non-zero real root, ξ gets ± and 1, if this real root is less than zero ξ, be 1, if this real root is greater than zero ξ, be-1; When system stability, the whole characteristic roots of system all have negative real part, the characteristic parameter ξ that simultaneously can release all characteristic roots all gets the span that the modified-image of controlling parameter with each group on the occasion of, the characteristic parameter ξ that can present according to controlled device is thus determined the control parameter that makes system stability;

Step 5: the changing trend diagram that the mathematical model of the turbine regulating system of setting up according to abovementioned steps 1 to 3 and step 4 are drawn, adopt method of trial and error to finely tune, adjust out and be really practically applicable to the optimal control parameter of unit.

The present invention proposes a kind of turbine regulating system based on stability of power system and control the setting method of parameter, because the model of the method has comprised grid side system, more similar to real model, so relatively greatly dwindled with setting method in the past the zone of reasonableness that does not cause the controller parameter of system unstability; And have very strong practically, and can not look like former setting method, although be stable during unit operation, during multiple unit operation, may there is vibration; This arranges for further standard steam turbine control system parameter, and the generation tool that reduces low frequency oscillations is of great significance.

Accompanying drawing explanation

Fig. 1 is the embodiment schematic flow sheet of governor control system parameter tuning method of the present invention;

Fig. 2 is the structural drawing that governing system of the present invention is controlled the embodiment of parameter tuning method;

Fig. 3 is the control system model schematic diagram of the invention process example;

Fig. 4 is the electrohydraulic servomechanism model schematic diagram of the invention process example;

Fig. 5 is the steam turbine model schematic diagram of the invention process example;

Fig. 6 is the one machine infinity bus system model schematic diagram of the invention process example;

Fig. 7 is that characteristic parameter ξ controls the changing trend diagram of parameter with speed regulator.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

Fig. 3 is the realistic model of control system, ignore nonlinear element after its transport function be t wherein ₁represent rotating speed transducer time constant, value 0.02; Speed governing dead-band value 0.025; Speed governing dead-band link K below represents primary frequency modulation difference coefficient (being speed diversity factor), and value is 20; K _p, K _i, K _dbe respectively rate mu-factor, integration time constant, the derivative time constant of load governor PID, value is 1,0.05,0 respectively; K ₂represent rotating speed feedforward control amplification coefficient, it is rotating speed transducer that parameter is taken as in 1, Fig. 31.2 is PID load governor, P _reffor given active power, P _efeedback power for grid side.

Fig. 4 is the realistic model of electrohydraulic servomechanism, and its transport function is p wherein _cvfor pitch instruction; K _p1, K _i1, K _d1be respectively valve positioner pid parameter, value is 9,0,0 respectively; Tc and To are servomotor opening and closing time constants, and parameter is taken as respectively 1.24 and 1.33; T wherein ₂represent Linear displacement transducer time constant, in Fig. 4,3 is valve PID controller, and 4 is valve on-off controller, and 5 open, close delay link for servomotor, and 6 is servomotor, and 7 is linear displacement transmitter, and parameter is taken as 0.02.

Fig. 5 is the realistic model of a reheat turbine, and its transport function is

$G_T=\frac{((1+\mathrm{\λ})(1+T_{\mathrm{rh}}s)(1+T_{\mathrm{co}}s)F_{\mathrm{hp}}+(F_{\mathrm{ip}}-\mathrm{\λ}{F}_{\mathrm{hp}})(1+T_{\mathrm{co}}s)+F_{1p})}{\left((1+T_{\mathrm{ch}}s)(1+\stackrel{}{T_{\mathrm{rh}}}s)(1+T_{\mathrm{co}}s)\right)},$ P wherein _gVfor pitch aperture; P _mmechanical output for output; Time constant T _ch, T _rhand T _cothe time delay that corresponding expression is produced by steam chest and air inlet duct, reheater and intersection piping, parameter is taken as 0.1,12,1; F _hp, F _ipand F _lprepresent the share of high, medium and low cylinder pressure acting amount in total mechanical output, value is 0.32,0.68,0 (it is to regard mesolow cylinder as an integral body that low pressure (LP) cylinder work done factor gets 0); λ represents high pressure cylinder power natural power overshooting coefficient, parameter, and value is in 0.9, Fig. 58 to be high pressure steam volume, 9 is reheated steam volume, 10Wei low pressure UNICOM vapor volume.

Fig. 6 is one machine infinity bus system realistic model, ignores after nonlinear element, and its transport function is

$G_1\left(s\right)=\frac{\mathrm{\Δ}{P}_e}{\mathrm{\Δ\δ}}=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A}),$ K wherein ₁, K ₂, K ₃, K ₄, K ₅, K ₆be respectively scale-up factor; Δ w _rfor rotating speed disturbed value, Δ δ is generator's power and angle deviation; 19 Δ T _mfor mechanical output increment; 18 Δ T _efor electromagnetic power increment; Δ ψ _fd is energized circuit magnetic linkage increment; Δ E _fdfor exciter output voltage increment; U _pSSfor power system stabilizer, PSS output signal; T ₃for energized circuit time constant; T _rfor voltage sensor time constant; K _afor exciter scale-up factor, Δ V _reffor reference output voltage, Δ V ₁voltage sensor output voltage.Its parameter is all got representative value, and in Fig. 6,11 is exciter, and 12 is the transport function of rotating speed with power.13 is the transport function of generator speed with phase angle, and 14 is voltage sensor, and 15 is energized circuit.

As shown in the schematic flow sheet of the method for governing system control parameter tuning as of the present invention in Fig. 1, the governing system in the embodiment of the present invention is controlled parameter tuning method and is comprised step:

Step 1 (S101): the mathematical model of setting up the turbine regulating system of the one machine infinity bus system while having comprised electric network model, set up the realistic model figure of current embodiment, the process of identifying the mathematical model of current object is generally to utilize corresponding object model identification module in existing working condition system to obtain mathematical model and the various parameter of controlled device, the mathematical model of the transport function between each major parameter that is the turbine regulating system while comprising electric network model, is shown below:

$-\mathrm{\Δ}{P}_m=(\frac{1}{(1+T_{1}s)\mathrm{\δ}}(1+G_{\mathrm{pid}})+\frac{1}{s}{G}_1{G}_{\mathrm{pid}})G_e{G}_t\mathrm{\Δ\ω};$

$(\mathrm{\Δ}{P}_m-\mathrm{\Δ}{P}_e)\frac{1}{T_{\mathrm{\σ}}s}=\mathrm{\Δ\ω};$

$\mathrm{\Δ}{P}_e=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A})\mathrm{\Δ\δ};$

$\⇒\frac{\mathrm{\Δ}{P}_m}{\mathrm{\Δ}{\mathrm{\ω}}_r}=\frac{G_2(1+G_{\mathrm{pid}})G_e{G}_t}{1+G_3{G}_4};$

K in above-mentioned formula ₁, K ₂, K ₃, K ₄, K ₅, K ₆be respectively scale-up factor, K _afor exciter scale-up factor, s is the differentiating operator after Laplace transformation, the difference coefficient that δ is rotating speed, and Δ w is rotating speed angular velocity deviator, Δ w _rfor rotating speed disturbed value, Δ δ is generator's power and angle deviation, Δ P _mfor mechanical output increment, Δ P _efor electromagnetic power increment, T ₁represent rotating speed transducer time constant, T ₃for energized circuit time constant, T _rfor voltage sensor time constant, T _σfor the time constant of turbine rotor, the transport function that G1 is one machine infinity bus system, G2 is the one order inertia transport function of the rotating speed transducer in control system, G _efor the transport function of electrohydraulic servomechanism, G _tfor the transport function of tandem compound, single reheat steam turbine, G _pidfor the transport function of controller, G3 is turbine regulating system ground transport function, G ₄there is no a corresponding physical meaning for what reduced form was set up.

Wherein G1, G2, G3, G4 are defined as:

$G_1=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A});$

$G_2=\frac{1}{(1+T_{1}s)};$

$G_3=(\frac{1}{(1+T_{1}s)\mathrm{\δ}}(1+G_{\mathrm{pid}})+\frac{1}{s}{G}_1{G}_{\mathrm{pid}})G_e{G}_t;$

$G_4=\frac{1}{T_{\mathrm{\σ}}s+G_1\frac{1}{s}};$

Step 2 (S102): to following formula control system model transport function in governing system control parameter K p the different arrays of many groups be set in 0～10 scope with Ki, obtain respectively the characteristic root of respectively organizing the transport function of controlled device under array parameter, because this system features equation exponent number is higher, can not try to achieve by asking for the mode of analytic solution the span of each parameter in governing system, and can only ask for by asking for numerical method the numerical solution of characteristic root, and then ask for the span of the control parameter of governing system.

Because high order system all can turn to the combination of zeroth order, single order, second order link, oscillating component is mainly order Oscillating link wherein.By analyzing the transport function of controlled device, there is not zeroth order link in known its, and non-zero root and conjugate complex that the characteristic root of the transport function of controlled device can be on real axis are several, can represent with following formula:

s＝A+Bj，

In formula, A and B are respectively real part and the imaginary part of characteristic root;

For order Oscillating link, its characteristic root is that a pair of conjugate complex is several, and expression formula is as follows:

$s_{\mathrm{1,2}}=-\mathrm{\ξ}{\mathrm{\ω}}_n\±j{\mathrm{\ω}}_n\sqrt{1-{\mathrm{\ξ}}^2},$

Wherein characteristic parameter ξ is damping ratio, ω _nfor undamped oscillation frequency.

Step 3 (S103): obtain the size of the characteristic parameter ξ of every stack features root, and obtain the ξ of its intermediate value minimum.As shown from the above formula,

A＝-ξω _n，

$B=\±j{\mathrm{\ω}}_n\sqrt{1-{\mathrm{\ξ}}^2},$

A, B in above-mentioned equation are used as known, can simultaneous equations try to achieve damping ratio

$\mathrm{\ξ}=\frac{-A}{\sqrt{A^2+B^2},}$

While knowing that by above formula ξ is less than zero, system features root real part is not for negative, and second-order system is unstable, so the damping ratio of second-order system can reflect whether stablizing of second-order system.So when whether the turbine regulating system of analyzing consideration electric network model is stablized, can ask for its characteristic parameter ξ to each characteristic root.

Step 4 (S104): draw characteristic parameter ξ with the parameter K of speed regulator according to the minimal characteristic parameter ξ that respectively organizes parameter characteristic of correspondence root in the governing system of trying to achieve in step 3 _p, K _ithe curve changing, as shown in Figure 6.When this characteristic root is Conjugate complex roots, ξ is the damping ratio of its second order link; When this characteristic root is non-zero real root, ξ gets ± and 1, if this real root is less than zero ξ, be 1, if this real root is greater than zero ξ, be-1.When system stability, the whole characteristic roots of system all have negative real part, the characteristic parameter ξ that simultaneously can release all characteristic roots all get on the occasion of.So the characteristic parameter ξ that can present according to controlled device controls the definite span that makes the control parameter of system stability of modified-image of parameter with each group.

Step 5 (S105): by the controlled device realistic model that step has been set up before, use method of trial and error to finely tune within the scope of this, adjust out and be really practically applicable to the optimal control parameter of unit.

The method of trial and error of taking in the invention process example be with reference to the accompanying drawings in 7 characteristic parameter ξ with speed regulator, control the changing trend diagram of parameter, make the integration control parameter K in governing system _ia numerical value between getting 0～3.1, and guarantee in its constant situation the proportional control parameter K to governing system _pin 0～4 scope, change a little, by the simulation result of observing system, choose optimal control system array parameter.

Claims (1)

1. turbine regulating system is controlled a parameter tuning method, it is characterized in that comprising the steps:

Step 1: the mathematical model of setting up the turbine regulating system of the one machine infinity bus system while having comprised electric network model, utilize in existing working condition system corresponding object model identification module to obtain mathematical model and the various parameter of controlled device, the transport function of the mathematical model of the transport function between each major parameter that is the turbine regulating system while comprising electric network model, is shown below:

$-\mathrm{\Δ}{P}_m=(\frac{1}{(1+T_{1}s)\mathrm{\δ}}(1+G_{\mathrm{pid}})+\frac{1}{s}{G}_1{G}_{\mathrm{pid}})G_e{G}_t\mathrm{\Δ\ω};$

$(\mathrm{\Δ}{P}_m-\mathrm{\Δ}{P}_e)\frac{1}{T_{\mathrm{\σ}}s}=\mathrm{\Δ\ω};$

$\mathrm{\Δ}{P}_e=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A})\mathrm{\Δ\δ};$

$\⇒\frac{\mathrm{\Δ}{P}_m}{\mathrm{\Δ}{\mathrm{\ω}}_r}=\frac{G_2(1+G_{\mathrm{pid}})G_e{G}_t}{1+G_3{G}_4};$

K in above-mentioned formula ₁, K ₂, K ₃, K ₄, K ₅, K ₆be respectively scale-up factor, K _afor exciter scale-up factor, s is the differentiating operator after Laplace transformation, the difference coefficient that δ is rotating speed, and Δ w is rotating speed angular velocity deviator, Δ w _rfor rotating speed disturbed value, Δ δ is generator's power and angle deviation, Δ P _mfor mechanical output increment, Δ P _efor electromagnetic power increment, T ₁represent rotating speed transducer time constant, T ₃for energized circuit time constant, T _rfor voltage sensor time constant, T _σfor the time constant of turbine rotor, the transport function that G1 is one machine infinity bus system, G2 is the one order inertia transport function of the rotating speed transducer in control system, G _efor the transport function of electrohydraulic servomechanism, G _tfor the transport function of tandem compound, single reheat steam turbine, G _pidfor the transport function of controller, G3 is turbine regulating system ground transport function, G ₄there is no a corresponding physical meaning for what reduced form was set up.Wherein G1, G2, G3, G4 are defined as:

$G_1=(K_1-\frac{K_2{K}_3\left[K_4(1+s{T}_R+K_5{K}_A)\right]}{s^2{T}_3{T}_R+s(T_3+T_R)+1+K_3{K}_6{K}_A});$

$G_2=\frac{1}{(1+T_{1}s)};$

$G_3=(\frac{1}{(1+T_{1}s)\mathrm{\δ}}(1+G_{\mathrm{pid}})+\frac{1}{s}{G}_1{G}_{\mathrm{pid}})G_e{G}_t;$

$G_4=\frac{1}{T_{\mathrm{\σ}}s+G_1\frac{1}{s}};$

Step 2: to control system model transport function in governing system control parameter K p the different arrays of many groups be set in 0～10 scope with Ki, obtain respectively the characteristic root of respectively organizing the transport function of controlled device under array parameter, by asking for numerical method, ask for the numerical solution of characteristic root, and then ask for the span of the control parameter of governing system, K in formula _ifor governing system integration control parameter, K _pfor proportional control parameter, K _dfor differential, control parameter, s is differentiating operator;

Analyze the transport function of controlled device, obtain non-zero root and conjugate complex that the characteristic root of controlled device transport function can be on real axis several, with following formula, represent:

s＝A+Bj，

In formula, A and B are respectively real part and the imaginary part of characteristic root;

For order Oscillating link, its characteristic root is that a pair of conjugate complex is several, and expression formula is as follows:

$s_{\mathrm{1,2}}=-\mathrm{\ξ}{\mathrm{\ω}}_n\±j{\mathrm{\ω}}_n\sqrt{1-{\mathrm{\ξ}}^2},$

Wherein characteristic parameter ξ is damping ratio, ω _nfor undamped oscillation frequency.

Step 3: obtain the size of the characteristic parameter ξ of every stack features root, and obtain the ξ of its intermediate value minimum, as shown from the above formula,

A＝-ξω _n，

$B=\±j{\mathrm{\ω}}_n\sqrt{1-{\mathrm{\ξ}}^2},$

A, B in above-mentioned equation are used as known, simultaneous equations are tried to achieve damping ratio

$\mathrm{\ξ}=\frac{-A}{\sqrt{A^2+B^2},}$

While knowing that by above formula ξ is less than zero, system features root real part is not for negative, and second-order system is unstable, and the damping ratio of second-order system can reflect whether stablizing of second-order system, when whether the turbine regulating system of analyzing consideration electric network model is stablized, each characteristic root is asked for to its characteristic parameter ξ;

Step 4: draw characteristic parameter ξ with the parameter K of speed regulator according to the minimal characteristic parameter ξ that respectively organizes parameter characteristic of correspondence root in the governing system of trying to achieve in step 3 _p, K _ithe curve changing, when this characteristic root is Conjugate complex roots, ξ is the damping ratio of its second order link; When this characteristic root is non-zero real root, ξ gets ± and 1, if this real root is less than zero ξ, be 1, if this real root is greater than zero ξ, be-1; When system stability, the whole characteristic roots of system all have negative real part, the characteristic parameter ξ that simultaneously can release all characteristic roots all gets the span that the modified-image of controlling parameter with each group on the occasion of, the characteristic parameter ξ that can present according to controlled device is thus determined the control parameter that makes system stability;

Step 5: the change changing trend diagram that the mathematical model of the turbine regulating system of setting up according to abovementioned steps 1 to 3 and step 4 are drawn, adopt method of trial and error to finely tune, adjust out and be really practically applicable to the optimal control parameter of unit.