CN110377970A - The hydrogovernor parameter optimization method and system of underdamping low frequency oscillation mode - Google Patents

The hydrogovernor parameter optimization method and system of underdamping low frequency oscillation mode Download PDF

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CN110377970A
CN110377970A CN201910566804.0A CN201910566804A CN110377970A CN 110377970 A CN110377970 A CN 110377970A CN 201910566804 A CN201910566804 A CN 201910566804A CN 110377970 A CN110377970 A CN 110377970A
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hydraulic turbine
mode
underdamping
regulating system
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CN110377970B (en
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陈亦平
杨若朴
杨荣照
张勇
唐卓尧
刘清晨
李家璐
杜旭
何越
高琴
方必武
黄济宇
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China Southern Power Grid Co Ltd
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03BMACHINES OR ENGINES FOR LIQUIDS
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
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Abstract

The invention discloses the hydrogovernor parameter optimization method and system of underdamping low frequency oscillation mode, method comprises determining that the relevant underdamping mode of unit to be optimized and its frequency of oscillation;The open-loop transfer function of the hydraulic turbine and its regulating system is established, and calculates damping coefficient of the open-loop transfer function of the hydraulic turbine and its regulating system under the frequency of oscillation of weakly damped oscillation mode;The integral square error of the hydraulic turbine and its regulating system output mechanical power under step signal is calculated according to the hydraulic turbine and its open-loop transfer function of regulating system;Calculate the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system;Objective function is established according to the damping coefficient of calculating, integral square error and the damping ratio of calculating;Optimized parameter using the optimal solution of PSO Algorithm objective function as hydrogovernor.The present invention avoids the deterioration of underdamping low frequency oscillation mode while improving system frequency stability, can be widely applied to electric power system optimization field.

Description

The hydrogovernor parameter optimization method and system of underdamping low frequency oscillation mode
Technical field
The present invention relates to the hydrogovernor parameters of electric power system optimization field, especially underdamping low frequency oscillation mode Optimization method and system.
Background technique
In the high water power ratio sending of Asynchronous Interconnection, it is unstable that the water hammer effect of the hydraulic turbine may cause governor, Since LOAD FREQUENCY mediating effect+6 coefficient is smaller, system damping is lower, and then causes low-frequency oscillation.
After south electric network Asynchronous Interconnection scheme is implemented, Yunnan Power System independent operating is connected through direct current with major network.Yunnan Power System Generation load specific gravity, water power ratio is more than 75%, and for thermoelectricity ratio less than 10%, it is typical that remaining, which is wind-powered electricity generation and photovoltaic, High water power ratio power grid.Yunnan Power System saves internal loading Zhan and always generates electricity about 1/3, and direct current sends load Zhan outside and always generates electricity about 2/3, due to straight Stream load is approximately rigid load in frequency limit device dead zone, is enabled in 49.9Hz~50.1Hz frequency range internal loading The damping of offer is greatly decreased.The reduction of out-damping coefficient and the influence of water hammer effect, repeatedly having caused cycle of oscillation is about The hunting of frequency phenomenon of 10~20s, therefore in Setting of PID Parameters for Hydro-Turbine Governor, often it is with the small interference stability of frequency Target optimizes.
When hydro turbine governor and big net operation, PI control is generallyd use.And 2.5 are greater than for water hammer time constant Tw The hydraulic turbine, due to differential control be conducive to improve the biggish unit of water hammer effect constant Tw dynamic property, so need adopt With PID type governor.The Tw measured value of Yunnan Power System main force Hydropower Unit is universal (Tw=3~4) bigger than normal, therefore differential coefficient is arranged It is necessary, but part may reduce angle stability while inhibiting hunting of frequency studies have shown that improving differential coefficient Property, low-frequency oscillation is induced, so when being optimized to governor parameter, only using the small interference stability of frequency as the optimization of target There are risks for method.
Summary of the invention
In order to solve the above technical problems, it is an object of the invention to: a kind of water wheels of underdamping low frequency oscillation mode are provided Machine governor parameter optimization method and system, to avoid underdamping low frequency oscillation mode while improving system frequency stability Deterioration.
First aspect of the embodiment of the present invention is adopted the technical scheme that:
The hydrogovernor parameter optimization method of underdamping low frequency oscillation mode, comprising the following steps:
Determine the relevant underdamping mode of unit to be optimized and its frequency of oscillation;
The open-loop transfer function of the hydraulic turbine and its regulating system is established, and the open loop for calculating the hydraulic turbine and its regulating system passes Damping coefficient of the delivery function under the frequency of oscillation of weakly damped oscillation mode;
The hydraulic turbine and its regulating system under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The integral square error of output mechanical power;
Calculate the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system;
Objective function is established according to the damping ratio of the damping coefficient of calculating, the integral square error of calculating and calculating;
Optimized parameter using the optimal solution of PSO Algorithm objective function as hydrogovernor.
Further, the relevant underdamping mode of determination unit to be optimized and its step for frequency of oscillation is specific to wrap It includes:
Total system characteristic value is calculated by power system small signal stability analysis program;
Underdamping mode relevant to unit to be optimized is found out according to total system characteristic value, it is described related to unit to be optimized Underdamping mode be damping ratio be lower than preset threshold low frequency oscillation mode;
Determine the frequency of oscillation for the underdamping mode found out.
Further, the open-loop transfer function for establishing the hydraulic turbine and its regulating system, and calculate the hydraulic turbine and its adjusting It is the step for damping coefficient of the open-loop transfer function of system under the frequency of oscillation of weakly damped oscillation mode, specific to wrap It includes:
Establish the open-loop transfer function of PID governor, the open-loop transfer function G of the PID governorGm(s) expression formula Are as follows:
Wherein, KP1、KI1And KD1The respectively proportional gain of PID governor, integral gain and the differential gain, s La Pula This operator, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor the gain of measured value, TR1When for frequency measurement link Between constant;
Establish the open-loop transfer function of electrohydraulic servo system, the open-loop transfer function G of the electrohydraulic servo systemGA(s) Expression formula are as follows:
Wherein, KP2For the gain of electrohydraulic servo system, s is Laplace operator, T2When for oil motor travel feedback link Between, TocTime constant is opened or closed for oil motor;
Establish the open-loop transfer function of prime mover, the open-loop transfer function G of described prime moverTw(s) expression formula are as follows:
Wherein, s is Laplace operator, TwFor open loop water hammer time constant;
According to the open loop of the open-loop transfer function of PID governor, the open-loop transfer function of electrohydraulic servo system and prime mover Transmission function obtains the hydraulic turbine and its regulating system open-loop transfer function, the hydraulic turbine and its regulating system open-loop transfer function Gsys(s) expression formula are as follows:
Gsys(s)=GGm(s)·GGA(s)·GTw(s)
Calculate the damping of the hydraulic turbine and its regulating system open-loop transfer function under the frequency of oscillation of weakly damped oscillation mode The frequency of oscillation s=j ω of torque coefficient, the hydraulic turbine and its regulating system open-loop transfer function in weakly damped oscillation modei Under damping coefficient DmExpression formula are as follows:
Dm=Re (Gsys(jωi))
Wherein, Re (Gsys(jωi)) it is Gsys(jωi) real part, ωiFor in the relevant underdamping mode of unit to be optimized The oscillation angular frequency of i-th of mode, i=1, the mode that 2,3 ... n, n include by the relevant underdamping mode of unit to be optimized Sum.
Further, it is described according to the hydraulic turbine and its open-loop transfer function of regulating system calculate under step signal the hydraulic turbine and The step for integral square error of its regulating system output mechanical power, specifically:
The hydraulic turbine and its regulating system under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The integral square error of output mechanical power, square of the hydraulic turbine and its regulating system output mechanical power under the step signal Error intergal J1(K) expression formula are as follows:
Wherein, Δ PmIt (t) is value of the step response in t moment of the hydraulic turbine and its regulating system, tfIt is the hydraulic turbine and its tune Section system reaches the time of steady-state value, Δ Pm(tf) it is the hydraulic turbine and its regulating system step response in tfThe steady-state value at moment,bpFor difference coefficient, K is the ginseng of the hydraulic turbine and its regulating system PID governor Number, KP、KIAnd KDRespectively proportional gain, integral gain and the differential gain of the hydraulic turbine and its regulating system PID governor.
Further, the step for the maximum characteristic value of the calculating primary frequency modulation closed-loop system corresponding damping ratio, specifically Include:
Obtain the state space of the hydraulic turbine and its regulating system PID governor, electrohydraulic servo system, prime mover and synchronous machine Equation, and then form the state space equation of single machine primary frequency modulation closed-loop system, the shape of the single machine primary frequency modulation closed-loop system State space equation expression formula are as follows:
Wherein, x is the state variable of single machine primary frequency modulation closed-loop system, and t is the time,
KP1、KI1And KD1Respectively proportional gain, integral gain and the differential of the hydraulic turbine and its regulating system PID governor Gain, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor the gain of measured value, TR1For frequency measurement link time Constant, KP2For the gain of electrohydraulic servo system, T2For oil motor travel feedback link time, TocWhen being opened or closed for oil motor Between constant, TWFor the water hammer time constant of primary frequency modulation closed-loop system, TJFor inertia time constant, D is synchronous machine damped coefficient;
The maximum eigenvalue λ of state space equation real part=σ+j ω of single machine primary frequency modulation closed-loop system is solved, and is found out Its corresponding damping ratio
Further, the damping ratio according to the damping coefficient of calculating, the integral square error of calculating and calculating is built It the step for vertical objective function, specifically includes:
Determine the upper limit value and lower limit value of the hydraulic turbine and its regulating system PID governor parameter, the hydraulic turbine and its tune Section system PID governor parameter K=[Kp,KI,KD] upper limit value KuWith lower limit value KlMeet: Kl≤K≤Ku, wherein KP、KIWith KDRespectively proportional gain, integral gain and the differential gain of the hydraulic turbine and its regulating system PID governor;
According to the damping coefficient of calculating, the integral square error of calculating, the damping ratio of calculating and the hydraulic turbine and its The upper limit value and lower limit value of regulating system PID governor parameter establish objective function, the expression formula of the objective function J (K) are as follows:
Wherein, J1It (K) is the integral square error calculated, M is punishment amount constant, and max () is to be maximized function, and ξ is The damping ratio of calculating, ξ0For the limit value of damping ratio, Dmi) it is the damping coefficient calculated,It is solved for optimization process Low-frequency oscillation damping torque coefficient, ωiFor the oscillation angular frequency of i-th of mode in the relevant underdamping mode of unit to be optimized, i The mode sum that=1,2,3 ... n, n include by the relevant underdamping mode of unit to be optimized.
Further, optimal ginseng of the optimal solution using PSO Algorithm objective function as hydrogovernor It the step for number, specifically includes:
Using the hydraulic turbine and its regulating system PID governor parameter K as the particle of optimization problem, particle populations are initialized Initial value and speed, and initialize the parameter value of primary frequency modulation closed-loop system;
According to the hydraulic turbine and its parameter value and target letter of regulating system PID governor parameter K, primary frequency modulation closed-loop system Number determines population fitness function K*=minJ (K), and then calculate the fitness value of particle individual;
The history optimal location of each particle and the optimal position of the population overall situation are determined according to the fitness value of particle individual It sets,;
The speed of each particle and position in Population Regeneration, wherein the speed of h-th particle and position after the g times iteration More new formula are as follows:
In above formula,WithThe g generation and g+1 for respectively indicating h-th of particle, which subrogate, sets,WithIt respectively indicates The diverse vector in the g generation and g+1 generation of h-th of particle, w are inertia coeffeicent, c1And c2Respectively letter of the particle to particle itself Appoint degree and the degree of belief to group, r1,r2It is the random number between [0,1], pbesthFor the optimal location of h-th of particle, Gbest is group's optimal location;
Judge whether the termination condition for meeting setting, if so, output population global optimum and its corresponding position As the solution of optimization problem, conversely, then returning according to PID governor parameter K, the parameter value and target of primary frequency modulation closed-loop system Function determines population fitness function K*=minJ (K), and then the step for the fitness value of calculating particle individual.
Second aspect of the embodiment of the present invention is adopted the technical scheme that:
The hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode, comprises the following modules:
Determining module, for determining the relevant underdamping mode of unit to be optimized and its frequency of oscillation;
Damping coefficient computing module for establishing the open-loop transfer function of the hydraulic turbine and its regulating system, and calculates The damping coefficient of the hydraulic turbine and its open-loop transfer function of regulating system under the frequency of oscillation of weakly damped oscillation mode;
Integral square error computing module, for calculating step according to the open-loop transfer function of the hydraulic turbine and its regulating system The integral square error of the hydraulic turbine and its regulating system output mechanical power under signal;
Damping ratio computing module, for calculating the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system;
Objective function establishes module, for according to the damping coefficient of calculating, the integral square error of calculating and calculating Damping ratio establish objective function;
Optimized parameter solves module, for the optimal solution using PSO Algorithm objective function as water turbine governing The optimized parameter of device.
Further, the determining module office specifically includes:
Total system characteristic value computing unit, it is special for calculating total system by power system small signal stability analysis program Value indicative;
Underdamping mode finds unit, for finding out underdamping mould relevant to unit to be optimized according to total system characteristic value Formula, the underdamping mode relevant to unit to be optimized are the low frequency oscillation mode that damping ratio is lower than preset threshold;
Frequency of oscillation determination unit, for determining the frequency of oscillation for the underdamping mode found out.
The third aspect of the embodiment of the present invention is adopted the technical scheme that:
The hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode, comprising:
At least one processor;
At least one processor, for storing at least one program;
When at least one described program is executed by least one described processor, so that at least one described processor is realized The hydrogovernor parameter optimization method of underdamping low frequency oscillation mode of the present invention.
One or more technical solutions in the embodiments of the present invention have the advantages that the comprehensive root of the embodiment of the present invention According to turbine and its regulating system in the damping coefficient under the frequency of oscillation of weakly damped oscillation mode, the hydraulic turbine under step signal And its integral square error and the maximum characteristic value of primary frequency modulation closed-loop system of regulating system output mechanical power are corresponding Damping ratio establishes objective function, and using the optimal solution of PSO Algorithm objective function as the optimal of hydrogovernor Parameter, it is contemplated that the influence to underdamping low frequency oscillation mode is kept away to the maximum extent while improving system frequency stability Exempt from the deterioration of underdamping low frequency oscillation mode, robustness is good.
Detailed description of the invention
Fig. 1 is the hydrogovernor parameter optimization method stream of underdamping low frequency oscillation mode provided in an embodiment of the present invention Cheng Tu;
Fig. 2 is the control block diagram of the hydraulic turbine of the embodiment of the present invention and its regulating system;
Fig. 3 is the control block diagram of single machine of embodiment of the present invention primary frequency modulation closed-loop system;
Fig. 4 is the hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode provided in an embodiment of the present invention A kind of structural block diagram;
Fig. 5 is the hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode provided in an embodiment of the present invention Another structural block diagram.
Specific embodiment
The present invention will be further explained with specific embodiment with reference to the accompanying drawings of the specification.For following implementation Step number in example, is arranged only for the purposes of illustrating explanation, does not do any restriction to the sequence between step, embodiment In each step execution sequence can be adaptively adjusted according to the understanding of those skilled in the art.
Referring to Fig.1, the embodiment of the invention provides a kind of hydrogovernor parameter of underdamping low frequency oscillation mode is excellent Change method, comprising the following steps:
S101, the relevant underdamping mode of unit to be optimized and its frequency of oscillation are determined;
Specifically, the present embodiment can be calculated by PSD-SSAP software and screen underdamping mould relevant to unit to be optimized Formula, and determine its frequency of oscillation.Step S101 is avoided that deterioration underdamping low frequency oscillation mode during parameter optimization.
S102, the open-loop transfer function for establishing the hydraulic turbine and its regulating system, and calculate the hydraulic turbine and its regulating system Damping coefficient of the open-loop transfer function under the frequency of oscillation of weakly damped oscillation mode;
S103, the hydraulic turbine and its adjusting under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The integral square error of system output mechanical power;
Specifically, this embodiment introduces the integral square errors of output mechanical power, can be in the base for inhibiting hunting of frequency The quick-action (i.e. single machine movement speed) of the hydraulic turbine and its regulating system is improved on plinth as far as possible to guarantee the performance of system.
S104, the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system is calculated;
Specifically, primary frequency modulation closed-loop system can be selected single machine primary frequency modulation closed-loop system (i.e. PID governor, electro-hydraulic watch Dress system, prime mover and synchronous machine only one).
S105, target is established according to the damping ratio of the damping coefficient of calculating, the integral square error of calculating and calculating Function;
S106, the optimized parameter using the optimal solution of PSO Algorithm objective function as hydrogovernor.
Specifically, particle swarm algorithm, and a kind of algorithm that based on group is iterated similar with genetic algorithm, but it is not There are the intersection and variation using genetic algorithm, but optimal particle is followed in solution space by particle and is scanned for.It is preferred that The optimized parameter on ground, hydrogovernor is indicated using the pid parameter of the hydraulic turbine and its regulating system PID governor.
By above content as it can be seen that the present embodiment first determines the relevant underdamping low frequency oscillation mode of unit to be optimized, then count It calculates the damping coefficient under the mode, integral square error and damping ratio and the mesh under the mode is established according to the result of calculating Scalar functions, it is contemplated that influence of the Small signal stability analysis of frequency to underdamping low frequency oscillation mode is finally calculated using population The optimizing of method iteration obtains optimized parameter until restraining, and while improving system frequency stability, avoids weak resistance to the maximum extent The deterioration of Buddhist nun's low frequency oscillation mode, robustness is good, can be widely applied to electric power system optimization field.
It is further used as preferred embodiment, the relevant underdamping mode of the determination unit to be optimized and its oscillation frequency The step for rate S101, specifically include:
S1011, total system characteristic value is calculated by power system small signal stability analysis program;
Specifically, PSD-SSAP software can be used in power system small signal stability analysis program.
S1012, underdamping mode relevant to unit to be optimized, described and machine to be optimized are found out according to total system characteristic value The relevant underdamping mode of group is the low frequency oscillation mode that damping ratio is lower than preset threshold;
Specifically, in order to avoid deteriorating underdamping low frequency oscillation mode during parameter optimization, preset threshold can be 0.1 or other relatively small numerical value.
S1013, the frequency of oscillation for determining the underdamping mode found out.
Specifically, the frequency of oscillation of underdamping mode can be angular frequency.
Assuming that the relevant underdamping mode λ of unit to be optimizediThere are n, i.e. i=1,2,3 ... n, correspondingly, underdamping mould Formula λiOscillation angular frequency also have n.
It is further used as preferred embodiment, the open-loop transfer function for establishing the hydraulic turbine and its regulating system, and The damping torque system of the calculating hydraulic turbine and its open-loop transfer function of regulating system under the frequency of oscillation of weakly damped oscillation mode The step for counting S102, specifically includes:
S1021, the open-loop transfer function for establishing PID governor, the open-loop transfer function G of the PID governorGm(s) Expression formula are as follows:
Wherein, KP1、KI1And KD1The respectively proportional gain of PID governor, integral gain and the differential gain, s La Pula This operator, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor the gain of measured value, TR1When for frequency measurement link Between constant;
S1022, the open-loop transfer function for establishing electrohydraulic servo system, the open-loop transfer function G of the electrohydraulic servo systemGA (s) expression formula are as follows:
Wherein, KP2For the gain of electrohydraulic servo system, s is Laplace operator, T2When for oil motor travel feedback link Between, TocTime constant is opened or closed for oil motor;
S1023, the open-loop transfer function for establishing prime mover, the open-loop transfer function G of described prime moverTw(s) expression formula Are as follows:
Wherein, s is Laplace operator, TwFor open loop water hammer time constant;
S1024, according to the open-loop transfer function of PID governor, the open-loop transfer function of electrohydraulic servo system and prime mover Open-loop transfer function obtain the hydraulic turbine and its regulating system open-loop transfer function, the hydraulic turbine and its regulating system open loop pass Delivery function Gsys(s) expression formula are as follows:
Gsys(s)=GGm(s)·GGA(s)·GTw(s)
S1025, the hydraulic turbine and its regulating system open-loop transfer function are calculated under the frequency of oscillation of weakly damped oscillation mode Damping coefficient, the frequency of oscillation s of the hydraulic turbine and its regulating system open-loop transfer function in weakly damped oscillation mode =j ωiUnder damping coefficient DmExpression formula are as follows:
Dm=Re (Gsys(jωi))
Wherein, Re (Gsys(jωi)) it is Gsys(jωi) real part, ωiFor in the relevant underdamping mode of unit to be optimized The oscillation angular frequency of i-th of mode, i=1, the mode that 2,3 ... n, n include by the relevant underdamping mode of unit to be optimized Sum.
Specifically, as shown in Fig. 2, the present embodiment hydraulic turbine and its regulating system by PID governor, electrohydraulic servo system with And the hydraulic turbine collectively constitutes, and after the open-loop transfer function for obtaining this three parts respectively, can pass through the open loop of this three parts Transmission function is multiplied to obtain the open-loop transfer function of the hydraulic turbine and its regulating system.And obtain opening for the hydraulic turbine and its regulating system After ring transmission function, the frequency of oscillation of the weakly damped oscillation mode of step S101 determination can be combined s=j ωiThis is substituted into open Ring transmission function simultaneously takes its real part, and corresponding damping coefficient can be obtained.
It is further used as preferred embodiment, it is described to be calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The S103 the step for integral square error of the hydraulic turbine and its regulating system output mechanical power under step signal, specifically:
The hydraulic turbine and its regulating system under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The integral square error of output mechanical power, square of the hydraulic turbine and its regulating system output mechanical power under the step signal Error intergal J1(K) expression formula are as follows:
Wherein, Δ PmIt (t) is value of the step response in t moment of the hydraulic turbine and its regulating system, tfIt is the hydraulic turbine and its tune Section system reaches the time of steady-state value, Δ Pm(tf) it is the hydraulic turbine and its regulating system step response in tfThe steady-state value at moment,bpFor difference coefficient, K is the ginseng of the hydraulic turbine and its regulating system PID governor Number, KP、KIAnd KDRespectively proportional gain, integral gain and the differential gain of the hydraulic turbine and its regulating system PID governor.
Specifically, in order to improve the quick-action of the hydraulic turbine and its regulating system as far as possible on the basis of inhibiting hunting of frequency (i.e. single machine movement speed) is defeated this embodiment introduces the integral square error of output mechanical power to guarantee the performance of system The integral square error of mechanical output is smaller out, and the quick-action of the hydraulic turbine and its regulating system is better.The hydraulic turbine and its adjusting system System reaches steady-state value Δ Pm(tf) time tfGenerally take 200s to 400s.
It is further used as preferred embodiment, the corresponding resistance of the maximum characteristic value of the calculating primary frequency modulation closed-loop system The step for Buddhist nun's ratio S104, specifically include:
S1041, the shape for obtaining the hydraulic turbine and its regulating system PID governor, electrohydraulic servo system, prime mover and synchronous machine State space equation, and then form the state space equation of single machine primary frequency modulation closed-loop system, the single machine primary frequency modulation closed loop system The state space equation expression formula of system are as follows:
Wherein, x is the state variable of single machine primary frequency modulation closed-loop system, and t is the time,
KP1、KI1And KD1Respectively proportional gain, integral gain and the differential of the hydraulic turbine and its regulating system PID governor Gain, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor the gain of measured value, TR1For frequency measurement link time Constant, KP2For the gain of electrohydraulic servo system, T2For oil motor travel feedback link time, TocWhen being opened or closed for oil motor Between constant, TWFor the water hammer time constant of primary frequency modulation closed-loop system, TJFor inertia time constant, D is synchronous machine damped coefficient;
S1042, the maximum eigenvalue λ of the state space equation real part=σ+j ω for solving single machine primary frequency modulation closed-loop system, And find out its corresponding damping ratio
Specifically, as shown in figure 3, the single machine primary frequency modulation closed-loop system of the present embodiment is by synchronous machine and the water wheels of Fig. 2 Machine and its regulating system composition, i.e. single machine primary frequency modulation closed-loop system are by PID governor, electrohydraulic servo system, prime mover and same This four most of composition of step machine, by obtaining this four most of all dynamic element of single machine closed-loop system near steady-state operation point Lienarized equation, state equation (the i.e. single machine primary frequency modulation closed loop after total system linearizes near the steady-state value can be formed The state space equation of system).After the state space equation for obtaining single machine primary frequency modulation closed-loop system, it can be asked by complex operation The maximum characteristic value of its real part and corresponding damping ratio are taken, to lay the foundation for the foundation of objective function.
In Fig. 3, the transmission function of synchronous machine can be simplified shown as:
It is further used as preferred embodiment, it is described long-pending according to the damping coefficient of calculating, the square error of calculating The step for damping ratio divided and calculated establishes objective function S105, specifically includes:
S1051, the upper limit value and lower limit value for determining the hydraulic turbine and its regulating system PID governor parameter, the hydraulic turbine And its regulating system PID governor parameter K=[Kp,KI,KD] upper limit value KuWith lower limit value KlMeet: Kl≤K≤Ku, wherein KP、KIAnd KDRespectively proportional gain, integral gain and the differential gain of the hydraulic turbine and its regulating system PID governor;
S1052, according to the damping coefficient of calculating, the integral square error of calculating, the damping ratio of calculating and water wheels The upper limit value and lower limit value of machine and its regulating system PID governor parameter establish objective function, the table of the objective function J (K) Up to formula are as follows:
Wherein, J1It (K) is the integral square error calculated, M is punishment amount constant, and max () is to be maximized function, and ξ is The damping ratio of calculating, ξ0For the limit value of damping ratio, Dmi) it is the damping coefficient calculated,It is solved for optimization process Low-frequency oscillation damping torque coefficient, ωiFor the oscillation angular frequency of i-th of mode in the relevant underdamping mode of unit to be optimized, i The mode sum that=1,2,3 ... n, n include by the relevant underdamping mode of unit to be optimized.
Specifically, constraint condition problem is converted unconfined condition problem using penalty function by the present embodiment, obtains objective function. Punishment amount constant M can use a biggish value, and such as 10000.
It is further used as preferred embodiment, the optimal solution using PSO Algorithm objective function is as water The step for optimized parameter of turbine governor S106, specifically include:
S1061, using the hydraulic turbine and its regulating system PID governor parameter K as the particle of optimization problem, initialize particle The initial value and speed of population, and initialize the parameter value of primary frequency modulation closed-loop system;
S1062, according to the hydraulic turbine and its regulating system PID governor parameter K, primary frequency modulation closed-loop system parameter value and Objective function determines population fitness function K*=minJ (K), and then calculate the fitness value of particle individual;
S1063, the history optimal location that each particle is determined according to the fitness value of particle individual and population are global most Excellent position,;
The speed of each particle and position in S1064, Population Regeneration, wherein after the g times iteration the speed of h-th of particle and The more new formula of position are as follows:
In above formula,WithThe g generation and g+1 for respectively indicating h-th of particle, which subrogate, sets,WithRespectively indicate The diverse vector in the g generation and g+1 generation of h particle, w are inertia coeffeicent, c1And c2Respectively trust of the particle to particle itself Degree and to the degree of belief of group, r1,r2It is the random number between [0,1], pbesthFor the optimal location of h-th of particle, Gbest is group's optimal location;
S1065, judge whether the termination condition for meeting setting, if so, output population global optimum and its correspondence Solution of the position as optimization problem, conversely, then returning according to PID governor parameter K, the parameter value of primary frequency modulation closed-loop system Population fitness function K is determined with objective function*=minJ (K), and then the step for the fitness value of calculating particle individual S1062。
Specifically, in step S1061 and S1062, the parameter value of primary frequency modulation closed-loop system refers to that single machine primary frequency modulation closes Other parameters of the loop system other than PID governor parameter K.
The present embodiment during parameter optimization in order to avoid not deteriorating underdamping low frequency oscillation mode, it is required that mesh Scalar functions J (K) acquirement minimum value, therefore the population fitness function K of particle swarm algorithm*=minJ (K).The present embodiment passes through weight The iteration optimizing operation of multiple step S1062~S1065, finally can be obtained optimal solution (the i.e. population fitness letter of objective function Several solution).
The termination condition of setting, which refers to, to be met the minimal error of setting, reaches maximum number of iterations or grain of continuous 100 generation The forward speed of son is less than pre-set velocity threshold value (forward speed of i.e. continuous 100 generation particle is excessively slow).
Referring to Fig. 4, the embodiment of the invention also provides a kind of hydrogovernor parameters of underdamping low frequency oscillation mode Optimization system comprises the following modules:
Determining module 201, for determining the relevant underdamping mode of unit to be optimized and its frequency of oscillation;
Damping coefficient computing module 202 for establishing the open-loop transfer function of the hydraulic turbine and its regulating system, and is counted The damping coefficient of the calculation hydraulic turbine and its open-loop transfer function of regulating system under the frequency of oscillation of weakly damped oscillation mode;
Integral square error computing module 203, for being calculated according to the open-loop transfer function of the hydraulic turbine and its regulating system The integral square error of the hydraulic turbine and its regulating system output mechanical power under step signal;
Damping ratio computing module 204, for calculating the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system;
Objective function establishes module 205, by according to the damping coefficient of calculating, the integral square error of calculating and based on The damping ratio of calculation establishes objective function;
Optimized parameter solves module 206, for the optimal solution using PSO Algorithm objective function as the hydraulic turbine The optimized parameter of governor.
Referring to Fig. 4, it is further used as preferred embodiment, the determining module 201 specifically includes:
Total system characteristic value computing unit 2011, for calculating complete set by power system small signal stability analysis program System characteristic value;
Underdamping mode finds unit 2012, for finding out weak resistance relevant to unit to be optimized according to total system characteristic value Buddhist nun's mode, the underdamping mode relevant to unit to be optimized are the low frequency oscillation mode that damping ratio is lower than preset threshold;
Frequency of oscillation determination unit 2013, for determining the frequency of oscillation for the underdamping mode found out.
Suitable for this system embodiment, this system embodiment is implemented content in above method embodiment Function is identical as above method embodiment, and the beneficial effect reached and above method embodiment beneficial effect achieved It is identical.
Referring to Fig. 5, the embodiment of the invention also provides a kind of hydrogovernor parameters of underdamping low frequency oscillation mode Optimization system, comprising:
At least one processor 301;
At least one processor 302, for storing at least one program;
When at least one described program is executed by least one described processor 301, so that at least one described processor 301 realize the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode of the present invention.
Suitable for this system embodiment, this system embodiment is implemented content in above method embodiment Function is identical as above method embodiment, and the beneficial effect reached and above method embodiment beneficial effect achieved It is identical.
It is to be illustrated to preferable implementation of the invention, but the present invention is not limited to the embodiment above, it is ripe Various equivalent deformation or replacement can also be made on the premise of without prejudice to spirit of the invention by knowing those skilled in the art, this Equivalent deformation or replacement are all included in the scope defined by the claims of the present application a bit.

Claims (10)

1. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode, it is characterised in that: the following steps are included:
Determine the relevant underdamping mode of unit to be optimized and its frequency of oscillation;
The open-loop transfer function of the hydraulic turbine and its regulating system is established, and calculates the open loop transmitting letter of the hydraulic turbine and its regulating system Damping coefficient of the number under the frequency of oscillation of weakly damped oscillation mode;
The hydraulic turbine and its regulating system output under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The integral square error of mechanical output;
Calculate the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system;
Objective function is established according to the damping ratio of the damping coefficient of calculating, the integral square error of calculating and calculating;
Optimized parameter using the optimal solution of PSO Algorithm objective function as hydrogovernor.
2. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode according to claim 1, feature It is: the step for the relevant underdamping mode of the determination unit to be optimized and its frequency of oscillation, specifically includes:
Total system characteristic value is calculated by power system small signal stability analysis program;
Underdamping mode relevant to unit to be optimized is found out according to total system characteristic value, it is described relevant to unit to be optimized weak Damping mode is the low frequency oscillation mode that damping ratio is lower than preset threshold;
Determine the frequency of oscillation for the underdamping mode found out.
3. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode according to claim 1, feature It is: the open-loop transfer function for establishing the hydraulic turbine and its regulating system, and calculate the open loop of the hydraulic turbine and its regulating system It the step for damping coefficient of the transmission function under the frequency of oscillation of weakly damped oscillation mode, specifically includes:
Establish the open-loop transfer function of PID governor, the open-loop transfer function G of the PID governorGm(s) expression formula are as follows:
Wherein, KP1、KI1And KD1The respectively proportional gain of PID governor, integral gain and the differential gain, s are Laplce's calculation Son, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor the gain of measured value, TR1It is normal for frequency measurement link time Number;
Establish the open-loop transfer function of electrohydraulic servo system, the open-loop transfer function G of the electrohydraulic servo systemGA(s) expression Formula are as follows:
Wherein, KP2For the gain of electrohydraulic servo system, s is Laplace operator, T2For oil motor travel feedback link time, Toc Time constant is opened or closed for oil motor;
Establish the open-loop transfer function of prime mover, the open-loop transfer function G of described prime moverTw(s) expression formula are as follows:
Wherein, s is Laplace operator, TwFor open loop water hammer time constant;
It is transmitted according to the open loop of the open-loop transfer function of PID governor, the open-loop transfer function of electrohydraulic servo system and prime mover Function obtains the hydraulic turbine and its regulating system open-loop transfer function, the hydraulic turbine and its regulating system open-loop transfer function Gsys (s) expression formula are as follows:
Gsys(s)=GGm(s)·GGA(s)·GTw(s)
Calculate the damping torque of the hydraulic turbine and its regulating system open-loop transfer function under the frequency of oscillation of weakly damped oscillation mode The frequency of oscillation s=j ω of coefficient, the hydraulic turbine and its regulating system open-loop transfer function in weakly damped oscillation modeiUnder Damping coefficient DmExpression formula are as follows:
Dm=Re (Gsys(jωi))
Wherein, Re (Gsys(jωi)) it is Gsys(jωi) real part, ωiIt is i-th in the relevant underdamping mode of unit to be optimized The oscillation angular frequency of mode, i=1, the mode sum that 2,3 ... n, n include by the relevant underdamping mode of unit to be optimized.
4. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode according to claim 1, feature It is: described that the hydraulic turbine and its regulating system under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The step for integral square error of output mechanical power, specifically:
The hydraulic turbine and its regulating system output under step signal are calculated according to the hydraulic turbine and its open-loop transfer function of regulating system The integral square error of mechanical output, the square error of the hydraulic turbine and its regulating system output mechanical power under the step signal Integrate J1(K) expression formula are as follows:
Wherein, Δ PmIt (t) is value of the step response in t moment of the hydraulic turbine and its regulating system, tfIt is the hydraulic turbine and its adjusting system System reaches the time of steady-state value, Δ Pm(tf) it is the hydraulic turbine and its regulating system step response in tfThe steady-state value at moment,bpFor difference coefficient, K is the ginseng of the hydraulic turbine and its regulating system PID governor Number, KP、KIAnd KDRespectively proportional gain, integral gain and the differential gain of the hydraulic turbine and its regulating system PID governor.
5. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode according to claim 1, feature It is: the step for the maximum characteristic value of the calculating primary frequency modulation closed-loop system corresponding damping ratio, specifically includes:
Obtain the state space side of the hydraulic turbine and its regulating system PID governor, electrohydraulic servo system, prime mover and synchronous machine Journey, and then form the state space equation of single machine primary frequency modulation closed-loop system, the state of the single machine primary frequency modulation closed-loop system Space equation expression formula are as follows:
Wherein, x is the state variable of single machine primary frequency modulation closed-loop system, and t is the time,
KP1、KI1And KD1Respectively proportional gain, integral gain and the differential gain of the hydraulic turbine and its regulating system PID governor, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor the gain of measured value, TR1For frequency measurement link time constant, KP2For the gain of electrohydraulic servo system, T2For oil motor travel feedback link time, TocIt is normal that the time is opened or closed for oil motor Number, TWFor the water hammer time constant of primary frequency modulation closed-loop system, TJFor inertia time constant, D is synchronous machine damped coefficient;
The maximum eigenvalue λ of state space equation real part=σ+j ω of single machine primary frequency modulation closed-loop system is solved, and it is right to find out its The damping ratio answered
6. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode according to claim 1, feature Be: the damping ratio according to the damping coefficient of calculating, the integral square error of calculating and calculating establishes objective function The step for, it specifically includes:
Determine the upper limit value and lower limit value of the hydraulic turbine and its regulating system PID governor parameter, the hydraulic turbine and its adjusting system Unite PID governor parameter K=[Kp,KI,KD] upper limit value KuWith lower limit value KlMeet: Kl≤K≤Ku, wherein KP、KIAnd KDPoint Not Wei the hydraulic turbine and its regulating system PID governor proportional gain, integral gain and the differential gain;
According to the damping coefficient of calculating, the integral square error of calculating, the damping ratio of calculating and the hydraulic turbine and its adjusting The upper limit value and lower limit value of system PID governor parameter establish objective function, the expression formula of the objective function J (K) are as follows:
Wherein, J1It (K) is the integral square error calculated, M is punishment amount constant, and max () is to be maximized function, and ξ is to calculate Damping ratio, ξ0For the limit value of damping ratio, Dmi) it is the damping coefficient calculated,The low frequency solved for optimization process Oscillation damping torque coefficient, ωiFor the oscillation angular frequency of i-th of mode in the relevant underdamping mode of unit to be optimized, i=1, The mode sum that 2,3 ... n, n include by the relevant underdamping mode of unit to be optimized.
7. the hydrogovernor parameter optimization method of underdamping low frequency oscillation mode according to claim 6, feature Be: the optimal solution using PSO Algorithm objective function is as this step of the optimized parameter of hydrogovernor Suddenly, it specifically includes:
Using the hydraulic turbine and its regulating system PID governor parameter K as the particle of optimization problem, the initial value of particle populations is initialized And speed, and initialize the parameter value of primary frequency modulation closed-loop system;
It is true according to the hydraulic turbine and its regulating system PID governor parameter K, the parameter value of primary frequency modulation closed-loop system and objective function Determine population fitness function K*=minJ (K), and then calculate the fitness value of particle individual;
The history optimal location of each particle and the optimal location of the population overall situation are determined according to the fitness value of particle individual,;
The speed of each particle and position in Population Regeneration, wherein after the g times iteration the speed of h-th particle and position update Formula are as follows:
In above formula,WithThe g generation and g+1 for respectively indicating h-th of particle, which subrogate, sets,WithIt respectively indicates h-th The diverse vector in the g generation and g+1 generation of particle, w are inertia coeffeicent, c1And c2Respectively degree of belief of the particle to particle itself With the degree of belief to group, r1,r2It is the random number between [0,1], pbesthFor the optimal location of h-th of particle, gbest For group's optimal location;
Judge whether the termination condition for meeting setting, if so, output population global optimum and its corresponding position conduct The solution of optimization problem, conversely, then returning according to PID governor parameter K, the parameter value and objective function of primary frequency modulation closed-loop system Determine population fitness function K*=minJ (K), and then the step for the fitness value of calculating particle individual.
8. the hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode, it is characterised in that: comprise the following modules:
Determining module, for determining the relevant underdamping mode of unit to be optimized and its frequency of oscillation;
Damping coefficient computing module for establishing the open-loop transfer function of the hydraulic turbine and its regulating system, and calculates water wheels The damping coefficient of machine and its open-loop transfer function of regulating system under the frequency of oscillation of weakly damped oscillation mode;
Integral square error computing module, for calculating step signal according to the open-loop transfer function of the hydraulic turbine and its regulating system The integral square error of the lower hydraulic turbine and its regulating system output mechanical power;
Damping ratio computing module, for calculating the corresponding damping ratio of the maximum characteristic value of primary frequency modulation closed-loop system;
Objective function establishes module, for the resistance according to the damping coefficient of calculating, the integral square error of calculating and calculating Buddhist nun's ratio establishes objective function;
Optimized parameter solves module, for the optimal solution using PSO Algorithm objective function as hydrogovernor Optimized parameter.
9. the hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode according to claim 8, feature Be: the determining module office specifically includes:
Total system characteristic value computing unit, for calculating total system feature by power system small signal stability analysis program Value;
Underdamping mode finds unit, for finding out underdamping mode relevant to unit to be optimized according to total system characteristic value, The underdamping mode relevant to unit to be optimized is the low frequency oscillation mode that damping ratio is lower than preset threshold;
Frequency of oscillation determination unit, for determining the frequency of oscillation for the underdamping mode found out.
10. the hydrogovernor Parameter Optimization System of underdamping low frequency oscillation mode, it is characterised in that: include:
At least one processor;
At least one processor, for storing at least one program;
When at least one described program is executed by least one described processor, so that at least one described processor is realized as weighed Benefit requires the hydrogovernor parameter optimization method of the described in any item underdamping low frequency oscillation modes of 1-7.
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