CN108107720A - Hydrogovernor parameter tuning method and system based on state space analysis - Google Patents
Hydrogovernor parameter tuning method and system based on state space analysis Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
- G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
Abstract
The invention discloses a kind of hydrogovernor parameter tuning methods based on state space analysis and system, method to include：Calculate the frequency response coefficient of Asynchronous Interconnection sending load；Hydraulic turbine system open-loop transfer function is established, and solves corresponding step response functions；The hydraulic turbine and its state space equation of speed governing closed-loop system under Asynchronous Interconnection are established according to the frequency response coefficient of calculating, and solve the characteristic value of the state space equation real part maximum of foundation and its corresponding damping ratio；According to the corresponding damping ratio of characteristic value of the step response functions of solution, the state space equation established and state space equation real part maximum, population fitness function is established using penalty function method；It is optimal for target with primary frequency modulation acting characteristic of the Hydropower Unit under step response according to population fitness function, using the optimized parameter of PSO Algorithm hydrogovernor.Strong robustness of the present invention and primary frequency modulation performance is good, can be widely applied to field of power.
Description
Technical field
The present invention relates to field of power, especially a kind of hydrogovernor parameter based on state space analysis is whole
Determine method and system.
Background technology
In the high water power ratio sending of Asynchronous Interconnection, the water hammer effect of the hydraulic turbine may cause governor unstable,
Since LOAD FREQUENCY mediating effect+6 coefficient is smaller, system damping is relatively low, and then triggers ultra-low frequency oscillation.And Hydropower Unit is presented and born
Damping characteristic is the main reason for causing low-frequency oscillation.In general, the hydraulic turbine and governor can generate negative damping in low-frequency range,
The delayed phase of steam turbine in itself is smaller, and when the delayed phase also very little of governor, positive damping can be generated in low-frequency range.These
It is all related with the parameter tuning of hydrogovernor.
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 weight, water power ratio is more than 75%, and thermoelectricity ratio is less than 10%, remaining is wind-powered electricity generation and photovoltaic, is typical high
Water power ratio power grid.Yunnan Power System saves internal loading and accounts for total power generation about 1/3, and direct current sends load outside and accounts for total power generation about 2/3, due to direct current
Load is approximately rigid load in frequency limit device dead zone so that can be carried in 49.9Hz~50.1Hz frequency ranges internal loading
The damping of confession is greatly decreased.The reduction of out-damping coefficient and the influence of water hammer effect, cause ultra-low frequency oscillation.Yunnan Power System is different
Step experiment and simulation report also turn out, if still using synchronous networking parameters, ultra-low frequency oscillation will occur for Yunnan Power System；And significantly
It is again that the primary frequency modulation rate for causing Hydropower Unit is excessively slow to reduce parameter.
At present caused by reply hydrogovernor negative resistance character during low-frequency oscillation, the solution generally taken be by
Generator primary frequency modulation the dead time is dead more than direct current frequency limiter (Frequency Limit Controller, FLC)
Area, but this method is not particularly suited for Asynchronous Interconnection sending.Therefore, there is an urgent need for one kind in the industry to be directed to Asynchronous Interconnection sending
Hydrogovernor parameter tuning scheme, avoid generate ultra-low frequency oscillation while ensure Hydropower Unit to greatest extent
Primary frequency modulation acting characteristic.
The content of the invention
In order to solve the above technical problems, it is an object of the invention to：A kind of strong robustness is provided and primary frequency modulation performance is good
, hydrogovernor parameter tuning method and system based on state space analysis.
The first technical solution for being taken of the present invention is：
Hydrogovernor parameter tuning method based on state space analysis, comprises the following steps：
Calculate the frequency response coefficient of Asynchronous Interconnection sending load；
Hydraulic turbine system open-loop transfer function is established, and solves corresponding step response functions；
The hydraulic turbine and its state space of speed governing closed-loop system under Asynchronous Interconnection are established according to the frequency response coefficient of calculating
Equation, and solve the characteristic value of the state space equation real part maximum of foundation and its corresponding damping ratio；
According to the spy of the step response functions of solution, the state space equation established and state space equation real part maximum
The corresponding damping ratio of value indicative establishes population fitness function using penalty function method；
It is optimal for mesh with primary frequency modulation acting characteristic of the Hydropower Unit under step response according to population fitness function
Mark, using the optimized parameter of PSO Algorithm hydrogovernor.
Further, the step for the frequency response coefficient of the calculating Asynchronous Interconnection sending load, it is specially：
The disturbance occurred close to Asynchronous Interconnection sending under the rich small limit method of operation is chosen, Asynchronous Interconnection is calculated and send
The frequency response coefficient of end system load, the rich small limit method of operation refers to operate in abundance of water Smaller load pattern, described different
The frequency response COEFFICIENT K of step networking sending loadfCalculation formula be：
Wherein, Δ P/P0It comes off percentage for power, Δ P is that the power of Asynchronous Interconnection sending before and after disturbance occurs becomes
Change value, P0The power of Asynchronous Interconnection sending, Δ ff before occurring for disturbance0For stable state frequency drop percentage, Δ f is disturbance
The frequency departure of front and rear Asynchronous Interconnection sending, Δ f is without departing from frequency limit device dead zone, f0Asynchronous Interconnection before occurring for disturbance
The frequency of sending, R are the difference coefficient of unit.
Further, it is described to establish hydraulic turbine system open-loop transfer function, and solve corresponding step response functions this steps
Suddenly, specifically include：
Establish the open-loop transfer function of Hydropower Unit regulating system, the open-loop transfer function of the Hydropower Unit regulating system
GGm(s) expression formula is：
Wherein, KP1、KI1And KD1The respectively proportional gain of Hydropower Unit regulating system PID controller, storage gain and micro-
Point gain, s are Laplace operator, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor frequency departure times magnification
Number, TR1For frequency measurement link time 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 is：
Wherein, KP2、KI2And KD2Respectively the proportional gain of electrohydraulic servo system PID controller, storage gain and differential increase
Benefit, s are Laplace operator, T1For servomotor travel feedback link time, TocTime constant is turned on and off for servomotor；
Establish the open-loop transfer function of prime mover, the open-loop transfer function G of described prime moverTw(s) expression formula is：
Wherein, s is Laplace operator, TwStart the time for open loop water；
Hydraulic turbine system is obtained according to the open-loop transfer function of Hydropower Unit regulating system, electrohydraulic servo system and prime mover
Open-loop transfer function, the hydraulic turbine system open-loop transfer function Gsys(s) expression formula is：
Gsys(s)=GGm(s)·GGA(s)·GTw(s)；
According to hydraulic turbine system open-loop transfer function, corresponding step response functions x (t) is solved.
Further, the frequency response coefficient according to calculating establishes the hydraulic turbine and its speed governing closed-loop system under Asynchronous Interconnection
State space equation, and solve the characteristic value of the state space equation real part maximum of foundation and its corresponding damping ratio this step
Suddenly, specifically include：
The linearisation state space equation of Hydropower Unit regulating system, electrohydraulic servo system, prime mover and synchronous machine is obtained,
And then form the hydraulic turbine and its state space equation of speed governing closed-loop system under Asynchronous Interconnection, under the Asynchronous Interconnection hydraulic turbine and
The state space equation of its speed governing closed-loop system is：
Wherein, x is the state variable of the hydraulic turbine and its speed governing closed-loop system, and t is the time,
KP1、KI1And KD1Respectively the proportional gain of Hydropower Unit regulating system PID controller, storage gain and differential increase
Benefit, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor frequency departure amplification factor, TR1For frequency measurement link when
Between constant, KP2、KI2And KD2The respectively proportional gain of electrohydraulic servo system PID controller, storage gain and the differential gain, T1
For servomotor travel feedback link time, TocTime constant, T are turned on and off for servomotorWWhen starting for the water of closed-loop system
Between, TJFor inertia time constant, KfFor the frequency response coefficient of Asynchronous Interconnection sending load, D is synchronous machine damped coefficient；
Solve Asynchronous Interconnection under the state space equation real part maximum of the hydraulic turbine and its speed governing closed-loop system eigenvalue λ=
σ ± j ω, and its corresponding damping ratio is obtained
Further, the step response functions according to solution, the state space equation and state space equation established
The corresponding damping ratio of characteristic value of real part maximum, the step for establishing population fitness function using penalty function method be specially：
According to the spy of the step response functions of solution, the state space equation established and state space equation real part maximum
The corresponding damping ratio of value indicative calculates population fitness function, the population fitness function J (K using penalty function methodP1,
KD1,KI1) expression formula be：
Wherein, M1And M2It is the penalty factor of penalty function method, ξ0For the minimum damping ratio of setting, tfStable state is reached for system
Time, xtFor solution step response functions time t value,For solution step response functions in time tfValue,
x∞For steady-state value,bpFor difference coefficient, s is Laplace operator, Gsys(s) it is water
Expander system open-loop transfer function.
Further, it is described according to population fitness function, it is acted with primary frequency modulation of the Hydropower Unit under step response
Characteristic is optimal for target, using PSO Algorithm hydrogovernor optimized parameter the step for, specifically include following
Step：
With the proportional gain K of Hydropower Unit regulating systemP1, storage gain KI1With differential gain KD1Parameter is asked as an optimization
The particle of topic initializes particle populations；
According to KP1、KI1And KD1Ask for corresponding population fitness function J (KP1,KD1,KI1), and then calculate in population
The fitness value of particle individual；
The history optimal location of particle individual and the optimal location of the population overall situation are determined according to the fitness value of calculating；
The speed of particle individual and position in Population Regeneration；
Judge whether the end condition for meeting setting, if so, output population global optimum and its corresponding position
Solution as problem；Conversely, it then returns according to KP1、KI1And KD1Ask for corresponding population fitness function J (KP1,KD1,KI1),
And then the step for calculating the fitness value of each particle in population.
Further, the speed of particle individual and the step for position in the Population Regeneration is specially：
The speed of each particle and position in Population Regeneration, wherein the speed of i-th particle and position after the g times iteration
More new formula is：
In above formula,WithIt represents the g generations of i-th particle respectively and g+1 subrogates and puts,WithIs represented respectively
The g generations of i particle and the diverse vector in g+1 generations, w are inertia coeffeicent, c1And c2Respectively particle is to the trust of particle itself
Degree and the degree of belief to group, r1,r2It is the random number between [0,1], pbestiFor the optimal location of i-th of particle,
Gbest is group's optimal location.
Further, the end condition for meeting setting refers to meet the minimal error of setting, reaches maximum iteration
Or the pace of continuous 100 generation particle is less than pre-set velocity threshold value.
The second technical solution for being taken of the present invention is：
Hydrogovernor parameter tuning system based on state space analysis, including：
Frequency response coefficients calculation block, for calculating the frequency response coefficient of Asynchronous Interconnection sending load；
Open-loop transfer function and step response functions acquisition module, for establishing hydraulic turbine system open-loop transfer function, and
Solve corresponding step response functions；
State space equation is established with solving module, and water under Asynchronous Interconnection is established for the frequency response coefficient according to calculating
The state space equation of turbine and its speed governing closed-loop system, and solve the state space equation real part maximum of foundation characteristic value and
Its corresponding damping ratio；
Population fitness function establishes module, for according to solution step response functions, establish state space side
The corresponding damping ratio of characteristic value of journey and state space equation real part maximum establishes population fitness letter using penalty function method
Number；
The optimized parameter acquisition module of hydrogovernor, for according to population fitness function, being existed with Hydropower Unit
Primary frequency modulation acting characteristic under step response is optimal for target, using the optimal ginseng of PSO Algorithm hydrogovernor
Number.
The 3rd technical solution taken of the present invention is：
Hydrogovernor parameter tuning system based on state space analysis, including：
Memory, for storing program；
Processor, for loading described program to perform the water based on state space analysis as described in the first technical solution
Turbine governor parameter setting method.
The beneficial effects of the invention are as follows：The present invention is based on state space analysis hydrogovernor parameter tuning method and
System draws governor parameter to the hydraulic turbine and its shadow of speed governing closed-loop system characteristic value and damping ratio based on state space analysis
It rings, and then with reference to particle cluster algorithm, iteration optimal for target with primary frequency modulation acting characteristic of the Hydropower Unit under step response
The optimized parameter of hydrogovernor is solved, synthesis is by state space analysis and particle cluster algorithm come to Asynchronous Interconnection sending end system
The hydrogovernor of system carries out parameter tuning, protects in the ultra-low frequency oscillation for avoiding generating under Asynchronous Interconnection while to greatest extent
Demonstrate,prove the primary frequency modulation acting characteristic of Hydropower Unit, strong robustness and primary frequency modulation performance is good.
Description of the drawings
Fig. 1 is the overall flow figure of the hydrogovernor parameter tuning method the present invention is based on state space analysis；
Fig. 2 is the hydraulic turbine of the present invention and its a kind of control block diagram of speed governing closed-loop system.
Specific embodiment
The present invention is further explained and illustrated with reference to Figure of description and specific embodiment.For the present invention with
Step number in lower embodiment, sets only for the purposes of illustrating explanation, does not do any restriction to the order between step,
The execution sequence of each step in embodiment can carry out accommodation according to the understanding of those skilled in the art.
With reference to Fig. 1, the hydrogovernor parameter tuning method based on state space analysis comprises the following steps：
S1, the frequency response coefficient for calculating Asynchronous Interconnection sending load；
S2, hydraulic turbine system open-loop transfer function is established, and solves corresponding step response functions；
S3, the state of the hydraulic turbine and its speed governing closed-loop system sky under Asynchronous Interconnection is established according to the frequency response coefficient of calculating
Between equation, and solve the characteristic value of the state space equation real part maximum of foundation and its corresponding damping ratio；
It is S4, maximum according to the step response functions of solution, the state space equation established and state space equation real part
The corresponding damping ratio of characteristic value, population fitness function is established using penalty function method；
S5, according to population fitness function, it is optimal with primary frequency modulation acting characteristic of the Hydropower Unit under step response
For target, using the optimized parameter of PSO Algorithm hydrogovernor.
In the present embodiment, the frequency response coefficient of Asynchronous Interconnection sending load can be under the rich small limit method of operation
Frequency response coefficient.Preferably, the optimized parameter of hydrogovernor is represented using the pid parameter of PID controller.
Particle cluster algorithm, and a kind of algorithm that based on group is iterated similar with genetic algorithm, but its there is no using losing
The intersection of propagation algorithm and variation, but optimal particle is followed in solution space by particle and is scanned for.
The present invention is based on state space analysis, by the hydraulic turbine and its speed governing closed-loop system are carried out state space analysis this
One small interference analytic approach analyzes influence of the governor parameter to the hydraulic turbine and its speed governing closed-loop system characteristic value and damping ratio, and
With primary frequency modulation acting characteristic of the Hydropower Unit under step response optimal (such as primary frequency modulation rate is most fast) for target, use
The optimizing of particle cluster algorithm iteration is avoiding generating the ultra-low frequency oscillation while most under Asynchronous Interconnection until convergence obtains optimized parameter
Ensure to limits the primary frequency modulation acting characteristic of Hydropower Unit, strong robustness and primary frequency modulation performance is good.
Be further used as preferred embodiment, the frequency response coefficient for calculating Asynchronous Interconnection sending load this
One step, specially：
The disturbance occurred close to Asynchronous Interconnection sending under the rich small limit method of operation is chosen, Asynchronous Interconnection is calculated and send
The frequency response coefficient of end system load, the rich small limit method of operation refers to operate in abundance of water Smaller load pattern, described different
The frequency response COEFFICIENT K of step networking sending loadfCalculation formula be：
Wherein, Δ P/P0It comes off percentage for power, Δ P is that the power of Asynchronous Interconnection sending before and after disturbance occurs becomes
Change value, P0The power of Asynchronous Interconnection sending, Δ ff before occurring for disturbance0For stable state frequency drop percentage, Δ f is disturbance
The frequency departure of front and rear Asynchronous Interconnection sending, Δ f is without departing from frequency limit device dead zone, f0Asynchronous Interconnection before occurring for disturbance
The frequency of sending, R are the difference coefficient of unit.It is run in the present embodiment close to Asynchronous Interconnection sending in the rich small limit
The disturbance occurred under mode refers to the position of disturbance generation and value of the Asynchronous Interconnection sending under the rich small limit method of operation
Distance be less than predetermined threshold value (generally one close to 0 numerical value, numerical value is smaller).
In the present embodiment, coefficient 0.8 so that result of calculation is relatively conservative, ensure that the safety fortune of Asynchronous Interconnection sending
Row.The present embodiment make use of small interference analytic approach to calculate the frequency response coefficient of Asynchronous Interconnection sending load.
Preferred embodiment is further used as, it is described to establish hydraulic turbine system open-loop transfer function, and solve corresponding
The step for step response functions, specifically includes：
S21, the open-loop transfer function for establishing Hydropower Unit regulating system, the open loop of the Hydropower Unit regulating system are transferred
Function GGm(s) expression formula is：
Wherein, KP1、KI1And KD1The respectively proportional gain of Hydropower Unit regulating system PID controller, storage gain and micro-
Point gain, s are Laplace operator, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor frequency departure times magnification
Number, TR1For frequency measurement link time constant；
S22, the open-loop transfer function for establishing electrohydraulic servo system, the open-loop transfer function G of the electrohydraulic servo systemGA
(s) expression formula is：
Wherein, KP2、KI2And KD2Respectively the proportional gain of electrohydraulic servo system PID controller, storage gain and differential increase
Benefit, s are Laplace operator, T1For servomotor travel feedback link time, TocTime constant is turned on and off for servomotor；
S23, the open-loop transfer function for establishing prime mover, the open-loop transfer function G of described prime moverTw(s) expression formula is：
Wherein, s is Laplace operator, TwStart the time for open loop water；
S24, the hydraulic turbine is obtained according to the open-loop transfer function of Hydropower Unit regulating system, electrohydraulic servo system and prime mover
System open loop transmission function, the hydraulic turbine system open-loop transfer function Gsys(s) expression formula is：
Gsys(s)=GGm(s)·GGA(s)·GTw(s)；
S25, according to hydraulic turbine system open-loop transfer function, solve corresponding step response functions x (t).
The open cycle system structure of the hydraulic turbine system of the present embodiment is by the Hydropower Unit regulating system based on PID controller
(i.e. hydro turbine governor), electrohydraulic servo system and prime mover this three parts composition, obtain opening for this three parts respectively
After ring transmission function, you can be multiplied to obtain hydraulic turbine system open-loop transfer function by the open-loop transfer function of this three parts.
And after obtaining hydraulic turbine system open-loop transfer function, it can be converted by frequency-time domain (such as inverse Laplace transformation), you can
Solve corresponding step response functions x (t).
With reference to Fig. 2, preferred embodiment is further used as, the frequency response coefficient according to calculating is established asynchronous
The state space equation of the hydraulic turbine off the net and its speed governing closed-loop system, and solve the spy of the state space equation real part maximum of foundation
It the step for value indicative and its corresponding damping ratio, specifically includes：
S31, by describe Hydropower Unit regulating system dynamic characteristic non-linear differential-Algebraic Equation set at operating point line
Property, the linearisation state space equation for obtaining Hydropower Unit regulating system (when describing its mathematical model, has ignored variable
Increment sign Δ), the expression formula of the linearisation state space equation of the Hydropower Unit regulating system is：
Wherein, x1、x2、x3、x4、x5、x6And x7It is the state variable of Hydropower Unit regulating system, t is the time, KWFor frequency
Rate deviation amplification factor, TR1For frequency measurement link time constant, KP1、KI1And KD1Respectively Hydropower Unit regulating system PID is controlled
Proportional gain, storage gain and the differential gain of device processed, bpFor difference coefficient, T1vTo measure inertia time constant；
S32, the linearisation state space equation for obtaining electrohydraulic servo system, the linearisation state of the electrohydraulic servo system
The expression formula of space equation is：
Wherein, x8、x9、x10、x11、x12、x13、x14And x15It is the state variable of electrohydraulic servo system, KP2、KI2And KD2Point
Not Wei electrohydraulic servo system PID controller proportional gain, storage gain and the differential gain, T1For servomotor travel feedback link
(LVDT) time, TOCTime constant is turned on and off for servomotor；
S33, the linearisation state space equation for obtaining prime mover, the table of the linearisation state space equation of described prime mover
It is up to formula：
Wherein, x16For the state variable of prime mover, TWStart the time for the water of closed-loop system；
S34, the linearisation state space equation for obtaining synchronous machine, the table of the linearisation state space equation of the synchronous machine
It is up to formula：
Wherein, x17For the state variable of prime mover, KfFor the frequency response coefficient of Asynchronous Interconnection sending load, TJFor
Inertia time constant；
According to the linearisation state space equation of Hydropower Unit regulating system, electrohydraulic servo system, prime mover and synchronous machine,
Obtain the hydraulic turbine and its state space equation of speed governing closed-loop system under Asynchronous Interconnection, the hydraulic turbine and its tune under the Asynchronous Interconnection
The state space equation of fast closed-loop system is：
Wherein, x is the state variable of the hydraulic turbine and its speed governing closed-loop system, and t is the time,
T1For servomotor travel feedback link time, D is synchronous machine damped coefficient；
S35, the feature for solving the state space equation real part maximum of the hydraulic turbine and its speed governing closed-loop system under Asynchronous Interconnection
Value λ=σ ± j ω, and its corresponding damping ratio is obtained
As shown in Fig. 2, the hydraulic turbine and its speed governing closed-loop system are by based on PID controller under the Asynchronous Interconnection of the present embodiment
This four most of composition of Hydropower Unit regulating system (i.e. hydro turbine governor), electrohydraulic servo system, prime mover and synchronous machine,
It, can group by obtaining this lienarized equation of the four most of all dynamic elements of unit closed-loop system near steady-state operation point
State equation (the i.e. state space side of the hydraulic turbine and its speed governing closed-loop system after being linearized into total system near steady-state value
Journey).After obtaining the hydraulic turbine and its state space equation of speed governing closed-loop system, its real part maximum can be asked for by complex operation
Characteristic value and corresponding damping ratio are laid the foundation with being established for population fitness function with iteration optimizing.
Be further used as preferred embodiment, according to the step response functions of solution, establish state space equation with
And the corresponding damping ratio of characteristic value of state space equation real part maximum, using penalty function method establish population fitness function this
One step, specially：
According to the spy of the step response functions of solution, the state space equation established and state space equation real part maximum
The corresponding damping ratio of value indicative calculates population fitness function, the population fitness function J (K using penalty function methodP1,
KD1,KI1) expression formula be：
Wherein, M1And M2It is the penalty factor of penalty function method, ξ0For the minimum damping ratio of setting, tfStable state is reached for system
Time (generally taking 300s), xtFor solution step response functions time t value,For the step response functions of solution
In time tfValue, x∞For steady-state value,bpFor difference coefficient, s calculates for Laplce
Son, Gsys(s) it is hydraulic turbine system open-loop transfer function.
Population fitness function in the present embodiment is the object function of particle cluster algorithm.
Preferred embodiment is further used as, it is described according to population fitness function, it is rung with Hydropower Unit in step
Should under primary frequency modulation acting characteristic it is optimal for target, using PSO Algorithm hydrogovernor optimized parameter this
Step specifically includes following steps：
S51, the proportional gain K with Hydropower Unit regulating systemP1, storage gain KI1With differential gain KD1Parameter is as excellent
The particle of change problem initializes particle populations；
S52, according to KP1、KI1And KD1Ask for corresponding population fitness function J (KP1,KD1,KI1), and then calculate particle
The fitness value of particle individual in group；
The optimal location of S53, the history optimal location that particle individual is determined according to the fitness value of calculating and the population overall situation；
The speed of particle individual and position in S54, Population Regeneration；
S55, the end condition for meeting setting is judged whether, if so, (i.e. population is global for output population global optimum
Optimal value) and its solution of the corresponding position as problem；Conversely, then return to step S52.
Particle populations are initialized in the present embodiment includes the initial value of initialization particle populations, initialization kind group velocity etc..This
Embodiment first gives one group of K when initializing particle populationsP1、KI1And KD1, then it is obtained most by the continuous iteration of particle cluster algorithm
Excellent KP1、KI1And KD1。
In step response, frequency modulation acting characteristic is optimal for target next time with Hydropower Unit for the present embodiment, by using particle
The process that group's algorithm repeats step S52 to step S54 is iterated optimizing until converging on certain damping ratio.
It is further used as preferred embodiment, the speed of particle individual and the step for position in the Population Regeneration,
Specially：
The speed of each particle and position in Population Regeneration, wherein the speed of i-th particle and position after the g times iteration
More new formula is：
In above formula,WithIt represents the g generations of i-th particle respectively and g+1 subrogates and puts,WithIs represented respectively
The g generations of i particle and the diverse vector in g+1 generations, w are inertia coeffeicent, c1And c2Respectively particle is to the trust of particle itself
Degree and the degree of belief to group, r1,r2It is the random number between [0,1], pbestiFor the optimal location of i-th of particle,
Gbest is group's optimal location (i.e. the position of population global optimum).
Preferred embodiment is further used as, the end condition for meeting setting refers to meet the minimum set by mistake
Difference reaches the pace of maximum iteration or continuous 100 generation particle less than pre-set velocity threshold value (i.e. continuous 100 generation grain
The pace of son is excessively slow).
Corresponding with the method for Fig. 1, the present invention is based on the hydrogovernor parameter tuning system of state space analysis, bags
It includes：
Frequency response coefficients calculation block, for calculating the frequency response coefficient of Asynchronous Interconnection sending load；
Open-loop transfer function and step response functions acquisition module, for establishing hydraulic turbine system open-loop transfer function, and
Solve corresponding step response functions；
State space equation is established with solving module, and water under Asynchronous Interconnection is established for the frequency response coefficient according to calculating
The state space equation of turbine and its speed governing closed-loop system, and solve the state space equation real part maximum of foundation characteristic value and
Its corresponding damping ratio；
Population fitness function establishes module, for according to solution step response functions, establish state space side
The corresponding damping ratio of characteristic value of journey and state space equation real part maximum establishes population fitness letter using penalty function method
Number；
The optimized parameter acquisition module of hydrogovernor, for according to population fitness function, being existed with Hydropower Unit
Primary frequency modulation acting characteristic under step response is optimal for target, using the optimal ginseng of PSO Algorithm hydrogovernor
Number.
Corresponding with the method for Fig. 1, the present invention is based on the hydrogovernor parameter tuning system of state space analysis, bags
It includes：
Memory, for storing program；
Processor, for loading described program to perform the water turbine governing of the present invention based on state space analysis
Device parameter tuning method.
In conclusion the present invention is based on the hydrogovernor parameter tuning methods and system of state space analysis, it is based on
State space analysis carries out microvariations (i.e. small interference) to the hydraulic turbine and its speed governing closed-loop system by state space analysis and analyzes
Draw influence of the governor parameter to the hydraulic turbine and its speed governing closed-loop system characteristic value and damping ratio, and then with Hydropower Unit in rank
The optimal primary frequency modulation acting characteristic to jump under response is target, using the optimal of particle cluster algorithm iterative solution hydrogovernor
Parameter is so that iteration optimizing converges on certain damping ratio, the advantages of having merged state space analysis and particle cluster algorithm, is keeping away
Exempt to generate the ultra-low frequency oscillation under Asynchronous Interconnection while ensure the primary frequency modulation acting characteristic of Hydropower Unit, robust to greatest extent
The strong and primary frequency modulation performance of property is good.Power industry is the composite can be widely applied to, strong robustness is efficiently solved under Asynchronous Interconnection
Ultra-low frequency oscillation problem.
The above are implementing to be illustrated to the preferable of the present invention, but the present invention is not limited to the embodiment, ripe
A variety of equivalent variations 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 contained in the application claim limited range a bit.
Claims (10)
1. the hydrogovernor parameter tuning method based on state space analysis, it is characterised in that：Comprise the following steps：
Calculate the frequency response coefficient of Asynchronous Interconnection sending load；
Hydraulic turbine system open-loop transfer function is established, and solves corresponding step response functions；
The hydraulic turbine and its state space equation of speed governing closed-loop system under Asynchronous Interconnection are established according to the frequency response coefficient of calculating,
And solve the characteristic value of the state space equation real part maximum of foundation and its corresponding damping ratio；
According to the characteristic value of the step response functions of solution, the state space equation established and state space equation real part maximum
Corresponding damping ratio establishes population fitness function using penalty function method；
It is optimal for target with primary frequency modulation acting characteristic of the Hydropower Unit under step response according to population fitness function,
Using the optimized parameter of PSO Algorithm hydrogovernor.
2. the hydrogovernor parameter tuning method according to claim 1 based on state space analysis, feature exist
In：The step for frequency response coefficient of the calculating Asynchronous Interconnection sending load, it is specially：
The disturbance occurred close to Asynchronous Interconnection sending under the rich small limit method of operation is chosen, calculates Asynchronous Interconnection sending end system
The frequency response coefficient of system load, the rich small limit method of operation refers to operate in abundance of water Smaller load pattern, described asynchronous
The frequency response COEFFICIENT K of net sending loadfCalculation formula be：
<mrow>
<msub>
<mi>K</mi>
<mi>f</mi>
</msub>
<mo>=</mo>
<mn>0.8</mn>
<mo>*</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>P</mi>
<mo>/</mo>
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mi>&Delta;</mi>
<mi>f</mi>
<mo>/</mo>
<msub>
<mi>f</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mi>R</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Wherein, Δ P/P0It coming off percentage for power, Δ P is the power change values of Asynchronous Interconnection sending before and after disturbance occurs,
P0The power of Asynchronous Interconnection sending, Δ f/f before occurring for disturbance0For stable state frequency drop percentage, Δ f is before and after disturbance occurs
The frequency departure of Asynchronous Interconnection sending, Δ f is without departing from frequency limit device dead zone, f0Asynchronous Interconnection sending end before occurring for disturbance
The frequency of system, R are the difference coefficient of unit.
3. the hydrogovernor parameter tuning method according to claim 1 based on state space analysis, feature exist
In：It is described to establish hydraulic turbine system open-loop transfer function, and the step for solve corresponding step response functions, specifically include：
Establish the open-loop transfer function of Hydropower Unit regulating system, the open-loop transfer function G of the Hydropower Unit regulating systemGm
(s) expression formula is：
<mrow>
<msub>
<mi>G</mi>
<mrow>
<mi>G</mi>
<mi>m</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>Y</mi>
<mrow>
<mi>P</mi>
<mi>I</mi>
<mi>D</mi>
</mrow>
</msub>
<mrow>
<mi>&Delta;</mi>
<mi>&omega;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>P</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>D</mi>
<mn>1</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>T</mi>
<mrow>
<mn>1</mn>
<mi>v</mi>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>K</mi>
<mrow>
<mi>I</mi>
<mn>1</mn>
</mrow>
</msub>
<mi>s</mi>
</mfrac>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>I</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mi>P</mi>
</msub>
</mrow>
<mi>s</mi>
</mfrac>
</mrow>
</mfrac>
<mfrac>
<msub>
<mi>K</mi>
<mi>W</mi>
</msub>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>T</mi>
<mrow>
<mi>R</mi>
<mn>1</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
<mo>,</mo>
</mrow>
Wherein, KP1、KI1And KD1Respectively the proportional gain of Hydropower Unit regulating system PID controller, storage gain and differential increase
Benefit, s are Laplace operator, T1vTo measure inertia time constant, bpFor difference coefficient, KWFor frequency departure amplification factor, TR1
For frequency measurement link time 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 is：
<mrow>
<msub>
<mi>G</mi>
<mrow>
<mi>G</mi>
<mi>A</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>V</mi>
</mrow>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>C</mi>
<mi>V</mi>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>P</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>D</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
<mo>+</mo>
<mfrac>
<msub>
<mi>K</mi>
<mrow>
<mi>I</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>P</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>D</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
<mo>+</mo>
<mfrac>
<msub>
<mi>K</mi>
<mrow>
<mi>I</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>T</mi>
<mrow>
<mi>o</mi>
<mi>c</mi>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
<mo>,</mo>
</mrow>
Wherein, KP2、KI2And KD2The respectively proportional gain of electrohydraulic servo system PID controller, storage gain and the differential gain, s
For Laplace operator, T1For servomotor travel feedback link time, TocTime constant is turned on and off for servomotor；
Establish the open-loop transfer function of prime mover, the open-loop transfer function G of described prime moverTw(s) expression formula is：
<mrow>
<msub>
<mi>G</mi>
<mrow>
<mi>T</mi>
<mi>w</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>P</mi>
<mi>M</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>V</mi>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>T</mi>
<mi>w</mi>
</msub>
<mi>s</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>0.5</mn>
<msub>
<mi>T</mi>
<mi>w</mi>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
<mo>,</mo>
</mrow>
Wherein, s is Laplace operator, TwStart the time for open loop water；
Hydraulic turbine system open loop is obtained according to the open-loop transfer function of Hydropower Unit regulating system, electrohydraulic servo system and prime mover
Transmission function, the hydraulic turbine system open-loop transfer function Gsys(s) expression formula is：
Gsys(s)=GGm(s)·GGA(s)·GTw(s)；
According to hydraulic turbine system open-loop transfer function, corresponding step response functions x (t) is solved.
4. the hydrogovernor parameter tuning method according to claim 1 based on state space analysis, feature exist
In：The frequency response coefficient according to calculating establishes the state space side of the hydraulic turbine and its speed governing closed-loop system under Asynchronous Interconnection
Journey, and the step for solve the characteristic value of the state space equation real part maximum of foundation and its corresponding damping ratio, specifically include：
The linearisation state space equation of Hydropower Unit regulating system, electrohydraulic servo system, prime mover and synchronous machine is obtained, and then
The hydraulic turbine and its state space equation of speed governing closed-loop system under Asynchronous Interconnection are formed, the hydraulic turbine and its tune under the Asynchronous Interconnection
The state space equation of fast closed-loop system is：
<mrow>
<mi>T</mi>
<mfrac>
<mrow>
<mi>d</mi>
<mi>x</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mi>J</mi>
<mi>x</mi>
<mo>,</mo>
</mrow>
Wherein, x is the state variable of the hydraulic turbine and its speed governing closed-loop system, and t is the time,
KP1、KI1And KD1The respectively proportional gain of Hydropower Unit regulating system PID controller, storage gain and the differential gain, T1v
To measure inertia time constant, bpFor difference coefficient, KWFor frequency departure amplification factor, TR1It is normal for frequency measurement link time
Number, KP2、KI2And KD2The respectively proportional gain of electrohydraulic servo system PID controller, storage gain and the differential gain, T1For oil
Motivation travel feedback link time, TocTime constant, T are turned on and off for servomotorWStart time, T for the water of closed-loop systemJ
For inertia time constant, KfFor the frequency response coefficient of Asynchronous Interconnection sending load, D is synchronous machine damped coefficient；
Solve the hydraulic turbine and its eigenvalue λ=σ ± j of the state space equation real part of speed governing closed-loop system maximum under Asynchronous Interconnection
ω, and its corresponding damping ratio is obtained
5. the hydrogovernor parameter tuning method according to claim 4 based on state space analysis, feature exist
In：The spy of the step response functions according to solution, the state space equation established and state space equation real part maximum
The corresponding damping ratio of value indicative, the step for establishing population fitness function using penalty function method be specially：
According to the characteristic value of the step response functions of solution, the state space equation established and state space equation real part maximum
Corresponding damping ratio calculates population fitness function, the population fitness function J (K using penalty function methodP1,KD1,
KI1) expression formula be：
<mrow>
<mi>J</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>P</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>D</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>I</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<msub>
<mi>t</mi>
<mi>f</mi>
</msub>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>&infin;</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>M</mi>
<mn>1</mn>
</msub>
<mo>*</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<msub>
<mi>t</mi>
<mi>f</mi>
</msub>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>&infin;</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>M</mi>
<mn>2</mn>
</msub>
<mo>*</mo>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>&xi;</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mi>&xi;</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Wherein, M1And M2It is the penalty factor of penalty function method, ξ0For the minimum damping ratio of setting, tfFor system reach stable state when
Between, xtFor solution step response functions time t value,For solution step response functions in time tfValue, x∞For
Steady-state value,bpFor difference coefficient, s is Laplace operator, Gsys(s) it is the hydraulic turbine
System open loop transmission function.
6. the hydrogovernor parameter tuning method according to claim 5 based on state space analysis, feature exist
In：It is described according to population fitness function, it is optimal for mesh with primary frequency modulation acting characteristic of the Hydropower Unit under step response
Mark, using PSO Algorithm hydrogovernor optimized parameter the step for, specifically include following steps：
With the proportional gain K of Hydropower Unit regulating systemP1, storage gain KI1With differential gain KD1Parameter problem as an optimization
Particle initializes particle populations；
According to KP1、KI1And KD1Ask for corresponding population fitness function J (KP1,KD1,KI1), and then calculate particle in population
The fitness value of individual；
The history optimal location of particle individual and the optimal location of the population overall situation are determined according to the fitness value of calculating；
The speed of particle individual and position in Population Regeneration；
Judge whether the end condition for meeting setting, if so, output population global optimum and its corresponding position conduct
The solution of problem；Conversely, it then returns according to KP1、KI1And KD1Ask for corresponding population fitness function J (KP1,KD1,KI1), and then
The step for calculating the fitness value of each particle in population.
7. the hydrogovernor parameter tuning method according to claim 6 based on state space analysis, feature exist
In：The speed of particle individual and the step for position in the Population Regeneration is specially：
The speed of each particle and position in Population Regeneration, wherein after the g times iteration the speed of i-th particle and position update
Formula is：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>g</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mi>g</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>g</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>v</mi>
<mrow>
<mi>g</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>wv</mi>
<mi>g</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>r</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>pbest</mi>
<mi>i</mi>
</msup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mi>g</mi>
<mi>i</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<msub>
<mi>r</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>g</mi>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mi>g</mi>
<mi>i</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
In above formula,WithIt represents the g generations of i-th particle respectively and g+1 subrogates and puts,WithIt represents respectively i-th
The g generations of particle and the diverse vector in g+1 generations, w are inertia coeffeicent, c1And c2Respectively particle is to the degree of belief of particle itself
With the degree of belief to group, r1,r2It is the random number between [0,1], pbestiFor the optimal location of i-th of particle, gbest
For group's optimal location.
8. the hydrogovernor parameter tuning method according to claim 6 based on state space analysis, feature exist
In：The end condition for meeting setting refers to meet the minimal error of setting, reaches maximum iteration or continuous 100 generation
The pace of particle is less than pre-set velocity threshold value.
9. the hydrogovernor parameter tuning system based on state space analysis, it is characterised in that：Including：
Frequency response coefficients calculation block, for calculating the frequency response coefficient of Asynchronous Interconnection sending load；
Open-loop transfer function and step response functions acquisition module, for establishing hydraulic turbine system open-loop transfer function, and solve
Corresponding step response functions；
State space equation is established with solving module, and the hydraulic turbine under Asynchronous Interconnection is established for the frequency response coefficient according to calculating
And its state space equation of speed governing closed-loop system, and solve the characteristic value of the state space equation real part maximum of foundation and its right
The damping ratio answered；
Population fitness function establishes module, for according to solution step response functions, establish state space equation with
And the corresponding damping ratio of characteristic value of state space equation real part maximum, population fitness function is established using penalty function method；
The optimized parameter acquisition module of hydrogovernor, for according to population fitness function, with Hydropower Unit in step
The optimal lower primary frequency modulation acting characteristic of response is target, using the optimized parameter of PSO Algorithm hydrogovernor.
10. the hydrogovernor parameter tuning system based on state space analysis, it is characterised in that：Including：
Memory, for storing program；
Processor, for loading described program to perform such as claim 1-8 any one of them based on state space analysis
Hydrogovernor parameter tuning method.
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| CN110456780A (en) * | 2019-09-02 | 2019-11-15 | 润电能源科学技术有限公司 | Control platform method of adjustment, device and the readable storage medium storing program for executing of automatic control system |
| CN111736471A (en) * | 2020-07-14 | 2020-10-02 | 江南大学 | Iterative feedback setting control and robust optimization method of rotary inverted pendulum |
| CN113595065A (en) * | 2021-07-19 | 2021-11-02 | 北京交通大学 | Method for inhibiting ultralow frequency oscillation of water-light complementary system |
| CN117311138A (en) * | 2023-11-30 | 2023-12-29 | 华中科技大学 | Method and system for calculating stability margin domain of control parameter of water turbine adjusting system |
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