CN108107720B - Water turbine speed regulator parameter setting method and system based on state space analysis - Google Patents
Water turbine speed regulator parameter setting method and system based on state space analysis Download PDFInfo
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Abstract
The invention discloses a method and a system for setting parameters of a hydraulic turbine governor based on state space analysis, wherein the method comprises the following steps: calculating the frequency response coefficient of the load of the asynchronous networking transmitting end system; establishing an open-loop transfer function of a water turbine system, and solving a corresponding step response function; establishing a state space equation of the water turbine and the speed regulation closed loop system thereof in the asynchronous networking according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a corresponding damping ratio; establishing a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation; and solving the optimal parameters of the water turbine speed regulator by adopting a particle swarm algorithm according to the particle swarm fitness function and aiming at the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response. The invention has strong robustness and good primary frequency modulation performance, and can be widely applied to the field of power systems.
Description
Technical Field
The invention relates to the field of power systems, in particular to a method and a system for setting parameters of a water turbine speed regulator based on state space analysis.
Background
In an asynchronous networking high-hydropower-ratio delivery end system, the speed regulator is possibly unstable due to the water hammer effect of a water turbine, and ultralow-frequency oscillation is further caused due to the fact that the load frequency adjusting effect coefficient is small and the system damping is low. The hydroelectric generating set has negative damping characteristic and is the main reason of low-frequency oscillation. Generally, the turbine and governor produce negative damping in the low frequency band, the turbine itself has a small phase lag, and when the governor has a small phase lag, positive damping is produced in the low frequency band. These are all related to the parameter setting of the governor of the hydraulic turbine.
After the southern power grid asynchronous networking scheme is implemented, the Yunnan power grid operates independently and is connected with the main grid through direct current. The power generation load of the Yunnan power grid is that the proportion of water and electricity exceeds 75%, the proportion of thermal power is less than 10%, and the balance is wind power and photovoltaic power, so that the power grid is a typical high-water-electricity-proportion power grid. The load in Yunnan power grid province accounts for about 1/3 of total power generation, the direct current outgoing load accounts for about 2/3 of total power generation, and the direct current load is approximately rigid load in the dead zone of the frequency limiter, so that the damping provided by the load in the frequency range of 49.9 Hz-50.1 Hz is greatly reduced. The reduction of the external damping coefficient and the influence of the water hammer effect cause ultralow frequency oscillation. The asynchronous test and simulation report of the Yunnan power grid also proves that if synchronous networking parameters are still adopted, the Yunnan power grid generates ultralow frequency oscillation; and the great reduction of the parameters will lead to the over-slow primary frequency modulation rate of the hydroelectric generating set.
At present, when low-Frequency oscillation caused by negative damping characteristics of a speed governor of a water turbine is dealt with, a generally adopted solution is to set a primary Frequency modulation dead zone of a generator to be larger than a direct current Frequency Limiter (FLC) dead zone, but the method is not suitable for an asynchronous networking sending-end system. Therefore, a hydro governor parameter setting scheme for an asynchronous networking delivery end system is urgently needed in the industry, and the primary frequency modulation action characteristic of a hydroelectric generating set is ensured to the maximum extent while ultralow frequency oscillation is avoided.
Disclosure of Invention
To solve the above technical problems, the present invention aims to: the method and the system for setting the parameters of the water turbine speed regulator based on state space analysis are strong in robustness and good in primary frequency modulation performance.
The first technical scheme adopted by the invention is as follows:
the method for setting the parameters of the hydraulic turbine governor based on state space analysis comprises the following steps:
calculating the frequency response coefficient of the load of the asynchronous networking transmitting end system;
establishing an open-loop transfer function of a water turbine system, and solving a corresponding step response function;
establishing a state space equation of the water turbine and the speed regulation closed loop system thereof in the asynchronous networking according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a corresponding damping ratio;
establishing a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation;
and solving the optimal parameters of the water turbine speed regulator by adopting a particle swarm algorithm according to the particle swarm fitness function and aiming at the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response.
Further, the step of calculating the frequency response coefficient of the load of the asynchronous networking sending end system specifically comprises:
selecting disturbance which is close to an asynchronous networking sending end system and occurs in a small and large limit operation mode, and calculating the frequency response coefficient of the load of the asynchronous networking sending end system, wherein the small and large limit operation mode refers to a mode of operating in a large water and small load mode, and the frequency response coefficient K of the load of the asynchronous networking sending end system isfThe calculation formula of (2) is as follows:
wherein, Δ P/P0As percentage of power shedding, Δ P is the power change value of the asynchronous networked transmitting end system before and after the disturbance occurs, P0For asynchronous networking of the power of the transmitting end system before a disturbance occurs, Δ ff0The steady-state frequency drop percentage is obtained, delta f is the frequency deviation of an asynchronous networking sending end system before and after disturbance occurs, delta f does not exceed the dead zone of a frequency limiter, and f0R is the frequency of the asynchronous networking sending end system before disturbance occurs, and is the difference adjustment coefficient of the unit.
Further, the step of establishing an open-loop transfer function of the water turbine system and solving a corresponding step response function specifically includes:
establishing an open-loop transfer function of a hydroelectric generating set regulating system, the open-loop transfer function G of the hydroelectric generating set regulating systemGmThe expression of(s) is:
wherein, KP1、KI1And KD1Proportional gain, integral gain and differential gain of a PID controller of a hydroelectric generating set regulating system are respectively, s is Laplace operator, T1vTo measure the time constant of inertia, bpTo adjust the difference coefficient, KWFor frequency deviation amplification, TR1Measuring a link time constant for the frequency;
establishing an open-loop transfer function of an electro-hydraulic servo system, the open-loop transfer function G of the electro-hydraulic servo systemGAThe expression of(s) is:
wherein, KP2、KI2And KD2Proportional gain, integral gain and differential gain of the PID controller of the electro-hydraulic servo system respectively, and s is pullThe Prasiian, T1For the servomotor stroke feedback link time, TocA time constant for starting or closing the servomotor;
establishing an open-loop transfer function of a prime mover, the open-loop transfer function G of the prime moverTwThe expression of(s) is:
where s is the Laplace operator, TwStarting time for ring-opening water;
obtaining an open-loop transfer function of a water turbine system according to the open-loop transfer functions of a hydroelectric generating set adjusting system, an electro-hydraulic servo system and a prime motor, wherein the open-loop transfer function G of the water turbine systemsysThe expression of(s) is:
Gsys(s)＝GGm(s)·GGA(s)·GTw(s)；
and solving the corresponding step response function x (t) according to the open-loop transfer function of the water turbine system.
Further, the step of establishing a state space equation of the water turbine under the asynchronous networking and a speed regulation closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a corresponding damping ratio thereof specifically comprises the following steps:
the method comprises the following steps of obtaining linear state space equations of a hydroelectric generating set adjusting system, an electro-hydraulic servo system, a prime mover and a synchronous machine, and further forming a state space equation of an asynchronous networked water turbine and a speed regulation closed loop system thereof, wherein the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof is as follows:
wherein x is the state variable of the water turbine and the speed regulation closed loop system thereof, t is time,
KP1、KI1and KD1Proportional gain, integral gain and differential gain, T, of a PID controller of a hydroelectric generating set regulation system1vTo measure the time constant of inertia, bpTo adjust the difference coefficient, KWFor frequency deviation amplification, TR1For measuring the time constant of the link, KP2、KI2And KD2Proportional gain, integral gain and differential gain, T, of the PID controller of the electro-hydraulic servo system1For the servomotor stroke feedback link time, TocFor the time constant of the opening or closing of the servomotor, TWWater start-up time for closed loop system, TJIs an inertia time constant, KfThe frequency response coefficient of the load of the asynchronous networking transmitting end system is shown, and D is the damping coefficient of the synchronous machine;
solving the maximum characteristic value lambda of the real part of the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof to obtain the corresponding damping ratio
Further, the step of establishing the particle swarm fitness function by a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation specifically comprises the following steps:
calculating a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation, wherein the particle swarm fitness function J (K) isP1,KD1,KI1) The expression of (a) is:
wherein M is1And M2Penalty factors, ξ, both in penalty function law0To set minimum damping ratio, tfTime to steady state for the system, xtTo solve for the value of the step response function at time t,
step response function for solving at time tfValue of (a), x∞In the case of a steady-state value,
bpfor the adjustment coefficient, s is the Laplace operator, Gsys(s) is the turbine system open loop transfer function.
Further, the step of solving the optimal parameters of the water turbine speed regulator by adopting a particle swarm algorithm with the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response as a target according to the particle swarm fitness function specifically comprises the following steps:
proportional gain K of hydroelectric generating set regulating systemP1Integral gain KI1And a differential gain KD1Taking the parameters as particles of an optimization problem, and initializing a particle population;
according to KP1、KI1And KD1Calculating corresponding particle swarm fitness function J (K)P1,KD1,KI1) Further calculating the fitness value of the individual particles in the particle swarm;
determining the historical optimal position of the particle individual and the optimal position of the population global according to the calculated fitness value;
updating the speed and the position of the particle individuals in the population;
judging whether a set termination condition is met, if so, outputting a particle swarm global optimum value and a position corresponding to the particle swarm global optimum value as a solution of the problem; otherwise, return to according to KP1、KI1And KD1Calculating corresponding particle swarm fitness function J (K)P1,KD1,KI1) Then further countA step of calculating a fitness value for each particle in the population of particles.
Further, the step of updating the speed and the position of the individual particles in the population specifically comprises:
and updating the speed and the position of each particle in the population, wherein the updating formula of the speed and the position of the ith particle after the g iteration is as follows:
in the above formula, the first and second carbon atoms are,
and
respectively representing the g generation position and the g +1 generation position of the ith particle,
and
respectively representing the g-th generation and the g + 1-th generation of the ith particle, w is an inertia coefficient, c1And c2The confidence of the particle to the particle itself and the confidence of the group, r1,r2Are all [0,1]Random number between, pbestiThe optimal position of the ith particle is the gbest optimal position of the population.
Further, the condition that the set termination condition is met is that a set minimum error is met, a maximum number of iterations is reached, or the advancing speed of the continuous 100 generations of particles is smaller than a preset speed threshold.
The second technical scheme adopted by the invention is as follows:
a hydraulic turbine speed regulator parameter setting system based on state space analysis comprises:
the frequency response coefficient calculation module is used for calculating the frequency response coefficient of the load of the asynchronous networking sending end system;
the open-loop transfer function and step response function acquisition module is used for establishing an open-loop transfer function of the water turbine system and solving a corresponding step response function;
the state space equation establishing and solving module is used for establishing a state space equation of the water turbine under the asynchronous networking and the speed regulating closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a damping ratio corresponding to the characteristic value;
the particle swarm fitness function establishing module is used for establishing a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation;
and the optimal parameter acquisition module of the hydraulic turbine speed regulator is used for solving the optimal parameters of the hydraulic turbine speed regulator by adopting a particle swarm algorithm according to the particle swarm fitness function and aiming at the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response.
The third technical scheme adopted by the invention is as follows:
a hydraulic turbine speed regulator parameter setting system based on state space analysis comprises:
a memory for storing a program;
and the processor is used for loading the program to execute the hydraulic turbine governor parameter setting method based on the state space analysis according to the first technical scheme.
The invention has the beneficial effects that: the invention relates to a method and a system for setting parameters of a water turbine speed regulator based on state space analysis, which are used for obtaining the influence of speed regulator parameters on the characteristic value and the damping ratio of a water turbine and a speed regulation closed loop system thereof based on the state space analysis, further combining a particle swarm algorithm, iteratively solving the optimal parameters of the water turbine speed regulator by taking the optimal primary frequency modulation action characteristic of a hydroelectric generating set under step response as a target, and comprehensively performing parameter setting on the water turbine speed regulator of an asynchronous networking transmitting end system through the state space analysis and the particle swarm algorithm, thereby avoiding the generation of ultra-low frequency oscillation under asynchronous networking, simultaneously maximally ensuring the primary frequency modulation action characteristic of the hydroelectric generating set, and having strong robustness and good primary frequency modulation performance.
Drawings
FIG. 1 is an overall flow chart of a state space analysis based hydro turbine governor parameter tuning method of the present invention;
fig. 2 is a control block diagram of the water turbine and its speed regulation closed loop system.
Detailed Description
The invention will be further explained and explained with reference to the drawings and the embodiments in the description. The step numbers in the following embodiments of the present invention are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.
Referring to fig. 1, the method for setting parameters of a hydraulic turbine governor based on state space analysis comprises the following steps:
s1, calculating the frequency response coefficient of the asynchronous networking sending end system load;
s2, establishing an open-loop transfer function of the water turbine system, and solving a corresponding step response function;
s3, establishing a state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a damping ratio corresponding to the characteristic value;
s4, establishing a particle swarm fitness function by a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation;
and S5, solving the optimal parameters of the water turbine speed regulator by adopting a particle swarm algorithm according to the particle swarm fitness function and aiming at the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response.
In this embodiment, the frequency response coefficient of the load of the asynchronous networking sending end system may be a frequency response coefficient in a small-large limit operation mode. Preferably, the optimal parameter of the hydro governor is represented by a PID parameter of a PID controller.
The particle swarm algorithm is similar to the genetic algorithm and is also an algorithm based on population iteration, but the intersection and variation of the genetic algorithm are not adopted, and the particle swarm algorithm searches by following the optimal particles in a solution space.
The method is based on state space analysis, the influence of the parameters of the speed regulator on the characteristic value and the damping ratio of the water turbine and the speed regulating closed loop system of the water turbine is analyzed through a small interference analysis method of state space analysis of the water turbine and the speed regulating closed loop system of the water turbine, the optimal primary frequency regulation action characteristic (such as the fastest primary frequency regulation rate) of the hydroelectric generating set under step response is taken as a target, the particle swarm algorithm is adopted for iterative optimization until convergence to obtain the optimal parameter, the primary frequency regulation action characteristic of the hydroelectric generating set is guaranteed to the maximum extent while the generation of ultra-low frequency oscillation under asynchronous networking is avoided, and the method is strong in robustness and good in primary frequency.
Further as a preferred embodiment, the step of calculating the frequency response coefficient of the load of the asynchronous networking sending-end system specifically includes:
selecting disturbance which is close to an asynchronous networking sending end system and occurs in a small and large limit operation mode, and calculating the frequency response coefficient of the load of the asynchronous networking sending end system, wherein the small and large limit operation mode refers to a mode of operating in a large water and small load mode, and the frequency response coefficient K of the load of the asynchronous networking sending end system isfThe calculation formula of (2) is as follows:
wherein, Δ P/P0As percentage of power shedding, Δ P is the power change value of the asynchronous networked transmitting end system before and after the disturbance occurs, P0For asynchronous networking of the power of the transmitting end system before a disturbance occurs, Δ ff0The steady-state frequency drop percentage is obtained, delta f is the frequency deviation of an asynchronous networking sending end system before and after disturbance occurs, delta f does not exceed the dead zone of a frequency limiter, and f0R is the frequency of the asynchronous networking sending end system before disturbance occurs, and is the difference adjustment coefficient of the unit. In this embodiment, the near asynchronous networking send-end system occurs in the small-large limit operation modeThe disturbance of (2) means that the distance between the position where the disturbance occurs and the value of the asynchronous networking sending end system in the small-size limit operation mode is smaller than a preset threshold value (generally, the value is a numerical value close to 0, and the numerical value is smaller).
In this embodiment, the coefficient of 0.8 makes the calculation result relatively conservative, and ensures the safe operation of the asynchronous networking sending-end system. The embodiment utilizes a small interference analysis method to calculate the frequency response coefficient of the load of the asynchronous networking sending end system.
Further as a preferred embodiment, the step of establishing an open-loop transfer function of the turbine system and solving a corresponding step response function specifically includes:
s21, establishing an open-loop transfer function of a hydroelectric generating set adjusting system, wherein the open-loop transfer function G of the hydroelectric generating set adjusting systemGmThe expression of(s) is:
wherein, KP1、KI1And KD1Proportional gain, integral gain and differential gain of a PID controller of a hydroelectric generating set regulating system are respectively, s is Laplace operator, T1vTo measure the time constant of inertia, bpTo adjust the difference coefficient, KWFor frequency deviation amplification, TR1Measuring a link time constant for the frequency;
s22, establishing an open-loop transfer function of the electro-hydraulic servo system, wherein the open-loop transfer function G of the electro-hydraulic servo systemGAThe expression of(s) is:
wherein, KP2、KI2And KD2Proportional gain, integral gain and differential gain of the PID controller of the electro-hydraulic servo system respectively, s is Laplace operator, T1For the servomotor stroke feedback link time, TocA time constant for starting or closing the servomotor;
s23, establishing an open-loop transfer function of the prime mover, wherein the open-loop transfer function G of the prime moverTwThe expression of(s) is:
where s is the Laplace operator, TwStarting time for ring-opening water;
s24, obtaining an open-loop transfer function of the water turbine system according to the open-loop transfer functions of the hydroelectric generating set adjusting system, the electro-hydraulic servo system and the prime mover, wherein the open-loop transfer function G of the water turbine systemsysThe expression of(s) is:
Gsys(s)＝GGm(s)·GGA(s)·GTw(s)；
and S25, solving a corresponding step response function x (t) according to the open-loop transfer function of the water turbine system.
The open-loop system structure of the water turbine system of the embodiment is composed of three parts, namely a hydroelectric generating set regulating system (namely a hydroelectric generating set speed regulator) based on a PID controller, an electro-hydraulic servo system and a prime motor, and after the three parts of open-loop transfer functions are respectively obtained, the open-loop transfer functions of the water turbine system can be obtained by multiplying the three parts of open-loop transfer functions. After the open-loop transfer function of the water turbine system is obtained, the corresponding step response function x (t) can be solved through frequency domain-time domain conversion (such as inverse Laplace transform).
With reference to fig. 2, as a further preferred embodiment, the step of establishing a state space equation of the water turbine under the asynchronous networking and the speed regulation closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with a maximum real part of the established state space equation and a corresponding damping ratio thereof specifically includes:
s31, linearizing a nonlinear differential-algebraic equation set describing the dynamic characteristics of the hydroelectric generating set adjusting system at an operating point to obtain a linearized state space equation of the hydroelectric generating set adjusting system (neglecting an increment symbol delta of a variable when describing a mathematical model thereof), wherein the expression of the linearized state space equation of the hydroelectric generating set adjusting system is as follows:
wherein x is1、x2、x3、x4、x5、x6And x7Are all state variables of the regulating system of the hydroelectric generating set, t is time, KWFor frequency deviation amplification, TR1For measuring the time constant of the link, KP1、KI1And KD1Proportional gain, integral gain and differential gain of a PID controller of a hydroelectric generating set regulation system, bpFor adjustment coefficients, T1vTo measure the inertia time constant;
s32, acquiring a linearized state space equation of the electro-hydraulic servo system, wherein the expression of the linearized state space equation of the electro-hydraulic servo system is as follows:
wherein x is8、x9、x10、x11、x12、x13、x14And x15Are state variables of electrohydraulic servo systems, KP2、KI2And KD2Proportional gain, integral gain and differential gain, T, of the PID controller of the electro-hydraulic servo system1For the servomotor stroke feedback Link (LVDT) time, TOCA time constant for starting or closing the servomotor;
s33, acquiring a linearized state space equation of the prime mover, wherein the expression of the linearized state space equation of the prime mover is as follows:
wherein x is16Being state variables of prime movers, TWWater start-up for closed loop systemTime;
s34, acquiring a linearized state space equation of the synchronous machine, wherein the expression of the linearized state space equation of the synchronous machine is as follows:
wherein x is17As state variables of the prime mover, KfFrequency response coefficient, T, for asynchronous networked sender system loadingJIs the inertia time constant;
according to the linearized state space equation of the hydroelectric generating set adjusting system, the electro-hydraulic servo system, the prime mover and the synchronous machine, the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof is obtained, and the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof is as follows:
wherein x is the state variable of the water turbine and the speed regulation closed loop system thereof, t is time,
T1feeding back link time for the stroke of the servomotor, and D is a damping coefficient of the synchronous machine;
s35, solving the maximum characteristic value lambda of the real part of the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof, and solving the corresponding damping ratio
As shown in fig. 2, the asynchronous networked water turbine and its closed-loop system for speed regulation in this embodiment are composed of four major parts, namely, a hydroelectric generating set regulating system (i.e., a hydroelectric generating set speed regulator), an electro-hydraulic servo system, a prime mover and a synchronous machine, based on a PID controller, and by obtaining linearized equations of all dynamic elements of the four major parts of a single-machine closed-loop system in the vicinity of a steady-state operating point, a state equation (i.e., a state space equation of the water turbine and its closed-loop system for speed regulation) after linearization of the whole system in the vicinity of. After the state space equation of the water turbine and the speed regulation closed loop system thereof is obtained, the maximum characteristic value of the real part and the corresponding damping ratio can be obtained through complex operation, and a foundation is laid for establishing and iteratively optimizing a particle swarm fitness function.
Further as a preferred embodiment, the step of establishing the particle swarm fitness function by using a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation is specifically as follows:
calculating a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation, wherein the particle swarm fitness function J (K) isP1,KD1,KI1) The expression of (a) is:
wherein M is1And M2Penalty factors, ξ, both in penalty function law0To set minimum damping ratio, tfThe time for the system to reach steady state (typically 300s), xtTo solve for the value of the step response function at time t,
step response function for solving at time tfValue of (a), x∞In the case of a steady-state value,
bpfor adjusting the difference systemNumber, s is Laplace operator, Gsys(s) is the turbine system open loop transfer function.
The particle swarm fitness function in this embodiment is an objective function of the particle swarm algorithm.
Further, as a preferred embodiment, the step of solving the optimal parameter of the hydraulic turbine speed regulator by using a particle swarm algorithm based on the particle swarm fitness function and with the optimal primary frequency modulation operating characteristic of the hydroelectric generating set under the step response as a target specifically comprises the following steps:
s51, proportional gain K of hydroelectric generating set adjusting systemP1Integral gain KI1And a differential gain KD1Taking the parameters as particles of an optimization problem, and initializing a particle population;
s52, according to KP1、KI1And KD1Calculating corresponding particle swarm fitness function J (K)P1,KD1,KI1) Further calculating the fitness value of the individual particles in the particle swarm;
s53, determining the historical optimal position of the particle individual and the optimal position of the population global according to the calculated fitness value;
s54, updating the speed and the position of the particle individuals in the population;
s55, judging whether the set termination condition is met, if so, outputting a particle swarm global optimum value (namely a population global optimum value) and a corresponding position thereof as a solution of the problem; otherwise, the process returns to step S52.
Initializing the particle population in this embodiment includes initializing an initial value of the particle population, initializing a population velocity, and the like. In this embodiment, a set of K is first set when initializing the particle groupP1、KI1And KD1Then, continuously iterating through a particle swarm algorithm to obtain the optimal KP1、KI1And KD1。
In the embodiment, the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response is taken as a target, and iterative optimization is performed by adopting a particle swarm algorithm to repeat the process from the step S52 to the step S54 until the damping ratio is converged to a certain damping ratio.
Further as a preferred embodiment, the step of updating the speed and the position of the individual particles in the population specifically comprises:
and updating the speed and the position of each particle in the population, wherein the updating formula of the speed and the position of the ith particle after the g iteration is as follows:
in the above formula, the first and second carbon atoms are,
and
respectively representing the g generation position and the g +1 generation position of the ith particle,
and
respectively representing the g-th generation and the g + 1-th generation of the ith particle, w is an inertia coefficient, c1And c2The confidence of the particle to the particle itself and the confidence of the group, r1,r2Are all [0,1]Random number between, pbestiFor the optimal position of the ith particle, gbest is the group optimal position (i.e., the position of the particle group global optimal).
Further preferably, the meeting of the set termination condition is that a set minimum error is met, a maximum number of iterations is reached, or the advancing speed of the continuous 100 generations of particles is less than a preset speed threshold (i.e. the advancing speed of the continuous 100 generations of particles is too slow).
Corresponding to the method of fig. 1, the state space analysis-based parameter setting system of the hydraulic turbine governor of the present invention comprises:
the frequency response coefficient calculation module is used for calculating the frequency response coefficient of the load of the asynchronous networking sending end system;
the open-loop transfer function and step response function acquisition module is used for establishing an open-loop transfer function of the water turbine system and solving a corresponding step response function;
the state space equation establishing and solving module is used for establishing a state space equation of the water turbine under the asynchronous networking and the speed regulating closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a damping ratio corresponding to the characteristic value;
the particle swarm fitness function establishing module is used for establishing a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation;
and the optimal parameter acquisition module of the hydraulic turbine speed regulator is used for solving the optimal parameters of the hydraulic turbine speed regulator by adopting a particle swarm algorithm according to the particle swarm fitness function and aiming at the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response.
Corresponding to the method of fig. 1, the state space analysis-based parameter setting system of the hydraulic turbine governor of the present invention comprises:
a memory for storing a program;
and the processor is used for loading the program to execute the state space analysis-based hydraulic turbine governor parameter setting method.
In summary, the method and the system for setting the parameters of the water turbine speed governor based on state space analysis of the invention are based on state space analysis, and the influence of the speed governor parameters on the characteristic values and the damping ratio of the water turbine and the speed regulation closed loop system thereof is obtained by performing small disturbance (namely small interference) analysis on the water turbine and the speed regulation closed loop system thereof through the state space analysis, so that the optimal primary frequency modulation action characteristic of the hydroelectric generating set under step response is taken as a target, the optimal parameters of the water turbine speed governor are iteratively solved by adopting a particle swarm algorithm to enable iterative optimization to converge on a certain damping ratio, the advantages of the state space analysis and the particle swarm algorithm are fused, the generation of ultra-low frequency oscillation under asynchronous networking is avoided, the primary frequency modulation action characteristic of the hydroelectric generating set is maximally ensured, and the robustness. The invention can be widely applied to the power industry, has strong robustness and effectively solves the problem of ultralow frequency oscillation under asynchronous networking.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. A method for setting parameters of a water turbine speed regulator based on state space analysis is characterized by comprising the following steps: the method comprises the following steps:
calculating the frequency response coefficient of the load of the asynchronous networking transmitting end system;
establishing an open-loop transfer function of a water turbine system, and solving a corresponding step response function;
establishing a state space equation of the water turbine and the speed regulation closed loop system thereof in the asynchronous networking according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a corresponding damping ratio;
establishing a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation;
according to the particle swarm fitness function, the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response is taken as a target, and the particle swarm algorithm is adopted to solve the optimal parameters of the hydraulic turbine speed regulator;
the open-loop transfer function of the water turbine system is established according to the product of the open-loop transfer function of the hydroelectric generating set adjusting system, the open-loop transfer function of the electro-hydraulic servo system and the open-loop transfer function of the prime mover, and the corresponding step response function is obtained by frequency domain-time domain conversion solving; the particle swarm fitness function J (K)P1,KD1,KI1) The expression of (a) is:
wherein M is1And M2Penalty factors, ξ, both in penalty function law0To set minimum damping ratio, tfTime to steady state for the system, xtTo solve for the value of the step response function at time t,
step response function for solving at time tfValue of (a), x∞In the case of a steady-state value,
bpfor the adjustment coefficient, s is the Laplace operator, Gsys(s) is the turbine system open loop transfer function; and xi is the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation.
2. The state space analysis-based governor parameter tuning method of a hydraulic turbine according to claim 1, characterized in that: the step of calculating the frequency response coefficient of the load of the asynchronous networking sending end system comprises the following steps:
selecting disturbance which is close to an asynchronous networking sending end system and occurs in a small and large limit operation mode, and calculating the frequency response coefficient of the load of the asynchronous networking sending end system, wherein the small and large limit operation mode refers to a mode of operating in a large water and small load mode, and the frequency response coefficient K of the load of the asynchronous networking sending end system isfThe calculation formula of (2) is as follows:
wherein, Δ P/P0As percentage of power shedding, Δ P is the power change value of the asynchronous networked transmitting end system before and after the disturbance occurs, P0For asynchronous networked transmitting-end system power before disturbance occurs, Δ f/f0Is the steady-state frequency drop percentage, and delta f is the asynchronous connection before and after the disturbanceFrequency deviation of network sending end system, delta f does not exceed frequency limiter dead zone, f0R is the frequency of the asynchronous networking sending end system before disturbance occurs, and is the difference adjustment coefficient of the unit.
3. The state space analysis-based governor parameter tuning method of a hydraulic turbine according to claim 1, characterized in that: the step of establishing an open-loop transfer function of the water turbine system and solving a corresponding step response function specifically comprises the following steps:
establishing an open-loop transfer function of a hydroelectric generating set regulating system, the open-loop transfer function G of the hydroelectric generating set regulating systemGmThe expression of(s) is:
wherein, KP1、KI1And KD1Proportional gain, integral gain and differential gain of a PID controller of a hydroelectric generating set regulating system are respectively, s is Laplace operator, T1vTo measure the time constant of inertia, bpTo adjust the difference coefficient, KWFor frequency deviation amplification, TR1Measuring a link time constant for the frequency;
establishing an open-loop transfer function of an electro-hydraulic servo system, the open-loop transfer function G of the electro-hydraulic servo systemGAThe expression of(s) is:
wherein, KP2、KI2And KD2Proportional gain, integral gain and differential gain of the PID controller of the electro-hydraulic servo system respectively, s is Laplace operator, T1For the servomotor stroke feedback link time, TocA time constant for starting or closing the servomotor;
establishing an open-loop transfer function of a prime mover, the open-loop transfer function G of the prime moverTw(s) watchThe expression is as follows:
where s is the Laplace operator, TwStarting time for ring-opening water;
obtaining an open-loop transfer function of a water turbine system according to the open-loop transfer functions of a hydroelectric generating set adjusting system, an electro-hydraulic servo system and a prime motor, wherein the open-loop transfer function G of the water turbine systemsysThe expression of(s) is:
Gsys(s)＝GGm(s)·GGA(s)·GTw(s)；
and solving the corresponding step response function x (t) according to the open-loop transfer function of the water turbine system.
4. The state space analysis-based governor parameter tuning method of a hydraulic turbine according to claim 1, characterized in that: the step of establishing a state space equation of the water turbine under the asynchronous networking and a speed regulation closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a corresponding damping ratio thereof specifically comprises the following steps:
the method comprises the following steps of obtaining linear state space equations of a hydroelectric generating set adjusting system, an electro-hydraulic servo system, a prime mover and a synchronous machine, and further forming a state space equation of an asynchronous networked water turbine and a speed regulation closed loop system thereof, wherein the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof is as follows:
wherein x is the state variable of the water turbine and the speed regulation closed loop system thereof, t is time,
KP1、KI1and KD1Proportional gain, integral gain and differential gain, T, of a PID controller of a hydroelectric generating set regulation system1vTo measure the time constant of inertia, bpTo adjust the difference coefficient, KWFor frequency deviation amplification, TR1For measuring the time constant of the link, KP2、KI2And KD2Proportional gain, integral gain and differential gain, T, of the PID controller of the electro-hydraulic servo system1For the servomotor stroke feedback link time, TocFor the time constant of the opening or closing of the servomotor, TWWater start-up time for closed loop system, TJIs an inertia time constant, KfThe frequency response coefficient of the load of the asynchronous networking transmitting end system is shown, and D is the damping coefficient of the synchronous machine;
solving the maximum characteristic value lambda of the real part of the state space equation of the asynchronous networked water turbine and the speed regulation closed loop system thereof to obtain the corresponding damping ratio
5. The state space analysis based hydro governor parameter tuning method of claim 4, characterized in that: the method comprises the following steps of according to a particle swarm fitness function, aiming at optimizing the primary frequency modulation action characteristic of the hydroelectric generating set under the step response, and solving the optimal parameter of the water turbine speed regulator by adopting a particle swarm algorithm, wherein the step specifically comprises the following steps:
proportional gain K of hydroelectric generating set regulating systemP1Integral gain KI1And a differential gain KD1Taking the parameters as particles of an optimization problem, and initializing a particle population;
according to KP1、KI1And KD1Finding corresponding particle swarm adaptationResponse function J (K)P1,KD1,KI1) Further calculating the fitness value of the individual particles in the particle swarm;
determining the historical optimal position of the particle individual and the optimal position of the population global according to the calculated fitness value;
updating the speed and the position of the particle individuals in the population;
judging whether a set termination condition is met, if so, outputting a particle swarm global optimum value and a position corresponding to the particle swarm global optimum value as a solution of the problem; otherwise, return to according to KP1、KI1And KD1Calculating corresponding particle swarm fitness function J (K)P1,KD1,KI1) And further calculating a fitness value of each particle in the particle group.
6. The state space analysis-based governor parameter tuning method of a hydraulic turbine according to claim 5, characterized in that: the step of updating the speed and the position of the individual particles in the population specifically comprises the following steps:
and updating the speed and the position of each particle in the population, wherein the updating formula of the speed and the position of the ith particle after the g iteration is as follows:
in the above formula, the first and second carbon atoms are,
and
respectively representing the g generation position and the g +1 generation position of the ith particle,
and
are respectively provided withRepresenting the variation vectors of the ith generation and the g +1 th generation of the ith particle, w is the inertia coefficient, c1And c2The confidence of the particle to the particle itself and the confidence of the group, r1,r2Are all [0,1]Random number between, pbestiThe optimal position of the ith particle is the gbest optimal position of the population.
7. The state space analysis-based governor parameter tuning method of a hydraulic turbine according to claim 5, characterized in that: the condition that the set termination condition is met is that the set minimum error is met, the maximum iteration times are reached or the advancing speed of the continuous 100-generation particles is smaller than a preset speed threshold value.
8. A hydraulic turbine speed regulator parameter setting system based on state space analysis is characterized in that: the method comprises the following steps:
the frequency response coefficient calculation module is used for calculating the frequency response coefficient of the load of the asynchronous networking sending end system;
the open-loop transfer function and step response function acquisition module is used for establishing an open-loop transfer function of the water turbine system and solving a corresponding step response function;
the state space equation establishing and solving module is used for establishing a state space equation of the water turbine under the asynchronous networking and the speed regulating closed loop system thereof according to the calculated frequency response coefficient, and solving a characteristic value with the maximum real part of the established state space equation and a damping ratio corresponding to the characteristic value;
the particle swarm fitness function establishing module is used for establishing a particle swarm fitness function by adopting a penalty function method according to the solved step response function, the established state space equation and the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation;
the optimal parameter acquisition module of the hydraulic turbine speed regulator is used for solving the optimal parameters of the hydraulic turbine speed regulator by adopting a particle swarm algorithm according to a particle swarm fitness function and aiming at the optimal primary frequency modulation action characteristic of the hydroelectric generating set under the step response;
wherein the open loop transfer function of the turbine system is based on waterThe method comprises the following steps that the product of an open-loop transfer function of a motor set adjusting system, an open-loop transfer function of an electro-hydraulic servo system and an open-loop transfer function of a prime mover is established, and a corresponding step response function is obtained through frequency domain-time domain conversion solving; the particle swarm fitness function J (K)P1,KD1,KI1) The expression of (a) is:
wherein M is1And M2Penalty factors, ξ, both in penalty function law0To set minimum damping ratio, tfTime to steady state for the system, xtTo solve for the value of the step response function at time t,
step response function for solving at time tfValue of (a), x∞In the case of a steady-state value,
bpfor the adjustment coefficient, s is the Laplace operator, Gsys(s) is the turbine system open loop transfer function; and xi is the damping ratio corresponding to the characteristic value with the maximum real part of the state space equation.
9. A hydraulic turbine speed regulator parameter setting system based on state space analysis is characterized in that: the method comprises the following steps:
a memory for storing a program;
a processor for loading the program to perform the state space analysis based hydro governor parameter tuning method of any of claims 1-7.
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