CN110377970B - Method and system for optimizing parameters of water turbine speed regulator in weak damping low-frequency oscillation mode - Google Patents

Method and system for optimizing parameters of water turbine speed regulator in weak damping low-frequency oscillation mode Download PDF

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CN110377970B
CN110377970B CN201910566804.0A CN201910566804A CN110377970B CN 110377970 B CN110377970 B CN 110377970B CN 201910566804 A CN201910566804 A CN 201910566804A CN 110377970 B CN110377970 B CN 110377970B
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陈亦平
杨若朴
杨荣照
张勇
唐卓尧
刘清晨
李家璐
杜旭
何越
高琴
方必武
黄济宇
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract

The invention discloses a method and a system for optimizing parameters of a water turbine speed governor in a weak damping low-frequency oscillation mode, wherein the method comprises the following steps: determining a weak damping mode related to a unit to be optimized and an oscillation frequency of the weak damping mode; establishing an open-loop transfer function of the water turbine and a regulating system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the regulating system thereof under the oscillation frequency of the weak damping oscillation mode; calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof under the step signal according to the open-loop transfer function of the water turbine and the regulating system thereof; calculating a damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system; establishing an objective function according to the calculated damping torque coefficient, the square error integral and the calculated damping ratio; and solving the optimal solution of the objective function by adopting a particle swarm algorithm to serve as the optimal parameter of the water turbine speed regulator. The invention can avoid the deterioration of the weak damping low-frequency oscillation mode while improving the frequency stability of the system, and can be widely applied to the field of power system optimization.

Description

Method and system for optimizing parameters of water turbine speed regulator in weak damping low-frequency oscillation mode
Technical Field
The invention relates to the field of power system optimization, in particular to a method and a system for optimizing parameters of a water turbine speed regulator in a weak damping low-frequency oscillation mode.
Background
In an asynchronous networking high-hydropower-proportion delivery end system, the speed regulator is possibly unstable due to the water hammer effect of a water turbine, and low-frequency oscillation is further caused due to the fact that the load frequency adjusting effect coefficient is small and the system damping is low.
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 proportion 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 Yunnan power grid is a typical high-water-electricity-proportion power grid. The load in Yunnan power grid province accounts for about 1/3 of the total power generation, the direct current outgoing load accounts for about 2/3 of the total power generation, and the direct current load is similar to a rigid load in the dead zone of the frequency limiter, so that the damping which can be provided by the load in the frequency range of 49.9 Hz-50.1 Hz is greatly reduced. The reduction of external damping coefficient and the influence of water hammer effect cause the frequency oscillation phenomenon with the oscillation period of about 10-20 s for many times, so when the PID parameters of the hydraulic turbine governor are set, the optimization is usually carried out by taking the small interference stability of the frequency as the target.
When the speed regulator of the hydroelectric generating set operates in a large network, PI control is generally adopted. For a hydraulic turbine with a water hammer time constant Tw of more than 2.5, a PID-type governor is required because the differential control is advantageous for improving the dynamic performance of a unit with a large water hammer effect constant Tw. The actual Tw measurement value of the main hydroelectric generating set of the Yunnan power grid is generally large (Tw = 3-4), so it is necessary to set a differential coefficient, but some studies show that increasing the differential coefficient may reduce the power angle stability and induce low-frequency oscillation while suppressing the frequency oscillation, so when optimizing the governor parameters, an optimization method aiming at only small disturbance stabilization of the frequency is risky.
Disclosure of Invention
To solve the above technical problems, the present invention aims to: the method and the system for optimizing the parameters of the hydro governor in the weak damping low-frequency oscillation mode are provided, so that the deterioration of the weak damping low-frequency oscillation mode is avoided while the frequency stability of the system is improved.
The technical scheme adopted by the first aspect of the embodiment of the invention is as follows:
the method for optimizing the parameters of the governor of the hydraulic turbine in the weak damping low-frequency oscillation mode comprises the following steps of:
determining a weak damping mode related to a unit to be optimized and an oscillation frequency of the weak damping mode;
establishing an open-loop transfer function of the water turbine and a regulating system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the regulating system thereof under the oscillation frequency of the weak damping oscillation mode;
calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof under the step signal according to the open-loop transfer function of the water turbine and the regulating system thereof;
calculating a damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system;
establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral and the calculated damping ratio;
and solving the optimal solution of the objective function by adopting a particle swarm algorithm to serve as the optimal parameter of the water turbine speed regulator.
Further, the step of determining the weak damping mode and the oscillation frequency thereof related to the unit to be optimized specifically includes:
calculating a characteristic value of the whole system through a small interference stability analysis program of the power system;
finding out a weak damping mode related to the unit to be optimized according to the characteristic value of the whole system, wherein the weak damping mode related to the unit to be optimized is a low-frequency oscillation mode with a damping ratio lower than a preset threshold value;
the oscillation frequency of the found weakly damped mode is determined.
Further, the step of establishing an open-loop transfer function of the water turbine and the regulating system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the regulating system thereof under the oscillation frequency of the weak damping oscillation mode specifically includes:
setting up PID speed regulator switchLoop transfer function, open loop transfer function G of said PID regulator Gm The expression of(s) is:
Figure BDA0002109769380000021
wherein, K P1 、K I1 And K D1 Proportional gain, integral gain and differential gain of PID speed regulator, s is Laplace operator, T 1v To measure the time constant of inertia, b p Is the coefficient of variation, K W As gain of the measured value, T R1 Measuring 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 system GA The expression of(s) is:
Figure BDA0002109769380000022
wherein, K P2 Is the gain of the electrohydraulic servo system, s is the Laplace operator, T 2 For the servomotor stroke feedback link time, T oc A 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 mover Tw The expression of(s) is:
Figure BDA0002109769380000031
where s is the Laplace operator, T w Is the open loop water hammer time constant;
obtaining the open-loop transfer function of the water turbine and the regulating system thereof according to the open-loop transfer function of the PID speed regulator, the open-loop transfer function of the electro-hydraulic servo system and the open-loop transfer function of the prime mover, and obtaining the open-loop transfer function G of the water turbine and the regulating system thereof sys The expression of(s) is:
G sys (s)＝G Gm (s)·G GA (s)·G Tw (s)
calculating damping torque coefficient of the water turbine and the adjusting system open-loop transfer function thereof under the oscillation frequency of the weak damping oscillation mode, wherein the water turbine and the adjusting system open-loop transfer function thereof under the oscillation frequency of the weak damping oscillation mode are provided with the oscillation frequency s = j omega i Damping torque coefficient D m The expression of (a) is:
D m ＝Re(G sys (jω i ))
wherein, re (G) sys (jω i ) Is G) sys (jω i ) Real part of, ω i For the oscillation angular frequency of the ith mode in the weak damping modes related to the unit to be optimized, i =1,2,3 … … n, where n is the total number of modes included in the weak damping modes related to the unit to be optimized.
Further, the step of calculating the square error integral of the mechanical power output by the water turbine and the adjusting system thereof according to the open-loop transfer function of the water turbine and the adjusting system thereof comprises the following specific steps:
calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof according to the open-loop transfer function of the water turbine and the regulating system thereof, and calculating the square error integral J of mechanical power output by the water turbine and the regulating system thereof according to the step signal 1 (K) The expression of (a) is:
Figure BDA0002109769380000032
wherein, Δ P m (t) is the value of the step response of the turbine and its regulating system at time t, t f Is the time, Δ P, at which the turbine and its regulating system reach a steady state value m (t f ) Step response of water turbine and regulating system thereof at t f The steady-state value of the moment in time,
Figure BDA0002109769380000033
b p for the coefficient of variation, K is the parameter of the PID speed regulator of the turbine and its regulating system, K P 、K I And K D Respectively a water turbine and a regulating system thereofProportional gain, integral gain and differential gain of the PID governor.
Further, the step of calculating the damping ratio corresponding to the maximum eigenvalue of the primary frequency modulation closed loop system specifically includes:
acquiring state space equations of a water turbine and a regulating system PID speed regulator, an electro-hydraulic servo system, a prime motor and a synchronous machine thereof, and further forming a state space equation of a single-machine primary frequency modulation closed-loop system, wherein the state space equation expression of the single-machine primary frequency modulation closed-loop system is as follows:
Figure BDA0002109769380000041
wherein x is the state variable of the single-machine primary frequency modulation closed-loop system, t is time,
Figure BDA0002109769380000042
/>
Figure BDA0002109769380000043
K P1 、K I1 and K D1 Proportional gain, integral gain and differential gain, T, of the PID governor of the water turbine and its regulating system 1v To measure the time constant of inertia, b p To adjust the difference coefficient, K W As gain of the measured value, T R1 For measuring the time constant of the link, K P2 Gain, T, of electrohydraulic servo systems 2 For the servomotor stroke feedback link time, T oc For the time constant of the opening or closing of the servomotor, T W Water hammer time constant, T, for primary frequency modulated closed loop systems J The inertia time constant is obtained, and D is the damping coefficient of the synchronous machine;
solving the maximum characteristic value lambda = sigma + j omega of the real part of the state space equation of the single-machine primary frequency modulation closed-loop system, and solving the corresponding damping ratio
Figure BDA0002109769380000051
Further, the step of establishing an objective function according to the calculated damping torque coefficient, the calculated squared error integral and the calculated damping ratio specifically includes:
determining the upper limit value and the lower limit value of parameters of a water turbine and a regulating system PID speed regulator thereof, wherein the parameters K = [ K ] of the water turbine and the regulating system PID speed regulator thereof p ,K I ,K D ]Upper limit value K of u And a lower limit value K l Satisfies the following conditions: k l ≤K≤K u Wherein, K is P 、K I And K D Proportional gain, integral gain and differential gain of the water turbine and a PID speed regulator of a regulating system of the water turbine are respectively obtained;
establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral, the calculated damping ratio and the upper limit value and the lower limit value of parameters of the water turbine and a regulating system PID speed regulator thereof, wherein the expression of the objective function J (K) is as follows:
Figure BDA0002109769380000052
wherein, J 1 (K) For the calculated square error integral, M is a penalty constant, max () is a function taking the maximum value, xi is the calculated damping ratio, xi 0 Limit of damping ratio, D m (ω i ) In order to calculate the damping torque coefficient,
Figure BDA0002109769380000053
low frequency oscillation damping torque coefficient, omega, for optimization process solution i For the oscillation angular frequency of the ith mode in the weak damping modes related to the unit to be optimized, i =1,2,3 … … n, where n is the total number of modes included in the weak damping modes related to the unit to be optimized.
Further, the step of solving the optimal solution of the objective function by using the particle swarm optimization algorithm as the optimal parameter of the hydraulic turbine governor specifically includes:
initializing initial values and speeds of particle populations and initializing parameter values of a primary frequency modulation closed-loop system by taking parameters K of a water turbine and a PID governor of a regulation system of the water turbine as particles of an optimization problem;
determining a particle swarm fitness function K according to parameters K of a water turbine and a water turbine regulation system PID speed regulator, parameters of a primary frequency modulation closed loop system and a target function * = minJ (K), and then calculate fitness value of individual particles;
determining the historical optimal position of each particle and the optimal position of the population overall according to the fitness value of each particle;
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 h particle after the g iteration is as follows:
Figure BDA0002109769380000061
in the above formula, the first and second carbon atoms are,
Figure BDA0002109769380000062
and &>
Figure BDA0002109769380000063
Represents the g-th and g + 1-th generation positions of the h-th particle, respectively>
Figure BDA0002109769380000064
And &>
Figure BDA0002109769380000065
Respectively representing the g generation and the g +1 generation of the h particle, w is an inertia coefficient, c 1 And c 2 The confidence of the particle to the particle itself and the confidence of the group, r 1 ,r 2 Are all [0,1]Random number between, pbest h The optimal position of the h particle is the gbest, and the optimal position of the group is the gbest;
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 an optimization problem, otherwise, returning to the step of closing a primary frequency modulation according to a PID speed regulator parameter KDetermining particle swarm fitness function K by parameter values and target function of ring system * = minJ (K), and a step of calculating the fitness value of each particle.
The second aspect of the embodiment of the present invention adopts the following technical solutions:
the system for optimizing the parameters of the governor of the water turbine in the weak damping low-frequency oscillation mode comprises the following modules:
the determining module is used for determining a weak damping mode related to the unit to be optimized and the oscillation frequency of the weak damping mode;
the damping torque coefficient calculation module is used for establishing an open-loop transfer function of the water turbine and the adjusting system thereof and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the adjusting system thereof under the oscillation frequency of the weak damping oscillation mode;
the square error integral calculation module is used for calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof under the step signal according to the open-loop transfer function of the water turbine and the regulating system thereof;
the damping ratio calculation module is used for calculating the damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system;
an objective function establishing module for establishing an objective function according to the calculated damping torque coefficient, the calculated squared error integral and the calculated damping ratio;
and the optimal parameter solving module is used for solving the optimal solution of the target function by adopting a particle swarm algorithm to serve as the optimal parameter of the hydraulic turbine speed governor.
Further, the determining module may specifically include:
the system-wide characteristic value calculating unit is used for calculating a system-wide characteristic value through a small interference stability analysis program of the power system;
the weak damping mode searching unit is used for searching a weak damping mode related to the unit to be optimized according to the full-system characteristic value, wherein the weak damping mode related to the unit to be optimized is a low-frequency oscillation mode with a damping ratio lower than a preset threshold value;
and an oscillation frequency determination unit for determining the oscillation frequency of the found weak damping mode.
The third aspect of the embodiment of the present invention adopts the following technical solutions:
the hydraulic turbine governor parameter optimization system of weak damping low frequency oscillation mode includes:
at least one processor;
at least one memory for storing at least one program;
when the at least one program is executed by the at least one processor, the at least one processor is caused to implement the weakly damped low frequency oscillation mode turbine governor parameter optimization method of the present invention.
One or more of the above-described embodiments of the present invention have the following advantages: the embodiment of the invention establishes the target function comprehensively according to the damping torque coefficient of the turbine and the adjusting system thereof under the oscillation frequency of the weak damping oscillation mode, the square error integral of the mechanical power output by the turbine and the adjusting system thereof under the step signal and the damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system, solves the optimal solution of the target function by adopting the particle swarm algorithm as the optimal parameter of the water turbine speed regulator, considers the influence on the weak damping low-frequency oscillation mode, improves the frequency stability of the system, avoids the deterioration of the weak damping low-frequency oscillation mode to the maximum extent and has good robustness.
Drawings
Fig. 1 is a flow chart of a method for optimizing parameters of a hydro governor in a weakly damped low frequency oscillation mode according to an embodiment of the present invention;
FIG. 2 is a control block diagram of a water turbine and its regulating system according to an embodiment of the present invention;
FIG. 3 is a control block diagram of a single-machine primary frequency modulation closed-loop system according to an embodiment of the present invention;
fig. 4 is a block diagram of a configuration of a hydro governor parameter optimization system with weak damping low-frequency oscillation mode according to an embodiment of the present invention;
fig. 5 is another structural block diagram of a hydro governor parameter optimization system with weakly damped low frequency oscillation modes according to an embodiment of the present invention.
Detailed Description
The invention will be further explained and explained with reference to the drawings and the embodiments in the specification. The step numbers in the following embodiments 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 adapted according to the understanding of those skilled in the art.
Referring to fig. 1, an embodiment of the present invention provides a method for optimizing parameters of a hydro governor in a weak damping low-frequency oscillation mode, including the following steps:
s101, determining a weak damping mode and an oscillation frequency thereof related to a unit to be optimized;
specifically, the present embodiment may calculate and screen the weak damping mode associated with the unit to be optimized through the PSD-SSAP software, and determine the oscillation frequency thereof. Step S101 can avoid deteriorating the weakly damped low frequency oscillation mode during the parameter optimization.
S102, establishing an open-loop transfer function of the water turbine and a regulating system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the regulating system thereof under the oscillation frequency of the weak damping oscillation mode;
s103, calculating the square error integral of mechanical power output by the water turbine and the adjusting system thereof in the step signal according to the open loop transfer function of the water turbine and the adjusting system thereof;
specifically, the present embodiment introduces the square error integral of the output mechanical power, and can improve the fast-moving property (i.e. single-machine operation speed) of the water turbine and the regulating system thereof as much as possible on the basis of suppressing the frequency oscillation to ensure the performance of the system.
S104, calculating a damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system;
specifically, the primary frequency modulation closed-loop system can adopt a single primary frequency modulation closed-loop system (namely, only one of the PID speed regulator, the electro-hydraulic servo system, the prime motor and the synchronous machine).
S105, establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral and the calculated damping ratio;
and S106, solving the optimal solution of the objective function by adopting a particle swarm algorithm to serve as the optimal parameter of the hydraulic governor.
Specifically, the particle swarm algorithm is similar to the genetic algorithm and is 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 particle in a solution space. Preferably, the optimal parameters of the hydro turbine governor are represented by PID parameters of the PID governor of the hydro turbine and its regulating system.
It can be seen from the above contents that, in the embodiment, the weak damping low-frequency oscillation mode related to the unit to be optimized is determined, the damping torque coefficient, the square error integral and the damping ratio in the mode are calculated, the objective function in the mode is established according to the calculation result, the influence of the small interference stability analysis of the frequency on the weak damping low-frequency oscillation mode is considered, finally, the particle swarm algorithm is adopted to iterate and optimize until convergence is obtained to obtain the optimal parameter, the deterioration of the weak damping low-frequency oscillation mode is avoided to the maximum extent while the system frequency stability is improved, the robustness is good, and the method can be widely applied to the field of power system optimization.
Further as a preferred embodiment, the step S101 of determining the weak damping mode and the oscillation frequency of the weak damping mode related to the unit to be optimized specifically includes:
s1011, calculating a characteristic value of the whole system through a small interference stability analysis program of the power system;
in particular, the PSD-SSAP software can be adopted in the power system small interference stability analysis program.
S1012, finding out a weak damping mode related to the unit to be optimized according to the full-system characteristic value, wherein the weak damping mode related to the unit to be optimized is a low-frequency oscillation mode with a damping ratio lower than a preset threshold value;
in particular, to avoid worsening the weakly damped low frequency oscillation mode during parameter optimization, the preset threshold may be 0.1 or other relatively small value.
And S1013, determining the oscillation frequency of the found weak damping mode.
In particular, the oscillation frequency of the weakly damped mode may be an angular frequency.
Supposing weak damping mode lambda related to unit to be optimized i There are n, i =1,2,3 … … n, respectively, the weak damping mode λ i There are also n oscillation angular frequencies.
Further as a preferred embodiment, the step S102 of establishing an open-loop transfer function of the water turbine and the regulating system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the regulating system thereof at the oscillation frequency of the weak damping oscillation mode specifically includes:
s1021, establishing an open-loop transfer function of the PID speed regulator, wherein the open-loop transfer function G of the PID speed regulator Gm The expression of(s) is:
Figure BDA0002109769380000091
wherein, K P1 、K I1 And K D1 Proportional gain, integral gain and differential gain of PID speed regulator, s is Laplace operator, T 1v To measure the time constant of inertia, b p To adjust the difference coefficient, K W As gain of the measured value, T R1 Measuring a link time constant for the frequency;
s1022, establishing an open-loop transfer function of the electro-hydraulic servo system, wherein the open-loop transfer function G of the electro-hydraulic servo system GA The expression of(s) is:
Figure BDA0002109769380000092
/>
wherein, K P2 Is the gain of the electrohydraulic servo system, s is the Laplace operator, T 2 For the feedback of the link time, T, of the servomotor stroke oc A time constant for starting or closing the servomotor;
s1023, establishing an open-loop transfer function of the prime mover, the open-loop transfer function G of the prime mover Tw The expression of(s) is:
Figure BDA0002109769380000093
where s is the Laplace operator, T w Is the open loop water hammer time constant;
s1024, obtaining an open-loop transfer function of the water turbine and a regulating system thereof according to the open-loop transfer function of the PID speed regulator, the open-loop transfer function of the electro-hydraulic servo system and the open-loop transfer function of the prime mover, and obtaining an open-loop transfer function G of the water turbine and the regulating system thereof sys The expression of(s) is:
G sys (s)＝G Gm (s)·G GA (s)·G Tw (s)
s1025, calculating a damping torque coefficient of the water turbine and the adjusting system open-loop transfer function thereof under the oscillation frequency of the weak damping oscillation mode, wherein the water turbine and the adjusting system open-loop transfer function thereof under the oscillation frequency of the weak damping oscillation mode are S = j ω i Damping torque coefficient D m The expression of (c) is:
D m ＝Re(G sys (jω i ))
wherein, re (G) sys (jω i ) Is G) sys (jω i ) Real part of, ω i And i =1,2,3 … … n, wherein n is the total number of modes contained in the weak damping modes related to the unit to be optimized.
Specifically, as shown in fig. 2, the water turbine and the adjusting system thereof in this embodiment are composed of a PID governor, an electro-hydraulic servo system, and the water turbine, and after the three most open-loop transfer functions are obtained respectively, the open-loop transfer functions of the water turbine and the adjusting system thereof can be obtained by multiplying the three most open-loop transfer functions. After obtaining the open-loop transfer function of the water turbine and its regulating system, S = j ω is the oscillation frequency of the weakly damped oscillation mode, which can be determined in conjunction with step S101 i And substituting the open-loop transfer function and taking the real part of the open-loop transfer function to obtain the corresponding damping torque coefficient.
Further as a preferred embodiment, the step S103 of calculating the square error integral of the mechanical power output by the water turbine and the adjusting system thereof according to the open-loop transfer function of the water turbine and the adjusting system thereof is specifically:
calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof according to the open-loop transfer function of the water turbine and the regulating system thereof, and calculating the square error integral J of mechanical power output by the water turbine and the regulating system thereof according to the step signal 1 (K) The expression of (a) is:
Figure BDA0002109769380000101
wherein, Δ P m (t) is the value of the step response of the turbine and its regulating system at time t, t f Is the time, Δ P, for the turbine and its regulating system to reach a steady state value m (t f ) Step response of water turbine and regulating system thereof at t f The steady-state value of the moment in time,
Figure BDA0002109769380000102
b p for the coefficient of variation, K is the parameter of the turbine and its regulation system PID governor, K P 、K I And K D Respectively the proportional gain, integral gain and differential gain of the water turbine and the PID speed regulator of the regulating system thereof.
Specifically, in order to improve the quick-acting performance (i.e., the single-machine operation speed) of the water turbine and the regulating system thereof as much as possible on the basis of suppressing the frequency oscillation to ensure the performance of the system, the present embodiment introduces the square error integral of the output mechanical power, and the smaller the square error integral of the output mechanical power, the better the quick-acting performance of the water turbine and the regulating system thereof. Water turbine and regulating system thereof reaching steady state value delta P m (t f ) Time t of f Typically 200s to 400s.
Further as a preferred embodiment, the step S104 of calculating the damping ratio corresponding to the maximum eigenvalue of the primary frequency modulation closed-loop system specifically includes:
s1041, obtaining state space equations of a water turbine and a regulating system PID speed regulator, an electro-hydraulic servo system, a prime motor and a synchronous machine of the water turbine, and further forming a state space equation of a single-machine primary frequency modulation closed-loop system, wherein the state space equation expression of the single-machine primary frequency modulation closed-loop system is as follows:
Figure BDA0002109769380000111
wherein x is the state variable of the single-machine primary frequency modulation closed-loop system, t is time,
Figure BDA0002109769380000112
Figure BDA0002109769380000121
/>
K P1 、K I1 and K D1 Proportional gain, integral gain and differential gain, T, of the PID governor of the water turbine and its regulating system 1v To measure the time constant of inertia, b p To adjust the difference coefficient, K W As gain of the measured value, T R1 Measuring the time constant, K, of the cell for frequency P2 For gain of electrohydraulic servo systems, T 2 For the servomotor stroke feedback link time, T oc For the time constant, T, of the opening or closing of the servomotor W Water hammer time constant, T, for primary frequency modulation closed loop system J Is an inertia time constant, and D is a damping coefficient of the synchronous machine;
s1042, solving the maximum characteristic value lambda = sigma + j omega of the real part of the state space equation of the single-machine primary frequency modulation closed-loop system, and solving the corresponding damping ratio
Figure BDA0002109769380000122
Specifically, as shown in fig. 3, the single-machine primary frequency modulation closed-loop system of this embodiment is composed of a synchronous machine, the water turbine of fig. 2 and a regulating system thereof, that is, the single-machine primary frequency modulation closed-loop system is composed of four major parts, namely, a PID speed regulator, an electro-hydraulic servo system, a prime mover and a synchronous machine, and by obtaining linearized equations of all dynamic elements of the four major parts of the single-machine closed-loop system near steady-state operating points, a state equation after linearization of the whole system near a steady-state value (that is, a state space equation of the single-machine primary frequency modulation closed-loop system) can be formed. After the state space equation of the single-machine primary frequency modulation closed-loop system is obtained, the maximum characteristic value of the part of the single-machine primary frequency modulation closed-loop system and the corresponding damping ratio can be obtained through complex operation, and a foundation is laid for establishing the target function.
In fig. 3, the transfer function of the synchronous machine can be simplified as:
Figure BDA0002109769380000123
further preferably, the step S105 of establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral and the calculated damping ratio specifically includes:
s1051, determining the upper limit value and the lower limit value of parameters of a water turbine and a PID speed regulator of a regulating system of the water turbine, wherein the parameters K = [ K ] of the water turbine and the PID speed regulator of the regulating system of the water turbine p ,K I ,K D ]Upper limit value K of u And a lower limit value K l Satisfies the following conditions: k l ≤K≤K u Wherein, K is P 、K I And K D Respectively the proportional gain, integral gain and differential gain of the water turbine and the PID speed regulator of the regulating system thereof;
s1052, establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral, the calculated damping ratio and the upper limit value and the lower limit value of the parameters of the PID speed regulator of the water turbine and the regulating system thereof, wherein the expression of the objective function J (K) is as follows:
Figure BDA0002109769380000131
wherein, J 1 (K) For the calculated square error integral, M is a penalty constant, max () is a function taking the maximum value, xi is the calculated damping ratio, xi 0 Limit of damping ratio, D m (ω i ) For the purpose of the calculated damping torque coefficient,
Figure BDA0002109769380000132
low frequency oscillation damping torque coefficient, omega, for optimization process solution i And i =1,2,3 … … n, wherein n is the total number of modes contained in the weak damping modes related to the unit to be optimized.
Specifically, the present embodiment converts the constraint problem into the unconstrained problem by using a penalty function, so as to obtain an objective function. The penalty constant M may take a larger value such as 10000.
Further as a preferred embodiment, the step S106 of solving the optimal solution of the objective function by using a particle swarm algorithm as the optimal parameter of the hydro governor specifically includes:
s1061, initializing initial values and speeds of particle populations by taking parameters K of a water turbine and a PID speed regulator of a regulating system of the water turbine as particles of an optimization problem, and initializing parameter values of a primary frequency modulation closed-loop system;
s1062, determining a particle swarm fitness function K according to parameters K of a water turbine and a water turbine regulation system PID speed regulator, parameters of a primary frequency modulation closed loop system and a target function * = minJ (K), and then calculating the fitness value of each particle;
s1063, determining the historical optimal position of each particle and the optimal position of the population global according to the fitness value of the particle individual;
s1064, updating the speed and the position of each particle in the population, wherein the updating formula of the speed and the position of the h particle after the g iteration is as follows:
Figure BDA0002109769380000133
in the above formula, the first and second carbon atoms are,
Figure BDA0002109769380000141
and &>
Figure BDA0002109769380000142
Represents the g-th and g + 1-th generation positions of the h-th particle, respectively>
Figure BDA0002109769380000143
And &>
Figure BDA0002109769380000144
Respectively representing the g generation and the g +1 generation of the h particle, w is an inertia coefficient, c 1 And c 2 The trust level of the particle to the particle and the trust level of the group, r 1 ,r 2 Are all [0,1]Random number between, pbest h The optimal position of the h particle is the gbest, and the optimal position of the group is the gbest;
s1065, judging whether the set termination condition is met, if so, outputting the global optimal value of the particle swarm and the corresponding position of the global optimal value as a solution of an optimization problem, otherwise, returning to determine a particle swarm fitness function K according to the PID speed regulator parameter K, the parameter value of the primary frequency modulation closed-loop system and the target function * = minJ (K), and step S1062 of calculating a fitness value of each particle.
Specifically, in steps S1061 and S1062, the parameter value of the primary frequency modulation closed-loop system refers to other parameters of the stand-alone primary frequency modulation closed-loop system except for the PID governor parameter K.
In this embodiment, in order to avoid not deteriorating the weak damping low-frequency oscillation mode in the parameter optimization process, the objective function J (K) needs to be the minimum value, so the particle swarm fitness function K of the particle swarm algorithm * = minJ (K). In this embodiment, the optimal solution of the objective function (i.e., the solution of the particle swarm fitness function) can be finally obtained by repeating the iterative optimization operations in steps S1062 to S1065.
The set termination condition means that a set minimum error is met, a maximum number of iterations is reached, or the advancing speed of the continuous generation 100 particles is smaller than a preset speed threshold (i.e. the advancing speed of the continuous generation 100 particles is too slow).
Referring to fig. 4, an embodiment of the present invention further provides a system for optimizing parameters of a hydro governor in a weak damping low-frequency oscillation mode, including the following modules:
the determining module 201 is used for determining a weak damping mode related to the unit to be optimized and the oscillation frequency of the weak damping mode;
the damping torque coefficient calculation module 202 is used for establishing an open-loop transfer function of the water turbine and the adjusting system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the adjusting system thereof under the oscillation frequency of the weak damping oscillation mode;
the square error integral calculation module 203 is used for calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof according to the open-loop transfer function of the water turbine and the regulating system thereof;
the damping ratio calculation module 204 is used for calculating a damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed-loop system;
an objective function establishing module 205 for establishing an objective function based on the calculated damping torque coefficient, the calculated squared error integral and the calculated damping ratio;
and the optimal parameter solving module 206 is configured to solve the optimal solution of the objective function by using a particle swarm algorithm as the optimal parameter of the hydraulic governor.
Referring to fig. 4, as a further preferred embodiment, the determining module 201 specifically includes:
a total-system characteristic value calculation unit 2011, configured to calculate a total-system characteristic value through a small interference stability analysis program of the power system;
the weak damping mode searching unit 2012 is configured to find a weak damping mode related to the unit to be optimized according to the full-system characteristic value, where the weak damping mode related to the unit to be optimized is a low-frequency oscillation mode with a damping ratio lower than a preset threshold;
an oscillation frequency determining unit 2013 for determining the oscillation frequency of the found weak damping mode.
The contents in the above method embodiments are all applicable to the present system embodiment, the functions specifically implemented by the present system embodiment are the same as those in the above method embodiment, and the beneficial effects achieved by the present system embodiment are also the same as those achieved by the above method embodiment.
Referring to fig. 5, an embodiment of the present invention further provides a system for optimizing parameters of a hydro governor in a weakly damped low-frequency oscillation mode, including:
at least one processor 301;
at least one memory 302 for storing at least one program;
when executed by the at least one processor 301, causes the at least one processor 301 to implement the weakly damped low frequency oscillation mode governor parameter optimization method of the present invention.
The contents in the above method embodiments are all applicable to the present system embodiment, the functions specifically implemented by the present system embodiment are the same as those in the above method embodiment, and the beneficial effects achieved by the present system embodiment are also the same as those achieved by the above method embodiment.
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 (10)

1. The method for optimizing the parameters of the water turbine speed regulator in the weak damping low-frequency oscillation mode is characterized by comprising the following steps of: the method comprises the following steps:
determining a weak damping mode related to a unit to be optimized and an oscillation frequency of the weak damping mode;
establishing an open-loop transfer function of the water turbine and the adjusting system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the adjusting system thereof under the oscillation frequency of the weak damping oscillation mode;
calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof under the step signal according to the open-loop transfer function of the water turbine and the regulating system thereof;
calculating a damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system;
establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral and the calculated damping ratio;
and solving the optimal solution of the objective function by adopting a particle swarm algorithm to serve as the optimal parameter of the water turbine speed regulator.
2. The weakly damped low frequency oscillation mode hydro governor parameter optimization method of claim 1 further comprising: the step of determining the weak damping mode and the oscillation frequency thereof related to the unit to be optimized specifically comprises the following steps:
calculating a characteristic value of the whole system through a small interference stability analysis program of the power system;
finding out a weak damping mode related to the unit to be optimized according to the full-system characteristic value, wherein the weak damping mode related to the unit to be optimized is a low-frequency oscillation mode with a damping ratio lower than a preset threshold;
the oscillation frequency of the found weakly damped mode is determined.
3. The weakly damped low frequency oscillation mode hydro governor parameter optimization method of claim 1 further comprising: the method comprises the steps of establishing an open-loop transfer function of the water turbine and a regulating system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the regulating system thereof under the oscillation frequency of a weak damping oscillation mode, and specifically comprises the following steps:
establishing an open loop transfer function of a PID governor, the open loop transfer function G of the PID governor Gm The expression of(s) is:
Figure FDA0004094085500000011
wherein, K P1 、K I1 And K D1 Proportional gain, integral gain and differential gain of PID speed regulator, s is Laplace operator, T 1v To measure the time constant of inertia, b p To adjust the difference coefficient, K W As gain of the measured value, T R1 Measuring a link time constant for the frequency;
establishing an electrohydraulic servo systemThe open-loop transfer function of the electro-hydraulic servo system, and the open-loop transfer function G of the electro-hydraulic servo system GA The expression of(s) is:
Figure FDA0004094085500000021
wherein, K P2 Is the gain of the electrohydraulic servo system, s is the Laplace operator, T 2 For the feedback of the link time, T, of the servomotor stroke oc A 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 mover Tw The expression of(s) is:
Figure FDA0004094085500000022
where s is the Laplace operator, T w Is the open loop water hammer time constant;
obtaining the open-loop transfer function of the water turbine and the regulating system thereof according to the open-loop transfer function of the PID speed regulator, the open-loop transfer function of the electro-hydraulic servo system and the open-loop transfer function of the prime mover, and obtaining the open-loop transfer function G of the water turbine and the regulating system thereof sys The expression of(s) is:
G sys (s)＝G Gm (s)·G GA (s)·G Tw (s)
calculating damping torque coefficient of the water turbine and the adjusting system open-loop transfer function thereof under the oscillation frequency of the weak damping oscillation mode, wherein the water turbine and the adjusting system open-loop transfer function thereof under the oscillation frequency of the weak damping oscillation mode are provided with the oscillation frequency s = j omega i Damping torque coefficient D m The expression of (a) is:
D m ＝Re(G sys (jω i ))
wherein, re (G) sys (jω i ) Is G) sys (jω i ) Real part of, ω i For the oscillation angular frequency of the ith mode in the weak damping mode related to the unit to be optimized, i =1,2,3 … … n is the unit to be optimizedThe total number of modes contained by the group-related weakly damped modes.
4. The method for optimizing parameters of a governor of a hydro turbine having weakly damped low frequency oscillation modes of claim 1, wherein: the step of calculating the square error integral of mechanical power output by the water turbine and the adjusting system thereof according to the step signal by the open-loop transfer function of the water turbine and the adjusting system thereof is specifically as follows:
calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof according to the open-loop transfer function of the water turbine and the regulating system thereof, and calculating the square error integral J of mechanical power output by the water turbine and the regulating system thereof according to the step signal 1 (K) The expression of (a) is:
Figure FDA0004094085500000031
wherein, Δ P m (t) is the value of the step response of the turbine and its regulating system at time t, t f Is the time, Δ P, at which the turbine and its regulating system reach a steady state value m (t f ) Step response of water turbine and regulating system thereof at t f The steady-state value of the moment in time,
Figure FDA0004094085500000032
s is Laplace operator, b p For the coefficient of variation, K is the parameter of the turbine and its regulation system PID governor, K P 、K I And K D Respectively the proportional gain, integral gain and differential gain of the water turbine and the PID speed regulator of the regulating system thereof.
5. The weakly damped low frequency oscillation mode hydro governor parameter optimization method of claim 1 further comprising: the step of calculating the damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system specifically comprises the following steps:
acquiring state space equations of a water turbine and a regulating system PID speed regulator, an electro-hydraulic servo system, a prime motor and a synchronous machine thereof, and further forming a state space equation of a single-machine primary frequency modulation closed-loop system, wherein the state space equation expression of the single-machine primary frequency modulation closed-loop system is as follows:
Figure FDA0004094085500000033
wherein x is the state variable of the single-machine primary frequency modulation closed-loop system, t is time,
Figure FDA0004094085500000034
Figure FDA0004094085500000041
K P1 、K I1 and K D1 Proportional gain, integral gain and differential gain, T, of the PID governor of the water turbine and its regulating system 1v To measure the time constant of inertia, b p To adjust the difference coefficient, K W As gain of the measured value, T R1 For measuring the time constant of the link, K P2 For gain of electrohydraulic servo systems, T 2 For the servomotor stroke feedback link time, T oc For the time constant of the opening or closing of the servomotor, T W Water hammer time constant, T, for primary frequency modulation closed loop system J The inertia time constant is obtained, and D is the damping coefficient of the synchronous machine;
solving the maximum characteristic value lambda = sigma + j omega of the real part of the state space equation of the single-machine primary frequency modulation closed-loop system, and solving the corresponding damping ratio
Figure FDA0004094085500000042
6. The weakly damped low frequency oscillation mode hydro governor parameter optimization method of claim 1 further comprising: the step of establishing an objective function according to the calculated damping torque coefficient, the calculated squared error integral and the calculated damping ratio specifically comprises:
determining the upper limit value and the lower limit value of parameters of a water turbine and a regulating system PID speed regulator thereof, wherein the parameters K = [ K ] of the water turbine and the regulating system PID speed regulator thereof p ,K I ,K D ]Upper limit value K of u And a lower limit value K l Satisfies the following conditions: k l ≤K≤K u Wherein, K is P 、K I And K D Proportional gain, integral gain and differential gain of the water turbine and a PID speed regulator of a regulating system of the water turbine are respectively obtained;
establishing an objective function according to the calculated damping torque coefficient, the calculated square error integral, the calculated damping ratio and the upper limit value and the lower limit value of parameters of the water turbine and a regulating system PID speed regulator thereof, wherein the expression of the objective function J (K) is as follows:
Figure FDA0004094085500000051
wherein, J 1 (K) For the calculated square error integral, M is a penalty constant, max () is a function taking the maximum value, xi is the calculated damping ratio, xi 0 Limit of damping ratio, D m (ω i ) For the purpose of the calculated damping torque coefficient,
Figure FDA0004094085500000057
low frequency oscillation damping torque coefficient, omega, for optimization process solution i For the oscillation angular frequency of the ith mode in the weak damping modes related to the unit to be optimized, i =1,2,3 … … n, where n is the total number of modes included in the weak damping modes related to the unit to be optimized.
7. The method for optimizing parameters of a governor of a hydro turbine having weakly damped low frequency oscillation modes of claim 6, wherein: the step of solving the optimal solution of the objective function by adopting the particle swarm algorithm as the optimal parameter of the hydraulic turbine governor specifically comprises the following steps:
initializing initial values and speeds of particle populations and initializing parameter values of a primary frequency modulation closed-loop system by taking parameters K of a water turbine and a PID speed regulator of a regulating system of the water turbine as particles of an optimization problem;
determining a particle swarm fitness function K according to parameters K of a water turbine and a water turbine regulation system PID speed regulator, parameters of a primary frequency modulation closed loop system and a target function * = min J (K), and then calculating the fitness value of each particle;
determining the historical optimal position of each particle and the optimal position of the population overall situation according to the fitness value of each particle;
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 h particle after the g iteration is as follows:
Figure FDA0004094085500000052
in the above-mentioned formula, the compound has the following structure,
Figure FDA0004094085500000053
and &>
Figure FDA0004094085500000054
Represents the g-th and g + 1-th generation positions of the h-th particle, respectively>
Figure FDA0004094085500000055
And &>
Figure FDA0004094085500000056
Respectively representing the g generation and the g +1 generation of the h particle, w is an inertia coefficient, c 1 And c 2 The confidence of the particle to the particle itself and the confidence of the group, r 1 ,r 2 Are all [0,1]Random number between, pbest h The optimal position of the h particle is the gbest, and the optimal position of the group is the gbest;
judging whether the set termination condition is met, if so, outputting particlesAnd taking the global optimal value of the group and the corresponding position thereof as a solution of an optimization problem, otherwise, returning to determine a particle swarm fitness function K according to the PID speed regulator parameter K, the parameter value of the primary frequency modulation closed-loop system and the target function * And (K) = min J (K), and calculating the fitness value of each particle.
8. The hydraulic turbine governor parameter optimization system of weak damping low frequency oscillation mode, its characterized in that: the system comprises the following modules:
the determining module is used for determining a weak damping mode related to the unit to be optimized and the oscillation frequency of the weak damping mode;
the damping torque coefficient calculation module is used for establishing an open-loop transfer function of the water turbine and the adjusting system thereof, and calculating a damping torque coefficient of the open-loop transfer function of the water turbine and the adjusting system thereof under the oscillation frequency of the weak damping oscillation mode;
the square error integral calculation module is used for calculating the square error integral of mechanical power output by the water turbine and the regulating system thereof under the step signal according to the open-loop transfer function of the water turbine and the regulating system thereof;
the damping ratio calculation module is used for calculating the damping ratio corresponding to the maximum characteristic value of the primary frequency modulation closed loop system;
an objective function establishing module for establishing an objective function according to the calculated damping torque coefficient, the calculated squared error integral and the calculated damping ratio;
and the optimal parameter solving module is used for solving the optimal solution of the target function by adopting a particle swarm algorithm to serve as the optimal parameter of the water turbine speed regulator.
9. The weakly damped low frequency oscillation mode hydro governor parameter optimization system of claim 8, wherein: the determining module specifically includes:
the system-wide characteristic value calculating unit is used for calculating a system-wide characteristic value through a small interference stability analysis program of the power system;
the weak damping mode searching unit is used for searching a weak damping mode related to the unit to be optimized according to the full-system characteristic value, wherein the weak damping mode related to the unit to be optimized is a low-frequency oscillation mode with a damping ratio lower than a preset threshold value;
and the oscillation frequency determining unit is used for determining the oscillation frequency of the found weak damping mode.
10. The hydraulic turbine governor parameter optimization system of weak damping low frequency oscillation mode, its characterized in that: the method comprises the following steps:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the weakly damped low frequency oscillation mode hydro governor parameter optimization method of any of claims 1-7.
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