CN113093523A - Regional load frequency fractional order PID (proportion integration differentiation) optimization control method for pumped storage power station - Google Patents

Regional load frequency fractional order PID (proportion integration differentiation) optimization control method for pumped storage power station Download PDF

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CN113093523A
CN113093523A CN202110358946.5A CN202110358946A CN113093523A CN 113093523 A CN113093523 A CN 113093523A CN 202110358946 A CN202110358946 A CN 202110358946A CN 113093523 A CN113093523 A CN 113093523A
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骆钊
高培淇
王菁慧
林铮
刘可真
沈赋
耿家璐
代莹皓
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Kunming University of Science and Technology
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Abstract

The invention discloses a fractional order PID (proportion integration differentiation) optimization control method for regional load frequency of a pumped storage power station, which comprises the steps of firstly, building a two-regional load frequency control model of the pumped storage power station based on an IEEE (institute of electrical and electronics engineers) standard; secondly, designing a fractional order PID controller, and optimizing parameters of the fractional order PID controller by adopting a PSO algorithm; and finally, performing simulation verification on a two-region load frequency control model containing the pumped storage power station built based on the IEEE standard, wherein simulation results show that a fractional order PID controller optimized by a PSO algorithm shows stronger robustness and stability in region load frequency control, and for load frequency control participated by the pumped storage power station, the frequency recovery time can be shortened, and the dynamic performance of the system is improved.

Description

Regional load frequency fractional order PID (proportion integration differentiation) optimization control method for pumped storage power station
Technical Field
The invention belongs to the technical field of electric power, and particularly relates to a fractional order PID (proportion integration differentiation) optimization control method for regional load frequency of a pumped storage power station.
Background
The pumped storage is used as a mature energy storage technology, has the advantages of large capacity, good economy, environmental protection, cleanness and the like, can fully exert the frequency modulation potential of the traditional unit through the pumped storage power station, improves the frequency modulation performance of the conventional unit, effectively solves the problem of power grid frequency fluctuation caused by large-scale grid connection of new energy, and has great significance.
In recent years, domestic and foreign scholars have made a great deal of research on controllers in two-region models in order to improve the dynamic performance of power grids. The currently common controller is a proportional-integral-derivative (PID) controller, has the characteristics of simple structure, convenient design, high operational reliability and the like, and is widely used for actual industrial control. The Monausa-nux et al provides a load frequency control method for a multi-region interconnected power system by combining the advantages of synovial membrane control and PI control, and simultaneously exerts the advantages of proportional-integral control and sliding mode control based on new region control deviation. A research room of Shanghai university of traffic establishes two-region control models of the power generation condition and the pumping condition of a pumped storage power station, designs a nonlinear-based fuzzy logic controller of a load frequency control model, and adopts a traditional PI (proportional integral) controller and the fuzzy logic controller to perform simulation research on the nonlinear load frequency control model.
As the fractional order theory introduces additional parameters, the dynamic adjustment range of the system is expanded, and the regulation and control capability is better. The robustness of a Fractional Order PID (proportional integral PID) controller and the robustness of a traditional PID controller are analyzed and compared in a two-region load frequency control model, and the fact that the Fractional Order PID (FOPID) controller has stronger robustness is proved in a multi-region interconnection model. The fractional order PID controller is applied to the simulation analysis of the two-region pumped storage power station, the approximation of the fractional order differential operator is realized through an indirect approximation algorithm, and the result shows that the fractional order PID controller has a better control effect compared with the traditional PID controller.
However, the PID control and the fractional PID control are mainly based on empirical parameters, so that on one hand, the control difference of the two controllers under actual conditions cannot be objectively compared, and on the other hand, the simulation result obtained by the empirical parameters is difficult to objectively verify whether the difference of the simulation result is the advantage of the controller or the defect caused by insufficient parameter setting, and the control performance of the controller is easily limited. Therefore, it is a research focus to improve the control performance of the controller through parameter optimization. A fractional order PID control parameter is set by using a self-adaptive Particle Swarm Optimization algorithm, the method is applied to a typical nonlinear system, a PSO (Particle Swarm Optimization) algorithm is used for optimizing key parameters in an active disturbance rejection controller, simulation verification is carried out in a pumped storage two-region interconnected power grid model, and researches show that the frequency modulation effect of a pumped storage power station can be better played through iterative Optimization of the PSO algorithm.
Disclosure of Invention
The technical problem is as follows: the technical problem to be solved by the invention is as follows: the control method has stronger robustness and stability in regional load frequency control, and can shorten the frequency recovery time and improve the dynamic performance of the system for the load frequency control participated by the pumped storage power station.
The technical scheme is as follows: in order to solve the technical problem, the invention provides a regional load frequency fractional order PID optimization control method of a pumped storage power station, which specifically comprises the following steps:
step S1: building a two-region load frequency control model containing a pumped storage power station based on an IEEE standard;
step S2: establishing a fractional order PID controller model;
step S3: setting a fitness function by adopting a particle swarm algorithm PSO, and optimizing parameters of a fractional order PID controller model;
step S4: and (4) adding the optimized fractional order PID controller model in the step (S3) into the two-region load frequency control model established in the step (S1), and respectively simulating and verifying the frequency regulation effect under the working conditions of power generation and water pumping.
In step S1, the process of building a two-region load frequency control model of the pumped storage power station based on the IEEE standard includes:
step S11: set up unit model
The transfer function model of the steam turbine set is:
Figure BDA0003004690520000021
the transfer function model of the hydraulic turbine set is as follows:
Figure BDA0003004690520000022
in the above formula, KτT tau is the reheater time constant, tau is the ratio of the power generated by the steam in the high pressure cylinder section to the total power of the turbinetIs the time constant of the steam chamber and the main steam inlet volume; t iswThe starting time of water is s is a Laplace transform operator;
the transfer function model of the speed regulator of the steam turbine set is as follows:
Figure BDA0003004690520000031
the transfer function model of the water turbine set speed regulator is as follows:
Figure BDA0003004690520000037
in the above formula, in the above formula: t isgThe time constant of the speed regulator is shown, s is a Laplace transform operator, and R is a difference adjustment coefficient of the hydraulic turbine set; digital electrohydraulic governor system for describing governor of water turbineOperating conditions, Kp， Ki，KdRespectively the proportional, integral and differential gains of the digital electro-hydraulic speed regulating system, and f is the system frequency;
step S12: constructing a transfer function model of the tie line power deviation as follows:
Figure BDA0003004690520000032
in the formula, delta PtieijA slight increment of tie line flow power; delta fi，△fjFrequency deviations of i and j regions, respectively; t isijFor the tie line synchronization coefficient, the calculation formula is as follows:
Figure BDA0003004690520000033
in the formula, XijIs a circuit reactance;
Figure BDA0003004690520000034
rated power for zone i; thetai，θjVoltage angles at two ends of a connecting line; vi，VjIs the voltage across the tie line;
synchronous power coefficient aijThe expression of (a) is:
Figure BDA0003004690520000035
in the formula (I), the compound is shown in the specification,
Figure BDA0003004690520000036
the rated power of the generator set of the control area j;
step S13: determining the area control error ACE as:
ACE＝ΔPtie+βΔf (8)
where Δ f is the system frequency deviation at the time of disturbance, Δ PtieExchanging power offsets for a tieAnd β is a regional frequency response coefficient defined as:
βi＝Di+1/Ri (9)
in the formula, RiIs the adjustment coefficient; diIs the load damping coefficient;
step S14: the transfer function model after the speed regulator linearization with the speed regulation dead zone is constructed as follows:
Figure BDA0003004690520000041
in the formula, N1And N2Coefficients of a second term and a third term of the nonlinear function after Fourier series expansion; t isgIs the time constant of the governor; omega0Is the sinusoidal input signal frequency.
In step S2, the design procedure of the fractional PID controller is as follows:
step S21: the transfer function model for constructing the fractional order PID controller model is as follows:
C(s)＝Kp+Kis-λ+Kdsμ (11)
in the formula, Kp，Ki，KdProportional, integral and differential coefficients; 1/sλIs an integral operator; sμFor the differential operator, λ and μ are the integral order and the differential order, respectively;
step S22: the fractional calculus operator is defined as follows:
Figure BDA0003004690520000042
in the above formula, a and t are upper and lower limits of differentiation or integration, and alpha is the order of calculus;
step S23: setting fractional calculus operator in frequency band [ omega ]b,ωh]The description is performed by using a fractional transfer function K(s), which is:
Figure BDA0003004690520000043
in the above formula, alpha is more than 0 and less than 1, and alpha is the differential order of fractional order; s is a differential operator; b is greater than 0, d is greater than 0 and is an adjustable parameter;
the specific expression of the Oustaloup approximation is as follows:
Figure BDA0003004690520000044
in the formula: k is 1, 2, …, N,
where the pole ωkZero ω'kAnd the gain K is expressed as:
Figure BDA0003004690520000051
constructing an Oustaloup filter based on the formulas (10) and (11), and determining omega by the formula (11)k，ω’kAnd K, constructing a transfer function of the Oustaloup filter through the formula (10), and obtaining a final fractional order controller PID model through a standard integer order transfer function module.
In step S3, a particle swarm algorithm PSO is used to set a fitness function, and the process of optimizing the parameters of the fractional PID controller model is as follows:
step S31: the velocity update and the position update of the particles in the particle swarm are:
Figure BDA0003004690520000052
in the above formula, ω is the inertia factor, c1And c2For the acceleration factor, rand represents [0, 1 ]]Random number between, PiFor individual history optimization, PgThe global optimization is achieved; x is the number ofiIs the position vector of the ith particle, viIs the velocity vector of the ith particle, and t represents the t iteration;
step S32: the fitness function is set as:
Figure BDA0003004690520000053
in the formula: kp，Ki，KdProportional, integral and differential coefficients; λ and μ are the integration order and the differentiation order, respectively; t is tsFor a stabilization time, trFor rise time, xi1，ξ2，ξ3Is a weight coefficient;
step S33: determining optimization parameters of the fractional order controller PID:
step 1: initializing a particle swarm, and setting the particle swarm scale, the maximum iteration times and related parameters;
step 2: step S31 is executed to update the particle positions and then assign the parameters K in the fitness function in step S32p、Ki、Kdμ and λ;
and step 3: running a two-region load frequency control model and returning an adaptive value f'fitness；
And 4, step 4: f 'is judged'fitness(t)＜FitminOr Iter>MaxIter, where f'fitness(t) is the fitness function, FitminFor the minimum adaptation value, Iter is the iteration number, and MaxIter is the maximum iteration number; if the condition is met, directly jumping to the step 6, and if the condition is not met, executing the step 5;
and 5: updating the particle speed and position according to the individual optimal adaptive value and the global optimal adaptive value, returning to the step 2, and continuously executing optimization;
step 6: outputting an optimized parameter K of a fractional order controller PIDp、Ki、KdMu and lambda.
Has the advantages that:
compared with the prior art, the invention has the following advantages: the invention provides a fractional order PID optimization control method for regional load frequency of a pumped storage power station, which is based on a fractional order calculus theory and designs a fractional order PID controller, wherein the fractional order PID controller has better dynamic performance and can fully play the frequency modulation potential of the traditional unit; the particle swarm optimization PSO is introduced to optimize the parameters of the fractional order PID controller, and a fitness function containing various performance indexes is adopted as an optimization target, so that the control performance of the fractional order PID controller is improved, and the robustness of the system is enhanced; the results of simulation verification under power generation and water pumping working conditions show that under two working conditions, the fractional order PID controller with the fitness function optimized provided by the invention can effectively stabilize power grid frequency fluctuation caused by disturbance, and has certain guiding significance on frequency control research of a power grid.
Drawings
FIG. 1 is a schematic structural framework diagram of a two-region load frequency control model of a pumped storage power station;
FIG. 2 is a schematic diagram of a fractional order PID controller (FOPID) architecture;
FIG. 3 is a schematic diagram of frequency deviation of a disturbance area under a power generation condition;
FIG. 4 is a schematic diagram of frequency deviation of a disturbance zone under a pumping condition.
Detailed Description
For better understanding of the technical solution of the present invention, the following detailed description of the technical solution of the present invention is provided with reference to the accompanying drawings and specific examples:
the invention provides a regional load frequency fractional order PID optimization control method of a pumped storage power station, which comprises the following steps:
step S1: building a two-region load frequency control model containing a pumped storage power station based on an IEEE standard;
in step S1, the process of building a two-region load frequency control model of the pumped storage power station based on the IEEE standard includes:
step S11: set up unit model
The transfer function model of the steam turbine set is:
Figure BDA0003004690520000071
the transfer function model of the hydraulic turbine set is as follows:
Figure BDA0003004690520000072
in the above formula, KτT tau is the reheater time constant, tau is the ratio of the power generated by the steam in the high pressure cylinder section to the total power of the turbinetIs the time constant of the steam chamber and the main steam inlet volume; t iswThe starting time of water is s is a Laplace transform operator;
the transfer function model of the speed regulator of the steam turbine set is as follows:
Figure BDA0003004690520000073
the transfer function model of the water turbine set speed regulator is as follows:
Figure BDA0003004690520000074
in the above formula, in the above formula: t isgThe time constant of the speed regulator is shown, s is a Laplace transform operator, and R is a difference adjustment coefficient of the hydraulic turbine set; description of the operating conditions of governor of water turbine by digital electrohydraulic governor system, Kp， Ki，KdRespectively the proportional, integral and differential gains of the digital electro-hydraulic speed regulating system, and f is the system frequency;
step S12: constructing a transfer function model of the tie line power deviation as follows:
Figure BDA0003004690520000075
in the formula, delta PtieijA slight increment of tie line flow power; delta fi，△fjFrequency deviations of i and j regions, respectively; t isijFor the tie line synchronization coefficient, the calculation formula is as follows:
Figure BDA0003004690520000076
in the formula, XijIs a circuit reactance;
Figure BDA0003004690520000077
rated power for zone i; thetai，θjVoltage angles at two ends of a connecting line; vi，VjIs the voltage across the tie line;
synchronous power coefficient aijThe expression of (a) is:
Figure BDA0003004690520000078
in the formula (I), the compound is shown in the specification,
Figure BDA0003004690520000079
the rated power of the generator set of the control area j;
step S13: determining the area control error ACE as:
ACE＝ΔPtie+βΔf (8)
where Δ f is the system frequency deviation at the time of disturbance, Δ PtieFor tie line exchange power deviation, β is the regional frequency response coefficient, which is defined as:
βi＝Di+1/Ri (9)
in the formula, RiIs the adjustment coefficient; diIs the load damping coefficient;
step S14: the transfer function model after the speed regulator linearization with the speed regulation dead zone is constructed as follows:
Figure BDA0003004690520000081
in the formula, N1And N2Coefficients of a second term and a third term of the nonlinear function after Fourier series expansion; t isgIs the time constant of the governor;ω0is the sinusoidal input signal frequency.
Step S2: establishing a fractional order PID controller model;
in step S2, the design procedure of the fractional PID controller is as follows:
step S21: the transfer function model for constructing the fractional order PID controller model is as follows:
C(s)＝Kp+Kis-λ+Kdsμ (11)
in the formula, Kp，Ki，KdProportional, integral and differential coefficients; 1/sλIs an integral operator; sμFor the differential operator, λ and μ are the integral order and the differential order, respectively;
step S22: the fractional calculus operator is defined as follows:
Figure BDA0003004690520000082
in the above formula, a and t are upper and lower limits of differentiation or integration, and alpha is the order of calculus;
step S23: setting fractional calculus operator in frequency band [ omega ]b,ωh]The description is performed by using a fractional transfer function K(s), which is:
Figure BDA0003004690520000083
in the above formula, alpha is more than 0 and less than 1, and alpha is the differential order of fractional order; s is a differential operator; b is greater than 0, d is greater than 0 and is an adjustable parameter;
the specific expression of the Oustaloup approximation is as follows:
Figure BDA0003004690520000091
in the formula: k is 1, 2, …, N,
where the pole ωkZero ω'kAnd the gain K is expressed as:
Figure BDA0003004690520000092
constructing an Oustaloup filter based on the formulas (10) and (11), and determining omega by the formula (11)k，ω’kAnd K, constructing a transfer function of the Oustaloup filter through the formula (10), and obtaining a final fractional order controller PID model through a standard integer order transfer function module.
Step S3: setting a fitness function by adopting a particle swarm algorithm PSO, and optimizing parameters of a fractional order PID controller model;
in step S3, a particle swarm algorithm PSO is used to set a fitness function, and the process of optimizing the parameters of the fractional PID controller model is as follows:
step S31: the velocity update and the position update of the particles in the particle swarm are:
Figure BDA0003004690520000093
in the above formula, ω is the inertia factor, c1And c2For the acceleration factor, rand represents [0, 1 ]]Random number between, PiFor individual history optimization, PgThe global optimization is achieved; x is the number ofiIs the position vector of the ith particle, viIs the velocity vector of the ith particle, and t represents the t iteration;
step S32: the fitness function is set as:
Figure BDA0003004690520000094
in the formula: kp，Ki，KdProportional, integral and differential coefficients; λ and μ are the integration order and the differentiation order, respectively; t is tsFor a stabilization time, trFor rise time, xi1，ξ2，ξ3Is a weight coefficient;
step S33: determining optimization parameters of the fractional order controller PID:
step 1: initializing a particle swarm, and setting the particle swarm scale, the maximum iteration times and related parameters;
step 2: step S31 is executed to update the particle positions and then assign the parameters K in the fitness function in step S32p、Ki、Kdμ and λ;
and step 3: running a two-region load frequency control model and returning an adaptive value f'fitness；
And 4, step 4: f 'is judged'fitness(t)＜FitminOr Iter>MaxIter, where f'fitness(t) is the fitness function, FitminFor the minimum adaptation value, Iter is the iteration number, and MaxIter is the maximum iteration number; if the condition is met, directly jumping to the step 6, and if the condition is not met, executing the step 5;
and 5: updating the particle speed and position according to the individual optimal adaptive value and the global optimal adaptive value, returning to the step 2, and continuously executing optimization;
step 6: outputting an optimized parameter K of a fractional order controller PIDp、Ki、KdMu and lambda.
Step S4: and (4) adding the optimized fractional order PID controller model in the step (S3) into the two-region load frequency control model established in the step (S1), and respectively simulating and verifying the frequency regulation effect under the working conditions of power generation and water pumping.
Examples
For ease of understanding, in the following the PID controller is abbreviated PID, fractional order PID controller is abbreviated FOPID; in order to better compare the frequency control effect of PID and FOPID in the two-region load frequency control model, a specific case is used for illustration. Parameter K of PIDp、Ki、KdAre respectively [0, 20 ]]、[0，20]、[0，10](ii) a FOPID parameter Kp、Ki、KdAre respectively [0, 80 ]]、[0，50]、[0，40]The value ranges of the integral order mu and the differential order lambda are both [0, 2%]。
The particle swarm optimization PSO is a random optimization algorithm based on a population, and the convergence of multiple experimental analyses is very important; setting 30 sub-optimization, and comparing optimization results of the controller parameters under different working conditions, wherein the optimization results are shown in table 1 specifically; optimizing the controller parameters by Particle Swarm Optimization (PSO) to obtain optimized control parameters, wherein the optimized control parameters are shown in a table 2; the basic parameters of energy transfer and power regulation of the unit in the two-region load frequency control model are set as shown in table 3, wherein Tij is a synchronous coefficient of a connecting line, aij is a synchronous power coefficient, beta i is a region frequency response constant, Ri is a speed regulator speed regulation constant, T tau is a time constant of a reheater, tau is a steam chamber time constant and a main steam inlet volume, K tau is a steam chamber time constant and a main steam inlet volumeτTw is the water starting time, Tg is the time constant of a speed regulator, K is the proportion of the power generated by steam in a high-pressure cylinder section to the total power of the steam turbineiIs the integral gain of the digital electro-hydraulic speed regulation system.
TABLE 1 f'fitnessController performance parameters optimized for 30 PSO fitness functions
Figure BDA0003004690520000111
Controller optimization control parameters after 230 PSO optimizations in Table
Figure BDA0003004690520000112
TABLE 3 basic parameters of two-region load frequency control model
Parameter(s) Numerical value Parameter(s) Numerical value
Tij 0.545 τt 10
aij -1 K i 5
βi 0.425 T W 1
Ri 2.4 Tg 0.08
Tτ 0.3 Kτ 0.5
A simulation model is built in Matlab/Simulink 2018b, parameters of PID and FOPID are optimized respectively by adopting a particle swarm algorithm PSO, the population scale of the particle swarm algorithm PSO is 10 times of the parameters to be optimized, and the maximum iteration steps are set to be 50.
And (4) analyzing an optimization result:
is prepared from'fitnessFOPID and PID online optimization as fitness functionThe control effect comparison after the chemical reaction shows that: (1) the two controllers have similar effects on frequency deviation indexes; (2) in the face of the same disturbance, the required regulation time of the FOPID is reduced by 3-4 seconds, the frequency fluctuation range is obviously shortened, the oscillation frequency is reduced, and the advantages of the FOPID are reflected in the regulation time and the frequency fluctuation.
FOPID controls the pumped storage power station to participate in frequency modulation condition analysis:
a pumped storage unit is connected to the two-region model to participate in power grid frequency regulation, and the fitness function f 'provided by the invention is adopted'fitnessThe controller parameters are optimized.
The FOPID control is mainly set parameters according to experience, on one hand, the control difference of two controllers under the actual condition cannot be objectively compared, on the other hand, the simulation result obtained through the experience parameters is difficult to objectively verify whether the difference of the simulation result is the advantage of the controller or the defect caused by insufficient parameter setting, and the control performance of the controller is easily limited. Therefore, the invention designs FOPID with better dynamic performance based on fractional calculus theory, and can fully exert the frequency modulation potential of the traditional unit; the particle swarm optimization PSO is introduced to optimize the FOPID parameters, so that the control performance of the controller is improved, and the robustness of the system is enhanced; simulation verification is carried out under the power generation working condition and the water pumping working condition, and results show that under the two working conditions, power grid frequency fluctuation caused by disturbance can be effectively stabilized through the FOPID optimized by the fitness function provided by the invention, and the FOPID has certain guiding significance on frequency control research of a power grid.
The frequency deviation curve of the pumped storage group working under the power generation working condition is shown in fig. 3. As can be seen from fig. 3: (1) due to the introduction of the water turbine set, the system can quickly react and make up for frequency fluctuation caused by disturbance of the system; (2) under the operating mode of drawing water, when the frequency fluctuation takes place in the electric wire netting, PID and FOPID can both effectually guarantee the dynamic stability of system, reduces the frequency deviation simultaneously, shortens the regulation time, has improved the dynamic behavior of system. The simulation result intuitively shows that the frequency fluctuation range of the power system is shortened, the oscillation frequency is obviously reduced, and the power system can be restored to be close to the reference value at a higher speed. When the pumped storage is not contained, the frequency still slightly fluctuates above and below the reference value after the recovery for a period of time; therefore, the frequency control of the disturbance area after the pumped storage power station is added has stronger anti-interference performance, and meanwhile, the reliability of the FOPID control method is further verified. From the change of the exchange power of the tie line, after the pumped storage is added, the exchange power of the tie line is increased to some extent, the amplitude is increased, but the recovery speed is obviously accelerated, the recovery time is shortened by nearly 10s, and although a small amount of overshoot occurs, the system plays a great role in overall stability.
The frequency deviation curve of the pumped-storage unit working under the pumping condition is shown in fig. 4. As can be seen from fig. 4: (1) the unit realizes the generator tripping according to the fluctuation of the power grid frequency, cuts off part of the load to make up the power shortage of the power grid caused by disturbance, so as to reduce the frequency fluctuation; (2) after pumped storage is added, the influence of disturbance on the power grid frequency is reduced, the recovery time of the power grid frequency is reduced, the oscillation frequency is reduced, and the frequency deviation is reduced; (3) the FOPID model has the advantages of smaller fluctuation, shorter recovery time, smaller frequency deviation value and better stability. After the pumped storage is added, the influence on the frequency disturbance of the power grid is reduced, the recovery speed is accelerated, but a small amount of overshoot occurs, because the unit under the pumped working condition can compensate the power loss of the power grid caused by the disturbance by quickly cutting off part of the load, so that the frequency fluctuation is reduced, and the stable operation of the power grid is maintained; the exchange power on the connecting line is less than that when the pumped storage is not contained, the oscillation frequency is obviously reduced to a large extent, the recovery speed is obviously accelerated, and the fluctuation is smooth.
In conclusion, the FOPID optimized by the PSO algorithm provided by the invention has stronger robustness and stability in regional load frequency control, and can shorten the frequency recovery time and improve the dynamic performance of the system for load frequency control participated by the pumped storage power station.

Claims (4)

1. A regional load frequency fractional order PID optimization control method of a pumped storage power station is characterized in that the analysis method comprises the following steps:
step S1: building a two-region load frequency control model containing a pumped storage power station based on an IEEE standard;
step S2: establishing a fractional order PID controller model;
step S3: setting a fitness function by adopting a particle swarm algorithm PSO, and optimizing parameters of a fractional order PID controller model;
step S4: and (4) adding the optimized fractional order PID controller model in the step (S3) into the two-region load frequency control model established in the step (S1), and respectively simulating and verifying the frequency regulation effect under the working conditions of power generation and water pumping.
2. The fractional order PID optimization control method for the regional load frequency of the pumped-storage power station as claimed in claim 1, wherein in the step S1, the process of building the two regional load frequency control model of the pumped-storage power station based on the IEEE standard comprises:
step S11: set up unit model
The transfer function model of the steam turbine set is:
Figure FDA0003004690510000011
the transfer function model of the hydraulic turbine set is as follows:
Figure FDA0003004690510000012
in the above formula, KτThe proportion of the power generated by the steam in the high-pressure cylinder section to the total power of the steam turbine, T tau is the time constant of the reheater, tautIs the time constant of the steam chamber and the main steam inlet volume; t iswThe starting time of water is s is a Laplace transform operator;
the transfer function model of the speed regulator of the steam turbine set is as follows:
Figure FDA0003004690510000013
the transfer function model of the water turbine set speed regulator is as follows:
Figure FDA0003004690510000014
in the above formula, in the above formula: t isgThe time constant of the speed regulator is shown, s is a Laplace transform operator, and R is a difference adjustment coefficient of the hydraulic turbine set; description of the operating conditions of governor of water turbine by digital electrohydraulic governor system, Kp，Ki，KdRespectively the proportional, integral and differential gains of the digital electro-hydraulic speed regulating system, and f is the system frequency;
step S12: constructing a transfer function model of the tie line power deviation as follows:
Figure FDA0003004690510000021
in the formula, delta PtieijA slight increment of tie line flow power; delta fi，△fjFrequency deviations of i and j regions, respectively; t isijFor the tie line synchronization coefficient, the calculation formula is as follows:
Figure FDA0003004690510000022
in the formula, XijIs a circuit reactance;
Figure FDA0003004690510000026
rated power for zone i; thetai，θjVoltage angles at two ends of a connecting line; vi，VjIs the voltage across the tie line;
synchronous power coefficient aijThe expression of (a) is:
Figure FDA0003004690510000023
in the formula (I), the compound is shown in the specification,
Figure FDA0003004690510000025
the rated power of the generator set of the control area j;
step S13: determining the area control error ACE as:
ACE＝ΔPtie+βΔf (8)
where Δ f is the system frequency deviation at the time of disturbance, Δ PtieFor tie line exchange power deviation, β is the regional frequency response coefficient, which is defined as:
βi＝Di+1/Ri (9)
in the formula, RiIs the adjustment coefficient; diIs the load damping coefficient;
step S14: the transfer function model after the speed regulator linearization with the speed regulation dead zone is constructed as follows:
Figure FDA0003004690510000024
in the formula, N1And N2Coefficients of a second term and a third term of the nonlinear function after Fourier series expansion; t isgIs the governor time constant; omega0Is the sinusoidal input signal frequency.
3. The regional load frequency fractional order PID optimization control method of the pumped storage power station according to claim 1 or 2, wherein in the step S2, the design fractional order PID controller process is:
step S21: the transfer function model for constructing the fractional order PID controller model is as follows:
C(s)＝Kp+Kis-λ+Kdsμ (11)
in the formula, Kp，Ki，KdProportional, integral and differential coefficients; 1/sλIs an integral operator; sμFor the differential operator, λ and μ are the integral order and the differential order, respectively;
step S22: the fractional calculus operator is defined as follows:
Figure FDA0003004690510000031
in the above formula, a and t are upper and lower limits of differentiation or integration, and alpha is the order of calculus;
step S23: setting fractional calculus operator in frequency band [ omega ]b,ωh]The description is performed by using a fractional transfer function K(s), which is:
Figure FDA0003004690510000032
in the above formula, alpha is more than 0 and less than 1, and alpha is the differential order of fractional order; s is a differential operator; b is greater than 0, d is greater than 0 and is an adjustable parameter;
the specific expression of the Oustaloup approximation is as follows:
Figure FDA0003004690510000033
in the formula: k is 1, 2, …, N,
where the pole ωkZero ω'kAnd the gain K is expressed as:
Figure FDA0003004690510000034
constructing an Oustaloup filter based on the formulas (10) and (11), and determining omega by the formula (11)k，ω’kAnd K, constructing a transfer function of the Oustaloup filter by the formula (10), and obtaining a final transfer function through a standard integer order transfer function moduleThe fractional order controller PID model of (1).
4. The method according to claim 3, wherein in step S3, the PSO is adopted to set a fitness function, and the optimization process of the parameters of the fractional order PID controller model is as follows:
step S31: the velocity update and the position update of the particles in the particle swarm are:
Figure FDA0003004690510000041
in the above formula, ω is the inertia factor, c1And c2For the acceleration factor, rand represents [0, 1 ]]Random number between, PiFor individual history optimization, PgThe global optimization is achieved; x is the number ofiIs the position vector of the ith particle, viIs the velocity vector of the ith particle, and t represents the t iteration;
step S32: the fitness function is set as:
Figure FDA0003004690510000042
in the formula: kp，Ki，KdProportional, integral and differential coefficients; λ and μ are the integration order and the differentiation order, respectively; t is tsFor a stabilization time, trFor rise time, xi1，ξ2，ξ3Is a weight coefficient;
step S33: determining optimization parameters of the fractional order controller PID:
step 1: initializing a particle swarm, and setting the particle swarm scale, the maximum iteration times and related parameters;
step 2: step S31 is executed to update the particle positions and then assign the parameters K in the fitness function in step S32p、Ki、Kdμ and λ;
and step 3: running a two-region load frequency control model and returning an adaptive value f'fitness；
And 4, step 4: f 'is judged'fitness(t)＜FitminOr Iter>MaxIter, where f'fitness(t) is the fitness function, FitminFor the minimum adaptation value, Iter is the iteration number, and MaxIter is the maximum iteration number; directly jumping to the step 6 if the condition is met, and executing the step 5 if the condition is not met;
and 5: updating the particle speed and position according to the individual optimal adaptive value and the global optimal adaptive value, returning to the step 2, and continuously executing optimization;
step 6: outputting an optimized parameter K of a fractional order controller PIDp、Ki、KdMu and lambda.
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