CN113093523B - 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 PDFInfo
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Abstract
The invention discloses a regional load frequency fractional order PID (proportion integration differentiation) optimization control method of a pumped storage power station, which comprises the steps of firstly, building two regional load frequency control models of the pumped storage power station based on IEEE (institute of Electrical and electronics Engineers) standards; secondly, designing a fractional order PID controller, and optimizing parameters of the fractional order PID controller by adopting a PSO algorithm; finally, simulation verification is carried out on two area load frequency control models which are built based on IEEE standards and contain the pumped storage power station, and simulation results show that the fractional order PID controller optimized by the PSO algorithm shows stronger robustness and stability in area load frequency control, and can shorten frequency recovery time and improve dynamic performance of the system for the load frequency control which the pumped storage power station participates in.
Description
Technical Field
The invention belongs to the technical field of electric power, and particularly relates to a regional load frequency fractional order PID (proportion integration differentiation) optimization control method 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 traditional unit, effectively solves the problem of power grid frequency fluctuation caused by large-scale grid connection of new energy, and has great significance.
In order to improve dynamic performance of a power grid, students at home and abroad develop a great deal of research on controllers in two-area models. The current common controller is a proportional-integral-derivative (PID) controller, has the characteristics of simple structure, convenient design, high operation reliability and the like, and is widely used for actual industrial control. Meng Xiangping et al combine the advantages of slip film control and PI control to provide a load frequency control method for a multi-zone interconnected power system while taking advantage of proportional-integral control and slip-mode control based on new zone control bias. A research room of Shanghai transportation university establishes two-area control models of a power generation working condition and a water pumping working condition of a water pumping energy storage power station, designs a nonlinear-based load frequency control model fuzzy logic controller, and adopts a traditional PI controller and a fuzzy logic controller to carry out simulation research on the nonlinear load frequency control model.
Because the fractional order theory expands the dynamic adjustment range of the system by introducing additional parameters, the system has better regulation and control capability. The robustness of the Fractional Order PID controller and the conventional PID controller is analyzed and compared in the two-region load frequency control model, and the Fractional Order PID (FOPID) controller has stronger robustness in the multi-region interconnection model. The fractional order PID controller is applied to simulation analysis of the two-region pumped storage power station, approximation of the fractional order differential operator is realized through an indirect approximation algorithm, and compared with the traditional PID controller, and the result shows that the fractional order PID controller has better control effect.
However, the PID control and fractional PID control mainly set parameters according to experience, on one hand, the control differences of the two controllers in actual situations cannot be objectively compared, on the other hand, the simulation results obtained through the experience parameters are difficult to objectively verify whether the differences of the simulation results are the advantages of the controllers or defects caused by insufficient parameter setting, and the control performance of the controllers is easy to be limited. Therefore, improving the control performance of the controller through parameter optimization is a current research hotspot. The method utilizes a self-adaptive particle swarm optimization algorithm to set fractional order PID control parameters, is applied to a typical nonlinear system, optimizes key parameters in an active disturbance rejection controller by adopting a PSO (Particle Swarm Optimization, PSO) algorithm, and performs simulation verification in an interconnection power grid model containing two areas of pumped storage, and researches show that the frequency modulation effect of the pumped storage power station can be better exerted by iterative optimization of the PSO algorithm.
Disclosure of Invention
Technical problems: the technical problems to be solved by the invention are as follows: the regional load frequency fractional order PID optimization control method with the pumped storage power station is provided, stronger robustness and stability are shown in regional load frequency control by adopting the control method, and the frequency recovery time can be shortened and the dynamic performance of the system can be improved for the load frequency control participated in the pumped storage power station.
The technical scheme is as follows: in order to solve the technical problems, 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 two-region load frequency control models of the pumped storage power station based on the IEEE standard;
step S2: establishing a fractional order PID controller model;
step S3: adopting a particle swarm algorithm PSO, setting a fitness function, and optimizing parameters of a fractional order PID controller model;
step S4: and (3) adding the fractional order PID controller model optimized in the step (S3) into the two-region load frequency control model constructed in the step (S1), and respectively simulating and verifying the frequency regulation effect under the power generation and water pumping working conditions.
In the step S1, the process of building the two-region load frequency control model of the pumped storage power station based on the IEEE standard is as follows:
step S11: building unit model
The transfer function model of the turbine unit is as follows:
the transfer function model of the water turbine unit is as follows:
in the above, K τ For the 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 t Is the steam chamber time constant and the main steam inlet volume; t (T) w S is the Laplace transformation operator for the water start time;
the transfer function model of the turbine unit speed regulator is as follows:
the transfer function model of the turbine group speed regulator is as follows:
in the above formula, in the above formula: t (T) g S is a Laplace transformation operator, R is a difference adjustment coefficient of the hydraulic turbine set; digital electrohydraulic speed regulating system is used to describe the running state of speed regulator of water turbine p ， K i ，K d Proportional, integral and differential gains of the digital electro-hydraulic speed regulation system are respectively calculated, and f is the system frequency;
step S12: the transfer function model of the tie line power deviation is constructed as follows:
wherein DeltaP tieij Flowing a power micro increment for the tie line; Δf i ，△f j Frequency deviations of i region and j region respectively; t (T) ij The calculation formula of the synchronous coefficient of the tie line is as follows:
wherein X is ij Is the reactance of the circuit;rated power for region i; θ i ，θ j The voltage angles at two ends of the connecting line; v (V) i ，V j Is the voltage at two ends of the connecting line;
synchronous power coefficient a ij The expression of (2) is:
in the method, in the process of the invention,rated power of the generator set for control region j;
step S13: the determination of the area control error ACE is:
ACE＝ΔP tie +βΔf (8)
wherein Δf is the system frequency deviation when disturbance occurs, ΔP tie For tie-line switching power offset, β is the regional frequency response coefficient, defined as:
β i ＝D i +1/R i (9)
wherein R is i Is a difference adjustment coefficient; d (D) i Is the load damping coefficient;
step S14: the transfer function model after the linearization of the speed regulator with the speed regulation dead zone is constructed as follows:
wherein N is 1 And N 2 Coefficients of the second term and the third term, which are the nonlinear function subjected to Fourier series expansion; t (T) g Is the speed regulator time constant; omega 0 Is the sinusoidal input signal frequency.
In the step S2, the process of designing the fractional order PID controller is as follows:
step S21: the transfer function model for constructing the fractional order PID controller model is as follows:
C(s)＝K p +K i s -λ +K d s μ (11)
wherein K is p ，K i ，K d Is the proportional, integral and differential coefficient; 1/s λ Is an integral operator; s is(s) μ As differential operators, lambda and mu are respectively the integral order and the differential order;
step S22: the fractional calculus operator is defined as follows:
in the above formula, a and t are upper and lower limits of differentiation or integration, and alpha is the order of the calculus;
step S23: setting fractional calculus operator to frequency band [ omega ] b ,ω h ]In this description, a fractional transfer function K(s) is used, which is:
in the above formula, 0< alpha <1, alpha is the differential order of fractional order; s is a differential operator; b >0, d >0, being an adjustable parameter;
the concrete expression of the eustaloup approximation is:
wherein: k=1, 2, …, N,
wherein the pole omega k Zero point omega' k And the gain K is expressed as:
constructing an Oustaloup filter based on formulas (10) and (11), determining ω from formula (11) k ，ω’ k And K, constructing a transfer function of the eustaloup filter through a formula (10), and obtaining a final fractional order controller PID model through a standard integer order transfer function module.
In the step S3, a particle swarm algorithm PSO is adopted, an fitness function is set, and the optimization process of the parameters of the fractional order PID controller model is as follows:
step S31: the velocity and position updates of the particles in the particle swarm are:
in the above formula, ω is an inertia factor, c 1 And c 2 As acceleration factor, rand represents [0,1 ]]Random number, P between i For the calendar Shi Zuiyou, P g Is globally optimal; x is x i Is the position vector of the ith particle, v i For the velocity vector of the ith particle, t represents the t-th iteration;
step S32: setting a fitness function as follows:
wherein: k (K) p ，K i ，K d Is the proportional, integral and differential coefficient; λ and μ are the integral order and the differential order, respectively; t is t s For the stabilization time, t r For rise time, ζ 1 ，ξ 2 ，ξ 3 Is a weight coefficient;
step S33: determining optimization parameters of the PID of the fractional order controller:
step 1: initializing a particle swarm, and setting the particle swarm scale, the maximum iteration number and related parameters;
step 2: step S31 is executed, the particle position is updated, and then the parameter K in the fitness function in step S32 is assigned p 、K i 、K d μ and λ;
step 3: running the load frequency control model of the two areas, and returning to the adaptive value f' fitness ；
Step 4: judging f' fitness (t)＜Fit min Or Iter>MaxIter where f' fitness (t) is an fitness function, fit min For the minimum adaptation value, iter is the iteration number, and MaxIter is the maximum iteration number; the step 6 is directly skipped when the condition is met, and the step 5 is executed when the condition is not met;
step 5: updating the particle speed and the position according to the individual optimal adaptation value and the global optimal adaptation value, returning to the step 2, and continuously executing optimization;
step 6: optimizing parameter K of output fractional order controller PID p 、K i 、K d μ and λ.
The beneficial effects are that:
compared with the prior art, the invention has the following advantages: according to the regional load frequency fractional order PID optimization control method containing the pumped storage power station, the fractional order PID controller is designed based on the fractional order calculus theory, and has better dynamic performance, so that the frequency modulation potential of the traditional unit can be fully exerted; the particle swarm algorithm PSO is introduced to optimize the parameters of the fractional order PID controller, and the 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; simulation verification is carried out under the power generation and water pumping working conditions, and the result shows that the fractional order PID controller with the fitness function optimization provided by the invention can effectively stabilize the power grid frequency fluctuation caused by disturbance under the two working conditions, and has a certain guiding significance on the frequency control research of the power grid.
Drawings
FIG. 1 is a schematic diagram of a structural framework of a two-zone load frequency control model of a pumped storage power plant;
FIG. 2 is a schematic diagram of a fractional order PID controller (FOPID) architecture;
FIG. 3 is a schematic diagram of the disturbance zone frequency deviation under power generation conditions;
FIG. 4 is a schematic diagram of the disturbance zone frequency deviation under pumping conditions.
Detailed Description
For a better understanding of the technical solution of the present invention, the following further details of the technical solution of the present invention are described with reference to the accompanying drawings and specific examples:
the invention provides a regional load frequency fractional order PID (proportion integration differentiation) optimization control method of a pumped storage power station, which comprises the following steps:
step S1: building two-region load frequency control models of the pumped storage power station based on the IEEE standard;
in the step S1, the process of building the two-region load frequency control model of the pumped storage power station based on the IEEE standard is as follows:
step S11: building unit model
The transfer function model of the turbine unit is as follows:
the transfer function model of the water turbine unit is as follows:
in the above, K τ For the 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 t Is the steam chamber time constant and the main steam inlet volume; t (T) w S is the Laplace transformation operator for the water start time;
the transfer function model of the turbine unit speed regulator is as follows:
the transfer function model of the turbine group speed regulator is as follows:
in the above formula, in the above formula: t (T) g S is a Laplace transformation operator, R is a difference adjustment coefficient of the hydraulic turbine set; digital electrohydraulic speed regulating system is used to describe the running state of speed regulator of water turbine p ， K i ，K d Proportional, integral and differential gains of the digital electro-hydraulic speed regulation system are respectively calculated, and f is the system frequency;
step S12: the transfer function model of the tie line power deviation is constructed as follows:
wherein DeltaP tieij Flowing a power micro increment for the tie line; Δf i ，△f j Frequency deviations of i region and j region respectively; t (T) ij The calculation formula of the synchronous coefficient of the tie line is as follows:
wherein X is ij Is the reactance of the circuit;rated power for region i; θ i ，θ j The voltage angles at two ends of the connecting line; v (V) i ，V j Is the voltage at two ends of the connecting line;
synchronous power coefficient a ij The expression of (2) is:
in the method, in the process of the invention,rated power of the generator set for control region j;
step S13: the determination of the area control error ACE is:
ACE＝ΔP tie +βΔf (8)
wherein Δf is the system frequency deviation when disturbance occurs, ΔP tie For tie-line switching power offset, β is the regional frequency response coefficient, defined as:
β i ＝D i +1/R i (9)
wherein R is i Is a difference adjustment coefficient; d (D) i Is the load damping coefficient;
step S14: the transfer function model after the linearization of the speed regulator with the speed regulation dead zone is constructed as follows:
wherein N is 1 And N 2 Coefficients of the second term and the third term, which are the nonlinear function subjected to Fourier series expansion; t (T) g Is the speed regulator time constant; omega 0 Is the sinusoidal input signal frequency.
Step S2: establishing a fractional order PID controller model;
in the step S2, the process of designing the fractional order PID controller is as follows:
step S21: the transfer function model for constructing the fractional order PID controller model is as follows:
C(s)＝K p +K i s -λ +K d s μ (11)
wherein K is p ，K i ，K d Is the proportional, integral and differential coefficient; 1/s λ Is an integral operator; s is(s) μ As differential operators, lambda and mu are respectively the integral order and the differential order;
step S22: the fractional calculus operator is defined as follows:
in the above formula, a and t are upper and lower limits of differentiation or integration, and alpha is the order of the calculus;
step S23: setting fractional calculus operator to frequency band [ omega ] b ,ω h ]In this description, a fractional transfer function K(s) is used, which is:
in the above formula, 0< alpha <1, alpha is the differential order of fractional order; s is a differential operator; b >0, d >0, being an adjustable parameter;
the concrete expression of the eustaloup approximation is:
wherein: k=1, 2, …, N,
wherein the pole omega k Zero point omega' k And the gain K is expressed as:
constructing an Oustaloup filter based on formulas (10) and (11), determining ω from formula (11) k ，ω’ k And K, constructing a transfer function of the eustaloup filter through a formula (10), and obtaining a final fractional order controller PID model through a standard integer order transfer function module.
Step S3: adopting a particle swarm algorithm PSO, setting a fitness function, and optimizing parameters of a fractional order PID controller model;
in the step S3, a particle swarm algorithm PSO is adopted, an fitness function is set, and the optimization process of the parameters of the fractional order PID controller model is as follows:
step S31: the velocity and position updates of the particles in the particle swarm are:
in the above formula, ω is an inertia factor, c 1 And c 2 As acceleration factor, rand represents [0,1 ]]Random number, P between i For the calendar Shi Zuiyou, P g Is globally optimal; x is x i Is the position vector of the ith particle, v i For the velocity vector of the ith particle, t represents the t-th iteration;
step S32: setting a fitness function as follows:
wherein: k (K) p ，K i ，K d Is the proportional, integral and differential coefficient; λ and μ are the integral order and the differential order, respectively; t is t s For the stabilization time, t r For rise time, ζ 1 ，ξ 2 ，ξ 3 Is a weight coefficient;
step S33: determining optimization parameters of the PID of the fractional order controller:
step 1: initializing a particle swarm, and setting the particle swarm scale, the maximum iteration number and related parameters;
step 2: step S31 is executed, the particle position is updated, and then the parameter K in the fitness function in step S32 is assigned p 、K i 、K d μ and λ;
step 3: running the load frequency control model of the two areas, and returning to the adaptive value f' fitness ；
Step 4: judging f' fitness (t)＜Fit min Or Iter>MaxIter where f' fitness (t) is an fitness function, fit min For the minimum adaptation value, iter is the iteration number, and MaxIter is the maximum iteration number; the step 6 is directly skipped when the condition is met, and the step 5 is executed when the condition is not met;
step 5: updating the particle speed and the position according to the individual optimal adaptation value and the global optimal adaptation value, returning to the step 2, and continuously executing optimization;
step 6: optimizing parameter K of output fractional order controller PID p 、K i 、K d μ and λ.
Step S4: and (3) adding the fractional order PID controller model optimized in the step (S3) into the two-region load frequency control model constructed in the step (S1), and respectively simulating and verifying the frequency regulation effect under the power generation and water pumping working conditions.
Examples
For ease of understanding, the PID controller is abbreviated as PID in the following, and the fractional order PID controller is abbreviated as FOPID; to better compare the frequency control effects of PID and FOPID in the two-zone load frequency control model, a specific case will be used below. Parameter K of PID p 、K i 、K d The value ranges of (2) are respectively [0, 20 ]]、[0，20]、[0，10]The method comprises the steps of carrying out a first treatment on the surface of the Parameter K of FOPID p 、K i 、K d The value ranges of (2) are 0, 80 respectively]、[0，50]、[0，40]The value ranges of the integral order mu and the differential order lambda are 0,2]。
The particle swarm algorithm PSO is a random optimization algorithm based on population, and the convergence of the particle swarm algorithm PSO is extremely important for multiple test analysis; setting 30 times of optimization, and comparing the optimization results of the controller parameters under different working conditions, wherein the optimization results are shown in a table 1; optimizing the controller parameters through a particle swarm algorithm 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 a unit in a load frequency control model of two areas are set as shown in a table 3, wherein Tij is a tie line synchronization coefficient, aij is a synchronous power coefficient, βi is an area frequency response constant, ri is a speed regulator speed regulation constant, Tτ is a reheater time constant, τt is a steam chamber time constant and a main steam inlet volume, K τ For the proportion of the power generated by the steam in the high-pressure cylinder section to the total power of the steam turbine, tw is the water start time, tg is the time constant of the speed regulator, K i Is the integral gain of the digital electrohydraulic speed regulating system.
Table 1 f' fitness Controller performance parameters after 30 PSO optimization for fitness function
TABLE 2 controller optimization control parameters after 30 PSO optimizations
TABLE 3 basic parameters of two-zone load frequency control model
| Parameters (parameters) | Numerical value | Parameters (parameters) | Numerical value |
| T ij | 0.545 | τ t | 10 |
| a ij | -1 | K i | 5 |
| βi | 0.425 | T W | 1 |
| Ri | 2.4 | T g | 0.08 |
| T τ | 0.3 | K τ | 0.5 |
Setting up a simulation model in Matlab/Simulink 2018b, adopting a particle swarm algorithm PSO to respectively optimize parameters of PID and FOPID, setting the population scale of the particle swarm algorithm PSO to be 10 times of the required optimized parameters, and setting the maximum iteration step number to be 50.
And (3) optimizing result analysis:
at f' fitness As a fitness function, the comparison of the control effects after the on-line optimization of the FOPID and the PID shows that: (1) The two controllers have similar effects on the frequency deviation index; (2) When the same disturbance is faced, the adjusting time required by the FOPID is reduced by 3-4 seconds, the frequency fluctuation range is obviously shortened, the oscillation times are reduced, and the advantages of the FOPID are shown to be in adjusting time and frequency fluctuation.
FOPID controls the pumped storage power station to participate in the frequency modulation condition analysis:
the pumped storage unit is connected into the two-region model to participate in the frequency regulation of the power grid, and the fitness function f 'provided by the invention is adopted' fitness The controller parameters are optimized.
The FOPID control mainly sets parameters according to experience, on one hand, the control difference of the two controllers under actual conditions 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 easy to limit. Therefore, the invention designs the FOPID with better dynamic performance based on fractional calculus theory, and can fully exert the frequency-regulating potential of the traditional unit; the particle swarm algorithm 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 the result shows that the FOPID optimized by the fitness function provided by the invention can effectively stabilize the power grid frequency fluctuation caused by disturbance under the two working conditions, and has certain guiding significance on the frequency control research of the power grid.
The frequency deviation curve of the pumped storage unit when working under the power generation working condition is shown in figure 3. As can be seen from fig. 3: (1) The introduction of the water turbine unit enables the system to react rapidly, and compensates the frequency fluctuation of the system caused by disturbance; (2) Under the pumping working condition, when the frequency fluctuation occurs in the power grid, the PID and the FOPID can effectively ensure the dynamic stability of the system, simultaneously reduce the frequency deviation, shorten the adjusting time and improve the dynamic performance of the 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 the vicinity of the reference value at a higher speed. When the pump storage is not contained, the frequency still slightly fluctuates above and below the reference value after a period of recovery; the frequency control of the disturbance area after the pumped storage power station is added has stronger anti-interference performance, and the reliability of the FOPID control method is further verified. From the change of exchange power of the tie line, after the pumped storage is added, the exchange power of the tie line is increased, the amplitude is increased, but the recovery speed is obviously accelerated, the recovery time is shortened by nearly 10 seconds, and a small amount of overshoot occurs, but the system overall stability is greatly improved.
The frequency deviation curve of the pumped storage unit in the pumping working condition is shown in figure 4. As can be seen from fig. 4: (1) The machine set realizes machine switching according to the fluctuation of the power grid frequency, and partial load is cut off to compensate the power shortage of the power grid caused by disturbance so as to reduce the frequency fluctuation; (2) After the pumped storage is added, the influence of disturbance on the frequency of the power grid is reduced, the recovery time of the frequency of the power grid is reduced, the oscillation frequency is reduced, and the frequency deviation is reduced; (3) The model fluctuation of the FOPID is smaller, the recovery time is shorter, the frequency deviation value is smaller, and the system has better stability. After the pumped storage is added, the influence on the frequency disturbance of the power grid is reduced and the recovery speed is accelerated, but a small amount of overshoot occurs, because the unit under the pumping working condition can make up the power loss of the power grid caused by disturbance by rapidly cutting off partial load, thereby reducing the frequency fluctuation and maintaining the stable operation of the power grid; the exchange power on the connecting line is smaller than the power without pumping energy storage, the oscillation frequency is obviously and greatly reduced, the recovery speed is obviously accelerated, and the fluctuation is smoother.
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 the load frequency control participated in the pumped storage power station.
Claims (1)
1. The regional load frequency fractional order PID optimization control method of the pumped storage power station is characterized by comprising the following steps of:
step S1: building two-region load frequency control models of the pumped storage power station based on the IEEE standard;
step S2: establishing a fractional order PID controller model;
step S3: adopting a particle swarm algorithm PSO, setting a fitness function, and optimizing parameters of a fractional order PID controller model;
step S4: adding the fractional order PID controller model optimized in the step S3 into the two-region load frequency control model constructed in the step S1, and respectively simulating and verifying the frequency regulation effect under the power generation and pumping working conditions;
in the step S1, the process of building the two-region load frequency control model of the pumped storage power station based on the IEEE standard is as follows:
step S11: building unit model
The transfer function model of the turbine unit is as follows:
the transfer function model of the water turbine unit is as follows:
in the above, K τ For the 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 t Is the steam chamber time constant and the main steam inlet volume; t (T) w S is the Laplace transformation operator for the water start time;
the transfer function model of the turbine unit speed regulator is as follows:
the transfer function model of the turbine group speed regulator is as follows:
in the above formula, in the above formula: t (T) g S is a Laplace transformation operator, R is a difference adjustment coefficient of the water turbine set; digital electrohydraulic speed regulating system is used to describe the running state of speed regulator of water turbine p ，K i ，K d Proportional, integral and differential gains of the digital electro-hydraulic speed regulation system are respectively calculated, and f is the system frequency;
step S12: the transfer function model of the tie line power deviation is constructed as follows:
wherein DeltaP tieij Flowing a power micro increment for the tie line; Δf i ，△f j Frequency deviations of i region and j region respectively; t (T) ij The calculation formula of the synchronous coefficient of the tie line is as follows:
wherein X is ij Is the reactance of the circuit; p (P) * i Rated power for region i; θ i ，θ j The voltage angles at two ends of the connecting line; v (V) i ，V j Is the voltage at two ends of the connecting line;
synchronous power coefficient a ij The expression of (2) is:
in the method, in the process of the invention,rated power of the generator set for control region j;
step S13: the determination of the area control error ACE is:
ACE＝ΔP tie +βΔf (8)
wherein Δf is the system frequency deviation when disturbance occurs, ΔP tie For tie-line switching power offset, β is the regional frequency response coefficient, defined as:
β i ＝D i +1/R i (9)
wherein R is i Is a difference adjustment coefficient; d (D) i Is the load damping coefficient;
step S14: the transfer function model after the linearization of the speed regulator with the speed regulation dead zone is constructed as follows:
wherein N is 1 And N 2 NonlinearCoefficients of the second term and the third term of the function developed by the Fourier series; t (T) g Is the time constant of the speed regulator; omega 0 Is the sinusoidal input signal frequency;
in the step S2, the process of designing the fractional order PID controller is as follows:
step S21: the transfer function model for constructing the fractional order PID controller model is as follows:
C(s)＝K p +K i s -λ +K d s μ (11)
wherein K is p ，K i ，K d Is the proportional, integral and differential coefficient; 1/s λ Is an integral operator; s is(s) μ As differential operators, lambda and mu are respectively the integral order and the differential order;
step S22: the fractional calculus operator is defined as follows:
in the above formula, a and t are upper and lower limits of differentiation or integration, and alpha is the order of the calculus;
step S23: setting fractional calculus operator to frequency band [ omega ] b ,ω h ]In this description, a fractional transfer function K(s) is used, which is:
in the above formula, 0< alpha <1, alpha is the differential order of fractional order; s is a differential operator; b >0, d >0, being an adjustable parameter;
the concrete expression of the eustaloup approximation is:
wherein: k=1, 2, …, N,
wherein the pole omega k Zero point omega' k And the gain K is expressed as:
constructing an Oustaloup filter based on formulas (10) and (11), determining ω from formula (11) k ，ω’ k And K, constructing a transfer function of the eustaloup filter through a formula (10), and obtaining a final fractional order controller PID model through a standard integer order transfer function module;
in the step S3, a particle swarm algorithm PSO is adopted, an fitness function is set, and the optimization process of the parameters of the fractional order PID controller model is as follows:
step S31: the velocity and position updates of the particles in the particle swarm are:
in the above formula, ω is an inertia factor, c 1 And c 2 As acceleration factor, rand represents [0,1 ]]Random number, P between i For individual history optimization, P g Is globally optimal; x is x i Is the position vector of the ith particle, v i For the velocity vector of the ith particle, t represents the t-th iteration;
step S32: setting a fitness function as follows:
wherein: k (K) p ，K i ，K d Is the proportional, integral and differential coefficient; λ and μ are the integral order and the differential order, respectively; t is t s For the stabilization time, t r For rise time, ζ 1 ，ξ 2 ，ξ 3 Is a weight coefficient;
step S33: determining optimization parameters of the PID of the fractional order controller:
step 1: initializing a particle swarm, and setting the particle swarm scale, the maximum iteration number and related parameters;
step 2: step S31 is executed, the particle position is updated, and then the parameter K in the fitness function in step S32 is assigned p 、K i 、K d μ and λ;
step 3: running the load frequency control model of the two areas, and returning to the adaptive value f' fitness ；
Step 4: judging f' fitness (t)<Fit min Or Iter>MaxIter where f' fitness (t) is an fitness function, fit min For the minimum adaptation value, iter is the iteration number, and MaxIter is the maximum iteration number; the step 6 is directly skipped to when the condition is met, and the step 5 is executed when the condition is not met;
step 5: updating the particle speed and the position according to the individual optimal adaptation value and the global optimal adaptation value, returning to the step 2, and continuously executing optimization;
step 6: optimizing parameter K of output fractional order controller PID p 、K i 、K d μ and λ.
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