CN115622131A - Micro-grid frequency robust optimal H with energy storage 2 /H ∞ Controller design method - Google Patents
Micro-grid frequency robust optimal H with energy storage 2 /H ∞ Controller design method Download PDFInfo
- Publication number
- CN115622131A CN115622131A CN202211389726.XA CN202211389726A CN115622131A CN 115622131 A CN115622131 A CN 115622131A CN 202211389726 A CN202211389726 A CN 202211389726A CN 115622131 A CN115622131 A CN 115622131A
- Authority
- CN
- China
- Prior art keywords
- controller
- robust
- grid
- frequency
- matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 44
- 238000004146 energy storage Methods 0.000 title claims abstract description 32
- 238000013461 design Methods 0.000 title claims abstract description 27
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 38
- 241000272168 Laridae Species 0.000 claims abstract description 32
- 230000008859 change Effects 0.000 claims abstract description 22
- 239000011159 matrix material Substances 0.000 claims description 62
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 37
- 238000011156 evaluation Methods 0.000 claims description 28
- 238000005457 optimization Methods 0.000 claims description 20
- 238000004458 analytical method Methods 0.000 claims description 15
- 210000004027 cell Anatomy 0.000 claims description 9
- 238000012546 transfer Methods 0.000 claims description 9
- 230000003044 adaptive effect Effects 0.000 claims description 7
- 230000008569 process Effects 0.000 claims description 7
- 238000004364 calculation method Methods 0.000 claims description 4
- 238000013016 damping Methods 0.000 claims description 4
- 230000007246 mechanism Effects 0.000 claims description 3
- 239000000203 mixture Substances 0.000 claims description 3
- 210000000352 storage cell Anatomy 0.000 claims description 3
- 230000010355 oscillation Effects 0.000 abstract description 3
- 238000011160 research Methods 0.000 abstract description 2
- 230000001052 transient effect Effects 0.000 abstract 2
- 238000004088 simulation Methods 0.000 description 7
- 238000010586 diagram Methods 0.000 description 4
- 238000004836 empirical method Methods 0.000 description 3
- 230000007547 defect Effects 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 2
- 230000004044 response Effects 0.000 description 2
- 238000013473 artificial intelligence Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000012512 characterization method Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000011217 control strategy Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
Images
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
- H02J3/241—The oscillation concerning frequency
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/28—Arrangements for balancing of the load in a network by storage of energy
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
- H02J2300/20—The dispersed energy generation being of renewable origin
- H02J2300/22—The renewable source being solar energy
- H02J2300/24—The renewable source being solar energy of photovoltaic origin
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
- H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
Landscapes
- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Feedback Control In General (AREA)
Abstract
The invention discloses a micro-grid frequency robust optimal H with energy storage 2 /H ∞ The design method of the controller aims at the problem of frequency oscillation caused by output fluctuation and load change of new energy such as wind, light and the like in a micro-grid, a micro-grid system which utilizes common frequency modulation of an energy storage unit and a hydroelectric generating set is constructed, and the transient stability of the micro-grid can be effectively improved by introducing an energy storage battery; the invention provides a method for solving output feedback robust H by utilizing an LMI tool 2 /H ∞ The controller optimizes related parameters of the controller by adopting a gull intelligent algorithm to optimize the control performance of the controller, and introduces the designed secondary frequency modulation loop of the water-light storage microgridThe controller is used for improving the transient state and steady state operation characteristics of the system by controlling the output of the hydroelectric generating set and the energy storage battery, so that the frequency deviation of the micro-grid is kept within an allowable range; the method is mainly characterized by taking the frequency control method of the state space model of the water-light storage micro-grid as a main characteristic, gives consideration to the robustness and the robustness stability of the system, and has theoretical research and engineering practical value.
Description
Technical Field
The invention belongs to the technical field of micro-grids, and particularly relates to output feedback robust optimal H based on intelligent algorithm optimization 2 /H ∞ A design method of a micro-grid frequency controller.
Background
With the expansion of the power demand of the current society, the power industry faces the problems of constructing high-cost power plants and transmission and distribution networks. The micro-grid is formed by supplying power to some local loads by using distributed energy sources such as wind, light, water and the like, and is an important scheme for solving the problem. Due to the fluctuation of the output power of new energy sources such as wind, light and the like and the randomness of the power consumption of the load side, the frequency oscillation of the micro-grid is easily caused, and the regional power supply quality is seriously influenced. Therefore, the research on the control method for improving the frequency stability of the microgrid is of great significance.
In order to keep the frequency of the microgrid stable, the traditional method adopts PID control, the principle of the PID controller is simple and easy to realize, but the robust stability and robust performance of the controller are not ideal. The prior document designs a frequency controller by using a fuzzy control method, and the method has better robustness on system parameter perturbation and has the defect that the control precision cannot be ensured. The method comprises sliding mode control and active disturbance rejection control, wherein the modern control theories obtain good robustness and dynamic performance in the frequency stability control of the micro-grid, but the calculation process is complex, the stability of the algorithm is proved to be a difficult point, and the application prospect of the intelligent algorithm in the aspect of micro-grid frequency stability is fully shown to be very wide.
The robust theoretical control strategy is considered as one of the best solutions for realizing the good operation of the microgrid under the conditions of unstable power output and load disturbance, but the design of many robust controllers only focuses on H ∞ Robust performance of norm representation refers toBidding, H for the robust stability performance index of the characterization system 2 The norm is not considered. H 2 /H ∞ The robust controller gives consideration to both robustness and dynamic stability, the overall performance of the robust controller is closely related to the selection of an evaluation function matrix and norm weight, the traditional method adopts an empirical method or a trial and error method for selection, the workload is large, the optimal solution is difficult to find, and the parameter optimization of the robust controller by using an intelligent algorithm is an important optimization direction in recent years.
Disclosure of Invention
Aiming at the problem of frequency fluctuation caused by power disturbance in a microgrid, the invention provides a microgrid frequency robust optimal H with energy storage 2 /H ∞ The controller design method enables the frequency of the micro-grid to be stable by controlling the output of the hydroelectric generating set and the energy storage battery to compensate the fluctuation of photovoltaic and load.
The technical scheme of the invention is as follows:
micro-grid frequency robust optimal H with energy storage 2 /H ∞ The controller design method is used for solving the problem of frequency stability caused by photovoltaic output and load fluctuation in the water-light storage micro-grid, and comprises the following steps:
step 1: establishing a load frequency regulation linear model of the water light storage micro-grid to obtain a state space equation of the water light storage micro-grid;
step 2: according to robust H ∞ Multi-objective control principle, design of output feedback robust H based on LMI tool solution 2 /H ∞ A controller; and step 3: application of gull intelligent algorithm to robust controller Z 2 /Z ∞ Optimizing the performance evaluation matrix parameters and the performance weight norm to obtain the optimal robust H 2 /H ∞ A frequency controller.
Preferably, step 1 is to establish a load frequency regulation linear model of the water-light storage microgrid to obtain a state space equation of the water-light storage microgrid, and the specific steps are as follows:
step 1-1, firstly, establishing a frequency change model of the water-light storage microgrid, wherein the frequency change can be caused by the power change in the microgrid, and the frequency change dynamic model signal analysis is represented as follows:
ΔP＝ΔP s -ΔP L
ΔP s ＝ΔP PV +ΔP HY +ΔP Be
in the formula: g MG (s) is a characteristic function of the frequency change of the water light storage micro-grid; s represents the Laplace operator, the same below; m is the inertia constant of the system; d is the system damping constant; Δ f is the system frequency variation; Δ P represents the system power; delta P s The total power output of the water light storage micro-grid is represented; delta P L Representing water light storage microgrid load; delta P HY Outputting power for the hydraulic turbine set; delta P PV Is the output power of the photovoltaic cell panel; delta P Be The output power of the energy storage battery;
step 1-2, analyzing the output model of each power supply
a. Dynamic model of water turbine
The model of water turbine can be divided into two parts of speed regulator and prime motor, and the characteristic function G of speed regulator y (s) the signal analysis is as follows:
in the formula: Δ X g The output quantity of the actuating mechanism of the hydraulic turbine speed regulator is provided; t is y And k y Respectively time constant and gain of the hydraulic turbine servomotor; r is a primary frequency modulation droop coefficient of the micro-grid; Δ u y (s) represents a control signal applied to the governor of the hydraulic turbine;Δu L is the control signal passed through the low pass filter; t is simulation time;
in the prime mover link of the water turbine, an IEEE (institute of Electrical and electronics Engineers) linearization model of the water turbine is adopted, and a characteristic function G of the model w (s) is represented as follows:
in the formula: t is w Is the water flow inertia time constant, Δ P HY And outputting power for the hydraulic turbine set.
b. Photovoltaic cell panel dynamic model
Photovoltaic cell panel output dynamic model and characteristic function G PV (s) the signal analysis is as follows:
in the formula: t is PV And k PV Time constant and gain of the photovoltaic panel; delta S PV Representing solar power.
c. Energy storage battery dynamic model
Energy storage battery output dynamic model and characteristic function G Be (s) is represented as follows:
in the formula: t is Be And k Be Respectively the time constant and the gain of the energy storage battery; Δ u Be Representing a control signal applied to the energy storage cell;
and (3) establishing a frequency adjustment linear model of the water light storage microgrid by combining the model analysis, wherein the characteristic function of the LPF is as follows:
in the formula: t is L Is the time constant of the LPF.
Step 1-3, establishing a state space equation according to the frequency regulation linear model of the water light storage micro-grid
The state space model is a dynamic time domain model taking time as an independent variable, and a state space equation of the water-light storage micro-grid frequency regulation linear model is expressed as follows:
in the formula: x is a state variable; u is a control input variable; w represents a disturbance variable of the system; y represents a system output variable; a is a system state space matrix, which is determined by system parameters; b is 1 A system disturbance matrix; b is 2 A system control matrix; c y For the system to output a matrix, D y1 And D y2 Respectively representing the disturbance and the control matrix of the system output representation;
according to the model structure analysis, the matrices take the values:
x＝[ΔδΔfΔX g ΔP HY ΔP PV ΔP Be Δu L ] T
w＝[ΔP L ΔS PV ] T
C y ＝[1 0 0 0 0 0 0]
D y1 ＝[0 0]D y2 ＝[0]。
preferably, step 2 is based on robust H ∞ Multi-objective control principle, design of output feedback robust H based on LMI tool solution 2 /H ∞ The controller comprises the following specific steps:
step 2-1, firstly, adding Z on the basis of a state space equation of the microgrid 2 /Z ∞ Two sets of performance evaluation function establishment H 2 /H ∞ State space equation of control:
in the formula: z 2 ，Z ∞ Is H 2 ，H ∞ Robust performance output evaluation function, C 1 、D 11 、D 12 、C 2 、D 21 、D 22 Are each Z 2 /Z ∞ The parameters of the performance evaluation matrix are specifically defined as follows:
C 1 ＝diag([x(1) x(2) x(3) 0 0 0 0])；
C 2 ＝diag([x(5) x(6) x(7) 0 0 0 0])；
D 11 ＝D 21 ＝0
x (1) -x (8) in the matrix are undetermined parameters of the evaluation matrix. Parameters x (1), x (2), x (3), x (5), x (6) and x (7) are used for tracking load change and suppressing interference by setting a performance target for a controlled output end; the parameters x (4) and x (8) suppress the overshoot by limiting the speed of change of the regulator load set point signal.
For mixture H 2 /H ∞ The control system introduces an output feedback controller so that u = K(s) y, and a corresponding closed-loop system state space equation is obtained as follows:
in the formula: a. The cl ＝A+B 2 KC y ；B cl ＝B 1 ；x cl ＝x；C cl1 ＝C 1 +D 12 KC y ；D cl1 ＝D 11 ；C cl2 ＝C 2 +D 22 KC y ；D cl2 ＝D 21 ；K＝K(s)。
Step 2-2, based on H 2 /H ∞ The design core of the robust output feedback controller of the state space equation is to minimize the control loop from w to Z in the closed loop system 2 /Z ∞ Closed loop root mean square gain of, H 2 /H ∞ The mathematical idea of controller design is to find a suitable controller K(s) to make the system go from disturbance w to performance evaluation Z ∞ Closed loop transfer function T of output wz∞ H of(s) ∞ Norm not exceeding a given upper bound gamma to ensure that the closed loop system is robust to uncertainty coming in from w, while allowing w to Z 2 Closed loop transfer function T of wz2 H of(s) 2 The norm is as small as possible to ensure the robust stability performance of the system to be at a good level, and the linear matrix inequality LMI can be described as follows:
a. optimum H ∞ The performance indexes of the control are as follows: from w to Z ∞ The closed loop rms gain of (a) does not exceed gamma. This condition can be expressed as if and only if there is a symmetric matrix X using the linear matrix inequality LMI ∞ Such that:
X ∞ ＞0
in the formula, I is a unit matrix, and the same is shown below; let γ =1 in order not to lose generality.
b. Optimum H 2 The performance indexes of the control are as follows: from w to Z 2 H of closed loop transfer function of 2 Norm does not exceed v, and likewise with LMI can be expressed as if and only if D cl2 =0 and there are two symmetric matrices X 2 And Q is such that:
Trace(Q)＜v 2
in the formula: trace (Q) represents tracing the matrix Q, and v is not limited.
For the above-described ease of manipulation in the LMI framework, to satisfy the generality, a single Lyapunov matrix X is set such that X ∞ ＝X 2 The pole configuration adopts a default pole left area, and the hybrid H is calculated by combining the LMI equation 2 /H ∞ The performance index that the controller needs to meet is that the closed-loop poles of the controlled object are all located in the left half-open complex plane, and the following functions are optimized to express the overall performance, and the expression is as follows:
in which alpha and beta represent H 2 /H ∞ The norm weight of the performance can obtain robust controllers with different performances by configuring different values of alpha and beta.
The above-described LMI-based goal implementation may be solved using a hinfmix solver of the LMI toolkit in MATLAB.
Preferably, step 3 applies a gull intelligence algorithm Z 2 /Z ∞ Optimizing the performance evaluation matrix parameters and the performance weight norm to obtainRobust optimal H 2 /H ∞ The frequency controller comprises the following specific steps:
step 3-1, setting a fitness function for gull algorithm optimization
The invention adopts ISE indexes commonly used in engineering as fitness functions for gull algorithm parameter optimization to improve the efficiency of algorithm optimization, and the fitness function formula is as follows:
in the formula, deltaf is the frequency deviation of the system output; and t is simulation time.
Step 3-2, applying gull algorithm to robust controller parameter optimization
From the above robust H 2 /H ∞ The controller finds out the solving process, Z 2 /Z ∞ Performance evaluation matrix C in (1) 1 、C 2 、D 11 、D 12 、D 21 、D 22 And the values of the alpha and beta weight coefficients directly influence the control performance of the controller, and the traditional method adopts an empirical method or a trial and error method to select, so that the workload is large, and the optimal solution is difficult to find.
The method applies the gull intelligent algorithm to the optimal selection of the parameters to be solved when the robust controller is used for solving. The optimization process can be roughly represented as: generating a gull individual group by an algorithm, carrying a parameter value to be solved by each individual, and sequentially assigning the numerical value carried by the group of individuals to a performance evaluation matrix C influencing the solving of the controller 1 、C 2 、D 11 、D 12 、D 21 、D 22 The undetermined coefficient and the two weight coefficients of alpha and beta in the matrix are calculated by using an LMI toolbox in Matlab to obtain a corresponding robust output feedback controller K(s), and an interference working condition is introduced into a closed loop system formed by the robust controller K(s) obtained by current calculation to obtain a corresponding performance evaluation index. And taking the performance index as an adaptive value of each individual gull in the improved gull algorithm, sorting the population adaptive values, and evaluating the optimal gull individual. According to the optimumIn the body, the seagull algorithm continues to perform optimization iteration towards the direction of reducing the fitness value until the condition of exiting the algorithm is reached;
substituting the obtained optimal weight coefficient and coefficient matrix into a state space equation of the system, and solving a linear matrix inequality LMI with corresponding performance to obtain a robust H 2 /H ∞ And outputting the feedback controller K(s).
The invention has the beneficial effects that:
(1) Aiming at the problem of frequency oscillation caused by output fluctuation and load change of new energy such as wind and light in a microgrid, the invention constructs a water-light Chu Weidian network system for jointly modulating the frequency by using energy storage and a hydroelectric generating set, and innovatively provides a robust H system based on LMI mode solution 2 /H ∞ Compared with the traditional weight function solving method, the method for outputting the feedback controller is more convenient and efficient in an LMI (local mean square) solving mode, and then the evaluation matrix parameters and H (H) influencing the control performance of the controller by the gull intelligent algorithm are introduced in the solving process of the controller 2 /H ∞ The norm weight coefficient is optimized and selected, so that the performance of the controller is optimized, and H is effectively improved 2 /H ∞ And the frequency stability of the hybrid robust output feedback controller in the water optical storage micro-grid.
(2) The design method of the controller fully considers the influence of the uncertainty of the output of new energy such as wind, light and the like and the uncertainty of load fluctuation on the frequency of the micro-grid, the micro-grid system adopting the method to design the controller is superior to the traditional control in the aspects of robustness and frequency dynamic stability, the method is suitable for micro-grid scenes with hydroelectric-photovoltaic-energy storage batteries and local loads, the load and the power change of the photovoltaic output have the characteristics of unpredictability and large fluctuation, and the method can also be popularized to the field of other new energy micro-grids with energy storage adjusting power supplies.
(3) Robust H proposed by the invention 2 /H ∞ The output feedback control method avoids the defect that the system state quantity needs to be acquired in real time in the state feedback control, and overcomes the accurate modeling required by the modern control theory on the controlled object by establishing a simple mathematical model of the controlled object, so that the controller is designedIs more effective and practical.
Drawings
FIG. 1 is a design flow chart of the present invention
FIG. 2 is a frequency regulation linear model of a microgrid;
FIG. 3 is a diagram of a standard robust hybrid H 2 /H ∞ A control schematic diagram;
FIG. 4 is a flow chart of algorithm optimization robust controller parameters;
FIG. 5 is a solar and load power interference graph;
FIG. 6 is a diagram of controller frequency control deviation response under power disturbance conditions.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
Micro-grid frequency robust optimal H with energy storage 2 /H ∞ The design method of the controller, which is combined with the figure 1, comprises the following steps:
step 1: establishing a load frequency regulation linear model of the water-light storage micro-grid to obtain a state space equation of the water-light storage micro-grid;
step 1-1, establishing a frequency change model of the water light storage micro-grid
The power change in the microgrid can cause the frequency change, and the frequency change dynamic model signal analysis is represented as follows:
ΔP＝ΔP s -ΔP L
ΔP s ＝ΔP PV +ΔP HY +ΔP Be
in the formula: g MG (s) is a characteristic function of the frequency change of the water light storage micro-grid; s represents the Laplace operator; m is the inertia constant of the system; d is the system damping constant; Δ f is the system frequency variation(ii) a Δ P represents the system power; delta P s The total power output of the water light storage micro-grid is represented; delta P L Representing water light storage microgrid load; delta P HY Outputting power for the hydraulic turbine set; delta P PV Is the output power of the photovoltaic cell panel; delta P Be The output power of the energy storage battery;
step 1-2, analyzing the output model of each power supply
a. Dynamic model of water turbine
The water turbine model is divided into two parts of a speed regulator and a prime motor, and the characteristic function G of the speed regulator y (s) the signal analysis is as follows:
in the formula: Δ X g The output quantity of the actuating mechanism of the hydraulic turbine speed regulator is provided; t is y And k y Respectively time constant and gain of the hydraulic turbine servomotor; r is a primary frequency modulation droop coefficient of the micro-grid; Δ u y (s) represents a control signal applied to the governor of the hydraulic turbine; Δ u L Is the control signal passed through the low pass filter; t is simulation time;
in the prime mover link of the water turbine, an IEEE (institute of Electrical and electronics Engineers) linearization model of the water turbine is adopted, and a characteristic function G of the model w (s) is represented as follows:
in the formula: t is w Is the water flow inertia time constant, Δ P HY Outputting power for the hydraulic turbine set;
b. photovoltaic cell panel dynamic model
Photovoltaic cell panel output dynamic model and characteristic function G PV (s) the signal analysis is as follows:
in the formula: t is PV And k PV Time constant and gain of the photovoltaic panel; delta S PV Representing solar power;
c. energy storage battery dynamic model
Energy storage battery output dynamic model and characteristic function G Be (s) is represented as follows:
in the formula: t is a unit of Be And k Be Respectively the time constant and the gain of the energy storage battery; Δ u Be Representing a control signal applied to the energy storage cell;
combining the model analysis, establishing a frequency adjustment linear model of the water light storage microgrid as shown in figure 2, wherein an LPF (low pass filter) in the figure is a low pass filter; Δ u represents a secondary frequency modulation control signal; Δ δ is a frequency deviation integral quantity; the characteristic function of the LPF is as follows:
in the formula: t is L Is the time constant of the LPF;
step 1-3, establishing a state space equation according to the frequency regulation linear model of the water light storage micro-grid
According to the load frequency regulation linear model of the water-light storage micro-grid in fig. 2, 7 state variables are selected, and a state space equation of the system is obtained through derivation by combining the relationship among system parameters as follows:
in the formula: x is a state variable; u is a control input variable; w represents a disturbance variable of the system; y represents a system output variable; a is a state space matrix, determined by system parameters; b is 1 A system disturbance matrix; b is 2 A control matrix for the system; c y For the system to output a matrix, D y1 And D y2 Respectively representing the disturbance and the control matrix of the system output representation;
according to the model structure analysis, the matrices take the values:
x＝[ΔδΔfΔX g ΔP HY ΔP PV ΔP Be Δu L ] T
w＝[ΔP L ΔS PV ] T
C y ＝[1 0 0 0 0 0 0]
D y1 ＝[0 0]D y2 ＝[0]。
step 2, solving robust H based on LMI 2 /H ∞ Controller design
Step 2-1, firstly, the state of the water-light storage micro-grid is required to be emptyAdding Z on the basis of the equation of space 2 /Z ∞ Two sets of performance evaluation function establishment H 2 /H ∞ State space equation of control:
in the formula: z 2 ，Z ∞ Is H 2 ，H ∞ Robust Performance output evaluation function, C 1 、D 11 、D 12 、C 2 、D 21 、D 22 Are each Z 2 /Z ∞ Performance evaluation matrix of (2), for Z 2 /Z ∞ Matrix C of performance evaluation function 1 、C 2 、D 11 、D 12 、D 21 、D 22 Is defined as:
C 1 ＝diag([x(1) x(2) x(3) 0 0 0 0])；
C 2 ＝diag([x(5) x(6) x(7) 0 0 0 0])；
D 11 ＝D 21 ＝0
in the formula, x (1) … x (8) is a matrix undetermined parameter and is also a weighting coefficient for system performance evaluation; selecting the performance combination with the optimal system stability and frequency regulation precision by changing the weighting coefficient by using an artificial intelligence optimization algorithm 2 /H ∞ And (3) introducing a controlled state space equation into the output feedback controller K(s) to enable u = K(s) y, and obtaining a corresponding closed-loop system state space equation as follows:
in the formula: a. The cl ＝A+B 2 KC y ；B cl ＝B 1 ；x cl ＝x；C cl1 ＝C 1 +D 12 KC y ；D cl1 ＝D 11 ；C cl2 ＝C 2 +D 22 KC y ；D cl2 ＝D 21 ；K＝K(s)；
Step 2-2, FIG. 3 is a standard robust mixture H 2 /H ∞ Control schematic diagram based on H 2 /H ∞ The design core of the robust output feedback controller of the state space equation is to minimize the control loop from w to Z in the closed loop system 2 /Z ∞ Closed loop rms gain. H 2 /H ∞ The mathematical idea of controller design is to find a suitable controller K(s) to make the system go from disturbance w to performance evaluation Z ∞ Closed loop transfer function T of output wz∞ H of(s) ∞ The norm does not exceed a given upper bound γ to ensure that the closed loop system is robust to uncertainties entered by w. At the same time, let w to Z 2 Closed loop transfer function T of wz2 H of(s) 2 The norm is as small as possible to ensure the robust and stable performance of the system to be at a better level. In this regard, the linear matrix inequality LMI is described as:
a. optimum H ∞ The performance indexes of the control are as follows: from w to Z ∞ Does not exceed gamma, which condition can be expressed as if and only if there is a symmetric matrix X, using the linear matrix inequality LMI ∞ Such that:
X ∞ ＞0
wherein I is a unit matrix, the same applies below; to be without loss of generality, let γ =1;
b. optimum H 2 The performance indexes of the control are as follows: from w to Z 2 H of closed loop transfer function of 2 Norm does not exceed v, and likewise with LMI can be expressed as if and only if D cl2 =0 and there are two symmetric matrices X 2 And Q is such that:
Trace(Q)＜v 2
in the formula: trace (Q) represents tracing the matrix Q, and v is not limited.
For the above-described ease of manipulation in the LMI framework, to satisfy the generality, a single Lyapunov matrix X is set such that X ∞ ＝X 2 The pole configuration adopts a default pole left area, and the hybrid H is calculated by combining the LMI equation 2 /H ∞ The performance index that the controller needs to meet is that the closed-loop poles of the controlled object are all located in the left half-open complex plane, and the following functions are optimized to express the overall performance, and the expression is as follows:
in which alpha and beta represent H 2 /H ∞ The norm weight of the performance can be used for obtaining robust controllers with different performances by configuring different values of alpha and beta;
the LMI-based goal implementation described above can be solved using the hinfmix solver of the LMI toolkit in MATLAB.
Step 3, applying the seagull intelligent algorithm to robust controller parameter optimization to enable the performance of the controller to reach the optimum
Step 3-1, the invention adopts ISE indexes commonly used in engineering as fitness functions for gull algorithm parameter optimization, so as to improve the efficiency of algorithm optimization, and the fitness function formula is as follows:
in the formula, deltaf is the frequency deviation of the system output; and t is simulation time.
Step 3-2, applying gull algorithm to robust controller parameter optimization
From the above robust H 2 /H ∞ The controller finds out in the solving process, Z 2 /Z ∞ Performance evaluation matrix C in (1) 1 、C 2 、D 11 、D 12 、D 21 、D 22 And the values of the alpha and beta weight coefficients directly influence the control performance of the controller, and the traditional method adopts an empirical method or a trial and error method to select, so that the workload is large, and the optimal solution is difficult to find. The method applies the gull intelligent algorithm to the optimal selection of the parameters to be solved when the robust controller is used for solving.
The optimization process, as shown in fig. 4, can be roughly expressed as: generating a gull individual group by an algorithm, wherein each individual carries 10 parameter values to be solved, and sequentially assigning the numerical values carried by the group of individuals to a matrix C 1 、C 2 、D 11 、D 12 、D 21 、D 22 The undetermined coefficient and the two weight coefficients of alpha and beta in the matrix are calculated by using an LMI tool kit in Matlab to obtain a corresponding robust output feedback controller K(s), and various interference working conditions are introduced into a closed-loop system formed by the robust controller K(s) obtained by current calculation to obtain a corresponding performance evaluation index; taking the performance index as an adaptive value of each individual gull in an improved gull algorithm, sorting the population adaptive values, and evaluating the optimal gull individual; according to the optimal individual, the gull algorithm continues to perform optimization iteration in the direction of reducing the fitness value until the condition of exiting the algorithm is reached.
Carrying out simulation:
the simulated system parameter is T y ＝0.08；k y ＝1；T w ＝0.5；T PV ＝1.8；k PV ＝1；T Be ＝0.1；k Be ＝1；T L ＝0.3；M＝0.2；D＝0.012；
The optimal coefficient matrix obtained after algorithm iteration is as follows:
C 1 ＝diag([0.6718 0.189 0.097 0 0 0 0])
C 2 ＝diag([0.9916 0.2007 0.2542 0 0 0 0])
two robust values H 2 /H ∞ The optimal weight coefficients are:
α＝0.5141 β＝0.1236
substituting the obtained coefficient matrix into a state space equation of the system, and solving a linear matrix inequality LMI with corresponding performance to obtain a robust H 2 /H ∞ The output feedback controller K(s) is:
in the formula: n is 1 ＝-28.23；n 2 ＝-1.513e06；n 3 ＝-4.745e07；n 4 ＝-4.631e08；n 5 ＝-1.656e09；n 6 ＝-2.94e09；n 7 ＝-3.815e09；n 8 ＝-1.662e09；d 1 ＝1；d 2 ＝198.7；d 3 ＝1.037e05；d 4 ＝3.887e06；d 5 ＝-1.24e07；d 6 ＝-1.515e08；d 7 ＝3.734e09；d 8 ＝2.115e09。
Based on the parameter setting, the SOA-H designed by the method of the invention 2 /H ∞ Controller and robust H using traditional self-tuning parameters 2 /H ∞ The simulation comparison of the controller and the PID controller optimized by the same method is carried out, the frequency deviation response of the controlled system under the power interference working condition shown in figure 5 is obtained as shown in figure 6, and the simulation result shows that the SOA-H obtained by the design method provided by the invention 2 /H ∞ The robust controller has stronger robustness to external power interference; at maximum overshoot, maximum steady state error and maximum settling timeEqual damping characteristic is superior to the traditional H 2 /H ∞ A controller and a PID controller.
In the embodiment, the controller is optimized by depending on the gull intelligent algorithm, and the key to solving the controller is to solve H 2 /H ∞ The controller realizes the LMI criterion conversion of the target and the calling of an LMI tool box in matlab, and the embodiment demonstrates the optimal H based on the intelligent algorithm optimization provided by the invention 2 /H ∞ The output feedback robust controller has more excellent control performance in the frequency control of the water optical storage micro-grid.
The above embodiments are merely illustrative of the technical concepts and features of the present invention, and the purpose of the embodiments is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.
Claims (4)
1. Micro-grid frequency robust optimal H with energy storage 2 /H ∞ A method for designing a controller, characterized in that,
step 1: establishing a load frequency regulation linear model of the water-light storage micro-grid to obtain a state space equation of the water-light storage micro-grid;
step 2: according to robust H ∞ Multi-objective control principle, design of output feedback robust H based on LMI tool solution 2 /H ∞ A controller;
and step 3: application of gull intelligent algorithm to robust controller Z 2 /Z ∞ Optimizing the performance evaluation matrix parameters and the performance weight norm to obtain the optimal robust H 2 /H ∞ A frequency controller.
2. Microgrid frequency robust optimal H with energy storage according to claim 1 2 /H ∞ The controller design method is characterized in that the step 1 of establishing a load frequency regulation linear model of the water-light storage micro-grid to obtain a state space equation of the water-light storage micro-grid comprises the following specific steps:
step 1-1, establishing a frequency change model of the water light storage micro-grid
The power change in the microgrid can cause the frequency change, and the frequency change dynamic model signal analysis is represented as follows:
ΔP＝ΔP s -ΔP L
ΔP s ＝ΔP PV +ΔP HY +ΔP Be
in the formula: g MG (s) is a characteristic function of the frequency change of the water light storage micro-grid; s represents the Laplace operator, the same below; m is the inertia constant of the system; d is the system damping constant; Δ f is the system frequency variation; Δ P represents the system power; delta P s The total power output of the water light storage micro-grid is represented; delta P L Representing water light storage microgrid load; delta P HY Outputting power for the hydraulic turbine set; delta P PV Is the output power of the photovoltaic cell panel; delta P Be The output power of the energy storage battery;
step 1-2, analyzing the output model of each power supply
a. Dynamic model of water turbine
The water turbine model is divided into two parts of a speed regulator and a prime motor, and the characteristic function G of the speed regulator y (s) the signal analysis is as follows:
in the formula: Δ X g The output quantity of the actuating mechanism of the hydraulic turbine speed regulator is provided; t is y And k y Respectively time constant and gain of the hydraulic turbine servomotor; r is a primary frequency modulation droop coefficient of the micro-grid; Δ u y (s) represents a control signal applied to the governor of the hydraulic turbine; Δ u L Is the control signal passed through the low pass filter; t is time;
in the prime mover link of the water turbine, an IEEE (institute of Electrical and electronics Engineers) linearization model of the water turbine is adopted, and a characteristic function G of the model w (s) is represented as follows:
in the formula: t is w Is the water flow inertia time constant, Δ P HY Outputting power for the hydraulic turbine set;
b. photovoltaic cell panel dynamic model
Photovoltaic cell panel output dynamic model and characteristic function G PV (s) the signal analysis is as follows:
in the formula: t is PV And k PV Time constant and gain of the photovoltaic panel; delta S PV Representing solar power;
c. energy storage battery dynamic model
Energy storage battery output dynamic model and characteristic function G Be (s) is represented as follows:
in the formula: t is Be And k Be Respectively the time constant and the gain of the energy storage battery; Δ u Be Representing a control signal applied to the energy storage cell;
and (3) establishing a frequency adjustment linear model of the water light storage micro-grid by combining the model analysis, wherein the LPF is a low-pass filter, and the characteristic function of the LPF is as follows:
in the formula: t is a unit of L Is the time constant of the LPF;
step 1-3, establishing a state space equation according to the frequency regulation linear model of the water light storage micro-grid
The state space equation of the water-light-storage micro-grid frequency regulation linear model is expressed as follows:
in the formula: x is a state variable; u is a control input variable; w represents a disturbance variable of the system; y represents a system output variable; a is a system state space matrix; b is 1 A system disturbance matrix; b is 2 A system control matrix; c y For the system output matrix, D y1 And D y2 Respectively representing the disturbance and the control matrix of the system output representation;
according to the model structure analysis, the matrices take the values:
x＝[ΔδΔfΔX g ΔP HY ΔP PV ΔP Be Δu L ] T
w＝[ΔP L ΔS PV ] T
C y ＝[1 0 0 0 0 0 0]
D y1 ＝[0 0]D y2 ＝[0]。
3. microgrid frequency robust optimal H with energy storage according to claim 1 2 /H ∞ Controller design method, characterized in that step 2 is based on robust H ∞ Multi-objective control principle, design of output feedback robust H based on LMI tool solution 2 /H ∞ The controller comprises the following specific steps:
step 2-1, adding Z on the basis of a state space equation of the water-light storage micro-grid 2 /Z ∞ Two sets of performance evaluation function establishment H 2 /H ∞ State space equation of control:
in the formula: z 2 ，Z ∞ Is H 2 ，H ∞ Robust performance output evaluation function, C 1 、D 11 、D 12 、C 2 、D 21 、D 22 Are each Z 2 /Z ∞ The specific definition of the matrix parameters is as follows:
C 1 ＝diag([x(1) x(2) x(3) 0 0 0 0])；
C 2 ＝diag([x(5) x(6) x(7) 0 0 0 0])；
D 11 ＝D 21 ＝0
x (1) -x (8) in the matrix are undetermined parameters of the evaluation matrix; parameters x (1), x (2), x (3), x (5), x (6) and x (7) are used for tracking load change and suppressing interference by setting a performance target for a controlled output end; parameters x (4) and x (8) restrain overshoot by limiting the change speed of the load fixed point signal of the regulator;
for mixture H 2 /H ∞ The control system introduces an output feedback controller K(s) such that u = K(s) y, resulting in the corresponding closed-loop system state-space equation as follows:
in the formula: a. The cl ＝A+B 2 KC y ；B cl ＝B 1 ；x cl ＝x；C cl1 ＝C 1 +D 12 KC y ；D cl1 ＝D 11 ；C cl2 ＝C 2 +D 22 KC y ；D cl2 ＝D 21 ；K＝K(s)；
Step 2-2, based on H 2 /H ∞ The design core of the robust output feedback controller of the state space equation is to minimize the control loop from w to Z in the closed loop system 2 /Z ∞ Closed loop rms gain of 2 /H ∞ The mathematical idea of controller design is to find a suitable controller K(s) to make the system go from disturbance w to performance evaluation Z ∞ Closed loop transfer function T of output wz∞ H of(s) ∞ Norm not exceeding a given upper bound gamma to ensure that the closed loop system is robust to uncertainties entered by w, while allowing w to Z 2 Closed loop transfer function T of wz2 H of(s) 2 The norm is as small as possible to ensure the robust stability performance of the system to be at a better level, and the linear matrix inequality LMI is described as follows:
a. optimum H ∞ The performance indexes of the control are as follows: from w to Z ∞ Does not exceed gamma, which condition is expressed as if and only if there is a symmetric matrix X, using the linear matrix inequality LMI ∞ Such that:
X ∞ ＞0
wherein I is a unit matrix, the same applies below; to be without loss of generality, let γ =1;
b. optimum H 2 The performance indexes of the control are as follows: from w to Z 2 H of closed loop transfer function of 2 Norm does not exceed v, and likewise LMI is taken to mean if and only if D cl2 =0 and there are two symmetric matrices X 2 And Q is such that:
Trace(Q)＜v 2
in the formula: trace (Q) represents tracing the matrix Q, and v is not limited;
setting a single Lyapunov matrix X such that X ∞ ＝X 2 The pole configuration adopts a default pole left area, and the hybrid H is calculated by combining the LMI equation 2 /H ∞ The performance index that the controller needs to meet is that the closed-loop poles of the controlled object are all located in the left half-open complex plane, and the following functions are optimized to express the overall performance, and the expression is as follows:
in which alpha and beta represent H 2 /H ∞ And the norm weight of the performance is configured with different alpha and beta values to obtain robust controllers with different performances.
4. Microgrid frequency robust optimal H with energy storage according to claim 1 2 /H ∞ A controller design method, characterized in that step 3 applies a gull intelligent algorithm to a robust controller Z 2 /Z ∞ Optimizing the performance evaluation matrix parameters and the performance weight norm to obtain the optimal robust H 2 /H ∞ The specific steps of the frequency controller are as follows:
step 3-1, setting a fitness function for gull algorithm optimization
The ISE index commonly used in engineering is used as a fitness function for optimizing the parameters of the gull algorithm, and the fitness function formula is as follows:
in the formula, deltaf is the frequency deviation of the system output; t is time;
step 3-2, applying the gull algorithm to robust controller parameter optimization, wherein the specific process is as follows:
generating a gull individual group, each individual carries a parameter value to be solved, and sequentially assigning the numerical value carried by the group of individuals to a performance evaluation matrix C influencing the solving of the controller 1 、C 2 、D 11 、D 12 、D 21 、D 22 The undetermined parameters and alpha and beta weight coefficients in the robust output feedback controller are calculated by using an LMI tool kit in Matlab to obtain a corresponding robust output feedback controller K(s), interference working conditions are introduced into a closed-loop system formed by the K(s) obtained by current calculation to obtain a corresponding performance evaluation index, the performance index is used as an adaptive value of each gull individual in an improved gull algorithm, the optimal gull individual is evaluated after sorting population adaptive values, and the gull individual is continuously optimized in the direction of reducing the adaptive value according to the optimal individual and the gull algorithmGeneration until reaching the condition of algorithm exit;
substituting the obtained optimal weight coefficient and coefficient matrix into a state space equation of the system, and solving a linear matrix inequality LMI with corresponding performance to obtain a robust H 2 /H ∞ And outputting the feedback controller K(s).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211389726.XA CN115622131A (en) | 2022-11-07 | 2022-11-07 | Micro-grid frequency robust optimal H with energy storage 2 /H ∞ Controller design method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211389726.XA CN115622131A (en) | 2022-11-07 | 2022-11-07 | Micro-grid frequency robust optimal H with energy storage 2 /H ∞ Controller design method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115622131A true CN115622131A (en) | 2023-01-17 |
Family
ID=84878384
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211389726.XA Pending CN115622131A (en) | 2022-11-07 | 2022-11-07 | Micro-grid frequency robust optimal H with energy storage 2 /H ∞ Controller design method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115622131A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117277400A (en) * | 2023-08-04 | 2023-12-22 | 昆明理工大学 | Control method for online optimization of water-light power generation system by objective function |
-
2022
- 2022-11-07 CN CN202211389726.XA patent/CN115622131A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117277400A (en) * | 2023-08-04 | 2023-12-22 | 昆明理工大学 | Control method for online optimization of water-light power generation system by objective function |
| CN117277400B (en) * | 2023-08-04 | 2024-04-30 | 昆明理工大学 | Control method for online optimization of water-light power generation system by objective function |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Yang et al. | Disturbance observer based fractional-order integral sliding mode frequency control strategy for interconnected power system | |
| Lin et al. | Controls of hybrid energy storage systems in microgrids: Critical review, case study and future trends | |
| CN110247438B (en) | Active power distribution network resource optimization configuration based on longicorn whisker algorithm | |
| CN108462212B (en) | Control method of new energy power system in multi-source multi-regulation-control-domain operation mode | |
| CN110048438B (en) | Power distribution network feeder level load power control method based on model predictive control | |
| CN114362267B (en) | Distributed coordination optimization method for AC/DC hybrid power distribution network considering multi-objective optimization | |
| CN111614110B (en) | Receiving-end power grid energy storage optimization configuration method based on improved multi-target particle swarm optimization | |
| CN115622131A (en) | Micro-grid frequency robust optimal H with energy storage 2 /H ∞ Controller design method | |
| Gupta et al. | Particle swarm optimization based automatic generation control of interconnected power system incorporating battery energy storage system | |
| Hu et al. | Deep reinforcement learning based coordinated voltage control in smart distribution network | |
| CN114722693A (en) | Optimization method of two-type fuzzy control parameter of water turbine regulating system | |
| CN113224769B (en) | Multi-time-scale power distribution network voltage optimization method considering photovoltaic multi-state adjustment | |
| Yang et al. | Coordination of generators and energy storage to smooth power fluctuations for multi-area microgrid clusters: A robust decentralized approach | |
| Cui et al. | Decentralized safe reinforcement learning for voltage control | |
| Swarup | Intelligent load frequency control of two-area interconnected power system and comparative analysis | |
| Gheisarnejad et al. | Reducing impact of constant power loads on DC energy systems by artificial intelligence | |
| CN115296309B (en) | Wind, light, water, fire and storage combined secondary frequency modulation method based on real-time inertia estimation | |
| CN109088418A (en) | A kind of electric distribution network reactive-voltage control method based on universal model | |
| Zadeh et al. | Frequency control of low inertia microgids in presence of wind and solar units using fuzzy-neural controllers | |
| Liu et al. | Deep-Q-network-based intelligent reschedule for power system operational planning | |
| CN114637204A (en) | Virtual synchronous machine control parameter setting method based on mixed H2/H infinity performance index | |
| Hburi et al. | Maximum power point tracking control for wind turbines with battery storage system | |
| CN108258732B (en) | Control method of new energy power system in normal regulation and control domain operation mode | |
| Yilmaz et al. | A smart grid robust optimization framework | |
| Gong et al. | ADRC & MPC Based Control Strategy of Bidirectional Buck-Boost Converter in Distributed Energy Storage Systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |