Networked robust stability analysis and optimization method for load frequency control

Abstract

The present invention discloses a method for networked robust stability analysis and optimization of load frequency control. The method first considers a simplified single-region power system and establishes a single-region system model with communication delay; then designs a PI controller, and converts the PI control into an output feedback control problem of the system, constructs a suitable Lyapunov-Krasovskii functional, and uses linear matrix inequality technology to derive a robust stability criterion of the system containing PI parameters; finally, in order to ensure the robust optimization of the system, the mincx function and the intelligent optimization algorithm are applied to optimize the obtained robust control law. The present invention takes into account the influence of time delay in the design of the PI controller, and obtains the stability criterion of the asymptotic stability and robust stability of the system by constructing a suitable Lyapunov-Krasovskii functional and LMI method; based on the linear matrix inequality, the maximum allowable delay of the system can be obtained under different delay types and different control gains.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and in particular relates to a networked robust stability analysis and optimization method for load frequency control. Background Art

[0002] Since it was proposed, load frequency control has been widely used in power systems due to its excellent ability to maintain the frequency and power exchange values ​​with neighboring areas at specified values, and has also laid a solid foundation for the development of smart grids.

[0003] In recent years, with the continuous development of power grids towards intelligence and networking and the deepening of control theory, many achievements have been made in the design and optimization of LFC controllers. With the dependence of signal transmission in power systems on open power communication networks, network communication delays inevitably affect system performance. In LFC systems, due to the introduction of communication networks, there will be a constant delay in the transmission of signals. However, due to the relatively small value of the delay, this delay is often ignored in the control and design of power systems. In addition, it is worth noting that packet loss and packet misordering in the communication channel may also cause time-varying delays. At present, LFC with delay has been studied in depth, but the impact of delay on LFC control performance has not been studied in depth. Summary of the invention

[0004] In order to solve the time lag phenomenon in the grid connection of new energy and the power system, the present invention provides a networked robust stability analysis and optimization method for load frequency control, which is used for the control of time delay-related robust stability of load frequency control in the power system.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A networked robust stability analysis and optimization method for load frequency control, comprising:

[0007] Step 1: Model analysis of load frequency control of power system, modeling of prime mover, speed regulator, generator, etc., and obtaining their related dynamic equations;

[0008] Step 2: Establish a simplified single-region power system model with communication delay;

[0009] Step 3: Design a PI controller, transform the PI control into the output feedback control of the system, and obtain the closed-loop control state space model of the system;

[0010] Step 4: In the absence of load disturbance, the asymptotically stable control law of the power system is obtained based on LMI and Lyapunov-Krasovskii functional;

[0011] Step 5: Taking the H∞ optimal performance index as the control target, solve the control law that satisfies the system state and input constraints, and thus design a robust H∞ controller;

[0012] Step 6: In order to reduce the conservatism of the results, the attenuation exponent γ of the system's H∞ optimal performance indicator is optimized through the mincx function, and the obtained robust controller is optimized using an intelligent algorithm to obtain the optimal control law.

[0013] Compared with the existing robust control method for power system load frequency control related to time delay, the present invention can achieve the following beneficial effects:

[0014] 1) The influence of time delay is considered in the design of PI controller, and the stability criteria of asymptotic stability and robust stability of the system are obtained by constructing appropriate Lyapunov-Krasovskii functional and LMI method;

[0015] 2) Compared with the existing optimization techniques, the present invention is effective and conservative; based on the linear matrix inequality, the maximum allowable delay of the system is obtained under different delay types and different control gains. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The present invention is a flow chart of a control method for delay-dependent robust stability of load frequency control in a power system.

[0017] Figure 2 It is a state response curve diagram of an example of the present invention when there is no load fluctuation and the transmission delay is constant.

[0018] Figure 3 It is a state response curve diagram of an example of the present invention when the load fluctuates and the transmission delay is constant.

[0019] Figure 4 It is a state response curve diagram of an example of the present invention when there is no load fluctuation and the transmission delay is a time-varying delay.

[0020] Figure 5 It is a state response curve diagram of an example of the present invention when the load fluctuates and the transmission delay is a time-varying delay. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0022] In order to solve the time lag phenomenon in the grid connection of new energy and the power system, the present invention proposes a time-delay-related robust control method, which belongs to the field of load frequency control of the power system. The method first considers a simplified single-region power system and establishes a single-region system model with communication delay; then designs a PI controller and transforms the PI control into the output feedback control problem of the system, constructs a suitable Lyapunov-Krasovskii functional, and uses linear matrix inequality technology to derive the robust stability criterion of the system containing PI parameters; finally, in order to ensure the robust optimization of the system, the mincx function and the intelligent optimization algorithm are applied to optimize the obtained robust control law.

[0023] The networked robust stability analysis and optimization method for load frequency control according to the embodiment of the present invention is as follows: Figure 1 As shown, the following steps are included:

[0024] Step 1: Model analysis of power system load frequency control, modeling the prime mover, speed regulator, generator, etc., and obtaining their related dynamic equations.

[0025] By studying the working principles and known power models of the prime mover, speed regulator, generator, etc., the transfer function models of the synchronous generator, speed regulator, and prime mover can be obtained:

[0026]

[0027]

[0028]

[0029] Among them, ΔP m , ΔP d , ΔP v They are respectively the mechanical output deviation of the prime mover, the change in the power system load, and the governor valve position deviation, K ps , T ps , T g , T ch are the generator gain coefficient, generator time constant, prime mover time constant, and speed regulator time constant. Δω is the generator speed change, ΔP g is the output power deviation of the speed regulator, and s is the Laplace operator.

[0030] Step 2: Establish a simplified single-area power system model with communication delay.

[0031] Based on the first step, the state space equation of the single-area load frequency control power system is obtained:

[0032]

[0033] where x(t) = [Δf(t) T ΔP m (t) T ΔP v (t) T ∫ACE T (s)] T , y(t)=[ACE ∫ACE] T ,

[0034]

[0035] ACE is the regional frequency error, which takes into account frequency change, load change and exchange power change. For load frequency control in a single area, the calculation formula is:

[0036] ACE=βΔf

[0037] Where R and β are the speed drop coefficient and frequency deviation factor of the speed regulator respectively.

[0038] Step 3: Considering the influence of the communication delay from sensor to controller in network transmission, design the PI controller:

[0039] u(t)=-K P ACE-K I ∫ACE

[0040] In the formula, K P , K I is the gain of the PI controller.

[0041] Define y(t) = [y(t) ∫y(t)] T , K=[K P K I ],but

[0042] u(t)=-Ky(t-τ(t))

[0043] τ(t) is the delay in the communication network, which can be a time-varying delay or a fixed delay.

[0044] In summary, the closed-loop system of the single-area model of power system load frequency control can be expressed as:

[0045]

[0046] Where L = -BKC, the time delay τ(t) is defined as follows:

[0047]

[0048] τ Mis the maximum allowed delay in the communication channel, α is the upper limit of the delay derivative, and for this system, the initial time of the continuous time equation is t∈[-τ,0]. -τ is the negative of the delay value.

[0049] Step 4: Obtain the control law of the asymptotic stability of the power system in the absence of load disturbances.

[0050] (1) Select the following Lyapunov-Krasovskii functional:

[0051] V(t)=V1(t)+V2(t)+V3(t)

[0052] Where V1(t) = x(t) T Px(t), P, S1, S2, and Z are real symmetric matrices.

[0053] (2) According to the definition of asymptotic stability in linear system theory, when the derivative of the Lyapunov functional is less than 0, the system is asymptotically stable.

[0054] Taking the first derivative of the functional in (1), we get:

[0055]

[0056]

[0057]

[0058] because therefore, It can also be expressed as:

[0059]

[0060] There is a lemma stating that there exists any matrix R=R T >0, scalar τ>0, and vector function Then the following holds:

[0061]

[0062] According to the above lemma, It can be expressed as:

[0063]

[0064] definition:

[0065] η(t)=[x(t) x(t-τ(t)) x(t-τ M )] T

[0066] but The derivative of :

[0067]

[0068] When Φ<0, the system is asymptotically stable. According to Lyapunov theory and Schur complement property, the control law of asymptotically stable system can be obtained as:

[0069] When ΔP d = 0, if there exists a real symmetric matrix P>0, S1, S2>0, Z>0, and scalars α, τ M , so that the following inequality holds, then the system is stable.

[0070]

[0071] Where M = A T P+PA+S1+S2, * indicates symmetry.

[0072] Step 5: Based on step 4, ∞ The optimal performance index is taken as the control target, the control law that satisfies the system state and input constraints is obtained, and the stability analysis is performed.

[0073] Because we need to consider the H∞ optimal performance index, we define the performance index as follows:

[0074]

[0075] Where γ is the attenuation exponent.

[0076] The above formula can also be expressed as:

[0077]

[0078] Consistent with the proof in step 4, we get:

[0079]

[0080] definition: but:

[0081]

[0082] According to the Schur complement property, the robust stability criterion of the system can be obtained:

[0083] For a given attenuation γ>0, with an initial value x(0)=0, the external disturbance ΔP d (t) and the output feedback y(t) satisfy H ∞ Norm Constraints And the following equation is satisfied, then the closed-loop system is robustly stable under the control of the PI controller:

[0084]

[0085] Step 6: In order to reduce the conservatism of the results, the attenuation exponent γ of the system's H∞ optimal performance indicator is optimized through the mincx function, and the obtained robust controller is optimized using an intelligent algorithm to obtain the optimal controller.

[0086] (1) Optimizing robust performance

[0087] The mincx function in the matlab toolbox is used to optimize the robust performance criteria to obtain the optimal attenuation coefficient γ and the corresponding PI controller parameters. The specific Mincx function is shown in the following formula:

[0088] mincx

[0089] stP>0,S1>0,S2>0,Z>0

[0090]

[0091] (2) Controller Optimization

[0092] For the optimization of the controller, the present invention uses some intelligent algorithms to optimize the obtained controller so that the obtained controller satisfies H ∞ The performance is standard and less conservative. By comparing the gray wolf algorithm, gray wolf + genetic algorithm, gray wolf + particle swarm algorithm, etc., a controller with better performance is obtained.

[0093] When the delay in the power system communication network is a constant delay, Figure 2 and Figure 3 When there is no load disturbance and when there is load disturbance and K P =0,K I =0.4 when the power system state response diagram. Figure 2 It can be seen that when there is no load change, each state gradually tends to be stable. Figure 3 In the figure, a step disturbance with an amplitude of 0.1 pu (pu is the per-unit value) is applied to the power system at t = 15s. It can be seen from the figure that the state of the system will fluctuate after the load disturbance is added, but under the action of the controller, the state response eventually returns to stability. The above proves that the design of the controller is effective. Figures 2 to 5 The solid line in the top middle is ACE.

[0094] When the delay in the power system communication network is time-varying, Figure 4 and Figure 5For the case where there is no load disturbance and there is a load disturbance and K P =0,K I =0.4 when the power system state response diagram. Figure 4 It can be seen that within the first 1s, the state of the system does not change, which is related to the upper limit of the maximum allowable delay of the system. The subsequent state change is basically consistent with the state change trend when the delay is constant, and the frequency deviation of the system will return to zero after a small fluctuation. Figure 5 The status response is Figure 4 Compared with the previous example, the system state fluctuated in the first second; after 1 second, the change in state response was roughly the same as Figure 4 After the load disturbance is added at 15s, the system state also changes to Figure 2 Similar small fluctuations, but also quickly returned to a stable state.

[0095] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0096] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A networked robust stability analysis and optimization method for load frequency control, characterized in that: The following steps are involved: Obtain transfer function models of generator, speed governor, and prime mover; Based on the transfer function model, a single-region power system model with communication delay is established; Design a PI controller, transform the PI control into output feedback control of the power system, and obtain a closed-loop control state space model of the power system; In the absence of load disturbance, the control law of asymptotic stability of the power system is obtained; Taking the H∞ optimal performance index as the control target, solve the control law that satisfies the system state and input constraints, and thus design a robust H∞ controller; Among them, based on the transfer function model, the single-region power system model with communication delay is established, including: Establish the state space equation of the load frequency control power system in a single area: Where x(t) = [Δf(t) T ΔP m (t) T ΔP v (t) T ∫ACE T (s)] T , y(t)=[ACE ∫ACE] T , u(t) is the controller control quantity, R is the speed drop coefficient of the speed regulator, ΔP m , ΔP d , ΔP v They are respectively the mechanical output deviation of the prime mover, the load variation of the power system, and the position deviation of the governor valve. ps , T ps , T g , T ch are the generator gain coefficient, the generator time constant, the prime mover time constant, and the speed regulator time constant, Δω is the generator speed change and Δω=2ΠΔf, s is the Laplace operator; ACE is the regional frequency error and the calculation formula is: ACE=βΔf Where β is the frequency deviation factor; Design a PI controller and transform the PI control into output feedback control of the power system. The closed-loop control state space model of the power system includes: Considering the influence of the communication delay from sensor to controller in network transmission, a PI controller is designed: u(t)=-K P ACE-K I ∫ACE In the formula, K P , K I P I The gain of the controller; Define y(t) = [y(t) ∫y(t)] T , K=[K P K I ],but: u(t)=-Ky(t-τ(t)) Where τ(t) is the delay in the communication network; Then the closed-loop system of the single-area model of load frequency control of the power system with time delay is expressed as: Where L = -BKC, and the delay τ(t) is defined as follows: In the formula, τ M is the maximum allowed delay in the communication channel, α is the upper limit of the delay derivative; In the absence of load disturbance, based on LMI and Lyapunov-Krasovskii functional, the asymptotically stable control law of the power system is obtained, including: (1) Select the following Lyapunov-Krasovskii functional: V(t)=V1(t)+V2(t)+V3(t) V1(t)=x(t) T Px(t) Where P, S1, S2, and Z are real symmetric matrices; (2) According to the definition of asymptotic stability in linear system theory, when the derivative of the Lyapunov functional is less than 0, the system is asymptotically stable. Then, taking the first derivative of the functional, we get: because therefore It is expressed as: There is a lemma stating that there exists any matrix R=R T >0, scalar τ>0, and vector function Then the following holds: According to the above lemma, It is expressed as: Definition: η(t) = [x(t)x(t - τ(t))x(t - τ M )] T but The derivative of : When Φ<0, the system is asymptotically stable. According to Lyapunov theory and Schur complement property, the control law of the asymptotically stable system is: When ΔP d = 0, if there exists a real symmetric matrix P>0, S1, S2>0, Z>0 and scalars α and τ M , so that the following inequality holds, then the system is stable: Where M = A T P+PA+S1+S2, * indicates symmetry.

2. The method for networked robust stability analysis and optimization of load frequency control according to claim 1, characterized in that: The transfer function model of the generator, speed regulator and prime mover is: In the formula, ΔP m , ΔP d , ΔP v They are respectively the mechanical output deviation of the prime mover, the load variation of the power system, and the position deviation of the governor valve. ps 、T ps 、T g 、T ch are the generator gain coefficient, generator time constant, prime mover time constant, and speed regulator time constant, Δω is the generator speed change, and Δω=2ΠΔf, ΔP g is the output power deviation of the speed regulator, and s is the Laplace operator.

3. The method for networked robust stability analysis and optimization of load frequency control according to claim 1, characterized in that: The delay can be time-varying delay or fixed delay.

4. The method for networked robust stability analysis and optimization for load frequency control according to claim 1, characterized in that: Taking the H∞ optimal performance index as the control target, solving the control law that satisfies the system state and input constraints, and then designing a robust H∞ controller includes: Define performance metrics: In the formula, γ is the attenuation exponent; the formula can also be expressed as: Right now: definition: but: According to the Schur complement property, the robust stability criterion of the system is obtained: For a given attenuation γ>0, with an initial value x(0)=0, the external disturbance ΔP d (t) and the output feedback y(t) satisfy H ∞ Norm Constraints And satisfy the following formula: Then the closed-loop system is robust and stable under the control of the PI controller.

5. The method for networked robust stability analysis and optimization for load frequency control according to claim 1 or 4, characterized in that: The method further comprises the steps of: Finally, the attenuation exponent γ of the system's H∞ optimal performance indicator is optimized through the mincx function, and the obtained robust controller is optimized using an intelligent algorithm to obtain the optimal control law.

6. The method for networked robust stability analysis and optimization for load frequency control according to claim 5, characterized in that: Optimizations for robust performance include: The robust performance criteria are optimized using the mincx function in the matlab toolbox to obtain the optimal attenuation coefficient γ and the corresponding PI controller parameters. Controller optimization includes: For the optimization of the controller, an intelligent algorithm is used to optimize the obtained controller so that the obtained controller meets H ∞ The performance is standard and less conservative; a controller with better performance is obtained by comparing the gray wolf algorithm, gray wolf + genetic algorithm or gray wolf + particle swarm algorithm.

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