MPC-PI hierarchical control method and system for improving frequency stability of power system

Abstract

The invention discloses an MPC-PI hierarchical control method and system for improving the frequency stability of a power system, and relates to the technical field of power system control and optimization, and the method comprises the steps: building a power system dynamic model containing inertia control, including a generator, a load, renewable energy and an interaction relation thereof, and determining a system state variable and a control input; in the MPC-PI mode, the upper MPC is responsible for optimizing the parameters of the PI controller in real time; in the MPC-PI mode, a lower PI controller needs to have an Anti-Window mechanism so as to prevent an integral saturation phenomenon caused by system constraint or a nonlinear effect; when the state change of the system is large or a saturation phenomenon occurs, the Anti-Window mechanism adjusts the integral part of the PI controller to avoid excessive accumulation of errors and ensure the stability and responsiveness of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of power system control and optimization, and specifically to an MPC-PI hierarchical control method and system for improving the frequency stability of a power system, including the combined application of model predictive control (MPC) and proportional integral (PI) control strategies. Background Art

[0002] With the rapid development of renewable energy, especially the widespread application of wind and solar energy, the power system is facing severe challenges in frequency stability. The intermittent and volatile nature of renewable energy makes it difficult for traditional frequency regulation methods to effectively cope with it. Slight fluctuations in frequency may cause equipment damage, system instability, and even cause large-scale power failures. Therefore, how to ensure the frequency stability of the power system in an environment with high penetration of renewable energy has become an important issue that needs to be solved in the field of power engineering.

[0003] Current frequency regulation technologies mainly include traditional PI control, model-based control methods, and distributed control strategies. Although PI controllers perform well in some cases, their parameter adjustment often relies on experience and is difficult to adapt to changes when facing fluctuations in renewable energy. In addition, PI controllers may not be sufficient to meet the needs of modern power systems in terms of dynamic response performance and anti-interference capabilities. Although model-based control methods take into account the dynamic characteristics of the system, they usually require complex models and long design times.

[0004] Model predictive control (MPC) is an advanced control strategy that has gradually attracted attention. MPC optimizes control strategies in real time by predicting future behaviors. It has good adaptability and predictability, and can effectively deal with the intermittency and uncertainty of renewable energy and ensure frequency stability. However, the practical application of MPC faces challenges, especially during implementation. Due to its complex optimization calculation requirements, it is often necessary to replace the supporting components of the existing PI controller, which may involve high costs and technical difficulties. Summary of the invention

[0005] The present invention proposes an MPC-PI hierarchical control method and system for improving the frequency stability of power systems. Based on the hierarchical control strategy of MPC, MPC is used as the upper controller to optimize the parameter trajectory of the traditional PI controller. This control strategy not only has the adaptability and foresight of MPC, but also retains the simplicity and reliability of the PI controller. By introducing MPC in hierarchical control, multi-level and multi-mode control operation can be achieved to adapt to different operation requirements and system states.

[0006] The technical solution of the present invention is as follows:

[0007] The MPC-PI hierarchical control method for improving the frequency stability of the power system is characterized by comprising the following contents:

[0008] S1: Establish a dynamic model of the power system including inertia control, including generators, loads, renewable energy and their interactions, and determine the system state variables and control inputs;

[0009] Determine the system state variables and control inputs, where: the overall system state variable is X = [Δf1, Pm1, Xg1, Pv1, ROCOF1, Δf2, Pm2, Xg2, Pv2

[0010] ,ROCOF2,Δf3,Pm3,Xg3,Pv3,ROCOF3,Ptie12,Ptie23

[0011] ,Ptie31]T;

[0012] Control input U = [u11,u21,u12,u22,u13,u23];

[0013] Control output

[0014] Y=[ACE1,ROCOF1,ACE2,ROCOF2,ACE3,ROCOF3] T ;

[0015] Introduce a nonlinear perturbation term and set it to w(t) = [PL1(t), PL2(t), PL3(t)];

[0016] If centralized control is adopted, the system dimension is 18. Considering the time delay caused by the distance factor, the system is divided into three subsystems;

[0017] Define the inertia-load frequency control parameters of the low-inertia multi-area power system, including but not limited to the following components: Governor: set the guide vane opening deviation Xgi, governor gain Kgovi, governor time constant Tgovi; Unit: set the unit output power Pmi, unit gain Kturi, unit time constant Tturi; Energy storage equipment: set the energy storage equipment output power PVi, energy storage equipment gain KESSi, energy storage equipment time constant TESSi; Equivalent generator: set the system inertia coefficient Hi and the system damping coefficient Di; Other parameters: including frequency deviation Δfi, frequency deviation change rate ROCOFi, tie line power deviation Ptieij;

[0018] Form the state space equations of the regional system:

[0019] The state space equations of each region are constructed as shown in formula (1):

[0020]

[0021] Where i = 1-3, X i =[Δf1,P m1 , X g1 , P v1 ,ROCOF1,P tie12 , P tie31 ] T , U i =[u 11 ,u 21 ],Y i =[ACE1,ROCOF1,ACE2,ROCOF2,ACE3,ROCOF3] T , A i , B i 、F i , C i They are:

[0022]

[0023] S2: Control mode selection;

[0024] S21: Assessing the stability of the power system:

[0025] During the operation of the power system, monitor the system status to determine whether there are major changes in operating conditions;

[0026] S22: Select control mode:

[0027] If the power system is relatively stable and there is no significant change in operating conditions during the period considered:

[0028] Select the traditional PI controller and disconnect the upper-level MPC model predictive control optimization;

[0029] S23: If the power system is in a state of high renewable energy penetration and the operating conditions vary greatly and are difficult to predict: select the MPC-PI control model to adapt to the dynamically changing power system needs;

[0030] S3: In MPC-PI mode, the upper-level MPC is responsible for real-time optimization of the parameters of the PI controller;

[0031] S4: In the MPC-PI mode, the lower-level PI controller needs to have an Anti-Windup mechanism to prevent integral saturation caused by system constraints or nonlinear effects. When the system state changes greatly or saturation occurs, the Anti-Windup mechanism will adjust the integral part of the PI controller to avoid excessive accumulation of errors and ensure the stability and responsiveness of the system.

[0032] S5: The PI controller automatically takes over when the system is stable and performs basic proportional-integral control tasks. The PI controller measures the error in real time and performs proportional and integral adjustments to maintain the steady-state operation of the system.

[0033] S6: Parameter optimization: Parameter optimization index setting method based on multi-objective GSA. The optimized parameters include conventional GPC parameters, important weights and anti-saturation strategy related parameters. The parameters to be optimized include: a1, N1, N P1 and Q i , R i Key weight.

[0034] The MPC-PI hierarchical control method for improving the frequency stability of the power system, S3 includes the following contents:

[0035] S31: Model Design

[0036] The frequency fluctuation is predicted using the system dynamic model to set the frequency stability as

[0037] Control objectives; at the same time, formulate optimization objective functions;

[0038] S32: Define the Laguerre function:

[0039] The discrete Laguerre function is introduced as the orthogonal basis of the controller to reduce the computational burden of the controller. The control trajectory is described by the Laguerre coefficient. The z-transform form of the Laguerre function is shown in formula (2).

[0040]

[0041] in,

[0042] S33: Determinant of control trajectory

[0043] Let ln be the inverse z-transform form of the nth Γn(z,a), equation (3) can be expressed as

[0044] The determinant L(k) is composed of l1 to lN, and equation (4) expresses

[0045] The conversion relationship between L(k+1) and L(k);

[0046] L(k)=[l1(k),l2(k)…l N (k)] T (3)

[0047] L(k+1)=A l L(k)

[0048]

[0049] S34: Control quantity prediction

[0050] According to equations (3) and (4), the control amount prediction of the system at the kth moment to the k+mth moment is shown in equation (5), where Δu(k+i|k) represents the control amount prediction value of the i-th step at the kth step, η=[c1,c2,...c N ] is the decision coefficient to be optimized, and the dimension N of the Laguerre coefficient has nothing to do with the prediction time domain length NP;

[0051]

[0052] S35: Building a prediction model

[0053] In the MIMO-MPC controller, the output Δui is the inertia control loop control quantity and the secondary frequency modulation control quantity, expressed as formula (6); the augmented equation of the common control area system is formula (7);

[0054] Δu i (k)=[Δu i1 (k),Δu i2 (k)] T (6)

[0055]

[0056] S36: State equations for multi-input multi-output systems

[0057] The state equation of the multi-input multi-output system including inertia control is shown in Equation (8), where the input and output of the system are represented by matrices Bi and Ci;

[0058]

[0059] S37: Incremental control quantity expression

[0060] The load-frequency control quantity increment Δui1 and the inertia control quantity increment Δui2 can be expressed in the form of Laguerre function, as shown in formula (9);

[0061]

[0062] Here, Li1T(k) and ηi1 are the parameters involved in the Laguerre function form of Δui1, and Li2T(k) and ηi2 are the parameters involved in the Laguerre function form of Δui2. Δui1 and Δui2 can be optimized independently, and the parameter selection does not affect each other;

[0063] S38: Laguerre function parameter definition

[0064] The newly defined LiT contains the Laguerre function z-transformation formal parameters involved in the two control quantities, as shown in equation (10);

[0065]

[0066] S39: State quantity expression

[0067] The state quantity of the system at the kth sampling time can be expressed as formula (11);

[0068]

[0069] S310: Cost Function and Optimization

[0070] The cost function of the system during rolling optimization can be expressed by formula (12), where Qi and Ri are weight matrices, and RL is shown in formula (13);

[0071]

[0072] In order to minimize the cost function J(k), it is necessary to directly obtain the optimal control parameters of the PI controller at the kth moment to ensure that the only independent variable in J(k) is K(k); the relationship expression between the matrix ΔU(k) ​​and K(k) needs to be derived.

[0073] In step S2, when the MPC-PI mode is adopted, steps S3 to S6 are performed.

[0074] The MPC-PI hierarchical control method for improving the frequency stability of the power system, S4 includes the following contents:

[0075] S41: Designing an Improved PI Controller

[0076] Combined with online learning algorithms, the gain of the PI controller is automatically adjusted according to the real-time operating status of the system;

[0077] S42: Calculate the control amount increment

[0078] At the kth moment, the control amount increment Δu(k) is calculated using the formula:

[0079] Δu(k)=i=1∑Nu-1Ki·e(k+i|k)·ΔT

[0080] Among them, the error e(k+i|k)=yr(k+i|k)-y^(k+i|k);

[0081] S43: Solving quadratic programming problems

[0082] When solving the quadratic programming problem, replace the control increments Δu1(k) and Δu2(k);

[0083] Consider the four key constraints of load frequency control: control value amplitude and its increment constraint; prime mover ramp rate constraint; system frequency fluctuation constraint; ROCOF constraint;

[0084] S44: Apply anti-windup mechanism

[0085] The anti-saturation PI control strategy is shown in formula (15):

[0086]

[0087] If the control quantity u(k-1) in the k-1th step is greater than the given limit u m If the kth step control is large, only the negative error will be considered for implementation; otherwise, only the positive error will be considered.

[0088] S45: Application Control Algorithm

[0089] The above control algorithm is applied to the load frequency controller and the inertia controller.

[0090] In the MPC-PI hierarchical control method for improving the frequency stability of the power system, in S41, an improved PI controller is designed:

[0091] The control quantity increment Δu(k) at time k can be obtained by the principle of the lower-level PI controller, as shown in formula (14):

[0092]

[0093] Where i∈[1,2...N u -1], ΔT is the integration step length, e is the error between the predicted output and the given trajectory, that is, the deviation of the system predicted ACE value from the softened given value,

[0094] When solving the quadratic programming problem shown in equation (8), Δu1(k) and Δu2(k) are replaced, and the key constraints of system load frequency control that need to be considered are increased to four: control quantity amplitude and its increment constraint, prime mover climbing rate constraint, system frequency fluctuation constraint and ROCOF constraint; they are solved and applied to the load frequency controller and inertia controller.

[0095] In the MPC-PI hierarchical control method for improving the frequency stability of the power system, in S3, the MPC and PI controllers are integrated to form a hierarchical control architecture:

[0096] The anti-saturation strategy is adopted in the lower PI controller to limit the integral control output to a lower order of magnitude, which can effectively shorten the time lag and suppress overshoot, so that the system can eliminate the deviation more quickly and reach a steady state again; the anti-saturation PI control strategy is shown in formula (15):

[0097]

[0098] If the control quantity u(k-1) in the k-1th step is greater than the given limit u m If is large, then the k-th step control will only consider the negative error for implementation; otherwise, only the positive error will be considered.

[0099] The MPC-PI hierarchical control method for improving the frequency stability of the power system, 6 includes the following contents:

[0100] S61: Define optimization goals

[0101] Determine the MPC parameters that need to be adjusted, such as the prediction horizon, control horizon, and weight coefficients, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption;

[0102] S62: Initialize GSA parameters

[0103] Initialize the parameters of GSA, including population size, gravity constant and maximum number of iterations, and randomly generate a set of initial solutions to form an initial population;

[0104] S63: Fitness evaluation

[0105] The fitness of each individual parameter combination is evaluated and the fitness value, i.e., J*, is calculated by running the MPC control simulation in the power system model;

[0106]

[0107] S64: Update individual quality

[0108] Update the mass of each individual according to the fitness value. The higher the fitness, the greater the mass. At the same time, calculate the gravity field between individuals.

[0109] S65: Location Update

[0110] The position of individuals is updated through the gravitational formula to generate new solutions, and random factors are introduced to maintain population diversity and prevent falling into local optimality;

[0111] S66: Boundary Processing

[0112] Perform boundary processing on parameter values ​​that exceed the defined range to ensure that the parameters are within the acceptable range;

[0113] S67: Iteration Check

[0114] During the iteration process, check whether the maximum number of iterations or fitness convergence conditions are reached. If not, return to the fitness evaluation and gravity update steps;

[0115] S68: Select the optimal solution

[0116] After the iteration, the individual with the best fitness is selected as the optimal solution of the MPC parameters and applied to the actual power system for frequency stability test. Finally, the performance indicators before and after optimization are compared to verify the effectiveness of GSA optimization.

[0117] In S63, an MPC control simulation is run in the power system model to calculate a fitness value, i.e., J*;

[0118]

[0119] Gravity Searching Algorithm, GSA optimizes the upper-level MPC parameters to achieve better control effects. The specific process is as follows:

[0120] (1) Define the optimization goal, determine the MPC parameters that need to be adjusted, such as the prediction horizon, control horizon, and weight coefficient, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption;

[0121] (2) Initialize the parameters of GSA, including population size, gravity constant, and maximum number of iterations, and randomly generate a set of initial solutions to form an initial population;

[0122] (3) Evaluate the fitness of each individual parameter combination and calculate the fitness value, i.e., J*, by running the MPC control simulation in the power system model;

[0123] (4) Update the mass of each individual according to the fitness value. The higher the fitness, the greater the mass. At the same time, calculate the gravity field between individuals.

[0124] (5) Update the position of individuals through the gravity formula, generate new solutions, and introduce random factors to maintain population diversity and prevent falling into local optimality;

[0125] For parameter values ​​that exceed the defined range, boundary processing is performed to ensure that the parameters are within the acceptable range. During the iteration process, check whether the maximum number of iterations or fitness convergence conditions are reached. If not, return to the fitness evaluation and gravity update steps. After the iteration, the individual with the best fitness is selected as the optimal solution for the MPC parameters, and it is applied to the actual power system for frequency stability testing. Finally, the performance indicators before and after optimization are compared to verify the effectiveness of GSA optimization.

[0126] The MPC-PI hierarchical control method for improving the frequency stability of the power system is characterized by adopting the MPC-PI mode or the PI controller mode, and adopting manual switching or automatic system switching.

[0127] A computer system includes a processor and a memory, wherein a computer program is stored in the memory, and is characterized in that when the processor executes the computer program, the MPC-PI hierarchical control method for improving the frequency stability of a power system with renewable energy penetration is implemented.

[0128] The present invention relates to a hierarchical control strategy based on the combination of model predictive control (MPC) and proportional-integral (PI) control, which aims to improve the frequency stability of power systems with high renewable energy penetration. First, the present invention constructs a dynamic model of the power system, describes the relationship between system frequency and load and power generation capacity, and achieves dynamic balance of frequency by controlling input power and load regulation. This process ensures that the system can effectively respond to changes in grid frequency, thereby improving power quality and system stability.

[0129] Secondly, the present invention establishes a model of the power system, uses the state space method to model the system, and realizes the prediction of future frequency fluctuations through multi-step prediction. This prediction capability enables the system to maintain a good operating state under the change of load and power generation conditions.

[0130] In terms of control strategy, the present invention adopts a dual-mode, hierarchical control structure, combined with MPC and PI control strategies, to dynamically adjust control inputs and parameter weights to optimize system performance. The objective function design takes into account the error between the system output and the predicted value to ensure the real-time and effectiveness of control decisions. Through the adaptive control algorithm, the control parameters are continuously optimized, thereby enhancing the application potential of this control strategy in high renewable energy penetration and grid dispatching.

[0131] The control strategy of the present invention can be operated in two modes:

[0132] First, when the system operating conditions are complex or the renewable energy fluctuates greatly, MPC will dominate the control process, and MPC is responsible for real-time optimization of the parameters of the PI controller to cope with frequency changes.

[0133] Secondly, when the system operating conditions are relatively stable, the PI controller will automatically take over and maintain the basic operating state of the system. This mode switching can effectively improve the flexibility and response speed of the control system.

[0134] In addition, the MPC-based hierarchical control strategy also has a certain fault tolerance. When the system is abnormal or the equipment fails, MPC can quickly adjust the control strategy to adapt to the new operating conditions and avoid the risk of system collapse. This feature is particularly important in modern power systems because the stability of the system is directly related to the reliability and economy of power supply.

[0135] In practical applications, this control strategy can be seamlessly integrated with the equipment when the existing power system is transformed into a smart grid, reducing the need for transformation of old equipment and reducing implementation costs. At the same time, the real-time optimization characteristics of MPC enable the system to maintain good performance when facing a higher proportion of renewable energy access in the future.

[0136] The MPC-based hierarchical control strategy proposed in the present invention has the following advantages and positive effects:

[0137] 1. Adaptability and foresight: Through real-time optimization, MPC can dynamically adjust the control strategy according to the system status and effectively respond to renewable energy fluctuations and complex operating conditions by optimizing the control parameters of the PI controller.

[0138] 2. Simplicity and reliability: Combining the advantages of traditional PI controllers, it retains the ease of use and stability of the control system while improving overall performance.

[0139] 3. Multi-level, multi-mode control: realize flexible switching between two operating modes, improve system response speed, and adapt to different operating requirements.

[0140] 4. Fault tolerance: In the event of equipment failure or abnormal conditions, MPC can quickly adjust the control strategy to reduce the risk of system collapse and ensure the stability of the power system.

[0141] 5. Seamless integration and cost-effectiveness: It can be seamlessly connected with the existing power system, reducing the need for transformation, lowering implementation costs, and facilitating the transformation to smart grids.

[0142] 6. Adapt to future development: When a high proportion of renewable energy is connected, maintain good control performance and system stability to meet the needs of future power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0143] Figure 1 Schematic diagram of the inertia-load frequency control structure of a multi-regional power system with high renewable energy penetration.

[0144] Figure 2 Structural diagram of the proposed MPC control principle.

[0145] Figure 3 Flow chart of load frequency control of low inertia power system based on MPC-PI controller and incorporating pumped storage characteristic line model. DETAILED DESCRIPTION

[0146] The MPC-PI hierarchical control method for improving power system frequency stability adopts an MPC-PI-based hierarchical control strategy to enhance the frequency stability of power systems with high renewable energy penetration, including:

[0147] S1: Establish a dynamic model of the power system including inertia control, including generators, loads, renewable energy and their interactions, and determine the system state variables and control inputs. Figure 1 .

[0148] The overall system state is X = [Δf1, P m1 , X g1 , P v1 ,ROCOF1,Δf2,P m2 , X g2 , P v2 ,ROCOF2,Δf3,P m3 , X g3 , P v3 ,ROCOF3,P tie12 , P tie23 , P tie31 ] T ,U=[u 11 ,u 21 ,u 12 ,u 22 ,u 13 ,u 23 ], Y=[ACE1,ROCOF1,ACE2,ROCOF2,ACE3,ROCOF3] T is the system output, and the nonlinear disturbance term is regarded as w(t) = [P L1 (t), P L2 (t), P L3 (t)]. If centralized control is adopted, the system will be 18-dimensional and involve many time delays caused by distance factors. Therefore, the present invention divides the overall system into three subsystems and adopts distributed control to achieve the purpose of reducing the model dimension.

[0149] Table 1 Parameters involved in inertia-load frequency control of low-inertia multi-region power system

[0150]

[0151]

[0152] The state space equation of each regional system is shown in formula (1):

[0153]

[0154] Where i = 1-3, X i =[Δf1,P m1 , X g1 , P v1 ,ROCOF1,P tie12 , P tie31 ] T , Ui =[u 11 ,u 21 ],Y i =[ACE1,ROCOF1,ACE2,ROCOF2,ACE3,ROCOF3] T , A i , B i 、F i , C i They are:

[0155]

[0156] S2: Manual selection of PI or MPC-PI control mode

[0157] S21: Assessing the stability of the power system:

[0158] During the operation of the power system, monitor the system status to determine whether there are major changes in operating conditions;

[0159] S22: Select control mode:

[0160] If the power system is relatively stable and there is no significant change in operating conditions during the period considered:

[0161] Select the traditional PI controller and disconnect the upper-level MPC model predictive control optimization;

[0162] S23: If the power system is in a state of high renewable energy penetration and the operating conditions vary greatly and are difficult to predict: select the MPC-PI control model to adapt to the dynamically changing power system needs;

[0163] S3: In MPC-PI mode, the upper-level MPC is responsible for real-time optimization of the parameters of the PI controller;

[0164] S31: Model Design

[0165] The frequency fluctuation is predicted using the system dynamic model to set the frequency stability as

[0166] Control objectives; at the same time, formulate optimization objective functions;

[0167] S32: Define the Laguerre function:

[0168] The discrete Laguerre function is introduced as the orthogonal basis of the controller to reduce the computational burden of the controller. The control trajectory is described by the Laguerre coefficient. The z-transform form of the Laguerre function is shown in formula (2).

[0169]

[0170] in,

[0171] S33: Determinant of control trajectory

[0172] Let ln be the inverse z-transform form of the nth Γn(z,a), equation (3) can be expressed as

[0173] The determinant L(k) is composed of l1 to lN, and equation (4) expresses

[0174] The conversion relationship between L(k+1) and L(k);

[0175] L(k)=[l1(k),l2(k)…l N (k)] T (3)

[0176] L(k+1)=A l L(k)

[0177]

[0178] S34: Control quantity prediction

[0179] According to equations (3) and (4), the control amount prediction of the system at the kth moment to the k+mth moment is shown in equation (5), where Δu(k+i|k) represents the control amount prediction value of the i-th step at the kth step, η=[c1,c2,...c N ] is the decision coefficient to be optimized, and the dimension N of the Laguerre coefficient has nothing to do with the prediction time domain length NP;

[0180]

[0181] S35: Building a prediction model

[0182] In the MIMO-MPC controller, the output Δui is the inertia control loop control quantity and the secondary frequency modulation control quantity, expressed as formula (6); the augmented equation of the common control area system is formula (7);

[0183] Δu i (k)=[Δu i1 (k),Δu i2 (k)] T (6)

[0184]

[0185] S36: State equations for multi-input multi-output systems

[0186] The state equation of the multi-input multi-output system including inertia control is shown in Equation (8), where the input and output of the system are represented by matrices Bi and Ci;

[0187]

[0188] S37: Incremental control quantity expression

[0189] The load-frequency control quantity increment Δui1 and the inertia control quantity increment Δui2 can be expressed in the form of Laguerre function, as shown in formula (9);

[0190]

[0191] Here, Li1T(k) and ηi1 are the parameters involved in the Laguerre function form of Δui1, and Li2T(k) and ηi2 are the parameters involved in the Laguerre function form of Δui2. Δui1 and Δui2 can be optimized independently, and the parameter selection does not affect each other;

[0192] S38: Laguerre function parameter definition

[0193] The newly defined LiT contains the Laguerre function z-transformation formal parameters involved in the two control quantities, as shown in equation (10);

[0194]

[0195] S39: State quantity expression

[0196] The state quantity of the system at the kth sampling time can be expressed as formula (11);

[0197]

[0198] S310: Cost Function and Optimization

[0199] The cost function of the system during rolling optimization can be expressed by formula (12), where Qi and Ri are weight matrices, and RL is shown in formula (13);

[0200]

[0201] In order to minimize the cost function J(k), it is necessary to directly obtain the optimal control parameters of the PI controller at the kth moment to ensure that the only independent variable in J(k) is K(k); the relationship expression between the matrix ΔU(k) ​​and K(k) needs to be derived.

[0202] S4: In the MPC-PI mode, the lower-level PI controller needs to have an Anti-Windup mechanism to prevent integral saturation caused by system constraints or nonlinear effects; when the system state changes greatly or saturation occurs, the Anti-Windup mechanism will adjust the integral part of the PI controller to avoid excessive accumulation of errors and ensure the stability and responsiveness of the system; S41: Design an improved PI controller

[0203] Combined with online learning algorithms, the gain of the PI controller is automatically adjusted according to the real-time operating status of the system;

[0204] S42: Calculate the control amount increment

[0205] At the kth moment, the control amount increment Δu(k) is calculated using the formula:

[0206] Δu(k)=i=1∑Nu-1Ki·e(k+i|k)·ΔT

[0207] Among them, the error e(k+i|k)=yr(k+i|k)-y^(k+i|k);

[0208] S43: Solving quadratic programming problems

[0209] When solving the quadratic programming problem, replace the control increments Δu1(k) and Δu2(k);

[0210] Consider the four key constraints of load frequency control: control value amplitude and its increment constraint; prime mover ramp rate constraint; system frequency fluctuation constraint; ROCOF constraint;

[0211] S44: Apply anti-windup mechanism

[0212] The anti-saturation PI control strategy is shown in formula (15):

[0213]

[0214] If the control quantity u(k-1) in the k-1th step is greater than the given limit u m If the kth step control is large, only the negative error will be considered for implementation; otherwise, only the positive error will be considered.

[0215] S45: Application Control Algorithm

[0216] The above control algorithm is applied to the load frequency controller and the inertia controller.

[0217] An improved proportional-integral (PI) controller is designed and combined with an online learning algorithm to automatically adjust the gain of the PI controller according to the real-time operating status of the system to improve its adaptability.

[0218] The control quantity increment Δu(k) at time k can be obtained by the principle of the lower-level PI controller, as shown in formula (14):

[0219]

[0220] Where i∈[1,2...N u-1], ΔT is the integration step length, e is the error between the predicted output and the given trajectory, that is, the deviation of the system predicted ACE value from the softened given value,

[0221] When solving the quadratic programming problem shown in equation (8), Δu1(k) and Δu2(k) are replaced, and the key constraints of system load frequency control that need to be considered increase to four: control quantity amplitude and its increment constraint, prime mover ramp rate constraint, system frequency fluctuation constraint and ROCOF constraint. Solve and apply to the load frequency controller and inertia controller.

[0222] S5: Integrate MPC and PI controller to form a hierarchical control architecture, in which MPC is responsible for the main control when the frequency fluctuation is large, and the PI controller performs auxiliary adjustment when the system is stable.

[0223] The PI controller automatically takes over when the system is stable and performs basic proportional-integral control tasks. The PI controller measures the error in real time and makes proportional and integral adjustments to maintain the steady-state operation of the system.

[0224] The anti-saturation strategy is adopted in the lower-level PI controller, which limits the integral control output to a lower order of magnitude, which can effectively shorten the time lag and suppress overshoot, so that the system can eliminate the deviation more quickly and reach a steady state again. Its rationality has been proved in, so it will not be expanded here. The anti-saturation PI control strategy is shown in formula (15):

[0225]

[0226] If the control quantity u(k-1) in the k-1th step is greater than the given limit u m If is large, then the k-th step control will only consider the negative error for implementation; otherwise, only the positive error will be considered.

[0227] S6: Parameter optimization: Parameter optimization index setting method based on multi-objective GSA. The optimized parameters include conventional GPC parameters, important weights and anti-saturation strategy related parameters. The parameters to be optimized include: a1, N1, N P1 and Q i , R i Key weight.

[0228] S61: Define optimization goals

[0229] Determine the MPC parameters that need to be adjusted, such as the prediction horizon, control horizon, and weight coefficients, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption;

[0230] S62: Initialize GSA parameters

[0231] Initialize the parameters of GSA, including population size, gravity constant and maximum number of iterations, and randomly generate a set of initial solutions to form an initial population;

[0232] S63: Fitness evaluation

[0233] The fitness of each individual parameter combination is evaluated and the fitness value, i.e., J*, is calculated by running the MPC control simulation in the power system model;

[0234]

[0235] S64: Update individual quality

[0236] Update the mass of each individual according to the fitness value. The higher the fitness, the greater the mass. At the same time, calculate the gravity field between individuals.

[0237] S65: Location Update

[0238] The position of individuals is updated through the gravitational formula to generate new solutions, and random factors are introduced to maintain population diversity and prevent falling into local optimality;

[0239] S66: Boundary Processing

[0240] Perform boundary processing on parameter values ​​that exceed the defined range to ensure that the parameters are within the acceptable range;

[0241] S67: Iteration Check

[0242] During the iteration process, check whether the maximum number of iterations or fitness convergence conditions are reached. If not, return to the fitness evaluation and gravity update steps;

[0243] S68: Select the optimal solution

[0244] After the iteration, the individual with the best fitness is selected as the optimal solution of the MPC parameters and applied to the actual power system for frequency stability test. Finally, the performance indicators before and after optimization are compared to verify the effectiveness of GSA optimization.

[0245] The frequency regulation performance index of the power system is shown in formula (16):

[0246]

[0247] The specific process of GSA optimizing upper-level MPC parameters:

[0248] (1) Define the optimization goal, determine the MPC parameters that need to be adjusted, such as the prediction horizon, control horizon, and weight coefficient, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption;

[0249] (2) Initialize the parameters of GSA, including population size, gravity constant, and maximum number of iterations, and randomly generate a set of initial solutions to form an initial population;

[0250] (3) Evaluate the fitness of each individual parameter combination and calculate the fitness value, i.e., J*, by running the MPC control simulation in the power system model;

[0251] (4) Update the mass of each individual according to the fitness value. The higher the fitness, the greater the mass. At the same time, calculate the gravity field between individuals.

[0252] (5) Update the position of individuals through the gravity formula, generate new solutions, and introduce random factors to maintain population diversity and prevent falling into local optimality;

[0253] For parameter values ​​that exceed the defined range, boundary processing is performed to ensure that the parameters are within the acceptable range. During the iteration process, check whether the maximum number of iterations or fitness convergence conditions are reached. If not, return to the fitness evaluation and gravity update steps. After the iteration, the individual with the best fitness is selected as the optimal solution for the MPC parameters, and it is applied to the actual power system for frequency stability testing. Finally, the performance indicators before and after optimization are compared to verify the effectiveness of GSA optimization.

[0254] Adopt MPC-PI mode or PI controller mode, and adopt manual switching or system automatic switching.

[0255] A computer system includes a processor and a memory, wherein a computer program is stored in the memory, and when the processor executes the computer program, an MPC-PI hierarchical control method for improving the frequency stability of a power system with renewable energy penetration is implemented.

[0256] Application Example 1:

[0257] For example, when the power system actually performs load frequency and inertia control, the method proposed in the present invention can be adopted.

[0258] First, sensors and monitoring equipment are installed to collect data such as current, voltage, and load in real time and transmit them to the control center to provide necessary input for MPC.

[0259] Next, we developed an MPC control module that uses real-time data for prediction and optimization, dynamically adjusting generator output to cope with fluctuations in renewable energy. When operating conditions are complex, MPC takes the lead in control and adjusts the generation mix in real time to maintain frequency stability; when conditions are stable, it automatically switches to PI control mode.

[0260] The system is also designed with fault detection and isolation mechanisms to quickly adjust control strategies to deal with equipment abnormalities.

[0261] In addition, the MPC control system is compatible with existing equipment, reducing the need for transformation, and provides real-time monitoring and visualization through a user-friendly interface. Finally, the control model is regularly evaluated and optimized to adapt to changes in the grid environment and the access of renewable energy, thereby improving the intelligence, stability and flexibility of the grid.

Claims

1. An MPC-PI hierarchical control method for improving power system frequency stability, characterized in that: Includes the following: S1: Establish a dynamic model of the power system including inertia control, including generators, loads, renewable energy and their interactions, and determine the system state variables and control inputs; Determine the system state variables and control inputs, where: the overall system state variables are X = [Δf1, Pm1, Xg1, Pv1, ROCOF1, Δf2, Pm2, Xg2, Pv2, ROCOF2, Δf3, Pm3, Xg3, Pv3, ROCOF3, Ptie12, Ptie23, Ptie31]T; Control input U = [u11,u21,u12,u22,u13,u23]; Control output Y=[ACE1,ROCOF1,ACE2,ROCOF2,ACE3,ROCOF3] T ; Introduce a nonlinear perturbation term and set it to w(t) = [PL1(t), PL2(t), PL3(t)]; If centralized control is adopted, the system dimension is 18. Considering the time delay caused by the distance factor, the system is divided into three subsystems; Define the inertia-load frequency control parameters of the low-inertia multi-area power system, including but not limited to the following components: Governor: set the guide vane opening deviation Xgi, governor gain Kgovi, governor time constant Tgovi; Unit: set the unit output power Pmi, unit gain Kturi, unit time constant Tturi; Energy storage equipment: set the energy storage equipment output power PVi, energy storage equipment gain KESSi, energy storage equipment time constant TESSi; Equivalent generator: set the system inertia coefficient Hi and the system damping coefficient Di; Other parameters: including frequency deviation Δfi, frequency deviation change rate ROCOFi, tie line power deviation Ptieij; Form the state space equations of the regional system: The state space equations of each region are constructed as shown in formula (1): Where i = 1-3, X i =[Δf1,P m1 , X g1 , P v1 ,ROCOF1,P tie12 , P tie31 ] T , U i =[u 11 ,u 21 ],Y i =[ACE1,ROCOF1,ACE2,ROCOF2,ACE3,ROCOF3] T , A i , B i 、F i , C i They are: S2: Control mode selection; S21: Assessing the stability of the power system: During the operation of the power system, monitor the system status to determine whether there are major changes in operating conditions; S22: Select control mode: If the power system is relatively stable and there is no significant change in operating conditions during the period considered: Select the traditional PI controller and disconnect the upper-level MPC model predictive control optimization; S23: If the power system is in a state of high renewable energy penetration and the operating conditions vary greatly and are difficult to predict: select the MPC-PI control model to adapt to the dynamically changing power system needs; S3: In MPC-PI mode, the upper-level MPC is responsible for real-time optimization of the parameters of the PI controller; S4: In the MPC-PI mode, the lower-level PI controller needs to have an Anti-Windup mechanism to prevent integral saturation caused by system constraints or nonlinear effects. When the system state changes greatly or saturation occurs, the Anti-Windup mechanism will adjust the integral part of the PI controller to avoid excessive accumulation of errors and ensure the stability and responsiveness of the system. S5: The PI controller automatically takes over when the system is stable and performs basic proportional-integral control tasks. The PI controller measures the error in real time and performs proportional and integral adjustments to maintain the steady-state operation of the system. S6: Parameter optimization: Parameter optimization index setting method based on multi-objective GSA. The optimized parameters include conventional GPC parameters, important weights and anti-saturation strategy related parameters. The parameters to be optimized include: a1, N1, N P1 and Q i , R i Key weight.

2. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1 is characterized in that: S3 includes the following: S31: Model Design The frequency fluctuation is predicted by using the system dynamic model, and the frequency stability is set as the control target. At the same time, the optimization objective function is formulated. S32: Define the Laguerre function: The discrete Laguerre function is introduced as the orthogonal basis of the controller to reduce the computational burden of the controller. The control trajectory is described by the Laguerre coefficient. The z-transform form of the Laguerre function is shown in formula (2). in, S33: Determinant of control trajectory Let ln be the inverse z-transform form of the nth Γn(z,a), equation (3) can be expressed as the determinant L(k) consisting of l1 to lN, and equation (4) expresses The conversion relationship between L(k+1) and L(k); L(k)=[l1(k),l2(k)…l N (k)] T (3) S34: Control quantity prediction According to equations (3) and (4), the control amount prediction of the system at the kth moment to the k+mth moment is shown in equation (5), where Δu(k+i|k) represents the control amount prediction value of the i-th step at the kth step, η=[c1,c2,...c N ] is the decision coefficient to be optimized, and the dimension N of the Laguerre coefficient has nothing to do with the prediction time domain length NP; S35: Building a prediction model In the MIMO-MPC controller, the output Δui is the inertia control loop control quantity and the secondary frequency modulation control quantity, expressed as formula (6); the augmented equation of the common control area system is formula (7); Δu i (k)=[Δu i1 (k),Δu i2 (k)] T (6) S36: State equations for multi-input multi-output systems The state equation of the multi-input multi-output system including inertia control is shown in Equation (8), where the input and output of the system are represented by matrices Bi and Ci; S37: Incremental control quantity expression The load-frequency control quantity increment Δui1 and the inertia control quantity increment Δui2 can be expressed in the form of Laguerre function, as shown in formula (9); Here, Li1T(k) and ηi1 are parameters related to the Laguerre function form of Δui1, and Li2T(k) and ηi2 are parameters related to the Laguerre function form of Δui2. Δui1 and Δui2 can be optimized independently, and the parameter selections do not affect each other; S38: Laguerre function parameter definition The newly defined LiT contains the Laguerre function z-transformation formal parameters involved in the two control quantities, as shown in equation (10); S39: State quantity expression The state quantity of the system at the kth sampling time can be expressed as formula (11); S310: Cost Function and Optimization The cost function of the system during rolling optimization can be expressed by formula (12), where Qi and Ri are weight matrices, and RL is shown in formula (13); In order to minimize the cost function J(k), it is necessary to directly obtain the optimal control parameters of the PI controller at the kth moment to ensure that the only independent variable in J(k) is K(k); the relationship expression between the matrix ΔU(k) ​​and K(k) needs to be derived.

3. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1 is characterized in that: In step S2, when the MPC-PI mode is adopted, steps S3 to S6 are performed.

4. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1 is characterized in that: S4 includes the following: S41: Designing an Improved PI Controller Combined with online learning algorithms, the gain of the PI controller is automatically adjusted according to the real-time operating status of the system; S42: Calculate the control amount increment At the kth moment, the control amount increment Δu(k) is calculated using the formula: Δu(k)=i=1∑Nu-1Ki·e(k+i|k)·ΔT Among them, the error e(k+i|k)=yr(k+i|k)-y^(k+i|k); S43: Solving quadratic programming problems When solving the quadratic programming problem, replace the control increments Δu1(k) and Δu2(k); Consider the four key constraints of load frequency control: control value amplitude and its increment constraint; prime mover ramp rate constraint; system frequency fluctuation constraint; ROCOF constraint; S44: Apply anti-windup mechanism The anti-saturation PI control strategy is shown in formula (15): If the control quantity u(k-1) in the k-1th step is greater than the given limit u m If the kth step control is large, only the negative error will be considered for implementation; otherwise, only the positive error will be considered. S45: Application Control Algorithm The above control algorithm is applied to the load frequency controller and the inertia controller.

5. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 4 is characterized in that: In S41, an improved PI controller is designed: The control quantity increment Δu(k) at time k can be obtained by the principle of the lower-level PI controller, as shown in formula (14): Where i∈[1,2...N u -1], ΔT is the integration step length, e is the error between the predicted output and the given trajectory, that is, the deviation of the system predicted ACE value from the softened given value, When solving the quadratic programming problem shown in equation (8), Δu1(k) and Δu2(k) are replaced, and the key constraints of system load frequency control that need to be considered are increased to four: control quantity amplitude and its increment constraint, prime mover climbing rate constraint, system frequency fluctuation constraint and ROCOF constraint; they are solved and applied to the load frequency controller and inertia controller.

6. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, characterized in that: In S3, MPC and PI controllers are integrated to form a hierarchical control architecture: The anti-saturation strategy is adopted in the lower PI controller to limit the integral control output to a lower order of magnitude, which can effectively shorten the time lag and suppress overshoot, so that the system can eliminate the deviation more quickly and reach a steady state again; the anti-saturation PI control strategy is shown in formula (15): If the control quantity u(k-1) in the k-1th step is greater than the given limit u m If is large, then the k-th step control will only consider the negative error for implementation; otherwise, only the positive error will be considered.

7. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, characterized in that: S6 includes the following: S61: Define optimization goals Determine the MPC parameters that need to be adjusted, such as the prediction horizon, control horizon, and weight coefficients, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption; S62: Initialize GSA parameters Initialize the parameters of GSA, including population size, gravity constant and maximum number of iterations, and randomly generate a set of initial solutions to form an initial population; S63: Fitness evaluation The fitness of each individual parameter combination is evaluated and the fitness value, i.e., J*, is calculated by running the MPC control simulation in the power system model; S64: Update individual quality Update the mass of each individual according to the fitness value. The higher the fitness, the greater the mass. At the same time, calculate the gravity field between individuals. S65: Location Update The position of individuals is updated through the gravitational formula to generate new solutions, and random factors are introduced to maintain population diversity and prevent falling into local optimality; S66: Boundary Processing Perform boundary processing on parameter values ​​that exceed the defined range to ensure that the parameters are within the acceptable range; S67: Iteration Check During the iteration process, check whether the maximum number of iterations or fitness convergence conditions are reached. If not, return to the fitness evaluation and gravity update steps; S68: Select the optimal solution After the iteration, the individual with the best fitness is selected as the optimal solution of the MPC parameters and applied to the actual power system for frequency stability test. Finally, the performance indicators before and after optimization are compared to verify the effectiveness of GSA optimization.

8. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, characterized in that: In S63, an MPC control simulation is run in the power system model to calculate a fitness value, i.e., J*; Gravity Searching Algorithm, GSA optimizes the upper-level MPC parameters to achieve better control effects. The specific process is as follows: (1) Define the optimization goal, determine the MPC parameters that need to be adjusted, such as the prediction horizon, control horizon, and weight coefficient, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption; (2) Initialize the parameters of GSA, including population size, gravity constant, and maximum number of iterations, and randomly generate a set of initial solutions to form an initial population; (3) Evaluate the fitness of each individual parameter combination and calculate the fitness value, i.e., J*, by running the MPC control simulation in the power system model; (4) Update the mass of each individual according to the fitness value. The higher the fitness, the greater the mass. At the same time, calculate the gravity field between individuals. (5) Update the position of individuals through the gravity formula, generate new solutions, and introduce random factors to maintain population diversity and prevent falling into local optimality; Boundary processing is performed on parameter values ​​that exceed the defined range to ensure that the parameters are within the acceptable range; During the iteration process, check whether the maximum number of iterations or fitness convergence conditions are reached. If not, return to the fitness evaluation and gravity update steps. After the iteration, select the individual with the best fitness as the optimal solution for the MPC parameters and apply it to the actual power system for frequency stability testing. Finally, compare the performance indicators before and after optimization to verify the effectiveness of GSA optimization.

9. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, characterized in that: Adopt MPC-PI mode or PI controller mode, and adopt manual switching or system automatic switching.

10. A computer system comprising a processor and a memory, wherein a computer program is stored in the memory, wherein: When the processor executes the computer program, the MPC-PI hierarchical control method for improving the frequency stability of a power system with renewable energy penetration as described in any one of claims 1 to 9 is implemented.

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