Mpc-pi hierarchical control method and system for improving power system frequency stability

Abstract

The application discloses an MPC-PI hierarchical control method and system for improving frequency stability of a power system, relates to the technical field of power system control and optimization, and establishes a dynamic model of the power system containing inertia control, including a generator, a load, renewable energy and their interaction, and determines system state variables and control inputs; in the MPC-PI mode, the upper MPC is responsible for real-time optimization of the parameters of the PI controller; in the MPC-PI mode, the lower 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.

Description

TECHNICAL FIELD

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

[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 intermittency and volatility of renewable energy make it difficult for traditional frequency regulation methods to effectively respond, and small fluctuations in frequency can cause equipment damage, system instability, and even large-scale power failures. Therefore, how to ensure the frequency stability of the power system in an environment with high renewable energy penetration has become an important problem that needs to be solved in the field of power engineering.

[0003] Current frequency regulation techniques 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 the volatility of renewable energy. In addition, PI controllers may not be sufficient in terms of dynamic response performance and anti-interference ability to meet the needs of modern power systems. Model-based control methods, although considering the dynamic characteristics of the system, often require complex models and longer design times.

[0004] Model predictive control (MPC) as an advanced control strategy has gradually attracted attention. MPC optimizes control strategies in real time through future behavior prediction, has good adaptability and predictability, and can effectively respond to the intermittency and uncertainty of renewable energy to ensure frequency stability. However, the practical application of MPC faces challenges, especially in the implementation process, as its complex optimization calculation requirements often require replacing the supporting components of existing PI controllers, which may involve high costs and technical difficulties. SUMMARY

[0005] The present application proposes a MPC-PI hierarchical control method and system for improving the frequency stability of a power system, which is based on the hierarchical control strategy of MPC, uses MPC as an 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 operating requirements and system states.

[0006] The technical solutions of the present application are as follows:

[0007] The MPC-PI hierarchical control method for improving the frequency stability of a power system, characterized in that it comprises the following contents:

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

[0009] Determine the system state variables and control inputs, wherein the overall system state variables are 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 disturbance term, set w(t) = [PL1(t), PL2(t), PL3(t)];

[0016] If centralized control is used, the system dimension is 18, considering the time delay caused by distance, the system is divided into three subsystems;

[0017] Define the inertia-load frequency control parameters of the low-inertia multi-region 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 device: set the energy storage device output power PV i, energy storage device gain KESSi, energy storage device 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 rate ROCOFi, tie-line power deviation Ptieij;

[0018] Form the regional system state space equation:

[0019] Construct the state space equation of each region as shown in equation (1):

[0020]

[0021] where i = 1-3, X i = [Af1, 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 respectively:

[0022]

[0023] S2: Control mode selection;

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

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

[0026] S22: Select control mode:

[0027] If the power system is relatively stable and there are no significant changes in operating conditions within the considered time period:

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

[0029] S23: If the power system is in a high new energy penetration state and the operating conditions change significantly and are difficult to predict: select the MPC-PI control model to adapt to the dynamic changes in the power system demand;

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

[0031] S4: In the MPC-PI mode, the lower 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 significantly or saturation occurs, the Anti-Windup mechanism will adjust the integral part of the PI controller to avoid excessive accumulation of errors, ensuring the stability and responsiveness of the system;

[0032] S5: PI controller automatically takes over when the system is stable, performs basic proportional-integral control tasks, and the PI controller measures the error in real time and adjusts the proportion and integral 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 system dynamic model is used to predict the frequency fluctuation, and the frequency stability is set as

[0037] the control target; at the same time, the optimization objective function is formulated;

[0038] S32: define Laguerre function:

[0039] Introduce discrete Laguerre function as the orthogonal basis of the controller to reduce the operation burden of the controller; the control trajectory is described by Laguerre coefficient, and the z transform form of the Laguerre function is shown in formula (2);

[0040]

[0041] Among them,

[0042] S33: determinant of control trajectory

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

[0044] The determinant L(k) is composed of l1 to lN, and formula (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 formula (3) and formula (4), the system predicts the control quantity at the k+m moment at the k moment as shown in formula (5), wherein Δu(k+i|k) represents the control quantity prediction value at the i step at the k step, η=[c1,c2,...c N ] is a decision coefficient to be optimized, and the dimension N of the Laguerre coefficient is irrelevant to the prediction time domain length NP.

[0051]

[0052] S35: Establishing 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, and is expressed as formula (6); the common control area system augmented equation is formula (7);

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

[0055]

[0056] S36: Multi-input multi-output system state equation

[0057] The multi-input multi-output system state equation containing inertia control is shown in formula (8), wherein the input and output of the system are represented by the matrix 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 based on the Laguerre function, as shown in formula (9);

[0061]

[0062] Here, Li1T(k) and ηi1 are the Laguerre function form related parameters of Δui1, and Li2T(k) and ηi2 are the Laguerre function form related parameters of Δui2. Δui1 and Δui2 can be independently optimized, and the parameter selection is independent of each other;

[0063] S38: Laguerre function parameter definition

[0064] The newly defined LiT contains the Laguerre function z transform form parameters related in the two control quantities, as shown in formula (10);

[0065]

[0066] S39: State quantity expression

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

[0068]

[0069] S310: Cost function and optimization

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

[0071]

[0072] In order to realize the minimization of the cost function J(k), the optimal control parameter of the k moment PI controller needs to be directly obtained, so as 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 the S2 step, when the MPC-PI mode is adopted, the S3-S6 steps 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: Design of improved PI controller

[0076] Combined with the online learning algorithm, the gain of the PI controller is automatically adjusted according to the real-time running state of the system;

[0077] S42: Calculation of control quantity increment

[0078] At the k moment, the control quantity increment Δu(k) is calculated, and the formula is:

[0079] Δu(k) = i = 1 ∑ Nu-1 Ki·e(k+i∣k)·ΔT

[0080] Wherein, the error e(k+i∣k) = yr(k+i∣k)-y^(k+i∣k);

[0081] S43: Solution of quadratic programming problem

[0082] In the solution of the quadratic programming problem, the control quantity increments Δu1(k) and Δu2(k) are replaced;

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

[0084] S44: applying an anti-windup mechanism

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

[0086]

[0087] If the k-1 step control quantity u(k-1) is greater than the given limit u m , the k step control only considers the negative error, otherwise, only the positive error is considered;

[0088] S45: applying the control algorithm

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

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

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

[0092]

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

[0094] When solving the quadratic programming problem shown in formula (8), Δu1(k) and Δu2(k) are replaced, and the key constraints of the system load frequency control are considered to be four: control quantity amplitude and its increment constraint, prime mover ramp rate constraint, system frequency fluctuation constraint, and ROCOF constraint; solving and applying on the load frequency controller and the inertia controller.

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

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

[0097]

[0098] If the k-1 step control amount u(k-1) is greater than the given limit u m , the k step control only considers the negative error, otherwise only the positive error.

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

[0100] S61: define optimization objective

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

[0102] S62: initialize GSA parameters

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

[0104] S63: fitness evaluation

[0105] Evaluate the fitness of each individual parameter combination, calculate the fitness value J* by running the MPC control simulation in the power system model;

[0106]

[0107] S64: update individual quality

[0108] Update the quality of each individual according to the fitness value, the higher the fitness, the greater the quality, and calculate the gravitational field between individuals;

[0109] S65: position update

[0110] Update the position of the individual through the gravitational formula to generate a new solution, and introduce random factors to maintain population diversity and prevent falling into local optimum;

[0111] S66: boundary processing

[0112] Boundary processing is performed on parameter values that exceed the defined range to ensure that parameters are within the acceptable range;

[0113] S67: iteration check

[0114] In the iteration process, check whether the maximum number of iterations or the fitness convergence condition is reached, if not, return to the fitness evaluation and gravity update steps;

[0115] S68: select optimal solution

[0116] After the iteration, the individual with the best fitness is selected as the optimal solution for the MPC parameters, which 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.

[0117] In S63, the fitness value J* is calculated by running MPC control simulation in the power system model.

[0118]

[0119] The Gravity Searching Algorithm (GSA) is used to optimize the upper MPC parameters to achieve better control effect. The specific process is as follows:

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

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

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

[0123] (4) Update the mass of each individual according to the fitness value, the higher the fitness, the greater the mass, and calculate the gravitational field between individuals;

[0124] (5) Update the position of the individual by the gravitational formula to generate new solutions, and introduce random factors to maintain population diversity and prevent falling into local optimum;

[0125] For parameter values outside 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 iteration number or fitness convergence condition is 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, which 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, characterized by using MPC-PI mode or PI controller mode, and using manual switching or system automatic switching.

[0127] The application discloses a computer system, which comprises a processor and a memory, and the memory stores a computer program, wherein the processor implements the MPC-PI hierarchical control method for improving the frequency stability of a power system with high renewable energy penetration when executing the computer program.

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

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

[0130] In terms of control strategy, the application adopts a dual-mode, hierarchical control structure, combines MPC and PI control strategies, dynamically adjusts control input and parameter weights, and optimizes system performance. The objective function design takes into account the error between the system output and the predicted value, ensuring the real-time and effectiveness of the control decision. Through the adaptive control algorithm, continuous optimization of the control parameters is implemented, thereby enhancing the application potential of the control strategy in high renewable energy penetration and power grid scheduling.

[0131] The control strategy of the application can operate in two modes:

[0132] Firstly, in the case of complex system operating conditions or large renewable energy fluctuations, MPC will dominate the control process, and MPC is responsible for real-time optimization of the parameters of the PI controller to respond to frequency changes.

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

[0134] In addition, the hierarchical control strategy based on MPC also has certain fault tolerance. When the system has an abnormality or equipment failure, MPC can quickly adjust the control strategy to adapt to the new operating conditions, avoiding 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 existing power system devices during the transformation to smart grids, reducing the need for modification of existing devices and lowering implementation costs. Meanwhile, the real-time optimization characteristics of MPC enable the system to maintain good performance when facing higher proportions of renewable energy access in the future.

[0136] The MPC-based hierarchical control strategy proposed by the present application 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 state, effectively dealing with 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, the control system retains ease of use and stability 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 device 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 integrated with existing power systems, reducing the need for modification and lowering implementation costs, helping the transformation of smart grids.

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

[0143] Figure 1 Inertia-load frequency control structure diagram of multi-region power system with high new energy penetration rate.

[0144] Figure 2 MPC control principle structure diagram.

[0145] Figure 3 Low-inertia power system load frequency control flowchart incorporating the MPC-PI controller based on the pumped storage characteristic line model. DETAILED DESCRIPTION

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

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

[0148] The overall system state quantity 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 The system output is w(t) = [P L1 (t), P L2 (t), P L3 (t)], and if centralized control is used, the system is 18-dimensional and involves many time delays due to distance factors, therefore, the present application divides the overall system into three subsystems and uses distributed control to reduce the model dimension.

[0149] Table 1 Inertia-load frequency control related parameters of low inertia multi-region power system

[0150]

[0151]

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

[0153]

[0154] Wherein, 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 are respectively:

[0155]

[0156] S2: Artificially select PI or MPC-PI control mode

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

[0158] During the operation of the power system, monitor the system state to determine whether there is a large change 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 within the considered period:

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

[0162] S23: If the power system is in a high new energy penetration state and the operating conditions change greatly and are difficult to predict: select the MPC-PI control model to adapt to the dynamic changes of the power system demand;

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

[0164] S31: Model design

[0165] Use the system dynamic model to predict frequency fluctuations to set frequency stability as

[0166] the control target; at the same time, formulate the optimization objective function;

[0167] S32: Define the Laguerre function:

[0168] Introduce a discrete Laguerre function as the orthogonal basis of the controller to reduce the computational burden of the controller; describe the control trajectory through the Laguerre coefficient, and the z-transform form of the Laguerre function is shown in equation (2);

[0169]

[0170] wherein,

[0171] S33: Determinant of the trajectory

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

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

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

[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 equation (3) and equation (4), the system predicts the control quantity at the k+m time at the k time as shown in equation (5), where Δu(k+i|k) represents the control quantity prediction value at the i step at the k step, η = [c1, c2, … c N ] is the decision coefficient to be optimized, and the dimension N of the Laguerre coefficient is irrelevant to the prediction time domain length NP;

[0180]

[0181] S35: Establishing 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 equation (6); the common control area system augmented equation is equation (7);

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

[0184]

[0185] S36: State equation of a multiple-input multiple-output system

[0186] The state equation of a multiple-input multiple-output system containing inertia control is shown in equation (8), wherein the input and output of the system are represented by the 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 based on the Laguerre function, as shown in equation (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 is independent of each other;

[0192] S38: Laguerre function parameter definition

[0193] The newly defined LiT contains the parameters of the Laguerre function z-transform form 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 equation (11);

[0197]

[0198] S310: Cost function and optimization

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

[0200]

[0201] To achieve the minimization of the cost function J(k), the optimal control parameter of the PI controller at the kth time is needed to be directly obtained, ensuring that the only independent variable in J(k) is K(k); the expression of the relationship between the matrix ΔU(k) and K(k) needs to be derived.

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

[0203] Combining with the online learning algorithm, the gain of the PI controller is automatically adjusted according to the real-time running state of the system;

[0204] S42: calculating the control amount increment

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

[0206] Δu(k) = i = 1 ∑Nu-1Ki·e(k+i|k)·ΔT

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

[0208] S43: solving the quadratic programming problem

[0209] When solving the quadratic programming problem, the control amount increment Δu1(k) and Δu2(k) are replaced;

[0210] Four key constraints of load frequency control are considered: control amount amplitude and increment constraint; prime mover climbing rate constraint; system frequency fluctuation constraint; ROCOF constraint;

[0211] S44: applying the anti-windup mechanism

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

[0213]

[0214] If the k-1 step control amount u(k-1) is greater than the given limit u m , the k step control only considers the negative error, otherwise, only the positive error is considered;

[0215] S45: applying the 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, which combines with the online learning algorithm to automatically adjust the gain of the PI controller according to the real-time running state of the system, and improves its adaptability.

[0218] The control amount increment Δu(k) at the kth moment can be obtained through the principle of the lower layer PI controller, as shown in formula (14):

[0219]

[0220] In the formula, i ∈ [1, 2...N u-1], AT is the integral step, e is the error between the predicted output and the given trajectory, i.e. the difference between the predicted ACE value and the softened given value,

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

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

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

[0224] An anti-windup strategy is used in the lower PI controller, which limits the integral control output to a lower order of magnitude, effectively shortening the time delay and suppressing overshoot, so that the system can eliminate the deviation more quickly and reach a new steady state. Its rationality has been proved in the literature, so it is not expanded here. The anti-windup PI control strategy is shown in equation (15):

[0225]

[0226] If the k-1 step control quantity u(k-1) is greater than the given limit u m , the k step control only considers the negative error for implementation, otherwise, only the positive error is considered.

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

[0228] S61: Define optimization objectives

[0229] Determine the MPC parameters that need to be adjusted, such as prediction horizon, control horizon and weight coefficient, 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, gravitational constant and maximum iteration number, and randomly generate a set of initial solutions to form the initial population;

[0232] S63: Fitness evaluation

[0233] Evaluate the fitness of each individual parameter combination by running MPC control simulation in the power system model to calculate the fitness value, i.e. J*;

[0234]

[0235] S64: Update individual quality

[0236] Update the quality of each individual according to the fitness value, the higher the fitness, the greater the quality, and calculate the gravitational force field between individuals;

[0237] S65: Position update

[0238] Update the position of the individual by the gravitational formula to generate a new solution, and introduce random factors to maintain population diversity and prevent falling into local optimum;

[0239] S66: Boundary processing

[0240] Boundary processing is performed on parameter values that exceed the defined range to ensure that parameters are within the acceptable range;

[0241] S67: Iteration check

[0242] During iteration, check if the maximum iteration number or fitness convergence condition is reached, if not, return to fitness evaluation and gravity update steps;

[0243] S68: Select optimal solution

[0244] After iteration, select the individual with the best fitness as the optimal solution of MPC parameters, apply it to the actual power system for frequency stability test, and finally compare the performance indicators before and after optimization to verify the effectiveness of GSA optimization.

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

[0246]

[0247] The specific process of GSA optimization of upper MPC parameters is as follows:

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

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

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

[0251] (4) Update the mass of each individual according to the fitness value, the higher the fitness, the greater the mass, and calculate the gravitational force between individuals;

[0252] (5) Update the position of the individual by the gravitational formula to generate new solutions, and introduce random factors to maintain population diversity and prevent falling into local optimum;

[0253] Boundary processing is performed on parameter values that exceed the defined range to ensure that parameters are within the acceptable range. During iteration, check if the maximum iteration number or fitness convergence condition is reached, if not, return to the fitness evaluation and gravity update steps. After iteration, select the individual with the optimal fitness as the optimal solution of MPC parameters, and apply it to the actual power system for frequency stability test, and finally compare the performance indicators before and after optimization to verify the effectiveness of GSA optimization.

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

[0255] A computer system includes a processor and a memory, the memory stores a computer program, and the processor executes the computer program to realize the MPC-PI hierarchical control method for improving the frequency stability of power system with renewable energy penetration.

[0256] Application Example 1:

[0257] For example, when performing load frequency and inertia control in the actual power system, the method proposed by the present application can be used.

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

[0259] Next, develop MPC control module, use real-time data for prediction and optimization, dynamically adjust generator output to respond to renewable energy fluctuations. When the operating conditions are complex, MPC dominates control, real-time adjusts the power combination to maintain frequency stability; while in stable conditions, automatically switch to PI control mode.

[0260] The system also designs a fault detection and isolation mechanism to quickly adjust the control strategy to respond to equipment abnormalities.

[0261] Furthermore, the MPC control system is compatible with existing equipment, reducing the need for modifications and providing 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 integration of renewable energy sources, enhancing the intelligence, stability, and flexibility of the grid.

Claims

1. An MPC-PI hierarchical control method for improving the frequency stability of a power system, characterized by, Comprise the following: S1: Establish a dynamic model of power system containing inertia control, including generators, loads, renewable energy and their interactions, determine system state variables and control inputs; Determine system state variables and control inputs, where: 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 nonlinear disturbance terms, set w(t) = [PL1(t), PL2(t), PL3(t)]; If centralized control is used, the system dimension is 18, considering the time delay caused by distance, the system is divided into three subsystems; Define the inertia-load frequency control parameters of low-inertia multi-region 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 device: set the energy storage device output power PV, energy storage device gain KESSi, energy storage device 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 rate ROCOFi, tie-line power deviation Ptieij; Form the regional system state space equation: Construct the state space equation of each region as shown in equation (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 , respectively: S2: Control mode selection; S21: Assess the stability of the power system: During the operation of the power system, monitor the system state to determine whether there are large changes in operating conditions; S22: Select control mode: If the power system is relatively stable and there are no significant changes in operating conditions within the considered time period: Select the traditional PI controller and disconnect the upper MPC model predictive control optimization; S23: If the power system is in a high new energy penetration state and the operating conditions change greatly and are difficult to predict: select the MPC-PI control model to adapt to the dynamic changes of the power system demand; S3: In MPC-PI mode, the upper MPC is responsible for real-time optimization of the parameters of the PI controller; S4: In MPC-PI mode, the lower 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, ensuring the stability and responsiveness of the system; S5: The PI controller automatically takes over when the system is stable, performing basic proportional-integral control tasks. The PI controller measures the error in real time and adjusts the proportion and integral 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 regular GPC parameters, important weight 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, characterized in that, S3 includes the following: S31: Model design Use the system dynamic model to predict frequency fluctuations to set the frequency stability as the control target; At the same time, formulate the optimization objective function; S32: Define the Laguerre function: The discrete Laguerre functions are introduced as the orthogonal basis of the controller to reduce the computational burden of the controller. The control trajectory is described by Laguerre coefficients, and the z-transform form of the Laguerre function is shown in equation (2); wherein S33: Determinant of the 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) composed 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) L(k+1) = A l L(k) S34: Control amount prediction According to the formula (3) and the formula (4), the system predicts the control quantity at the k+m moment at the k moment as shown in the formula (5), wherein Δu (k+i|k) represents the control quantity prediction value at the i step at the k step, η=[c1, c2,..., cN] is a decision coefficient to be optimized, the dimension N of the Laguerre coefficient is irrelevant to the prediction time domain length NP. N ] for the decision coefficient to be optimized, the dimension N of the Laguerre coefficient is irrelevant to the prediction time domain length NP. S35: Establishment of a prediction model In the MIMO-MPC controller, the output Δui is the inertia control loop control amount and the secondary frequency modulation control amount, expressed as equation (6); the augmented equation of the common control area system is equation (7); Δu i (k) = [Δu i1 (k), Δu i2 (k)] T (6) S36: State equation of a multiple-input multiple-output system The state equation of a multiple-input multiple-output system containing inertia control is shown in equation (8), wherein the inputs and outputs of the system are represented by matrices Bi and Ci; S37: Expression of the incremental control amount The load-frequency control amount increment Δui1 and the inertia control amount increment Δui2 can be expressed in the form of Laguerre functions, as shown in equation (9); Here, Li1T(k) and ηi1 are the Laguerre function form related parameters of Δui1, and Li2T(k) and ηi2 are the Laguerre function form related parameters of Δui2; Δui1 and Δui2 can be independently optimized, and the parameter selection is independent of each other; S38: Definition of Laguerre function parameters The newly defined LiT contains the z-transform form parameters of the Laguerre functions related to the two control amounts, as shown in equation (10); S39: Expression of state variables The state variables of the system at the kth sampling time can be expressed as equation (11); S310: Cost function and optimization The cost function of the system during the rolling optimization can be expressed by equation (12), wherein Qi and Ri are weight matrices, and RL is shown in equation (13); To achieve the minimization of the cost function J(k), the optimal control parameters of the PI controller at the kth time are directly obtained, ensuring that the only independent variable in J(k) is K(k); the expression of the relationship 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, characterized in that, In step S2, when the MPC-PI mode is adopted, steps S3-S6 are performed.

4. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, wherein, S4 includes the following contents: S41: Design of an improved PI controller Combined with an online learning algorithm, the gain of the PI controller is automatically adjusted according to the real-time running state of the system; S42: Calculation of the control amount increment At the kth time, the control amount increment Δu(k) is calculated, and the formula is: Δu(k) = i = 1 ∑Nu-1 Ki·e(k+i∣k)·ΔT Wherein, the error e(k+i∣k) = yr(k+i∣k)-y^(k+i∣k); S43: Solution of a quadratic programming problem In the solution of the quadratic programming problem, the control amount increments Δu1(k) and Δu2(k) are replaced; Four key constraints of load-frequency control are considered: control amount amplitude and increment constraints; prime mover ramp rate constraints; system frequency fluctuation constraints; ROCOF constraints; S44: Application of an anti-windup mechanism The anti-windup PI control strategy is shown in equation (15): If the control quantity u(k-1) of the (k-1)th step is greater than the given limit u m , then the control of the kth step is implemented only considering the negative error, otherwise only the positive error. S45: Application of the control algorithm The 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, characterized in that, In S41, the improved PI controller is designed: The control amount increment Δu(k) at time k can be obtained by the principle of the lower-layer PI controller, as shown in equation (14): where i ∈ [1, 2...N u -1], AT is the integration step, e is the error between the predicted output and the given trajectory, i.e. the size of 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 four key constraints of the system load frequency control need to be considered: control amount amplitude and its increment constraint, prime mover ramp rate constraint, system frequency fluctuation constraint, and ROCOF constraint; the solution is applied to the load frequency controller and the inertia controller.

6. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, wherein, In S3, the MPC and the PI controller are integrated to form a hierarchical control architecture: In the lower-layer PI controller, an anti-windup strategy is adopted, which limits the integral control output to a lower order of magnitude, effectively shortens the time delay, suppresses the overshoot, and enables the system to eliminate the deviation more quickly and reach the steady state again; the anti-windup PI control strategy is shown in equation (15): If the control quantity u(k-1) of the (k-1)th step is greater than the given limit u m , then the control quantity of the kth step is determined only by the negative error, otherwise only by the positive error.

7. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, characterized in that: S6 includes the following contents: S61: defining the optimization objective Determine the MPC parameters that need to be adjusted, such as the prediction time domain, the control time domain, and the weight coefficient, and formulate the objective function, which is usually the minimization of frequency deviation or control energy consumption; S62: initializing GSA parameters Initialize the parameters of GSA, including population size, gravitational constant, and maximum iteration number, and randomly generate a set of initial solutions to form the initial population; S63: fitness evaluation Evaluate the fitness of each individual parameter combination by running the MPC control simulation in the power system model to calculate the fitness value J*; S64: updating individual mass Update the mass of each individual according to the fitness value, and the higher the fitness, the greater the mass. At the same time, calculate the gravitational force field between individuals; S65: position update Update the position of the individual by the gravitational formula to generate a new solution, and introduce a random factor to maintain population diversity and prevent falling into local optimum; 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 iteration number or the fitness convergence condition is reached. If not, return to the fitness evaluation and gravity update steps; S68: select the optimal solution After the iteration is completed, select the individual with the optimal fitness as the optimal solution of the MPC parameters, and apply it to the actual power system for frequency stability test. Finally, compare the performance indicators before and after optimization to verify the effectiveness of GSA optimization.

8. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, wherein: In S63, the fitness value J* is calculated by running the MPC control simulation in the power system model; The GSA optimization of the upper-layer MPC parameters achieves better control effect, and the specific process is as follows: (1) Define the optimization objective, determine the MPC parameters that need to be adjusted, such as the prediction time domain, the control time domain, and the 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, gravitational constant, and maximum iteration number, and randomly generate a set of initial solutions to form the initial population; (3) Fitness evaluation is performed for each individual parameter combination by running MPC control simulation in the power system model to calculate the fitness value, i.e. J*; (4) The quality of each individual is updated according to the fitness value, the higher the fitness value, the greater the quality, and the gravitational force field between individuals is calculated at the same time; (5) The position of the individual is updated by the gravitational formula to generate a new solution, and a random factor is introduced to maintain population diversity and prevent falling into local optimum; 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, it is checked whether the maximum number of iterations or the fitness convergence condition is reached, if not, the fitness evaluation and gravity update steps are returned; after the iteration is completed, the individual with the optimal fitness is selected as the optimal solution of the MPC parameters, and it is applied to the actual power system for frequency stability test, and finally the performance indicators before and after optimization are compared to verify the effectiveness of GSA optimization.

9. The MPC-PI hierarchical control method for improving power system frequency stability according to claim 1, wherein, The MPC-PI mode or the PI controller mode is adopted, and manual switching or automatic switching of the system is adopted.

10. A computer system comprising a processor and a memory, the memory having stored therein a computer program, characterized in that, The processor implements the MPC-PI hierarchical control method for improving the frequency stability of the power system in any one of claims 1 to 9 when executing the computer program.

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