Power system frequency control system and method

Abstract

The invention discloses a power system frequency control system and method, and the system comprises a state sensing module which is used for obtaining a frequency deviation signal of a power system; the convex neural network control module is in communication connection with the state sensing module and is used for receiving the frequency deviation signal and generating a preliminary control instruction by utilizing gradient mapping of an output function of at least one strict convex neural network in the convex neural network control module; the security constraint processing module is in communication connection with the convex neural network control module and is used for performing constraint processing on the preliminary control instruction, and the constraint processing at least comprises input saturation constraint and state security filtering; and the instruction output module is in communication connection with the security constraint processing module and is used for issuing the processed final control instruction to a controllable power supply in the power system. According to the method, the problem that quick response, stable operation and state safety of power system frequency control under high-proportion new energy access are difficult to consider into account is solved.

Description

Technical Field

[0001] This invention relates to the field of power system automatic control technology, specifically to a power system frequency control system and method based on convex neural networks, for achieving rapid, stable and safe regulation of power system frequency. Background Technology

[0002] Power system frequency is a core operational indicator reflecting the balance between power generation and consumption, and its stability directly affects the safe and reliable operation of the power system. When the system is subjected to load fluctuations, changes in power output, or external disturbances, if the frequency deviation cannot be suppressed in time and restored to the rated value, it may trigger equipment protection actions, system oscillations, or even large-scale power outages. Therefore, frequency control has always been an important research direction in the field of power system operation control.

[0003] Traditional power systems are based on synchronous generators, and their frequency control is typically divided into three levels: inertial response, primary frequency regulation, and secondary frequency regulation. Inertial response mainly relies on the physical inertia of the synchronous generator rotor, releasing or absorbing rotor kinetic energy to suppress the rate of frequency change in the initial stages of system disturbance. Primary frequency regulation is usually achieved through droop control of the speed control system, proportionally adjusting mechanical power according to frequency deviation to establish a new power balance point. Secondary frequency regulation plays a role on a slower time scale, eliminating steady-state frequency differences, restoring the system frequency to its rated value, and coordinating power exchange between regions.

[0004] With the gradual integration of power electronic interface power supplies, energy storage systems and new energy units such as wind and solar power can also participate in system frequency regulation through inverter control. On the one hand, energy storage systems can use inverters to quickly adjust active power on a millisecond to second timescale, providing fast frequency response or equivalent inertia response to suppress frequency variations and lower the frequency minimum. On the other hand, some wind turbine units can participate in the primary frequency response by releasing rotor kinetic energy or achieving virtual inertia and droop characteristics through inverter control. This type of inverter-based frequency support method has a significant advantage in response speed, providing new regulation resources for system frequency stability.

[0005] In the traditional power grid operation framework, secondary frequency regulation is still mainly achieved by the Automatic Generation Control (AGC) system, which periodically adjusts the generator power setpoints through centralized dispatching to restore system frequency and tie-line power. This method has a mature structure, rich engineering practice, and good application results under conditions of sufficient system inertia and relatively stable operating conditions.

[0006] As power systems expand in scale and become more complex in operation, researchers have proposed various model-based frequency control methods, such as optimal control methods based on linearized models, linear quadratic regulators, and model predictive control (MPC). These methods can optimize frequency performance and control costs while considering the dynamic characteristics of the system, and can simultaneously handle input and state constraints. However, their control effectiveness is highly dependent on the accuracy of the system model, and the computational complexity of online optimization is high. Furthermore, they face significant engineering implementation challenges in scenarios with significant system nonlinearity, frequent changes in operating points, or complex constraints.

[0007] In recent years, with the increasing proportion of new energy grid connection and enhanced data acquisition capabilities, data-driven and neural network-based frequency control methods have gradually attracted attention. These methods learn the system's frequency response characteristics through historical or simulation data, reducing reliance on precise physical models to some extent and possessing strong nonlinear approximation and adaptive capabilities. However, most existing methods focus on control performance optimization, and their stability and safety often rely on empirical design or penalty term constraints, lacking rigorous theoretical guarantees and posing potential risks in safety-critical applications such as frequency control.

[0008] Meanwhile, distributed frequency control methods have gradually developed to adapt to large-scale interconnected systems and distributed power supply integration. These methods achieve coordinated regulation among multiple control units through local measurements and wired communication, exhibiting a certain degree of scalability and robustness. However, under conditions of high-proportion power electronic interface power supply integration, the coupling relationships between different controllers become complex, significantly increasing the difficulty of parameter tuning and stability analysis. Summary of the Invention

[0009] The present invention aims to address the deficiencies in the aforementioned background technology. Its primary technical problem is to provide a power system frequency control scheme that can simultaneously ensure the rapid response of frequency control, the asymptotic stability of the closed-loop system, and the safety of critical operating states in a complex power system environment with a high proportion of new energy access.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: A power system frequency control system includes: a state sensing module for acquiring a frequency deviation signal of the power system; a convex neural network control module, communicatively connected to the state sensing module, for receiving the frequency deviation signal and generating preliminary control commands using the gradient mapping of the output function of at least one strictly convex neural network within the module; a safety constraint processing module, communicatively connected to the convex neural network control module, for performing constraint processing on the preliminary control commands, the constraint processing including at least input saturation constraints and state safety filtering; and a command output module, communicatively connected to the safety constraint processing module, for issuing the processed final control commands to the controllable power sources in the power system.

[0011] In some embodiments, at least one of the following technical means is also included: The activation function of the strictly convex neural network is the Softplus-β function.

[0012] The state safety filtering is based on the comparison between state variables and preset safety thresholds, and the multiplicative filtering factor is calculated in combination with the direction of control commands.

[0013] The system also includes an integral state update module, which is used to update the integral state using an integral update mechanism with a projection operator.

[0014] The convex neural network control module and the safety constraint processing module are deployed in an automatic generation control (AGC) server or a site controller.

[0015] The present invention also adopts the following technical solutions: A power system frequency control method includes the following steps: acquiring a frequency deviation signal of the power system; inputting the frequency deviation signal into a pre-trained convex neural network controller, and generating a preliminary control command by calculating the gradient mapping of the output function of the strictly convex neural network in the controller; performing safety constraint processing on the preliminary control command, the processing including at least input saturation constraint and state safety filtering; and outputting the final control command after safety constraint processing to a controllable power source in the power system for frequency regulation.

[0016] Furthermore, The activation function of the strictly convex neural network is the Softplus-β function.

[0017] Furthermore, The state-based safety filtering includes: comparing the key operating state of the power resources with a preset safety threshold, and scaling the initial control command by calculating a multiplicative filter factor between 0 and 1 based on the directionality of the control command.

[0018] Furthermore, When generating the integral control term in the preliminary control instruction, an integral update mechanism with a projection operator is adopted.

[0019] The present invention also adopts the following technical solutions: A method for training the aforementioned convex neural network controller, characterized by comprising: constructing a differentiable closed-loop system model including a power system dynamics model and a parameterized control strategy; performing forward simulation on the differentiable closed-loop system to calculate a loss function based on initial conditions and disturbance scenarios obtained from multiple batches of random sampling; calculating the gradient of the loss function with respect to the neural network parameters using automatic differentiation techniques and backpropagation; and optimizing the neural network parameters using a stochastic gradient descent algorithm until the convergence condition is met.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention constructs a PI control law based on a strictly convex neural network gradient mapping, ensuring the control strategy itself possesses strict monotonicity and providing an inherent guarantee of asymptotic stability and zero steady-state frequency difference for the closed-loop system. Building upon this, by combining hard saturation constraints on the control input with a direction-aware multiplicative safety filtering mechanism for critical operating states, it ensures that control commands remain within the physical execution capabilities of the power equipment without requiring online solutions to complex optimization problems, and prevents critical states (such as generator power and energy storage state of charge) from exceeding limits, thus achieving a hard guarantee for the safe operation of the system. Ultimately, the synergistic effect of these technical features enables the control scheme of this invention to simultaneously achieve rapid frequency response, reliable system stability, and strict state safety constraints in complex power system environments with a high proportion of renewable energy integration, effectively overcoming the shortcomings of traditional methods in terms of adaptability, stability, and safety.

[0021] By employing the Softplus-β function as the activation function of the neural network, the strict convexity and smoothness of the neural network output function are further ensured, enhancing the mathematical robustness and universal approximation ability of the control law.

[0022] By calculating the directionality of the multiplicative factor in the state-safe filtering, intelligent attenuation of control commands is achieved. The filter is activated only when necessary, preserving control performance to the maximum extent and avoiding the impact of overly conservative constraint processing on control effectiveness.

[0023] By introducing an integral update mechanism with a projection operator, integral saturation is effectively avoided, ensuring the effectiveness of integral control in long-term operation and further improving the steady-state accuracy and dynamic performance of the control.

[0024] By deploying the core control module in existing AGC servers or field controllers, the existing infrastructure is fully utilized, enabling a deployment mode of offline training and rapid online execution, which significantly enhances the engineering feasibility and application value of the invention. Attached Figure Description

[0025] Figure 1 This is a diagram illustrating the structure and operation of a power system frequency control system according to an embodiment of the present invention.

[0026] Figure 2 This is a schematic diagram of the convergence trend of the loss function during offline training of a convex neural network controller in one embodiment of the present invention.

[0027] Figure 3 This is a schematic diagram of the response curves of the frequency deviation of each node when an embodiment of the present invention is applied to a test system.

[0028] Figure 4 This is a schematic diagram of the final control commands of each controllable power source in one embodiment of the present invention.

[0029] Figure 5 This is a schematic diagram of the actual frequency regulation power output curve of a synchronous generator in one embodiment of the present invention.

[0030] Figure 6 This is a schematic diagram of the state of charge (SOC) change curve of a grid-type energy storage system in one embodiment of the present invention. Detailed Implementation

[0031] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0032] It should be noted that when a component is referred to as "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as "connected to" another component, it can be directly connected to or indirectly connected to that other component. Furthermore, a connection can be used for both fixing and circuit / signal connectivity.

[0033] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0034] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0035] The basic concept of the embodiments of the present invention is as follows: The overall architecture and workflow of the control system proposed in this invention are as follows: Figure 1 As shown, this invention proposes a convex neural network-based frequency control method for power systems with guaranteed safety and stability. First, an optimal frequency control problem is constructed based on a linearized power system frequency response model. Second, in the neural network control design, a frequency control strategy with strict monotonicity is constructed by parameterizing the proportional-integral control law as a gradient mapping of the convex neural network output, and offline training of control parameters is achieved by combining differentiable closed-loop system modeling. Third, the control command is constrained through integral saturation, input saturation, and state-related safety filtering mechanisms, thereby achieving secondary frequency control in novel power systems that balances fast response, steady-state frequency recovery, and stability and safety constraints.

[0036] Example 1

[0037] Specifically, the method proposed in this invention includes the following steps: Step 1: Construct the optimal frequency control problem under safety and stability constraints 1.1 Power System Phase Angle-Frequency Model First, the power system model considered in this invention is introduced. It is assumed that the system consists of… n It consists of nodes. i, j All represent node sets The line index in the middle, Unordered pairs Representing edge set The system transmission line index, transmission line { i, j} connects two adjacent nodes in the system i and j The above-mentioned graph model connects nodes and lines. This describes a power system. Common resources found in modern power systems are connected to system nodes, including synchronous generators, grid-forming (GFM) inverter power supplies, grid-following (GFL) inverter power supplies, and controllable loads. This invention assumes that loads and power sources can exist at the same grid node; however, each node connects only one type of power source with unlimited capacity, namely, synchronous generator sets, wind power, photovoltaic power, or energy storage units.

[0038] For each node, there is a phase angle. d i and frequency oh i The phase angle dynamic response model is a frequency integral expression, and the frequency dynamic response model is described by the oscillation equation. The node frequency dynamics are affected by the inertia, damping, and power injection of the power resources at the node. The phase angle-frequency model of the power system is shown below: (1) in, d Represents the phase angle of all nodes in the system. d i The set, oh Represents the frequency of all nodes in the system oh i The set, M It is a diagonal matrix containing the inertia constants of all nodes in the system. D It is a diagonal matrix containing the damping constants of all nodes in the system. E This is the linear mapping matrix between the nodal frequency vector and the phase angle vector in the center of inertial coordinate system. J It is the Jacobian matrix that describes the power interaction between nodes. P f It is the active power output vector of the node's power resources. P d This is the node power disturbance vector. Controllable power sources on the node (synchronous generators, grid-connected power sources, and controllable loads) can be controlled via the input... u i Actively adjust the active power output to achieve frequency regulation.

[0039] The dynamic model of the node phase angle, frequency, and node power of a power system can be summarized in the following state-space set form: (2) Where the state vector x This includes the system's frequency, phase angle, and power frequency-power response state variables, as well as the control input vector. u Including control inputs for all controllable power supplies u i System state matrix A sys It consists of the phase angle and frequency variable matrices from (1) and the state matrices of each power source. B sys It is the system input matrix. B d It is the injection matrix of the disturbance power. The specific form of the state-space model (2) is not shown here. This invention is only used for illustrative purposes and is not the core part.

[0040] The linearized power system phase-frequency model used in step 1.1 is a small-signal linearized description of the system frequency dynamics near the rated operating condition or typical steady-state operating point. This model is primarily used to characterize the fundamental dynamic relationship between system frequency deviation and active power imbalance. Its purpose is to provide a unified and analytical control modeling framework for secondary frequency control problems, rather than to accurately reproduce all nonlinear transient processes of the power system under large disturbance conditions. For the frequency recovery and steady-state performance optimization problems in the secondary frequency control stage, the system frequency deviation has usually entered a relatively slow-changing range, and the frequency dynamics can be approximated as the deviation evolution process around the operating point. In this control stage, using the linearized frequency response model as the basis for controller design and training conforms to the general modeling assumptions in existing power system frequency control theory and engineering practice. Its applicability is premised on the operating range where the frequency deviation and control input do not exceed the allowable range of the equipment.

[0041] 1.2 Determination of Frequency Control Objectives

[0042] This invention addresses the secondary frequency control problem in power systems by optimizing frequency control performance during the transient process following system disturbances, ultimately restoring the frequency to its rated value. The controlled objects include all controllable power sources, namely synchronous generators, grid-connected inverters, and controllable loads.

[0043] The control objective is to achieve the following within a given time interval: t =0~ T Within this framework, the absolute value of the frequency deviation at each node of the system and the squared cost function of the control input are minimized, where the frequency deviation is weighted by coefficients. q i Adjustment and control costs are determined by weighting coefficients. r i Adjustments are made to balance frequency performance and control energy consumption.

[0044] (3)

[0045] in oh i ( t )express t Frequency deviation at time, u i ( t )express t Time-based control input.

[0046] 1.3 System Constraint Construction

[0047] (1) The system dynamics model is described by a unified state-space model (2), whose state equations are composed of node phase angles, frequencies and frequency response models of various energy units, serving as dynamic constraints for the frequency control problem.

[0048] (2) All types of frequency control inputs are limited by physical capacity and actuator capability, control input u It must be located at the upper limit of the preset range. and the lower limit of the interval Within a certain range, to ensure that the control input is within the engineering feasible range. Furthermore, the control input must guarantee the stability of the closed-loop system.

[0049] (4)

[0050] (3) Required node status x (Including the regulating power of synchronous generators and the state of charge of grid-connected energy storage systems) must not exceed the permissible upper limit. and the lower limit of the interval scope.

[0051] (5)

[0052] (4) Under steady-state conditions, the steady-state frequency deviation of the system should asymptotically converge to zero, thereby achieving accurate frequency recovery.

[0053] (6)

[0054] 1.4 Constructing a complete frequency control problem

[0055] In summary, the optimal frequency control problem of the system is modeled as follows: (7) Step 2: Construction of a PI frequency controller based on a convex neural network 2.1 PI Control Structure Design To eliminate frequency deviation, this method employs a proportional-integral (PI) control structure, where the control input consists of a proportional term. p ( oh ) and integral term i ( s (This is obtained by superimposing.)

[0056] (8)

[0057] Integral status s Updates are performed using an integral update mechanism with projection operators to prevent integral saturation. This indicates that the constraint integral state is within the allowed upper and lower bounds. The projection operator. When the integration state reaches the upper and lower limits and continuing integration would lead to exceeding the limits, a correction term is introduced. x ( s , oh )=- oh make Suppressing integral growth to achieve anti-integral saturation control; when the integral state is within the allowable range... x ( s , oh )=0 will not affect the integration state.

[0058] 2.2 Strictly Convex Neural Network Control Design

[0059] To achieve the system stability and frequency recovery constraints in (7), both the proportional and integral terms are designed as strictly monotonic mappings to ensure the stability of the closed-loop system and the output tracking performance. Therefore, the gradient of a strictly convex neural network (SCNN) is used as the functional expression of the PI control law. Compared to traditional PI controllers, PI control based on SCNN can ensure system stability while optimizing transient control performance through offline training, and can achieve rapid online solution of the control strategy.

[0060] The convex neural network used is k Composed of layered structures, consisting of l Index, the output of each layer is derived from the output of the previous layer. o l Input signal z and bias terms b l After a strictly convex and increasing activation function s l Generation. By imposing positive constraints on the network weights, the strict convexity of the network output function on the input variables can be guaranteed.

[0061] (9)

[0062] in, The first l The layered network consists of the layer-1 output weight matrix, the input signal weight matrix, and the bias term vector; the layer-2 output weight matrix, the layer-3 input signal weight matrix, and the layer-4 bias term vector. k Output of layer network o k Represented as a function , It is a set of trainable parameter matrices and bias term vectors for each layer of the neural network. β >0 is a trainable parameter of the activation function. In neural network weights... For positive Non-zero, and all activation functions s l In the case of strict convexity and increasing, the output function of this neural network It's about the input signal. z Strictly convex.

[0063] The network uses Softplus- β An activation function of the form that, while ensuring strict convexity, possesses good smoothness and general approximation ability, and can approximate any strictly convex function that is continuous with Lipschitz.

[0064] (10)

[0065] The activation function is continuously differentiable over the entire real number domain, and its first derivative is: (11) Therefore in all x ∈ R Strictly greater than 0 indicates Softplus- β Function with respect to input variables x Strictly increasing. Furthermore, its second derivative is: (12) when β When > 0, Softplus- β The first derivative of the activation function is strictly positive over the entire real number domain, and the second derivative is strictly positive. Therefore, the activation function satisfies both the requirements of strict increasing and strict convexity.

[0066] The SCNN network structure for the weight matrix Simultaneously applying positive value constraints and structural constraints maintains the strict convexity of the network's output function, ensuring its gradient mapping exhibits strict monotonicity. Based on this, the proportional control term in the proportional-integral control law... p (·) and integral control items i (·) are respectively constructed as the gradients of the output functions of the corresponding SCNN networks.

[0067] (13)

[0068] in and The output gradient functions of the SCNN networks with proportional control and integral control are respectively given. i (P) and i (I) These are the neural network parameter sets for proportional control and integral control, respectively.

[0069] Finally, proportional control itemsp (·) and integral control items i (·) is given by the gradient functions of two strictly convex neural networks, thus forming a neural network PI controller with asymptotic stability and zero steady-state deviation guarantee.

[0070] In this invention, the SCNN network employs a finite number of layers. k With a finite-width multi-layer structure, the network depth and width can be selected according to the specific system scale and control accuracy requirements. Increasing the network depth can improve the network's ability to represent complex nonlinear convex functions, while increasing the network width helps to improve the function approximation accuracy, but at the same time, it will increase computational complexity and training cost.

[0071] Considering the real-time and stability requirements of power system frequency control, this invention does not pursue an infinitely deep or wide network structure. Instead, it selects an appropriate number of network layers and nodes to achieve an effective approximation of the system frequency control mapping while ensuring convexity and strict monotonicity. Since the control law is given by the gradient form of the SCNN output function, both network forward propagation and gradient calculation can be efficiently implemented through matrix operations with a fixed structure. This ensures that the computational complexity of online control increases linearly with the network size, meeting the needs of real-time engineering applications.

[0072] Step 3: Offline Training Method for Neural Network Controllers

[0073] 3.1 Modeling of Differentiable Closed-Loop Control Problems

[0074] An automatic differentiation method is employed to compute the policy gradient used for optimization. The system's state-space model is combined with a neural PI control policy to construct a computational graph, forming a differentiable closed-loop system. This computational graph consists of the forward and backward propagation processes of the closed-loop system. During forward propagation, the system model is simulated along a given time interval to obtain the system state trajectory and compute the corresponding loss function. During backward propagation, the network weights of the SCNN are optimized by taking the backward derivative of the parameterized closed-loop dynamics.

[0075] This invention employs explicit discrete-time numerical integration methods to discretize continuous-time frequency dynamic models, such as forward Euler integration based on a fixed step size or an equivalent first-order differentiable integral scheme. These integration methods are characterized by simple computational structure and explicit numerical form, ensuring differentiability of the simulation process within an automatic differentiation framework while maintaining the basic dynamic response characteristics of the system. Since this invention focuses on the dynamic process of the secondary frequency control stage of a power system, whose frequency state changes relatively slowly, the aforementioned discretization method can meet the requirements for the approximate accuracy of the system frequency dynamics during the training phase, provided a reasonable simulation step size is selected. By representing the system dynamic model as a discrete-time state update form, the entire closed-loop system can be directly embedded into the computational graph for forward propagation and backward gradient calculation.

[0076] To achieve offline training of the SCNN neural network, this method employs initial conditions obtained from multiple batches of random sampling to perform forward propagation simulations on the closed-loop system. Accordingly, the offline training problem of the neural network controller is formulated as follows: a sample-based parameterized optimization objective and constraints: (14) in, This is the periodic index for discrete forward simulation, belonging to 0~ N natural numbers, N This represents the number of cycles in the forward simulation. This is the index of the training sample data batch, belonging to 1~ m natural numbers, m This represents the total number of batches of sample data. N and m All of this is reflected in the summation symbol of the loss function in formula (15). , , They represent k Time, Number b The batch frequency sample vector, input sample vector, and all state sample vectors. Initial condition state vector. For dimension n x real vector Through user-defined state distribution x Sampling is performed to generate an initial set of conditional states in the state space. Perturbation matrix d b For dimension N × n d Real matrix Through user-defined perturbation distribution dSampling is performed to generate a set of disturbances. Neural network parameters Θ:={ i (P) , β (P) , i (I) , β (I) The network parameters include the proportional control term and the integral control term, namely the weight parameters and activation function parameters corresponding to the proportional network and the integral network. The neural network optimal control problem proposed in the current step formula (14) originates from the system frequency optimal control problem in step 1 formula (7), the difference being that the system has been discretized, which can be used for offline training of neural networks.

[0077] The training objective is to minimize the average loss over a batch of samples, and this loss function... L The frequency deviation weight vector is composed of the 1-norm of the frequency deviation and the squared 2-norm of the control input. q and control cost weight vector r Used to balance frequency regulation performance.

[0078] (15)

[0079] It should be noted that the control input and state constraints in this invention are not implemented through soft constraint penalty terms, but through the safety filter introduced in step 4. In addition, as mentioned in step 2, the neural PI controller has provable asymptotic stability and a guarantee of zero steady-state deviation in its structure. Therefore, the system stability constraint and zero steady-state deviation constraint in formula (7) are omitted in formula (14).

[0080] 3.2 Gradient Backpropagation and Parameter Update

[0081] For a specific range of control parameters and initial condition samples from the synthesized dataset, a differentiable closed-loop system can use stochastic gradient descent-like algorithms to iteratively update the proportional and integral network parameters. The chain rule is then used to apply the loss function of the forward simulation results. L Differentiate the neural network parameter Θ.

[0082] (16)

[0083] These parameterized optimal control problems can be solved offline using algorithms based on stochastic gradient optimization.

[0084] In the controller parameter optimization process, an adaptive learning rate stochastic gradient optimization algorithm based on the AdamW optimizer is employed, combined with learning rate decay or scheduling strategies, to maintain stable convergence characteristics at different stages of the training process. These measures reduce the sensitivity of long-term differentiable simulations to numerical accuracy while ensuring training efficiency.

[0085] 3.3 Loss Function Convergence Judgment and Early Stopping Mechanism

[0086] The present invention sets up a loss function convergence judgment and an early stopping mechanism for early termination of training, and the implementation method is as follows.

[0087] Define parameters: check_period=10, improvement threshold min_delta=1e-2, number of non-converged epochs to terminate training patience = 8; initialization settings: best_loss=inf, number of non-converged epochs bad_count=0.

[0088] After training begins, every convergence check period contains `check_period` training rounds. In each period, a convergence check of the loss function's mean is performed. If the mean loss function after `check_period` training rounds in the current period (`avg_loss`) is less than `best_loss - min_delta`, then the model parameters trained in the current period are retained, and the number of non-converged periods (`bad_count`) is counted as 0. If `avg_loss` is greater than or equal to `best_loss - min_delta`, it indicates that the mean loss function in this period does not show a significant convergence trend, and the number of non-converged periods (`bad_count`) is incremented by 1. Finally, it checks if `bad_count` is greater than or equal to `patience`. If so, the training is terminated; otherwise, training continues until the next convergence check period.

[0089] In summary, the training of a neural network can be described by the following pseudocode process:

[0090] 3.4 Applicability of Neural Network Controllers

[0091] It should be noted that, since the steady-state operating point and dynamic characteristics of the power system differ significantly under different scheduling operation cycles (e.g., different daily load curves, renewable energy output structures, or operating modes), this invention does not assume that a single training dataset can cover the operating conditions of all scheduling cycles. Instead, the control strategy of this invention adopts a "training by scheduling cycle and deployment by cycle" approach. That is, for each type of typical scheduling operation condition, a corresponding initial state distribution and disturbance distribution are constructed, and neural network control parameters matching the operating cycle are obtained through offline training.

[0092] Under the above design, the training data distribution is not used to approximate any nonlinear mapping in the entire operating space, but rather to fully sample and optimize the frequency control input-output relationship within the operating interval corresponding to a given scheduling period, thereby ensuring that the controller has good generalization performance within this operating interval. Combined with the input saturation constraint and state-safe filtering mechanism introduced in this invention, even near boundary conditions not explicitly covered by the training data, the controller output is still protected by safety constraints, thereby reducing the risk of instability due to generalization errors.

[0093] Step 4: Design input saturation constraints and state-safe filtering mechanisms

[0094] 4.1 Design of control input saturation constraints

[0095] The control inputs of synchronous generators, grid-type energy storage systems and controllable loads are saturated to ensure that the control strategy output by the neural network does not exceed the physical allowable range of power resources and thus meets the input saturation constraint in formula (14) in step 3.1.

[0096] (17)

[0097] in, For synchronous generator G i The control input must be no lower than the lower limit. And not higher than the upper limit ; FM for grid-type energy storage systems i The control input must be no lower than the lower limit. And not higher than the upper limit ; For controllable load L i The control input must be no lower than the lower limit. And not higher than the upper limit .

[0098] 4.2 Design of a State-Multiplicative Security Filter

[0099] Corresponding to the state constraint requirements in formula (14) of step 3.1, the constrained state includes the synchronous generator frequency regulation power. Frequency regulation power of grid-type energy storage With state of charge E i Response power of controllable load No further state constraints are set, as hard saturation constraints have already been set for the control input in step 4.1.

[0100] (18)

[0101] Variables containing underscores , , The variable containing the overline represents the lower bound of the constrained state. , , This represents the upper limit of the constrained state.

[0102] Each power resource state in formula (18) x i All are controlled by a single input. u i The determined single control input u i This may affect multiple states simultaneously, and the "input-state" paths for different power resources are decoupled. To achieve state safety requirements, a state-dependent filtering factor is introduced. m i Control input to the output of the neural network u i Channel-by-channel scaling is performed. The filter factor ranges from 0 to 1 and is used to attenuate the control command when the state is close to the boundary and the control direction may cause constraint violation, thus obtaining the filtered control command. .

[0103] (19)

[0104] in m i The value depends on the state. x i Control input u i and symbolic factors s i Its expression is: (20) For a system state belonging to a certain power resource It is required that it does not exceed the lower limit. and the Upper Realm The range, and define the lower limit of the safety threshold. and upper limit ,satisfy The safety threshold for power resource status is generally set within the operating range of the status. A value of 5% to 10% is appropriate; choosing too high a value would be overly conservative and negatively impact the power supply's output efficiency. (Sign factor) s i The expression ∈{-1,1} describes the sign relationship between the input and state variables, and its value depends on the type of power resource. s i =1 indicates the current state of power resources. x i In other words, positive control input u i >0 tends to increase x i ; s i =-1 indicates the current state of power resources. x i In other words, positive control input u i >0 tends to decrease. x i Furthermore, we can utilize symbolic factors. s i To determine whether the role of input control should be reduced.

[0105] Formula (20) lists s i The first of the three possible values ​​can be interpreted as: when the state is below the lower limit of the safety threshold. ,and s i u i <0, meaning the control input will further reduce the state and bring it closer to the lower bound of the constraint. , m i Values This activates the security filter to reduce u i The effect, until hour, m i = =0, making the filter control command... =0, avoid x i Crossing the lower bound of the constraint The second line of formula (20) describes the state. x i Lower limit of safety threshold and upper limit Normal operating status between m i =1, does not affect the original control input, safety filter is not activated. = u i Similarly, the third line of formula (20) can be interpreted as: when the state is above the upper limit of the safety threshold. ,and s i u i A value greater than 0 indicates that the control input will cause the state to increase further and approach the upper bound of the constraint. , m i Values This activates the security filter to reduce u i The effect, until hour, m i = =0, making the filter control command... =0, avoid x i Exceeding the upper bound of the constraint .

[0106] Among the state variables of interest in this invention, the sign factor s i The values ​​of and the activation conditions of the security filter are summarized in the following table: Table 1 Activation conditions for security filtering with different state variables

[0107] In summary, the safety filtering mechanism is activated only when the control input may cause the state to further violate the constraints, thereby satisfying the state safety constraints in formula (18). This safety filtering method can achieve continuous, direction-aware protection of state constraints without solving the optimization problem online, and can be seamlessly embedded into a neural network PI control framework.

[0108] Step 5: Training and Implementation Based on the Proposed Method

[0109] 5.1 Training Implementation Environment and Procedures

[0110] The modeling method proposed in this embodiment can be implemented using mainstream programming software (such as Visual Studio Code and MATLAB) and programming languages ​​(such as Python and MATLAB). Here, Python is used as an example to illustrate the implementation method. Scientific computing and system simulation libraries such as PyTorch, NumPy, Pandas, and the Control Systems Library should be pre-installed in the computing environment to enable neural network construction and training, matrix calculation, state-space model construction, and dynamic response simulation. The simulation embodiment of this invention was developed using Visual Studio Code software, with Python version 3.12. The hardware environment is a personal computer with a 2.9GHz CPU, 16GB RAM, and a 4GB graphics card.

[0111] (1) Training parameter settings: Table 2 Training Parameter Settings

[0112] (2) Read the power system model data, including the node state space model matrix. A sys , B sys , B d Node index data, variable index data, and power resource control input upper and lower limit data (e.g., in step 4.1) , , , , , ), power resource status upper and lower limit data (e.g., in step 4.2) , , , , , ), and the upper and lower limits of the integral status (in step 2.1) The variable values ​​in the optimization control problem are summarized in the table below. The current power per-unit value used in the power system is 1 pu = 100 MW.

[0113] Table 3. Values ​​of the Problem Variables

[0114] (3) Define the loss function L The weights of each item r i Define the probability distribution and amplitude parameters of state sampling and perturbation sequence sampling; system initial state distribution. x and perturbation distribution d The initial state distribution is constructed using a uniform distribution within a preset interval. x The reasonable range of values ​​for frequency deviation, phase angle shift, and related power supply state variables that may occur in the coverage system during this scheduling cycle. Disturbance distribution. d This is used to describe external disturbances such as load abrupt changes and fluctuations in renewable energy output. One of the system nodes is randomly selected to apply an active power disturbance with an amplitude uniformly distributed in the interval [-1,1].

[0115] (4) Perform training according to the process of Algorithm 1 in step 3.2 and save the neural network parameters obtained from the training.

[0116] (5) Read the trained strategy and perform real-time simulation verification.

[0117] (6) Training results: With 1000 training rounds set, the early stopping mechanism in step 3.3 was triggered at round 880, and the final value of the loss function was 1.962. The convergence trend of the loss function of the neural network is as follows: Figure 2 As shown. The offline training time for the neural network in the current embodiment is 1068.57 seconds, which meets the requirements for offline training after day-to-day scheduling.

[0118] 5.2 Simulation Verification Results

[0119] The method proposed in this invention was simulated and verified on a two-region, 14-node power system. This system includes one synchronous generator, two grid-connected energy storage systems, two grid-connected power sources, and two controllable loads. The system frequency reference value is 50Hz. The initial state of charge (SOC) of the grid-connected energy storage systems is 60%, while the initial states of all other systems are 0. The simulation experiment lasted 50 seconds with a sampling period of 0.1 seconds. At 1 second of simulation time, a step power disturbance with an amplitude of 0.5 pu was triggered at system node 7, simulating the condition of sudden load connection / disconnection of renewable energy power plants. The system simulation results are as follows: Figure 3-Figure 6 As shown.

[0120] Figure 3 The system node frequency response results are shown. By applying the proposed neural network control strategy, the frequency deviation can be gradually reduced after the disturbance occurs, and the frequency of each node in the system converges to the reference value of 50Hz (±0.01Hz) in 39.55 seconds. Figure 4 The control input results of synchronous generators, grid-connected energy storage, and controllable loads are shown. While achieving frequency control, the saturation constraints of the control input are satisfied through the method in step 4.1. Figure 5The exhibition showcased the frequency regulation output power of synchronous generators, grid-connected energy storage, grid-connected power sources, and controllable loads. Figure 6 The results of the state of charge of grid-type energy storage are shown, and all of them meet the state safety constraints through the method in step 4.2.

[0121] 5.3 Engineering Implementation of the Proposed Method

[0122] In engineering implementation, the frequency control method proposed in this invention is achieved through a combination of offline training and online deployment. Offline training of the neural network control strategy can be completed on the existing Automatic Generation Control (AGC) server or equivalent dispatch computing platform of the power grid dispatching agency. Specifically, during the day-ahead or intraday dispatching phase, corresponding control strategy parameters are trained for the system operating conditions of different hourly dispatching cycles.

[0123] The trained neural network control model is deployed in the online control system as a fixed control function, such as in the AGC execution module of the dispatch center or the station controller of power plants and energy storage power stations. During real-time operation, the controller only needs to perform a neural network forward calculation based on the measured frequency deviation and related state variables and output active power regulation commands. It does not involve online optimization or gradient calculation, has low computational load, and strong deterministic execution time, which can meet the real-time requirements of secondary frequency control in power systems.

[0124] Furthermore, during specific engineering deployments, the neural network model can be appropriately pruned or its parameters quantized based on the computing power of the target hardware platform to further reduce computational and storage overhead, thereby adapting to the hardware resources of existing AGC servers or site controllers without affecting the stability and security of the control strategy.

[0125] Stability Analysis and Frequency Recovery Guarantee

[0126] The stability of the controller design of this invention is proven by following the Lyapunov stability analysis method.

[0127] (1) Stability assumption

[0128] The frequency dynamic model used in this invention is a phase angle-frequency small-signal model obtained by linearizing around a certain steady-state operating point (e.g., a typical operating point under rated conditions or during a dispatch period). Under the premise that the power system frequency dynamics satisfy strict equilibrium point independent dissipation (EIP), for the system state... x ,enter u Output variables y = oh There exists a definite storage function. S (x , ), satisfying only at the system equilibrium point x = , y = hour, S ( x , )=0, and constant r >0, making (twenty one) In the physical sense of a power system, the above conditions are consistent with the energy dissipation characteristics determined by the "inertia term + damping term + interconnection power coupling term" in frequency dynamics: when the operating point satisfies the following conditions—phase angle difference within a feasible range (e.g., phase angle difference not approaching the instability boundary), frequency deviation within an allowable narrow band, and damping parameter being positive—the frequency dynamics exhibit strict dissipation characteristics in this neighborhood, thus allowing the use of an energy storage function. S ( x , An EIP-type dissipation inequality is established. Therefore, the stability conclusion of this invention is limited to local asymptotic stability within the neighborhood of the operating point, and its applicability is consistent with the frequency deviation operating range in a second frequency modulation scenario.

[0129] Next, according to the integral control term in formula (13) in step 2.2... i ( s The SCNN network outputs a gradient function, and the Bregman distance function is defined.

[0130] (twenty two)

[0131] B ( s , The function is positive definite and lies at the equilibrium point of the integral state. s = Place B ( s , )=0.

[0132] (2) Construction of Lyapunov functions

[0133] A composite Lyapunov function consisting of the system's energy storage function and the Bregman distance is constructed to analyze the stability of the closed-loop system.

[0134] (twenty three)

[0135] This function V ( x , s )≥0, at the equilibrium point ( , ) V ( x , s )=0.

[0136] V ( x , s The time-domain differential expression of ) is: (twenty four) in sat (·) represents the input saturated static nonlinear operator. m This includes the filter factor from formula (19) in step 4.2. m i A diagonal matrix.

[0137] (3) The impact of saturated nonlinearity and state-safe filtering

[0138] The input-saturated channel-wise static nonlinear operator in step 4.1 sat (·) satisfies the sector constraint, that is, for any input ( u - u ) and output ( sat ( u ) - u There exists 0 ≤ k i ≤ 1 ensures that each channel satisfies: (25) That is, input saturation does not increase the system supply rate term, therefore the second term in the second row of formula (24) can be relaxed to: (26) Step 4.2 Formula (19) proposes a security filter that is a channel-by-channel multiplicative attenuation, where 0 ≤ m i ≤1, m For inclusion m i The diagonal matrix is ​​such that: (27) In other words, state-safe filtering also does not add a supply rate term. Combining the above three points, the actual closed-loop system can be viewed as an interconnection of "strict EIP frequency dynamics" and "static nonlinear operators satisfying sector constraints (saturation + safety filtering + projection)". Since none of these nonlinear elements add a supply rate term, the original Lyapunov inequality can be preserved. The integral projection operator proposed in step 2.1 is activated only when the integration state touches the boundary and continuing integration would lead to an out-of-bounds error; its correction term... x Always opposite in direction to the nominal integral, thus satisfying This avoids violating the negative definiteness of Lyapunov functions.

[0139] Finally, based on the strict monotonicity of the neural network PI control strategy, we can obtain... (28) The equation applies only at the system equilibrium point. y = and s = The office was established. Due to... V ( x , s )≥0, and The closed-loop system is locally asymptotically stable near the equilibrium point under steady-state conditions. The frequency deviation is strictly converged to zero, achieving accurate frequency recovery.

[0140] Example 2

[0141] The basic concept of this embodiment is as follows: The core of this invention lies in a power system frequency control system and method based on a convex neural network (SCNN). This system constructs an inherently stable control law using SCNN and integrates input saturation and state-safety filtering mechanisms to achieve fast, stable, and safe frequency control. This method employs an offline training and online deployment model, making it suitable for engineering applications.

[0142] The power system frequency control system includes: Status awareness module: Used to acquire the frequency deviation signal of the power system. In this embodiment, the module acquires the system frequency signal in real time through a frequency measurement unit (PMU) or SCADA system deployed at key nodes of the power grid, and compares it with the rated frequency (e.g., 50Hz) to obtain the deviation value.

[0143] The convex neural network control module is communicatively connected to the state-aware module. This module contains at least one strictly convex neural network. The strictly convex neural network is a neural network with positive constraint weights and a strictly convex increasing activation function; the gradient of its output function is used as the control law. This module receives the frequency deviation signal, performs forward propagation calculations on the neural network, and takes the gradient of its output function to generate preliminary control commands. In this embodiment, the neural network adopts a 3-layer structure (input layer, hidden layer, output layer), with 32 nodes in the hidden layer and the activation function being Softplus- β function( β =1.0).

[0144] Safety Constraint Processing Module: Communicates with the convex neural network control module. This module processes the initial control commands by applying constraints, including at least input saturation constraints and state safety filtering. Input saturation constraints limit the commands to the physical capabilities of the controllable power source; for example, the upper limit for a synchronous generator's power regulation command is +20 MW, and the lower limit is -20 MW. State safety filtering calculates a multiplicative filter factor between 0 and 1 based on a comparison of state variables (such as energy storage SOC and generator output power) with preset safety thresholds, combined with the direction of the control command, to scale the command.

[0145] Command output module: It communicates with the safety constraint processing module and is used to send the final control command after safety constraint processing to the local controller of the power plant or power station through the dispatch data network or dedicated line, so as to control the synchronous generator, grid-type energy storage inverter or controllable load for power regulation.

[0146] The power system frequency control method includes the following steps: Frequency deviation acquisition: The deviation between the current frequency and the rated frequency of the power system is acquired in real time through a frequency measuring device.

[0147] Initial command generation: The frequency deviation signal is input to a pre-trained convex neural network controller. This controller calculates the gradient mapping of the output function of its internal strictly convex neural network, generating initial control commands.

[0148] Safety constraint processing: Initial control commands are processed. First, input saturation constraint processing is performed, clamping the commands to the range [U_min, U_max]. Then, state-based safety filtering is performed based on key operating states (e.g., energy storage SOC = 60%) and their safety thresholds (e.g., SOC_min = 10%, SOC_max = 90%), combined with the direction of the control commands (e.g., increasing power output would decrease SOC, then...). s =-1), calculate the multiplicative filter factor. m If the state is safe (e.g., SOC is between 10% and 90%), then m =1; If the state is close to the boundary and the command direction is dangerous (e.g., SOC=85% and the command requires continued discharge), then m <1, attenuate the instruction.

[0149] Output final command: Send the processed final control command to the controllable power source in the power system. The command cycle can be the same as or shorter than the traditional AGC cycle (e.g., 4-8 seconds).

[0150] The specific shortcomings addressed by this embodiment are: the difficulty of traditional frequency control methods in simultaneously ensuring control performance, stability, and safety in complex and novel power systems.

[0151] Component names, connections, and working principles: Component names have been described above. The connections are sequential communication connections: State Awareness Module -> Convex Neural Network Control Module -> Safety Constraint Processing Module -> Command Output Module. Working principle: SCNN ensures control stability and performance, while safety constraint processing ensures command feasibility and state safety.

[0152] Dimensions: Neural network structure: 1 node in the input layer, 32 nodes in the hidden layer, and 1 node in the output layer.

[0153] Input saturation limit: [-20 MW, +20 MW].

[0154] State safety threshold (example energy storage SOC): [10%, 90%].

[0155] Control command issuance cycle: 1 second.

[0156] Implementation steps (in chronological order): Initialization: After power-on, load the pre-trained neural network parameter file (e.g., scnn_controller_params.pth).

[0157] Execute in a loop: a. Data Acquisition (Tool: PMU / SCADA): At the beginning of each control cycle, read the current system frequency measurement value from the data bus.

[0158] b. Calculate the deviation: Calculate the deviation between the current frequency and 50 Hz.

[0159] c. Neural Network Calculation (Condition: Frequency Deviation Value as Input): Perform forward propagation of the neural network and calculate the gradient of the output function to obtain the initial control command u. preliminary .

[0160] d. Input saturation handling: Compare u preliminary With preset limit [U] min U max ], to obtain u saturated .

[0161] e. Status Reading and Safety Filtering (Tool: Monitoring System): Reading key status values ​​(such as generator power P) from the monitoring system. gen Energy storage SOC). Based on the state value, its safety threshold, and u saturatedIn the direction of the filter factor μ for each channel, calculate the filter factor μ according to the established formula. i Calculate the final instruction u final = m i u saturated f. Instruction issuance (tool: scheduling instruction channel): This will send u... final The data is transmitted to the relevant power plant or energy storage station via standard communication protocols (such as IEC 60870-5-104).

[0162] Waiting for the next cycle.

[0163] Experimental Verification: To verify the effectiveness of this embodiment, a system was built as follows: Figure 3-5 The simulation test system is shown, and the data recorded is as follows:

[0164] In other embodiments, the activation function of the strictly convex neural network may also be the ReLU squared function. s ( x ) =(max(0, x )) 2 And by adjusting the network weight constraints, its overall strict convexity is ensured.

[0165] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A power system frequency control system, characterized in that, include: The state awareness module is used to acquire the frequency deviation signal of the power system; A convex neural network control module, which is communicatively connected to the state perception module, is used to receive the frequency deviation signal and generate preliminary control commands by using the gradient mapping of the output function of at least one strictly convex neural network within it. A safety constraint processing module, which is communicatively connected to the convex neural network control module, is used to perform constraint processing on the preliminary control command. The constraint processing includes at least input saturation constraints and state safety filtering. The instruction output module is communicatively connected to the safety constraint processing module and is used to send the processed final control instruction to the controllable power source in the power system.

2. The system according to claim 1, characterized in that, The activation function of the strictly convex neural network is the Softplus-β function.

3. The system according to claim 1, characterized in that, The state safety filtering is based on the comparison between state variables and preset safety thresholds, and the multiplicative filtering factor is calculated in combination with the direction of control commands.

4. The system according to claim 1, characterized in that, The system also includes an integral state update module, which is used to update the integral state using an integral update mechanism with a projection operator.

5. The system according to claim 1, characterized in that, The convex neural network control module and the safety constraint processing module are deployed in the automatic power generation control server or the station controller.

6. A power system frequency control method, characterized in that, Includes the following steps: Acquire the frequency deviation signal of the power system; input the frequency deviation signal into a pre-trained convex neural network controller, and generate preliminary control commands by calculating the gradient mapping of the output function of the strictly convex neural network in the controller; perform safety constraint processing on the preliminary control commands, the processing including at least input saturation constraints and state safety filtering; The final control command, after being processed by safety constraints, is output to the controllable power source in the power system for frequency regulation.

7. The method according to claim 6, characterized in that, The activation function of the strictly convex neural network is the Softplus-β function.

8. The method according to claim 6, characterized in that, The state-based safety filtering includes: comparing the key operating state of the power resources with a preset safety threshold, and scaling the initial control command by calculating a multiplicative filter factor between 0 and 1 based on the directionality of the control command.

9. The method according to claim 6, characterized in that, When generating the integral control term in the preliminary control instruction, an integral update mechanism with a projection operator is adopted.

10. A method for training the convex neural network controller of claim 6, characterized in that, include: Construct a differentiable closed-loop system model that includes a power system dynamics model and a parameterized control strategy; Based on initial conditions and disturbance scenarios using multiple batches of random sampling, a forward simulation is performed on the differentiable closed-loop system to calculate the loss function. Using automatic differentiation, the gradient of the loss function with respect to the neural network parameters is calculated via backpropagation. The neural network parameters are then optimized using a stochastic gradient descent algorithm until the convergence condition is met.

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