A method, system and related devices for flexible load restoration in power distribution networks

Abstract

This application discloses a method, system, and related devices for flexible load restoration in distribution networks, belonging to the field of power system fault recovery. The method includes: combining a flexible load extreme operation model with distribution network power flow constraints to form the constraints for the distribution network operator; transforming the opportunity constraints in the operator's constraints into deterministic constraints, and then calculating the distribution network's operational safety domain using a vertex search method based on Hausdorff distance; constructing a distribution network load restoration model based on the operational safety domain; solving the distribution network load restoration model based on the operational safety domain; and performing decision optimization at the distribution network level during power restoration based on the solution results. This method performs load restoration while considering the distribution network's operational safety domain, ensuring the safety and robustness of the power grid restoration process, and ultimately helping the distribution network operator make informed decisions.

Description

Technical Field

[0001] This application relates to a method, system, and related devices for flexible load restoration in a power distribution network, belonging to the field of power system dispatching technology. Background Technology

[0002] Extreme weather events and cyberattacks frequently cause power outages, resulting in significant economic losses and severe social impacts. Compared to transmission systems, distribution networks have lower levels of automation and insufficient redundancy, making them relatively weaker in responding to disasters, and their control and protection measures are also relatively limited. Data shows that distribution network outages account for 80% of total grid outage time, making them one of the main causes of power system failures. Furthermore, since the end loads of industrial, commercial, and residential users are mainly connected to the distribution network, any failures will severely impact daily production and life, leading to significant social consequences.

[0003] With the rapid popularization of renewable energy, power electronic equipment, and energy storage technologies on the user side, current distribution network load restoration strategies are gradually shifting from the traditional power-tracking load model to a source-grid-storage coordinated operation model. This involves improving the redundancy capacity of the distribution network through distributed generation, distribution network topology adjustments, and mobile energy storage. Load, as the core object of distribution network restoration, directly affects the restoration process. Currently, mainstream research focuses on achieving rapid load restoration through optimized coordination of the source-grid-storage system; however, research on the characteristics of user-side loads themselves is relatively limited. User-side loads are diverse and complex, requiring accurate modeling during restoration to more accurately describe the distribution network restoration process. However, current load restoration research pays little attention to the time-varying characteristics of loads, leading to discrepancies between theoretical models and actual conditions, and potentially causing safety hazards. Summary of the Invention

[0004] The purpose of this application is to address the shortcomings of existing technologies by proposing a flexible load restoration method, system, and related devices for power distribution networks to ensure the safety and stability of the load restoration process.

[0005] To achieve the above objectives, the technical solution adopted in this application is as follows:

[0006] In a first aspect, this application provides a flexible load restoration system for a distribution network, comprising:

[0007] Based on simulation, the operating data of flexible load under extreme conditions is obtained. The operating data of flexible load under extreme conditions is trained by MLP neural network to obtain an extreme operation model of flexible load with the input of power outage duration and power restoration duration and the output of load size.

[0008] The flexible load extreme operation model and the distribution network power flow constraints are combined to form the constraints of the distribution network operator; the chance constraints in the constraints of the distribution network operator are transformed into deterministic constraints, and then the operating safety domain of the distribution network is calculated by the vertex search method based on Hausdorff distance.

[0009] A distribution network load restoration model based on the operational safety domain is constructed, the model is solved, and the decision optimization at the distribution network level during power restoration is performed based on the solution results.

[0010] As a further improvement of this application, the input layer of the MLP neural network is provided with two neurons, which correspond to the power outage duration and the power restoration duration, respectively; the hidden layer is provided with 10 neurons; and the output layer is provided with 1 neuron, which corresponds to the load size.

[0011] As a further improvement of this application, the MLP neural network employs an error backpropagation algorithm for supervised learning during training, and utilizes gradient descent to optimize the network weights and biases to establish a flexible load extreme operation model with nonlinear dependencies; the MLP neural network uses the power outage duration... t 1 and the time it takes to restore power. t 2 is the input, and the output layer outputs data as... t 1, t 2. Related load size P tcl .

[0012] As a further improvement to this application, the calculation of the operating safety domain of the distribution network using the vertex search method based on Hausdorff distance includes:

[0013] By solving different objective functions step by step, each vertex is obtained, and then the polygon represented by the boundary of the safe operating region is approximately obtained. Finally, the search stops when the Hausdorff distance reaches the termination condition, and the safe operating region of the distribution network is obtained.

[0014] As a further improvement to this application, the vertex search method based on Hausdorff distance specifically includes:

[0015] 1) Determine the solution time t The operational safety domain of the distribution network, initialize the set of direction vectors: With the initial vertex set ; To initialize the set of direction vectors, This is the transpose of the direction vector, where T represents the transpose of the vector, and i is used to distinguish different direction vectors;

[0016] 2) Sequentially obtain the sets of initialization direction vectors belonging to different groups. The optimization problem is solved to obtain the optimal solution. And store it in the set of vertices of the optimal solution. ;

[0017] 3) Based on the optimal solution vertex set Calculate the unit outward normal vector between all adjacent vertices, and use it as the direction vector for the next round of search, thus obtaining the updated set of direction vectors. ;

[0018] 4) Calculate the Hausdorff distance for each vertex. d j If a vertex corresponds to Less than the set threshold If the threshold value is greater than or equal to the set threshold, then the search for the external normal vector determined by the corresponding vertex and its adjacent vertices will cease; Then repeat steps 2)-4) until all vertices are... d j Continue until all termination conditions are met;

[0019] 5) Based on each vertex, obtain t The operational safety domain of the distribution network at any given time is obtained, and then the polygon represented by the boundary of the operational safety domain is obtained.

[0020] As a further improvement to this application, the distribution network load recovery model based on the operational safety domain includes an objective function and constraints; wherein, the objective function is to maximize load recovery, and the constraints, in addition to the original distribution network power flow constraints, voltage limit constraints, power limit constraints, and current limit constraints, add main transformer constraints, gas turbine unit constraints, and distribution network operational safety domain constraints;

[0021] Wherein, the objective function is

[0022]

[0023] In the formula, t∈T indicates that t is an element belonging to the time set T, which contains all the time points involved in the load recovery process. α i It is the load weight. sload i,t It is a binary variable indicating whether the load is in use. Pload i,t It is a node i Load in time t The active power at time t, max{} represents solving for the maximum value, and I is the set of nodes.

[0024] Secondly, this application provides a flexible load restoration system for a distribution network, comprising:

[0025] The simulation training module is used to obtain the operation data of flexible load under extreme conditions based on simulation, and to train the operation data of flexible load under extreme conditions through MLP neural network to obtain an extreme operation model of flexible load with the input of power outage duration and power restoration duration and the output of load size.

[0026] The distribution network operation safety domain calculation module is used to form the constraint conditions of the distribution network operator together with the flexible load extreme operation model and the distribution network power flow constraints; the opportunity constraints in the constraint conditions of the distribution network operator are transformed into deterministic constraints, and then the operation safety domain of the distribution network is calculated by the vertex search method based on Hausdorff distance.

[0027] The model solving module is used to construct a distribution network load restoration model based on the operational safety domain, solve the distribution network load restoration model based on the operational safety domain, and optimize the decision-making at the distribution network level during power restoration based on the solution results.

[0028] Thirdly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the flexible load restoration method for the power distribution network.

[0029] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the flexible load restoration method for the power distribution network.

[0030] Fifthly, this application provides a computer program product, the computer program product including computer instructions, the computer instructions instructing a computer to execute the power distribution network flexible load restoration method.

[0031] The beneficial effects of the technical solution proposed in this application are:

[0032] To ensure accurate load restoration, this application analyzes the abnormal characteristics of flexible loads during power outage restoration from two perspectives: the inherent characteristics of flexible loads and user behavior. An extreme operation model of flexible loads, combined with the abnormal characteristics during restoration, proposes a strategy for handling abnormal flexible loads under extreme conditions. This strategy accurately describes the actual actions during load restoration and enables dynamic selection of diverse load behaviors in the distribution network. The application also studies the calculation method for the operating safety domain of the distribution network under extreme conditions and establishes a distribution network load restoration model based on the IEEE simulation system. Unlike previous methods that fixed load sizes during distribution network restoration, the proposed method considers the abnormal characteristics of loads under extreme conditions, aligning with actual load restoration. This allows distribution network operators to make correct restoration decisions, contributing to the safe and stable operation of the distribution network. During load restoration, the operating safety domain of the distribution network is calculated, ensuring that the distribution network does not exceed its limits during load restoration decisions. Making load restoration decisions based on the known operating safety domain guarantees safe and stable restoration of the distribution network under extreme conditions. Attached Figure Description

[0033] Figure 1 A schematic diagram illustrating the load evolution of the flexible load provided in this application under normal operating conditions;

[0034] Figure 2 A schematic diagram illustrating the load evolution of the flexible load provided in this application under different power outage durations;

[0035] Figure 3 A schematic diagram of the flexible load restoration method for distribution networks provided in this application;

[0036] Figure 4 The calculation results for the operational security domain of the distribution network provided in this application;

[0037] Figure 5 The restoration results of the flexible load restoration method for distribution networks provided in this application. Detailed Implementation

[0038] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0039] Terminology Explanation:

[0040] MLP (Multi-Layer Perceptron) is a feedforward artificial neural network consisting of an input layer, one or more hidden layers, and an output layer. Information is exchanged between layers through fully connected layers, and non-linear activation functions are used to introduce non-linear transformation capabilities, thereby solving complex problems that linear models cannot handle.

[0041] In the description of this application, unless otherwise expressly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0042] The first objective of this application is to provide a method for flexible load restoration in a distribution network, including the following:

[0043] Step (1): Analysis of abnormal characteristics of flexible loads under extreme conditions;

[0044] Specifically, the technical solution for step (1), which analyzes the abnormal characteristics of flexible loads under extreme conditions, is described in detail below:

[0045] Unlike traditional distribution network restoration processes that treat load as a fixed value, when a power outage occurs, a large number of flexible loads within the distribution network are lost due to the diversity of their operating states. This leads to a phenomenon in the initial stage of restoration where the power of the load to be restored is significantly higher than the baseline load for a short period of time, known as cold load return. This is one of the reasons why load restoration exhibits abnormal characteristics.

[0046] During power outages, changes in flexible loads can be categorized into three scenarios: short-term, medium-to-long-term, and long-term power outages. Different outage durations correspond to different load responses. When the outage is short, due to insufficient time, some flexible loads remain within their normal temperature range. Although restoring power will cause a load surge, it will not reach its maximum value. For medium-to-long-term power outages, the temperature of all flexible loads exceeds their normal operating range. Therefore, when power is restored, all flexible loads will activate, causing the total power to reach its peak, and the duration of this peak increases with the duration of the outage. Long-term power outages mean that the temperature of all flexible loads has reached the outdoor temperature. When power is restored, the load power reaches its maximum, and the phenomenon of cold load recirculation remains unchanged regardless of the duration of the outage.

[0047] On the other hand, human behavior is a subjective cause of abnormal load characteristics. After power is restored to the distribution network, users adjust their loads based on the impact of the power outage duration on their production and daily life to reduce economic losses. At this time, the load curve has changed significantly compared to before the power outage, and traditional fixed load curve modeling methods are no longer applicable. Taking industrial parks as an example, due to economic and other constraints, the baseline load after power restoration may be insufficient to meet user demand, thus requiring additional load, resulting in load surges. The magnitude of such subjectively driven load surges increases with the duration of the power outage, forming abnormal characteristics during load restoration.

[0048] Step (2), Strategy for handling abnormal flexible loads under extreme conditions;

[0049] Specifically, the technical solution for the extreme case handling strategy of step (2) is described in detail below:

[0050] The abnormal characteristics of flexible loads under extreme conditions are solved by training an MLP neural network.

[0051] Since the causes of load anomalies are mainly related to the duration of power outages, and the characteristics of flexible loads are complex and difficult to accurately describe through mechanistic modeling, an MLP neural network is used to train and solve for the characteristics of flexible loads under extreme conditions. Specifically, the input layer of the MLP neural network has two neurons, corresponding to the power outage duration and the power restoration duration, the hidden layer has 10 neurons, and the output layer has 1 neuron, corresponding to the load size. The final result is a flexible load extreme operation model with the power outage duration and power restoration duration as inputs and the load size as output.

[0052] The flexible load extreme operation model obtained from the MLP neural network, together with the power flow constraints of the distribution network, constitutes the constraint conditions for the distribution network operator.

[0053] Step (3): Calculation method of the operational safety domain of the distribution network under extreme conditions;

[0054] Specifically, the technical solution for calculating the operational safety domain of the distribution network under extreme conditions in step (3) is described in detail below:

[0055] After the anomalous characteristics of flexible loads in the distribution network are solved using an MLP neural network, a data- and knowledge-driven approach is adopted. The resulting constraints of the extreme operation model of flexible loads should be delivered to the distribution network operator for integration, and distribution network power flow constraints are added. Based on these constraints, the cumulative distribution function is fitted by transforming chance constraints into deterministic constraints. Finally, the operational safety domain of the distribution network is calculated using a vertex search method based on Hausdorff distance.

[0056] Regarding the mathematical solution method of the model, a vertex search method based on Hausdorff distance is adopted, which transforms the optimal solution of the optimization problem of the operating safety domain of the distribution network into a vertex of the corresponding operating safety domain of the distribution network. The process terminates when the relative displacement of the new vertex to the original line corresponding to it, i.e., the Hausdorff distance, is less than a certain specific value.

[0057] Based on the above scheme, this application establishes a calculation method model for the operational safety domain of the distribution network under extreme conditions, including model construction and solution of the operational safety domain of the distribution network. The model construction considers the characteristics of flexible loads that deviate from normal conditions under extreme circumstances. The model constraints include distribution network power flow constraints, voltage limitation constraints, power limitation constraints, and current limitation constraints, which together constitute the solution model for the operational safety domain of the distribution network under extreme conditions.

[0058] In solving the operational safety domain of the distribution network, the network operation constraints containing random variables are first expressed as chance constraints, and then the chance constraints are transformed into deterministic constraints. The vertex search method based on Hausdorff distance is used to calculate the polygon represented by the boundary of the operational safety domain of the distribution network when the load is restored in extreme cases.

[0059] By transforming the above model, the operational safety domain of the distribution network under extreme conditions for load restoration can be obtained, thereby guiding the distribution network to carry out safe and stable load restoration.

[0060] Step (4): Distribution network load recovery model based on the operational safety domain.

[0061] Specifically, step (4) of the distribution network load restoration model based on the operational safety domain is described in detail below:

[0062] After calculating the operating safety domain of the distribution network based on load characteristics and power flow constraints, the flexible load extreme operation model combines the actual situation of power grid recovery under extreme conditions such as the gradual increase of main transformer output, and incorporates IEEE 33 nodes to form a distribution network load recovery model based on the operating safety domain.

[0063] Among them, IEEE33 usually refers to the IEEE 33-node system, which is a standard test system widely used in the field of power system research.

[0064] Specifically, after the operational safety domain of the distribution network is calculated under extreme conditions, it is introduced into the distribution network load recovery model based on the operational safety domain, including the objective function and constraints. The objective function is to maximize load recovery, and the constraints are expanded from the original distribution network power flow constraints, voltage limit constraints, power limit constraints, and current limit constraints to include main transformer constraints, gas turbine unit constraints, and operational safety domain constraints of the distribution network.

[0065] After performing second-order cone relaxation on the power flow constraints of the distribution network, the distribution network load recovery model based on the operational safety domain can be transformed into a linear programming problem, which can be solved using a commercial solver.

[0066] Second-order cone relaxation is a convex relaxation technique that addresses nonlinear constraints in power flow in distribution networks (such as the relationship between power, voltage, and current) by mathematically transforming them into second-order cone constraints (which are convex constraints). Taking node power balance and voltage constraints in distribution networks as examples, relaxation transforms the originally nonlinear and difficult-to-solve power flow calculations into problems within a convex optimization framework, creating conditions for subsequent transformation into linear programming. Furthermore, under certain conditions, the relaxation gap is small, and the solution accuracy meets engineering requirements.

[0067] The present application will now be described in further detail with reference to the accompanying drawings. Figure 3 As shown, a specific implementation method for a flexible load restoration method for a power distribution network is described below.

[0068] (1) Analysis of abnormal characteristics of flexible loads under extreme conditions, detailed as follows:

[0069] During power system restoration, the operation of flexible loads such as building air conditioning is interrupted due to power outages, leading to an increase in indoor temperature. This temperature rise causes indoor objects and building structures to absorb and store a large amount of heat, creating potential load pressure. When power supply is restored, the stored heat is gradually released into the indoor air, resulting in additional cooling load. During this process, the initial power demand often significantly exceeds the normal baseline load level for a short period. Furthermore, the duration of the power outage directly affects the different manifestations of the load; short-term, medium-term, and long-term power outages correspond to different load states, manifested in differences in the magnitude and duration of the power surge during the initial restoration phase.

[0070] On the other hand, user behavior also plays a significant role in changes in electricity load. User-side load includes a large amount of adjustable flexible load, which can be flexibly adjusted according to electricity price fluctuations or equipment operating constraints. After power is restored, users typically adjust their electricity demand promptly based on the impact of the outage on production and daily life to minimize economic losses. Especially in production-oriented power consumption scenarios such as industrial parks, businesses often increase production scale after power is restored to compensate for production losses caused by the outage, resulting in initial power demand potentially significantly exceeding the baseline load before the outage. This load change not only puts greater pressure on the power grid for recovery but may also exacerbate load volatility in the power system, increasing the complexity and uncertainty of power restoration.

[0071] Unlike traditional distribution network restoration processes that treat load size as a constant, after a power outage, the loss of the diverse operating states of the flexible loads that constitute a large proportion of the distribution network leads to a phenomenon where the power of the load to be restored is much greater than the baseline load value in the initial short period of restoration. This phenomenon is known as cold load backflow and is an objective reason for the load's dependence on the duration of the power outage.

[0072] During normal operation, since the flexible load only has two operating states—ON (power at rated power P) and OFF (power at 0)—the internal temperature of the flexible load exhibits a periodic variation within a certain range. Specifically, the flexible load has a temperature dead zone width δ. If the set temperature of the flexible load is... T set When its internal temperature exceeds T max ( T max = T set When +δ), the flexible load begins to work, and the internal temperature decreases; when its internal temperature is less than δ, the flexible load starts to work, and the internal temperature decreases. T min ( T min = T set When -δ) is reached, the flexible load is turned off, the internal temperature rises, and the final result is... Figure 1 The normal operating status is shown.

[0073] like Figure 2 As shown, the evolution of flexible loads can be divided into three scenarios: short-term power outage, medium-to-long-term power outage, and long-term power outage. Different outage durations lead to differences in load performance. When a power outage occurs in the distribution network, all flexible loads are shut down due to the loss of power supply, and their internal temperature gradually rises over time. In the case of a short-term power outage, when power is restored, the temperature of some flexible loads is still within their normal operating cycle. Therefore, only those flexible loads whose temperature has exceeded their operating cycle will be restarted, while loads whose temperature is still within their operating cycle will remain in normal operation. This results in the load amplitude increasing somewhat due to a short-term power outage, but failing to reach its maximum value. T min Indicates the minimum temperature. T max This indicates the maximum temperature; OFF means off, and ON means on.

[0074] In the event of a medium- to long-term power outage, due to the extended duration of the outage, the internal temperatures of all flexible loads will exceed their normal operating range upon restoration of power. Therefore, at the moment power is restored, all flexible loads will activate, causing the total power to momentarily reach its maximum. Subsequently, as the internal temperatures of the flexible loads gradually decrease and return to their normal operating cycle, the total power will decrease accordingly. It is particularly important to note that in the event of a medium- to long-term power outage, the longer the outage, the closer the internal temperature of the flexible loads will be to the outdoor temperature. T out This means that the time required to return to normal operating cycles will increase, and the duration of peak power of flexible loads will also increase with the duration of power outages.

[0075] If the power outage in the distribution network is prolonged, the internal temperature of the flexible loads will be the same as the outdoor temperature when power is restored. In this case, similar to a medium- to long-term power outage, all flexible loads will activate instantly upon power restoration, causing the total power to reach its maximum. However, because the internal temperature of the flexible loads is the same as the outdoor temperature during a long-term power outage, the impact of the prolonged outage on the state of the flexible loads is weakened. Therefore, under the condition of a long-term power outage, the abnormal characteristics of the flexible loads remain unchanged.

[0076] Human behavior causes loads to exhibit a dependence on the duration of power outages. When power is restored to the distribution network, users adjust their loads promptly based on the impact of the outage on their lives and production to minimize economic losses; these loads are called profit-seeking loads. Therefore, the load curve after power restoration changes significantly compared to before the outage, rendering traditional fixed load curve modeling methods inapplicable. For example, in an industrial park, if production continues according to the original plan after a power outage, production targets often cannot be met, leading to economic losses. Therefore, the park needs to increase production to ensure the smooth completion of the production plan, resulting in a load exceeding the baseline load in the initial stage of power restoration.

[0077] Under normal operating conditions, the size of the profit-seeking load is the pre-planned baseline load. P base Without interrupting power supply, the daily production target can be successfully achieved by operating at the baseline load.

[0078] During power outages, profit-seeking loads may experience power failures due to extreme circumstances, causing their load to drop to zero instantly. This power outage results in a loss of load for profit-seeking loads, often preventing them from meeting planned production demands.

[0079] During the power restoration phase, the load loss caused by the power outage may prevent the achievement of daily production targets if production continues at the baseline load, resulting in economic losses. Therefore, after power is restored, profit-driven loads often increase production scale, exhibiting load behavior different from normal operation. The longer the power outage, the greater the load loss, and the more pronounced the load behavior upon power restoration. It should be noted that since daily production targets are fixed, although the load may be higher than the baseline level upon power restoration, the total overload will not exceed the total load loss during the power outage. This profit-driven load behavior, where the baseline load cannot meet user demand upon power restoration, ultimately leads to changes in load behavior, primarily influenced by the duration of the power outage.

[0080] (2) The strategy for handling abnormal flexible loads under extreme conditions is detailed below:

[0081] Due to the large number of flexible loads in the distribution network and the varying operating parameters of each flexible load, it is difficult to accurately describe the operating state of flexible loads using knowledge-driven modeling methods. Therefore, this application employs a data-driven modeling method to model the handling of flexible loads under extreme conditions, simulates the operating data of flexible loads, and uses this data to train a Multiple Layer Perception (MLP) model to accurately characterize the cold load recirculation phenomenon.

[0082] MLP neural networks are essentially nonlinear fits to the input and output. Their structure can be divided into three parts: an input layer, a hidden layer, and an output layer. We set the number of neurons in the input layer of the MLP neural network to 2, corresponding to the power outage duration and power restoration duration; the number of neurons in the hidden layer to 10; and the number of neurons in the output layer to 1, corresponding to the load magnitude. Its mathematical model can be represented by the following formula:

[0083] (1)

[0084] (2)

[0085] (3)

[0086] (4)

[0087] In the formula, W in and b in These are the weights and biases from the input layer to the hidden layer; W hid and b hid These are the weights and biases from the hidden layer to the output layer;t 1 and t 2 represents the duration of the power outage and the time it takes to restore power; N in This represents the set of neurons in the input layer, N1, N2, ... N. 10 , which is a neuron; N hid Represents the set of neurons in the hidden layer; P tcl Represents the output layer neurons; F ( ) is the activation function of the MLP neural network.

[0088] During training, the MLP neural network employs a backpropagation algorithm for supervised learning, utilizing gradient descent to optimize the network's weights and biases. Since the MLP neural network is a typical feedforward network, information processing proceeds from the input layer to the hidden layer and finally to the output layer. The hidden layer performs a non-linear mapping of the input layer neurons. Furthermore, the backpropagation method feeds back the output layer's error, correcting the MLP neural network's weights and biases, thereby establishing a flexible, extreme load operation model with good non-linear dependencies.

[0089] This application utilizes an MLP neural network to convert power outage duration into load quantity. The trained neural network is based on power outage duration. t 1 and the time it takes to restore power. t 2 is the input, and the output layer outputs data as... t 1, t 2. Related load size P tcl This refers to the magnitude of the load value that causes an abnormal state under extreme conditions. This method successfully models the abnormal state of flexible loads under extreme conditions using historical data, solving the problem of accurately describing the mechanism in modeling.

[0090] (3) The calculation method for the operational safety domain of the distribution network under extreme conditions is explained in detail below:

[0091] When load is restored, the distribution network has its own constraints:

[0092] 1) Current constraints

[0093] The branch power flow model adopts the DistFlow power flow model, which can be specifically described as follows.

[0094] (5)

[0095] (6)

[0096] (7)

[0097] (8)

[0098] In the formula, U i,t , U j,t Indicates the corresponding node i ,node j The square of the voltage, Iline ji,t Represents the square of the line current. Pline ji,t and Qline ji,t Indicates the active and reactive power on the line. r ji and x ji This indicates the resistance and reactance of the circuit. Pline k,t Indicates that at time t Time node k Active power injected into the node, sload i,t It's a 01 variable, indicating whether the load is in use. Pload i,t It is a node i In time t Active power of the load at time PGenerator i,t Represents a node In time t Active power of distributed gas turbine units PPV i,t Represents a node In time t The active power of distributed photovoltaic power at that time. Qline k,t Indicates that at time t Time node k The reactive power injected into the node, Qload i,t It is a node i In time t Reactive power of the load at time QGenerator i,t Represents a node i In time t The reactive power of distributed gas turbine units QPV i,t Represents a node In time t The reactive power of distributed photovoltaic power generation.

[0099] Since equation (6) is non-convex, it is relaxed, as specifically stated below.

[0100] (9)

[0101] 2) Load sequence constraints

[0102] Once the load is energized, power should not be interrupted during the recovery period, as specifically stated below.

[0103] (10)

[0104] 3) Voltage upper and lower limit constraints

[0105] Node voltages should be within specified limits, which can be specifically stated as follows:

[0106] (11)

[0107] In the formula, U min , U max These represent the upper and lower limits of the node voltage, respectively.

[0108] 4) Power upper and lower limit constraints

[0109] The active and reactive power of a distribution network should be limited by the line heat capacity, which can be specifically stated as follows:

[0110] (12)

[0111] (13)

[0112] In the formula, P line.max and Q line.max These represent the maximum active and reactive power that the line can withstand, respectively.

[0113] 5) Photovoltaic confinement

[0114] Photovoltaic output should be within the constraints, which can be specifically stated as follows:

[0115] (14)

[0116] (15)

[0117] In the formula, P PV.max and Q PV.max These represent the active and reactive power capacity limits of the substation, respectively.

[0118] Since constraints containing random variables cannot be directly calculated, this application transforms them into chance constraints, and then further transforms them into deterministic constraints by determining the confidence intervals of the chance constraints. Specifically, this can be represented as follows:

[0119] First, the network operation constraints containing random variables are expressed in the form of chance constraints:

[0120] (16)

[0121] In the formula: Probability represents the probability that the event will occur; Represented as random variables; This represents the confidence level corresponding to the opportunity constraint.

[0122] The above opportunity constraints are transformed into deterministic constraints as follows:

[0123] (17)

[0124] In the formula: For quantiles; It is the inverse function of the cumulative distribution function of photovoltaics.

[0125] Given confidence level α By substituting the corresponding photovoltaic CDF (Circuit Data File), the specific form of the above formula can be calculated.

[0126] Subsequently, a vertex search method based on Hausdorff distance is used to solve for the operational safety domain of the distribution network. The basic idea of ​​the vertex search method is to solve a series of optimization problems with different objective functions to obtain each vertex, thereby approximating the polygon represented by the boundary of the operational safety domain of the distribution network. The search stops when the Hausdorff distance (HD) reaches the termination condition. The optimization problems and algorithm termination conditions will be defined below, and the process of the vertex search method based on Hausdorff distance will be explained. The specific process is as follows:

[0127] (1) Optimization problem

[0128] First, the objective function for the vertex search of the operational security domain of the distribution network is determined as follows:

[0129] (18)

[0130] In the formula: The unit direction vector for searching new vertices; For the safe operation domain of the distribution network points within.

[0131] Therefore, the optimization problem is determined as follows:

[0132] Objective function: Equation (18).

[0133] Constraints: Equations (5) to (17).

[0134] The constraints of the optimization problem are a high-dimensional representation of the operational security domain of the distribution network. Its decision variables can be divided into coordination variables between the operational security domain and external interactions, and internal variables characterizing the internal resource and power allocation, i.e., coordination variables. Internal variables Among them, superscript T: indicates the transpose of a vector. P O The active power used in the interaction between the distribution network and the external environment; Q O Reactive power interacting between the distribution network and the external environment; P L The active power of the loads within the distribution network; Q L The reactive power of the loads within the distribution network; P PV The active power of new energy sources within the distribution network; Q PV This refers to the reactive power of new energy sources such as photovoltaics within the power distribution network.

[0135] Each different The optimal solution to the optimization problem is determined by the coordination variables. This represents a vertex of the operational security domain of the corresponding power distribution network.

[0136] (2) Termination conditions

[0137] The polygon representing the boundary of the operational safety domain of a power distribution network is a set of vertices and edges. Among the different characteristics of a new vertex and an original vertex, relative displacement is the most intuitive and effective. Therefore, the termination condition is set as the relative displacement from the new vertex to its corresponding original line, i.e., the Hausdorff distance, being less than a certain specific value. Let the relative displacement be... ,Right now:

[0138] (19)

[0139] In the formula: for t New vertices generated at each moment; The vertex on the clockwise side of the newly generated vertex; Let L2 be the norm of the search direction vector; This is the set termination condition.

[0140] (3) Algorithm Flow

[0141] The process for solving the operational safety domain of a distribution network using the vertex search method based on Hausdorff distance is as follows:

[0142] 1) Determine the solution time t The operational safety domain of the distribution network, initialize the set of direction vectors: With the initial vertex set ; To initialize the set of direction vectors, This is the transpose of the direction vector, where T represents the transpose of the vector, and i is used to distinguish different direction vectors;

[0143] 2) Sequentially obtain the sets of initialization direction vectors belonging to different groups. The optimization problem is solved to obtain the optimal solution. And store it in the set of vertices of the optimal solution. ;

[0144] 3) Based on the optimal solution vertex set Calculate the unit outward normal vector between all adjacent vertices, and use it as the direction vector for the next round of search, thus obtaining the updated set of direction vectors. ;

[0145] 4) Calculate the Hausdorff distance for each vertex. d j If a vertex corresponds to Less than the set threshold If the threshold value is greater than or equal to the set threshold, then the search for the external normal vector determined by the corresponding vertex and its adjacent vertices will cease; Then repeat steps 2)-4) until all vertices are... d j Continue until all termination conditions are met;

[0146] 5) Based on each vertex, obtain t The operational safety domain of the distribution network at any given time is obtained, and then the polygon represented by the boundary of the operational safety domain is obtained.

[0147] The solution yields the operational safety domain of the distribution network under extreme conditions, such as... Figure 4 As shown, different operational safety domain results for the distribution network will be obtained under different confidence intervals (0%, 10%, 15%, 50%, 90%, 95%, 100%).

[0148] Wherein, the horizontal axis P / MW: P is active power, the unit is "MW" (megawatt), which represents the amount of active power transmitted or consumed by components (such as lines, transformers, nodes, etc.) in the distribution network. Active power is mainly used to do useful work, such as driving motors, lighting, etc., and is one of the key indicators of energy transmission and consumption in the power system.

[0149] The vertical axis, Q / MVAr, represents reactive power, measured in megavars (MVAr). Reactive power is primarily used to establish magnetic fields and maintain voltage levels in electrical equipment. Although it doesn't directly perform useful work, it is crucial for voltage stability and power quality in the power system. The normal operation of equipment such as transformers and reactors relies on the support and exchange of reactive power. Different colored curves correspond to different proportions (e.g., 0%, 10%, 15%, 50%, 90%, 95%, 100%, etc., which are proportional parameters related to the operating boundaries and margins of the distribution network) of the safe operating range of the distribution network, reflecting the feasible operating range of active and reactive power under different operating conditions.

[0150] (4) The distribution network load restoration model based on the operational safety domain is described in detail below:

[0151] A distribution network load restoration model based on the operational safety domain is established, including the objective function and constraints. The objective function of this model is to maximize distribution network load restoration. The constraints include distribution network power flow constraints, load sequence constraints, voltage constraints, power constraints, substation capacity constraints, gas turbine unit constraints, and the operational safety domain constraints. These constraints collectively form the distribution network load restoration model, which is jointly transformed and solved by the distribution network operator to ultimately achieve decision optimization at the distribution network level during power restoration. Specifically, this can be represented as follows:

[0152] When restoring a distribution network, the goal is to maximize load recovery. Therefore, this distribution network load recovery model based on the operational safety domain has the following objective function:

[0153] (20)

[0154] In the formula, t ∈ T This indicates that t is an element belonging to the time set T, which contains all the time points involved in the load recovery process. α i It is the load weight. sload i,t It is a binary 01 variable, indicating whether the load is in use. Pload i,t It is a node i Load in time t The active power at time I is the set of nodes.

[0155] The constraints of the distribution network load recovery model based on the operational safety domain include distribution network power flow constraints, load sequence constraints, voltage limit constraints, power limit constraints, substation capacity limit constraints, gas turbine unit limit constraints, and load curve cluster constraints. Therefore, in addition to the constraints in equations (5) to (17), it also has the following constraints:

[0156] 1) Substation capacity limitations

[0157] The capacity of the substation should be within the specified limits, which can be specifically stated as follows:

[0158] (twenty one)

[0159] (twenty two)

[0160] In the formula, Pmax sub and Qmax sub These represent the active and reactive power capacity limits of the substation, respectively.

[0161] 2) Gas turbine unit limitations

[0162] Gas turbine units have capacity and ramp rate limitations, which can be specifically described as follows.

[0163] (twenty three)

[0164] (twenty four)

[0165] (25)

[0166] In the formula, Prate i It is the power ramp rate limitation of the gas turbine unit. sGenerator i,t It's a 01 variable, indicating whether the distributed generator is in use. PGenerator.max i,t , PGenerator.min i,t These represent the maximum and minimum active power of the gas turbine unit, respectively. QGenerator.max i,t , QGenerator.min i,t These represent the maximum and minimum reactive power of the distributed gas turbine unit, respectively.

[0167] 3) Operational safety domain constraints of the distribution network

[0168] During restoration, both active and reactive power must be within the safe operating range of the distribution network, which can be specifically stated as follows:

[0169] (26)

[0170] In the formula, Zone (P,Q) represents the operational security domain of the distribution network.

[0171] At this point, the distribution network load restoration model based on the operational safety domain has been established and can be effectively solved using a commercial solver. The resulting load restoration results are as follows: Figure 5 As shown, the load was successfully restored within five time steps (one time step being 15 minutes), and the characteristics of the proposed load were fully considered during the restoration process.

[0172] In the context of optimization problem solving (such as distribution network load recovery models, power system planning, and mathematical modeling), commercial solvers refer to commercially available software tools developed by specialized companies that possess mature algorithms and efficient computing capabilities. These tools are used to solve various mathematical optimization models (such as linear programming, integer programming, mixed integer programming, nonlinear programming, and quadratic programming). They typically undergo long-term technological accumulation and engineering verification, enabling them to handle large-scale and complex optimization problems, making them indispensable tools in scientific research, engineering, and business decision-making. This application directly uses existing commercial solvers for solving the problems, without specifying any limitations.

[0173] The second objective of this application is to provide a flexible load restoration system for a distribution network. Based on the aforementioned flexible load restoration method for a distribution network, the system includes:

[0174] The simulation training module is used to obtain the operation data of flexible load under extreme conditions based on simulation, and to train the operation data of flexible load under extreme conditions through MLP neural network to obtain an extreme operation model of flexible load with the input of power outage duration and power restoration duration and the output of load size.

[0175] The distribution network operation safety domain calculation module is used to form the constraint conditions of the distribution network operator together with the flexible load extreme operation model and the distribution network power flow constraints. It transforms the chance constraints in the distribution network operator's constraint conditions into deterministic constraints, and then calculates the operation safety domain of the distribution network through the vertex search method based on Hausdorff distance.

[0176] The model solving module is used to construct a distribution network load restoration model based on the operational safety domain, solve the distribution network load restoration model based on the operational safety domain, and optimize the decision-making at the distribution network level during power restoration based on the solution results.

[0177] A third objective of this application is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the aforementioned flexible load restoration method for power distribution networks. The device also includes a communication interface and a bus.

[0178] The fourth objective of this application is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned flexible load restoration method for power distribution networks.

[0179] The fifth objective of this application is to provide a computer program product, which includes computer instructions that instruct a computer to execute the above-described flexible load restoration method for power distribution networks.

[0180] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0181] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0182] This application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, readable storage media, optical storage, etc.) containing computer-usable program code.

[0183] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0184] Obviously, the described embodiments are only some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort should fall within the scope of protection of this application.

[0185] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation methods of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of this application.

Claims

1. A method for flexible load restoration in a distribution network, characterized in that, include: Based on simulation, the operating data of flexible load under extreme conditions is obtained. The operating data of flexible load under extreme conditions is trained by MLP neural network to obtain an extreme operation model of flexible load with the input of power outage duration and power restoration duration and the output of load size. The flexible load extreme operation model and the distribution network power flow constraints are combined to form the constraints of the distribution network operator; the chance constraints in the constraints of the distribution network operator are transformed into deterministic constraints, and then the operating safety domain of the distribution network is calculated by the vertex search method based on Hausdorff distance. A distribution network load restoration model based on the operational safety domain is constructed, the model is solved, and the decision optimization at the distribution network level during power restoration is performed based on the solution results. The operational safety domain of the distribution network, calculated using the vertex search method based on Hausdorff distance, includes: By solving different objective functions step by step, each vertex is obtained, and then the polygon represented by the boundary of the safe operating region is approximately obtained. Finally, the search stops when the Hausdorff distance reaches the termination condition, and the safe operating region of the distribution network is obtained. The vertex search method based on Hausdorff distance specifically includes: 1) Determine the solution time t The operational safety domain of the distribution network, initialize the set of direction vectors: With the initial vertex set ; To initialize the set of direction vectors, This is the transpose of the direction vector, where T represents the transpose of the vector, and i is used to distinguish different direction vectors; 2) Sequentially obtain the sets of initialization direction vectors belonging to different groups. The optimization problem is solved to obtain the optimal solution. And store it in the set of vertices of the optimal solution. ; 3) Based on the optimal solution vertex set Calculate the unit outward normal vector between all adjacent vertices, and use it as the direction vector for the next round of search, thus obtaining the updated set of direction vectors. ; 4) Calculate the Hausdorff distance for each vertex. d j If a vertex corresponds to Less than the set threshold If the threshold value is greater than or equal to the set threshold, then the search for the external normal vector determined by the corresponding vertex and its adjacent vertices will cease; Then repeat steps 2)-4) until all vertices are... d j Continue until all termination conditions are met; 5) Based on each vertex, obtain t The operational safety domain of the distribution network at any given time is obtained, and then the polygon represented by the boundary of the operational safety domain is obtained.

2. The method for flexible load restoration in a distribution network according to claim 1, characterized in that, The MLP neural network has two neurons in its input layer, corresponding to the power outage duration and the power restoration duration, respectively; ten neurons in its hidden layer; and one neuron in its output layer, corresponding to the load size.

3. The method for flexible load restoration in a distribution network according to claim 2, characterized in that, During training, the MLP neural network employs a backpropagation algorithm for supervised learning and utilizes gradient descent to optimize the network's weights and biases, establishing a flexible load extreme operation model with nonlinear dependencies. The MLP neural network is based on the power outage duration... t 1 and the time required to restore power t 2 is the input, and the output layer outputs data as... t 1, t 2. Related load size P tcl .

4. The method for flexible load restoration in a distribution network according to claim 1, characterized in that, The distribution network load recovery model based on the operational safety domain includes an objective function and constraints. The objective function is to maximize load recovery. The constraints, in addition to the original distribution network power flow constraints, voltage limit constraints, power limit constraints, and current limit constraints, also include main transformer constraints, gas turbine unit constraints, and the operational safety domain constraints of the distribution network. Wherein, the objective function is In the formula, t∈T indicates that t is an element belonging to the time set T, which contains all the time points involved in the load recovery process. α i It is the load weight. sload i,t It is a binary variable indicating whether the load is in use. Pload i,t It is a node i Load in time t The active power at time t, max{} represents solving for the maximum value, and I is the set of nodes.

5. A flexible load restoration system for a distribution network, based on the flexible load restoration method for a distribution network as described in any one of claims 1 to 4; characterized in that, include: The simulation training module is used to obtain the operation data of flexible load under extreme conditions based on simulation, and to train the operation data of flexible load under extreme conditions through MLP neural network to obtain an extreme operation model of flexible load with the input of power outage duration and power restoration duration and the output of load size. The distribution network operation safety domain calculation module is used to form the constraint conditions of the distribution network operator together with the flexible load extreme operation model and the distribution network power flow constraints; the opportunity constraints in the constraint conditions of the distribution network operator are transformed into deterministic constraints, and then the operation safety domain of the distribution network is calculated by the vertex search method based on Hausdorff distance. The model solving module is used to construct a distribution network load restoration model based on the operational safety domain, solve the distribution network load restoration model based on the operational safety domain, and optimize the decision-making at the distribution network level during power restoration based on the solution results.

6. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the flexible load restoration method for the distribution network as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the flexible load restoration method for power distribution networks as described in any one of claims 1 to 4.

8. A computer program product, the computer program product comprising computer instructions, characterized in that, The computer instructions instruct the computer to execute the flexible load restoration method for the power distribution network as described in any one of claims 1 to 4.

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