Power distribution system off-grid emergency control method considering island flexible self-configuration division

Abstract

The invention discloses a power distribution system off-grid emergency control method considering island flexible self-configuration division, and belongs to the technical field of power distribution network off-grid control. The invention discloses a power distribution system off-grid emergency control method considering island flexible self-configuration division. The method comprises the following steps: establishing a multi-resource power distribution system frequency response model; taking minimization of load loss and resource control quantity as objective functions, and constructing an optimization decision model fusing steady-state constraint and transient-state constraint; solving the optimization decision model based on an improved discrete particle swarm algorithm; and executing active island division according to the optimal island division scheme. The method comprehensively considers an optimization model of a transient process and a steady-state operation constraint condition, coordinates multiple resources to jointly execute emergency control in island switching, minimizes load loss, preferentially guarantees power supply of important loads, and improves the power supply efficiency. And the conditions of power supply transient instability, system frequency out-of-limit, large-area power failure accidents and the like caused by unreasonable island division of the power distribution system are avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of off-grid control of distribution networks, and particularly to an off-grid emergency control method for a distribution system considering flexible self-configuration division of islands. Background Art

[0002] In recent years, the frequency of extreme natural disasters has increased significantly globally, and its impact on distribution systems has become more severe. Such disasters may not only cause damage to the physical facilities of the distribution network, but also lead to the interruption of the electrical connection between the local distribution network and the main grid, further triggering large-scale power outages due to chain reactions, posing a major threat to social and economic activities and residents' daily lives. Against this background, how to effectively respond to emergencies and ensure the security and continuity of power supply has become a key research topic, and islanding division technology and frequency emergency control technology are regarded as important strategies to improve the resilience and stability of modern distribution systems.

[0003] When the off-grid distribution system suffers from a power deficit, the system frequency often drops rapidly. If no measures are taken in time, it may lead to excessive system frequency drop and cause the system to collapse. As a classic emergency control means, the core principle of under-frequency load shedding is to gradually unload non-critical loads through preset rules to maintain the frequency stability of the system. This method adopts fixed frequency thresholds and hierarchical load shedding strategies, with high reliability and engineering practicability. However, this rigid control method has obvious deficiencies: due to its lack of dynamic adaptability, it often leads to unnecessary load losses and may even cause significant economic losses. For example, in some cases, even if the system frequency deviates slightly from the safe range, under-frequency load shedding may still cut off a large number of loads according to fixed rules, which obviously does not conform to the principle of maximizing economic benefits. Therefore, in recent years, the research focus has gradually shifted to how to make refined decisions on the amount of load shedding to achieve "precision control". Specifically, by introducing mechanisms such as real-time state monitoring, dynamic optimization algorithms, and load priority assessment, combined with the specific operating conditions of the system, the load shedding strategy can be flexibly adjusted to minimize load losses while ensuring system safety.

[0004] Corresponding to under-frequency load shedding is the over-frequency generator tripping strategy, which is mainly used to deal with the situation of excessive system frequency. This method quickly cuts off the output power of some generators to prevent the frequency from exceeding the upper limit. Over-frequency generator tripping may have an adverse impact on the mechanical stability of the generator set, so its trigger conditions and action logic need to be carefully designed. Although over-frequency generator tripping is of great significance in specific scenarios, it is not applicable to the typical scenarios of off-grid distribution systems because in this case, the system is more likely to face the problem of frequency drop rather than increase.

[0005] In contrast, automatic generation control is a more advanced and flexible frequency control method. It dynamically adjusts the output of generating units by real-time monitoring of system frequency and load changes to achieve rapid frequency restoration and stability. The core advantage of automatic generation control lies in its ability to adaptively adjust according to the current operating state, thus avoiding the limitations brought by traditional fixed-threshold strategies. However, the effectiveness of automatic generation control highly depends on the reliability of the communication system and the accuracy of the control algorithm. Especially in extreme scenarios such as islanding switching, communication delays or data loss may cause automatic generation control to fail to respond in a timely manner, thereby affecting the overall control effect.

[0006] As an important means to improve the power supply reliability and resilience of distribution systems, islanding partitioning technology has received extensive attention from academia and industry in recent years. From the implementation perspective, islanding partitioning technology can be divided into two categories: active islanding partitioning and passive islanding partitioning. Active islanding partitioning is to proactively select the optimal islanding partitioning scheme through real-time monitoring of the power grid status, using advanced algorithms and optimization techniques when foreseeing possible faults or when the system experiences faults and abnormal conditions, and then implement islanding partitioning; passive islanding partitioning is to rely on pre-set protection devices to adjust the network structure in real time according to the system status to form an island after a fault occurs. Compared with passive islanding partitioning, active islanding partitioning emphasizes achieving rapid and reasonable islanding partitioning through active control strategies before or during a fault, so as to maximize power supply guarantee and improve system resilience.

[0007] In the problem of active islanding partitioning of distribution systems, due to the large scale and complex structure of distribution systems, traditional optimization algorithms are not convenient for considering the dynamic process of the system, with complex modeling and difficulties, and are often difficult to apply in distribution systems with rapidly changing situations. Summary of the Invention

[0008] The object of the present invention is to provide an off-grid emergency control method for a distribution system considering flexible self-configuration islanding partitioning, an optimization model that comprehensively considers transient process and steady-state operation constraint conditions, which can actively decide the islanding partitioning area, coordinate multiple resources to jointly execute emergency control during islanding switching, minimize load loss, give priority to ensuring the power supply of important loads, and avoid situations such as power source transient instability, system frequency over-limit, and large-scale power outages caused by unreasonable islanding partitioning of the distribution system.

[0009] To achieve the above object, the present invention provides an off-grid emergency control method for a distribution system considering flexible self-configuration islanding partitioning, including the following steps: S1. Establish a multi-resource frequency response model for the distribution system, and perform multi-resource frequency response modeling on synchronous generators, virtual synchronous machines, energy storage power sources, photovoltaic power sources, and load shedding. S2. Construct an optimization decision-making model that integrates steady-state constraints and transient constraints with the objective of minimizing load loss and resource control amount. The transient constraints include the lowest frequency point constraint, the frequency change rate constraint, the transient constraint of power source output, the maximum power angle constraint, and the critical clearing time constraint. S3. Solve the optimization decision-making model based on the improved discrete particle swarm algorithm, and improve the global search ability by introducing the crossover and mutation operations of the genetic algorithm to obtain the optimal islanding division scheme and emergency control strategy. S4. Perform active islanding division according to the optimal islanding division scheme, coordinately control the power source output, and cut off non-critical loads to ensure the transient stability of the island and the power supply to important loads.

[0010] The advantages and positive effects of the off-grid emergency control method for a distribution system considering flexible self-configuration islanding division of the present invention are as follows: 1. The present invention constructs the framework of the optimization decision-making model from a theoretical level. During the islanding division process, it ensures that the power capacity within each island can match the load demand, while maintaining key parameters such as voltage and frequency within a safe range. And for distributed energy with increasing penetration in the new distribution system, it is also an important variable to be considered in the islanding division decision. To avoid larger-scale power outages caused by the transient instability of the power source due to disturbances during the off-grid process and island operation, transient stability constraints are introduced in the decision-making process of the model. Emergency frequency control maintains the system frequency within a safe range by optimizing the cutting off of non-critical loads and adjusting the power source output, avoiding system collapse caused by frequency over-limit.

[0011] 2. The present invention models the synchronous generator, virtual synchronous machine, energy storage battery, photovoltaic power source, electric vehicle, and load that can be cut off respectively to describe the dynamic characteristics of various resources during the islanding switching process, providing a solid theoretical basis for subsequent optimization decision-making. On this basis, through the methods of aggregation equivalence and order reduction simplification, the complex multi-resource system is transformed into a low-dimensional model that is easy to analyze, significantly reducing the computational complexity while retaining the ability to describe key dynamic characteristics.

[0012] The technical solutions of the present invention will be further described in detail below through the accompanying drawings and embodiments. Description of the Drawings

[0013] Figure 1 It is the frequency response model structure of the multi-resource system of the present invention; Figure 2 It is the reduced-order model structure of the frequency response of the multi-resource system of the present invention; Figure 3 It is the structure of the two-machine parallel power supply system of the present invention; Figure 4 It is the structure diagram of the optimization decision-making model of the present invention; Figure 5 The solution structure of the optimization decision-making model of the present invention; Figure 6 The 33-node distribution system of the embodiment of the present invention; Figure 7 The objective function iteration curve of the embodiment of the present invention; Figure 8 The active islanding division result of the embodiment of the present invention; Figure 9 The total load shedding situation of the system in the embodiment of the present invention; Figure 10 The transient process data curve of the embodiment of the present invention, a) is the frequency of the islanded system, b) is the voltage of the islanded system, c) is the engine output curve, and d) is the energy storage output curve; Figure 11 The passive islanding division result; Figure 12 The total load shedding situation of the passive islanding division system; Figure 13 The transient process data curve of the passive islanding division, a) is the frequency of the islanded system, b) is the voltage of the islanded system, c) is the engine output curve, and d) is the energy storage output curve; Figure 14 The power angle characteristic curve of large-scale disturbances in a single-machine infinite bus system; Figure 15 The curve of the relationship between the system angular frequency deviation and time of large-scale disturbances in a single-machine infinite bus system; Figure 16 The power angle characteristic curve of small-scale disturbances in a single-machine infinite bus system. Specific implementation manners

[0014] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which this application belongs. In case of inconsistency, the meaning described in this specification or the meaning obtained according to the content recorded in this specification shall prevail. In addition, the terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0015] The following will describe in detail the embodiments of the present invention with reference to the accompanying drawings.

[0016] A distribution system off-grid emergency control method considering flexible self-configuration division of islanding includes the following steps: S1. Establish a multi-resource distribution system frequency response model, and perform multi-resource frequency response modeling on synchronous generators, virtual synchronous machines, energy storage power sources, photovoltaic power sources, and load shedding.

[0017] As the core equipment in the island system, the frequency response characteristics of the synchronous machine mainly consist of inertia response and primary frequency regulation. The frequency response model of inertia response is: ; (1) Where, represents the generator inertia time constant, is the generator damping coefficient, is the mechanical power, is the electromagnetic power, is the frequency deviation, .

[0018] By using the difference discretization method to transform the frequency response model into a differential-algebraic model, the relationship between adjacent step sizes of variables at each discrete time can be obtained. The forward Euler method is used for differentiation, and the differential frequency response model is: ; (2) Where, represents the change in the frequency deviation value at time represents the change in the frequency deviation value at time represents the differential time step, represents the change in power at time

[0019] Primary frequency regulation is the process in which synchronous generators and virtual synchronous machines automatically adjust the active power output according to the frequency deviation. Its control strategy is based on the droop characteristics of the governor. After considering the time delay of control through a first-order inertia link, the droop characteristics of the governor are expressed as: ; (3) Where, is the output power, is the power reference value, is the droop coefficient of the governor, is the Laplace operator, is the control time constant.

[0020] Similarly, after performing the differentiation process, the discrete differential equation of the output power of the synchronous machine during primary frequency regulation is: ; (4) Where, represents the output power at time represents the output power at time

[0021] The output power of the energy storage battery is highly controllable. The active power and reactive power injection can be directly changed by adjusting the current or voltage commands, and it can adapt to different power demands. PQ control is a classic method, aiming to make the energy storage battery output with given active power and reactive power as the target, make up for the power deficit, and ensure the overall power balance of the system. In PQ control, the outer-loop power control usually subtracts the target value of power from the reference value and then inputs it to the current inner-loop control through a PI controller. Since the bandwidth of the inner-loop control is much larger than that of the outer-loop control, the inner-loop control can be ignored during analysis.

[0022] After considering the characteristics of the outer-loop PI control and the control time delay of the energy storage power supply, the discrete difference equation of the output power of the energy storage power supply is: ; (5) In the formula, represents the battery output power at time represents the battery output power at time represents the PI control power at time represents the PI control power at time represents the PI control error at time represents the PI control error at time represents the power reference value, and are the proportional and integral gain coefficients of the PI control respectively, represents the differential time step, represents the control time constant, z is the index variable.

[0023] The uncertainty of the photovoltaic power output needs to be considered in islanding division and emergency control decision-making. When the photovoltaic power generation system is operating normally, its output power is mainly determined by solar radiation and environmental temperature. Generally, the maximum power point tracking strategy is adopted to ensure that the system operates in the best state. Due to the impact of extreme disasters that may occur at different times and being disturbed by environmental factors such as light intensity fluctuations and cloud cover, the photovoltaic output power will show a certain degree of uncertainty. Therefore, when calculating the power deficit, the output of the photovoltaic needs to be regarded as a random variable, and this uncertainty can be described by a probability distribution. Assume that the maximum photovoltaic output follows a normal distribution within a certain time period: ; (6) Among them, represents the predicted maximum output value of the photovoltaic, It reflects the fluctuation range of its output. N is a normal distribution.

[0024] Further considering the deviation in the actual scenario, an uncertainty coefficient can be introduced to characterize the upper and lower floating range of the photovoltaic output. The actual photovoltaic output of the photovoltaic power source is: ; (7) In the formula, is the maximum photovoltaic output value. is the uncertainty coefficient, and its value range can be determined according to specific situations, usually in [-0.2, +0.2], which is used to represent the possible deviation of the photovoltaic output.

[0025] In this way, the dynamic change characteristics of the rated output of the photovoltaic power source at different times can be considered to a certain extent, and during the islanding switching process, it can be considered that its output basically maintains the actual output and remains unchanged in a short time scale. Therefore, in emergency control, the photovoltaic power source only provides constant power support, and the output power during the transient process is not adjustable.

[0026] Modeling of the frequency response of the distribution system The system frequency response characteristics are represented by the widely used Center of Inertia (COI) frequency to represent the system frequency, as shown in the following formula: ; (8) In the formula, is the system inertia center frequency, is the overall inertia time constant of the system, is the generator 's inertia time constant (the unit types include synchronous generators and virtual synchronous machines, that is, units that can provide inertia support), is the generator node's frequency.

[0027] At the moment of disturbance the rate-of-change of frequency (RoCoF) of the system is: ; (9) In the formula, represents the power change amount of the system.

[0028] The control methods and control characteristics adopted by various resources in the system are shown in Table 1. The frequency response model structure of the multi-resource system is as Figure 1 shown.

[0029] Table 1 Frequency modulation methods and control characteristics of controlled resources ; Reduced - order modeling of frequency response of distribution system The frequency response model of the multi - resource system obtained by aggregating and equivalent reducing of similar resources is as Figure 2 shown.

[0030] The parameters of aggregation equivalence are: ; (10) In the formula, and are the equivalent aggregations of the power of energy storage batteries and load shedding respectively, is the equivalent aggregation of the rated power change of photovoltaic power sources considering uncertainty, , and are the numbers of energy storage batteries, photovoltaic power sources, and load shedding respectively.

[0031] The equivalent aggregations of the control parameters of power sources with inertia support ability are as follows: ; (11) In the formula, , , and represent the inertia time constant, damping coefficient, capacity, and control time constant of the overall system. , and represent the inertia time constant, damping coefficient, and capacity of the th synchronous generator, , and represent the inertia time constant, damping coefficient, and capacity of the th virtual synchronous machine.

[0032] ; (12) In the formula, and are proportionality coefficients, representing the proportion of the rated capacity of the th synchronous generator and the th virtual synchronous machine in the overall system capacity. and represent the droop coefficients of the th synchronous generator and the th virtual synchronous machine, represents the droop coefficient of the overall system. is the weighting coefficient of the th feedback control branch. Indicates the control time constant of the th generator. And are the numbers of synchronous generators and virtual synchronous machines respectively.

[0033] Finally, the established frequency response model of the multi-resource distribution system is: ; (13) In the formula, is the frequency deviation of the center of inertia of the system, represents the power change of the system, is the inertia time constant of the whole system, is the damping coefficient of the whole system, t is the time.

[0034] The differential model of the frequency response of the multi-resource distribution system after discrete difference is: ; (14) In the formula, is the frequency deviation of the center of inertia of the system at time, is the frequency deviation of the center of inertia of the system at time, represents the differential time step.

[0035] According to this model, the transient state of the system frequency can be constrained during emergency frequency control.

[0036] S2. Taking the minimization of load loss and resource control amount as the objective function, an optimization decision model integrating steady-state constraints and transient constraints is constructed. The transient constraints include the lowest frequency constraint, the frequency change rate constraint, the transient power output constraint of the power source, the maximum power angle constraint, and the critical clearing time constraint.

[0037] (I) Steady-state constraint conditions The steady-state constraint conditions include linear power flow constraints, power output constraints of power sources, node voltage constraints, line capacity constraints, and load shedding amount constraints.

[0038] After a fault occurs, the distribution system will be divided into multiple island systems for operation. It is necessary to introduce the node 01 state variable and the line 01 state variable to describe the internal topological structure of the island system after the fault.

[0039] The variables and need to satisfy: ; (15) ; (16) ; (17) ; (18) Wherein, is the set of multiple isolated islands divided, is an isolated island the set of nodes within, is an isolated island the set of nodes where the power source is located within, is an isolated island the set of lines within, represents the isolated island the parent node of the node within. represents the line the state of, represents the line is in the disconnected state.

[0040] Equation 15 means that a node belongs to at most one isolated island; Equation 16 means that the power source node must belong to the isolated island where the power source is located; Equation 17 means that the node belongs to the isolated island on the premise that the parent node also belongs to the isolated island and the line is not disconnected; Equation 18 means that the line belongs to the isolated island on the premise that both end nodes of the line and belong to the isolated island.

[0041] The linear DistFlow model ignores the non - linear terms in the traditional power flow model, making the solution more convenient. It is a simplified model suitable for power flow calculation of the radial network structure of the distribution system. The power flow constraints of the radial - structured isolated island are as follows: ; (19) ; (20) ; (21) ; (22) ; (23) Wherein, and are the active and reactive power flows on the line flowing from the parent node to the child node , and are the active and reactive power flows on the line flowing from the parent node Active and reactive power flows on the line flowing to the child node and represent the active and reactive power output from the power source at node g and represent the active and reactive power of the load at node and represent the active and reactive power of the load shedding at node M represents a very large constant in the large M method represents the square of the grid-connected node voltage amplitude before disconnection represents the square of the voltage amplitude of the power source node is the square of the rated voltage amplitude and are the squares of the voltage amplitudes of nodes and and are the resistances and reactances of the lines between nodes and and are the active and reactive power flowing through the line under maximum operation

[0042] Equation 19 represents the active and reactive power flow balance of each node; Equation 20 defines the voltage of the grid connection point and the power source node as the reference value; Equation 21 describes the voltage drop between adjacent nodes of the line. Equation 22 constrains the node voltage deviation; Equation 23 limits the magnitude of the power flowing through the line

[0043] The power output constraints of the power source include the upper and lower limits of the active and reactive power of the power source and the reserve capacity limit, and the constraints are as follows ; (24) In the formula and are the lower limits of the active and reactive power outputs of the power source g and are the upper limits of the active and reactive power outputs of the power source g represents the reserve capacity coefficient, and the range is (0, 1]

[0044] The load shedding quantity constraints are used to limit the range and proportion of the load shed in an emergency, and the constraints are as follows ; (25) ​​​​​​ ; (26) In the formula, and are the lower limits of active and reactive load shedding at node i . and are the upper limits of active and reactive load shedding at node i .

[0045] Formula 36 ensures that the load is shed according to the active and reactive power ratios of the original load at node i .

[0046] (II) Transient constraint conditions After islanding, due to the radial network structure, the power deficit of each island can be represented by the power flowing through the lines of the boundary nodes of the island, that is, the difference between the power flowing into the boundary node lines of the island and the power flowing out of the boundary node lines of the island: ; (27) In the formula, represents the power flowing through the boundary node line of the island flowing in, represents the power flowing through the boundary node line of the island flowing out.

[0047] After the island is disturbed, if the system frequency drops below the safety threshold or the frequency change rate is too large, the under-frequency load shedding protection will be triggered, causing system instability. Therefore, it is necessary to constrain the frequency transient process: ; (28) In the formula, represents the lowest safety value of the system frequency, and represent the minimum and maximum values of the frequency change rate respectively, represents the inertial center frequency of the system at time , represents the inertial center frequency of the system at time . For each step in the transient process of the system frequency of the island , the frequency transient constraint must be satisfied.

[0048] During the frequency regulation process, the power adjustment amount of the power source needs to satisfy the output ramp rate constraint, which limits the maximum rate of power change between adjacent times. Considering that the over-current tolerance of the power electronic interface power source is limited and too large power overshoot will cause equipment burnout, it is also necessary to limit the instantaneous maximum power. The transient constraint of the power source output is: ; (29) In the formula, and respectively represent the maximum rates of the power output of the power source ramping up and down, is the multiple of the maximum instantaneous power amount that the power source can withstand exceeding the maximum power limit, represents the maximum power of the power source, represents the instantaneous value of the power of the power source at time represents the instantaneous value of the power of the power source at time the power output within the island at each step during the transient process must satisfy the power transient constraint at time

[0049] The transient synchronization stability constraint ensures that the generators in the formed island system do not lose synchronization during the transient process after the disturbance, thus maintaining the overall stable operation of the system.

[0050] During the process of forming the island, the disturbance caused by the power deficit is a small disturbance, that is, when there is an intersection between the power angle characteristic curve and Considering the calculation error and the conservative requirements in actual engineering applications, the maximum power angle constraint does not exceed , ; (30) In the formula, is the maximum power angle of the system during the transient process of the island under the disturbance, is the set of islands, is the damping unbalanced power; Considering that the action time of the protection device is 100 ms, when subsequent secondary disasters attack the island system, if the critical clearing time of the island system when it withstands a large fault disturbance is less than the action time of the protection device, it may occur that the protection action cannot clear the fault in time, resulting in the loss of synchronization of the power sources within the island, and then the collapse of the island system. Therefore, the formed island must have a certain resilience, that is, the critical clearing time of the system is greater than 100 ms, and the critical clearing time constraint is as follows: ; (31) is the critical clearing time of the system during the transient process of the island under the disturbance.

[0051] The improved extended equal - area criterion is used to calculate the maximum power angle and the critical clearing time in a multi - machine system.

[0052] When extending the equal - area criterion from a single - machine infinite - bus system to a multi - machine system, the rotor motion equations of each generator are coupled with the state variables of other generators, and it is necessary to solve the complexity brought by multi - machine dynamic coupling and energy interaction. Therefore, the dynamic behavior of the system cannot be simply described by a single power - angle characteristic curve. Instead, the mutual influence between multiple power angles needs to be considered. Moreover, in a multi - machine system, the damping characteristics between generators will significantly affect the transient response of the system, introducing stronger non - linear characteristics, making it difficult to directly analyze using the traditional equal - area criterion. For a multi - machine system, it can be approximately transformed into a two - machine system through equivalent simplification, so as to apply the improved and extended equal - area criterion to analyze the system stability.

[0053] The structure of a two - machine parallel power supply system is established as Figure 3 shown, including two power sources connected to a common bus through lines, with a load connected to the common bus. The types of power sources are not limited and can be two SGs, two VSGs, or one SG and one VSG.

[0054] Figure 3 In and , the effective values of the phase voltages of power source 1 and power source 2 are and respectively, and the phase angles are and respectively. The effective value of the phase voltage at the load is , and the phase angle is . is the line admittance between nodes 1 - 3,

[0055] is the line admittance between nodes 2 - 3, and ; (32) In the formula, , and are the injection currents at nodes 1, 2, and 3 respectively.

[0056] Further derivation gives: ; (33) It is easy to know that , eliminating the intermediate variable and simplifying gives: ; (34) Define the variables , and as: ; (35) Combining formula (2-30) and formula (2-31), we can obtain: ; (36) wherein, and are the voltage amplitudes, , and are the admittance amplitudes, , and are the equivalent admittance angles.

[0057] The dynamic characteristics of the line are much faster than the response speed of the power source governor. After ignoring the line dynamic characteristics, the output power of the parallel system is: ; (37) wherein, and are the complex powers of power source 1 and power source 2 respectively, and are the conjugate vectors of currents and respectively.

[0058] Substituting formula 34 into formula 35 and taking the real part, the active powers output by the two power sources can be obtained as: ; (38) The rotor motion equations of the two power sources are as follows: ; (39) wherein, the relevant variables of power source 1 are represented by subscript 1, and the relevant variables of power source 2 are represented by subscript 2.

[0059] The phase angle difference between the two power sources is , and at this time, formula (2-35) can be changed to: ; (40) Reasonably setting the parameters of the VSG to make , the parallel power supply system can be converted into a single-machine infinite system, and the equivalent rotor motion equation can be obtained: ; (41) wherein, is the equivalent inertia, is the equivalent damping coefficient, is the equivalent rated power, is the equivalent electromagnetic power.

[0060] Finally, the equivalent rotor motion equation of the two-machine parallel power supply system is obtained as follows: ; (42) So far, the dynamic characteristics of the two-machine system have been equivalent to a comprehensive power angle characteristic curve. The advantage of this method is that it expands the applicable range of the equal area criterion, retains the simplicity of the equal area criterion, and can reflect the dynamic characteristics of the two-machine system to a certain extent. Based on the equivalent comprehensive power angle characteristic curve, the improved extended equal area method is used to analytically calculate CCA and CCT, and the quantization indexes of the maximum power angle constraint and the critical clearing time constraint required for the optimization decision simulation can be extracted.

[0061] Analytically calculate CCA and CCT in a single-machine infinite bus system using the improved extended equal area method In the research framework of a single-machine infinite bus system, when the system encounters a disturbance event, the power angle trajectory of the synchronous generator SG or the virtual synchronous generator VSG will gradually deviate from the initial equilibrium position. In this process, it first experiences an acceleration stage, and with the implementation of the fault clearing action, it then enters a deceleration stage. Based on the principle of energy conservation, if the energy accumulated in the deceleration stage can completely compensate for the energy consumed in the acceleration stage, the system can reach a new steady-state operating point again; otherwise, if the two cannot achieve balance, the system will face the risk of losing synchronism.

[0062] For traditional synchronous machines, the dynamic characteristics of their electromagnetic power and mechanical power can be described by the rotor motion equation. During a fault, due to the drop in the grid voltage, the electromagnetic power decreases while the mechanical power remains unchanged, resulting in the acceleration of the generator. After the fault is cleared, the electromagnetic power gradually recovers and the generator starts to decelerate.

[0063] For virtual synchronous machines, their control strategies simulate the mechanical and electromagnetic characteristics of synchronous generators. During a fault, although the physical structure of the VSG is different from that of the synchronous machine, its control strategy makes its dynamic characteristics during the transient process similar to those of the synchronous machine. Therefore, the equal area criterion is also applicable to the transient stability analysis of the VSG.

[0064] The active power transmitted from the power source to the power grid and the reactive power can be expressed by the following formula: (43) In the formula, , are the resistance and reactance of the line, is the output voltage of the power source, is the grid voltage, is the power angle of the power source.

[0065] In a single-machine infinite bus system, the rotor motion equations of SG and VSG can both be described by a simplified second-order nonlinear differential equation: (44) In the formula, is the inertia constant, is the damping coefficient, is the power angle, is the rated angular frequency, and are the initial mechanical power and electromagnetic power respectively.

[0066] When analyzing by the traditional equal - area method, it is assumed that the mechanical power remains unchanged, and it is also assumed that the damping can be ignored during the transient process. Since the damping coefficient of SG is usually small, its influence on the unbalanced power during the transient process is limited and only acts as a decay factor after stabilization. However, for VSG, its virtual damping is closely coupled with primary frequency regulation, and the set virtual damping is generally large. If the influence of virtual damping is ignored during the process of analyzing and calculating the acceleration and deceleration areas, the calculated critical clearing angle is often too conservative, thus affecting the judgment of the system's transient stability.

[88] .

[0067] To more accurately reflect the dynamic characteristics of VSG, the damping term needs to be incorporated into the analysis. Define the damping unbalanced power After that, formula (44) becomes: (45) In the traditional equal - area method, it is also assumed that the reactive power and voltage remain constant, ignoring the impact of their dynamic changes on system stability. However, there is a strong coupling relationship between reactive power and voltage, especially under weak grid conditions, this coupling effect is more significant. When a three - phase symmetrical short - circuit fault occurs in the grid, the instantaneous voltage drop of the grid will cause an increase in the reactive power output of small - scale SG and small - scale VSG. Since the reactive power and voltage amplitude have a droop relationship, the decrease in voltage amplitude will further lead to a decrease in the active power output of the power source, increasing the accelerating area. If this process is ignored, the transient instability risk of the system may be underestimated. The relationship between reactive power and voltage can be expressed by the following formula: (46) In the formula, is the power source output voltage, is the rated voltage, is the reactive - voltage droop coefficient, is the initial reactive power.

[0068] In summary, combining formula (43), formula (45) and formula (46) can establish the power - angle relationship at steady state: (47) When a fault occurs, the corresponding variables should take the values at the time of the fault, denoted by the subscript F. During the transient state the power - angle relationship is: (48) According to the different degrees of disturbance, the power angle characteristic curve can be divided into two categories. Category I: The disturbance is large, and the power angle characteristic curve has no intersection with ; Category II: The disturbance is small, and the power angle characteristic curve has an intersection with .

[0069] Based on the power angle characteristic curve, the constraint conditions required for optimization decisions can be refined to guide the islanding partition scheme. It should be noted that for these two types of faults, there are different focuses of attention.

[0070] (1)Calculation of CCT in the first category of situations The first category of situations usually corresponds to severe short-circuit grounding faults or other large-scale disturbances, and its power angle characteristic curve is as shown in Figure 14 . The accelerating area represents the increased kinetic energy of the generator during the disturbance, that is, the area enclosed by the power angle curve and the mechanical power horizontal line during the accelerating process of the system after the disturbance ; the decelerating area represents the reduced kinetic energy of the generator during the decelerating process, that is, the area enclosed by the power angle curve and the mechanical power horizontal line during the decelerating process of the system after the disturbance . During the fault occurrence period, at this time the power angle characteristic curve changes suddenly from to , resulting in the rotor experiencing an accelerating process, and the system operating point deviates from the initial equilibrium point ; after the fault is removed at , the power angle characteristic curve returns to , and the system enters the decelerating stage.

[0071] In the first category of situations, there is no stable equilibrium intersection between the power angle characteristic curve of the system under fault and , indicating that the system cannot return to the steady state by itself without clearing the fault after the disturbance. Due to the large disturbance amplitude, the critical clearing time CCT of the system is usually short, which means that the fault may not be removed in time, and the system will inevitably lose synchronous stability. Therefore, in this type of situation, the focus of research is more concentrated on the calculation of CCT. CCT directly reflects the critical stable time of the system under extreme disturbances, provides a scientific basis for the action time limit of protection equipment, and ensures that it can quickly remove the fault before instability, thus minimizing the impact of accidents.

[0072] When calculating and solving CCA considering damping, since varies dynamically with time, it is difficult to directly solve analytically. The simplified method is to approximate the curve graph area generated by damping as a triangular area for calculation.

[0073] The rotor motion equation of the power supply during a fault is as follows: ; (49) Furthermore, we obtain: ; (50) Integrate both sides of Equation (50): ; (51) Among them, the right side of the equation is the area of the curve graph , is the stable equilibrium point. Since is not an algebraic equation about , it is impossible to analytically calculate this integral term. It is necessary to assume that is the critical clearing angle of the system. When the system clears the fault at , the system is exactly in the critically stable state. At this time, the corresponding reaches the maximum value, defined as .

[0074] From Figure 14 , it can be seen that the length of the line segment is . The area of the triangle can be calculated as follows: ; (52) Approximate the area of the curve as the area of the triangle , that is: ; (53) Substitute Equation (53) into Equation (51) to obtain: ; (54) The left side of the equation represents the increased kinetic energy of the system when the system moves to . The right side of the equation represents the increased rotor kinetic energy when the excess input power of the rotor moves from to .

[0075] Solving Equation (54) gives the analytical expression of about as: ; (55) The calculation of the accelerating and decelerating areas of the single-machine infinite-bus system is as follows: ; (56) In the formula, is the accelerating area when the VSG system is critically stable; It is the deceleration area of the VSG system when it is critically stable.

[0076] The scaling method is used again to convert the unbalanced energy of the transient damping process (curve graph area) is reduced to a triangle Area, the final equal area formula is as follows: ; (57) Combining formula (55) and formula (57) can obtain the resection angle , defined as the system limit resection angle .

[0077] The method for calculating CCA is scaled twice. The first scaling makes The calculated value is less than The actual value, the second scaling causes the actual acceleration area to be smaller than the calculated value , and the actual deceleration area is greater than the calculated value This difference ultimately makes the limit resection angle calculated by the system smaller than the actual limit resection angle. Nevertheless, compared with the traditional method that completely ignores the damping effect, this method significantly reduces the conservatism, and the calculation results are still conservative to a certain extent, which can meet the conservative requirements in practical engineering applications.

[0078] Get the limit resection angle Then the limit removal time can be solved .because and It is difficult to obtain the analytical expression between - Here, we can use the triangle scaling method mentioned above to approximate the analytical expression. The scaling process is as follows: Figure 15 shown.

[0079] Figure 15 The system angular frequency deviation and time relationship curve are given. The point corresponds to the limit removal time. From the above analysis, it can be seen that the angular frequency deviation reaches the maximum value at the limit removal time. , at this time the power angle is the limit resection angle According to the VSG rotor motion equation, The area of the curve is ,Right now: ; (58) Will The area of the curve is reduced to The area of a triangle is: ; (59) By simultaneously solving Equation (55) and Equation (59), we can obtain The approximate solution is as follows: ; (60) Calculation of the maximum power angle in the second type of situation The second type of situation usually corresponds to a disturbance caused by a power deficit, and its power angle characteristic curve is as Figure 16 shown.

[0080] In this case, there is a stable equilibrium intersection point between the power angle characteristic curve under system fault and , indicating that the system still has the possibility of restoring to a new steady state without clearing the fault after the disturbance. Due to the small disturbance amplitude, the transient process of the system is relatively smooth, and the critical clearing time CCT is usually long, generally exceeding the typical value of 0.1 - 0.3 seconds of the inherent action delay of relay protection. This means that the action time limit threshold of the protection equipment can usually meet the requirements and will not become a limiting factor. Therefore, in this type of situation, the focus of research is more concentrated on the calculation of the maximum power angle reached after the disturbance. The maximum power angle directly reflects the power angle offset that the system can withstand at the moment of fault clearing and also represents the maximum margin for it to withstand disturbances.

[0081] During the disturbance the power angle characteristic curve and have two equilibrium intersection points and . At this time, the accelerating area should be the curve area within the interval , and the decelerating area should be the curve area within the interval . Here represents the maximum power angle that the rotor can run to after the disturbance. The physical meaning is that after the disturbance, the electromagnetic power is less than , the rotor deviates from the steady-state power angle , accelerates through the power angle . After exceeding , the electromagnetic power is greater than , the rotor enters the decelerating process, reaches the maximum power angle and no longer increases, but continues to decelerate and the power angle decreases until it oscillates and decays and stabilizes at the equilibrium intersection point , or just critically decelerates and stabilizes at the equilibrium intersection point . If is greater than the equilibrium intersection point , it means that the system will continue to accelerate until it loses synchronous stability under this disturbance. At this time, methods such as fault removal or reduction of power deficit need to be used to increase the decelerating area so that is within the interval to ensure the synchronous stability of the system.

[0082] Similarly, when considering damping to calculate the acceleration and deceleration area, it is also necessary to use the triangle scaling approximation. Accelerate to power angle When the damping effect mainly plays a hindering role, the acceleration area is reduced and the deceleration area is increased. Under small disturbance conditions, the maximum power angle Usually does not exceed the power angle , so when calculating the damping area, we only need to focus on the interval Internal area, negligible interval Internal area.

[0083] Correspondingly, the triangle The area calculation is modified as follows: ; (61) at this time Power Angle Hegong Angle The angular frequency corresponding to the midpoint of is modified to: ; (62) The intermediate process derivation will not be repeated, and the final equal area formula is modified as follows: ; (63) Combining formula (62) and formula (63) can obtain the maximum power angle .

[0084] Objective Function The objective function of the off-grid emergency control optimization decision model of the distribution system considering the flexible self-configuration partitioning of the island is to minimize the load loss and resource control amount, and the formula is as follows: ; (64) In the formula, is the objective function, is the battery control cost weight coefficient, is the control cost weight coefficient of the synchronous generator, is the control cost weight coefficient of the virtual synchronous machine, is the control cost weight coefficient of load shedding, For battery The control cost, For synchronous generator The control cost, For virtual synchronization machines The control cost, For load shedding The control volume cost, is the number of batteries, is the number of synchronous generators, is the number of virtual synchronous machines, is the number of load shedding, is the battery output power, is the synchronous generator output power, is the virtual synchronous machine output power, is the load shedding output power.

[0085] The setting of the weight coefficient reflects the priority of different resources in emergency control. The smaller the weight factor, the smaller the increment of the objective function, and the higher the control priority. Generally speaking, the control costs of power source side resources such as energy storage, SG and VSG are much lower than those of load shedding. Different control costs are set for first-class loads, second-class loads and third-class loads in emergency load shedding to ensure that non-important loads are removed first. In practical applications, the weight coefficients and control costs of different control resources can be set according to safety requirements.

[0086] After comprehensively considering the steady-state constraint conditions and transient constraint conditions, the complete structure of the optimization decision model is as Figure 4 , Figure 5 shown.

[0087] To sum up, the established optimization decision model for off-grid emergency control of a distribution system considering flexible self-configuration division of islands is as follows: . (65) S3. Solve the optimization decision model based on the improved discrete particle swarm algorithm. By introducing the crossover and mutation operations of the genetic algorithm to enhance the global search ability, the optimal island division scheme and emergency control strategy are obtained.

[0088] When making the island division decision, there are a large number of 0-1 variables for the line switch states. Traditional continuous optimization algorithms often face problems such as combinatorial explosion, local optimal trap and low convergence efficiency due to the discrete characteristics of the search space, and it is often difficult to solve efficiently. Heuristic optimization algorithms have shown good performance in solving optimization decision problems containing a large number of 0-1 variables.

[0089] The Particle Swarm Optimization (PSO) algorithm draws on the mechanism of birds sharing information and collaborating with each other during foraging, and its design goal is to solve complex global optimization problems. Since the PSO algorithm was proposed, due to its simplicity, ease of implementation, and high efficiency, it has been widely used in fields such as function optimization, neural network training, and data mining. However, traditional PSO algorithms mainly optimize continuous spaces, and their optimization effects on discrete spaces (such as optimization problems containing a large number of 0-1 variables) are limited. Therefore, the Discrete Particle Swarm Optimization (DPSO) algorithm emerged. Its basic idea is to discretize the concepts of position and velocity in the continuous PSO algorithm, and it has shown unique advantages in solving optimization decision-making problems containing a large number of 0-1 variables, becoming an effective tool for solving discrete optimization problems.

[0090] When solving the optimization decision model, a particle in DPSO is a topological structure. The position of the particle is represented as a point in the solution space, and the velocity represents the transition probability or direction of the solution in the discrete space. Different particles give different topological structures. According to the determined topological structure, the mixed integer linear programming problem is solved to obtain the objective function value of the optimization decision model, which is returned as the fitness value of the particle. The DPSO algorithm will guide the particles to move towards better solutions through information sharing and collaboration among the particles, and finally find the optimal solution of the objective function. The island division result in the best emergency control plan is the topological structure corresponding to the optimal particle.

[0091] The update formulas for the particle velocity and position in DPSO are as follows: ; (66) ; (67) In the formula, and respectively represent the velocity and position of particle i in the t th iteration. is the inertia weight, which controls the influence of the particle's historical movement on the current velocity. and are acceleration constants, which respectively adjust the tendency of the particle towards the individual optimal position and the global optimal position . A larger value helps the particle fully explore individual experience, while a larger value enhances the information sharing ability among the particles. Usually, the values of and are set to be close to achieve a balance between individual exploration and group collaboration. and are random numbers within the interval [0, 1], used to introduce randomness and enhance the search ability. Sigmoid The function maps the velocity to the interval [0, 1]. rand The function generates uniformly distributed random numbers within the interval [0, 1], allowing the particles to jump in the solution space in a probabilistic manner.

[0092] The inertia weight controls the influence of the particle's historical motion on the current velocity. A higher value helps the particle to explore a large range in the solution space, while a lower value tends to perform a fine search. In practical applications, a dynamic adjustment strategy is usually adopted to make the inertia weight decrease linearly. The formula is: ; (68) In the formula, is the inertia weight in the t th iteration, and are the maximum and minimum values of the inertia weight, is the maximum number of iterations.

[0093] When solving by DPSO, it may fall into a local optimal solution. By introducing the crossover and mutation operations of the genetic algorithm, the diversity of the population can be increased, and the probability of the particles converging to the global optimal solution can be improved. The basic steps are as follows: (1) Randomly generate the initial positions and velocities of a group of particles. Among them, the initial positions are represented by 01 variables, and the initial velocities are randomly generated between [-1, 1].

[0094] (2) Calculate the fitness value of each particle according to the objective function, and record the individual optimal solution and the global optimal solution.

[0095] (3) Use the velocity update formula and the position update formula to recalculate the velocities and positions of the particles in the population. The particle positions are mapped to 0 or 1 through the Sigmoid function.

[0096] (4) Calculate the fitness values of the newly generated particles, compare them with the previous individual optimal solutions, and update the individual optimal solutions and the group optimal solutions.

[0097] (5) Adopt the roulette wheel strategy to select a certain number of particles from the particle swarm to form a sub-population, and then randomly select two individuals within the sub-population for crossover operation to obtain new individuals and calculate their fitness. If the fitness of the new individual exceeds that of the original individual, replacement is made.

[0098] (6) In the updated particle swarm, some particles are mutated according to a preset mutation probability to generate new individuals, and their fitness values are calculated. If the fitness value of the new individual exceeds that of the original individual, the new individual replaces the old one.

[0099] (7) Check whether the termination condition is met, that is, whether the maximum number of iterations set is reached or the objective function value meets the requirements. If the condition is not met, return to step (3) to continue the next round of iteration; otherwise, output the global optimal solution.

[0100] S4. Perform active islanding division according to the optimal islanding division scheme, coordinately control the power output of the power supply, and cut off the non-critical loads to ensure the transient stability of the island and the power supply for important loads.

[0101] Embodiment To better illustrate the control process of the present invention, a specific numerical example test is given. The numerical example system is transformed based on the standard 33-node distribution system. As Figure 6 shown, synchronous generators with a maximum power of 600 kW are added at nodes 25 and 30, virtual synchronous machines with a maximum power of 450 kW are added at nodes 14 and 21, photovoltaic power sources with a maximum power of 200 kW are added at nodes 5 and 11, and energy storage power sources with a maximum power of 100 kW are added at nodes 8 and 24. The set power supplies all have different control parameters.

[0102] The original total active load of the 33-node distribution system is 3715 kW. After the transformation, the total installed capacity of the distributed power sources reaches 2700 kW, with local self-balancing ability. Moreover, various types of power sources and energy storage devices in the transformed system are coordinately configured: The photovoltaic power source provides a stable power output but cannot flexibly respond to the dynamic demands of the system, representing a type of resource that is uncontrollable or difficult to quickly adjust the power output, mainly used to provide constant power support; The energy storage power source (grid-connected power source) adopts the PQ control strategy and can quickly adjust the active power and reactive power output according to the dispatching instructions, mainly used to quickly respond to the power shortage situation in the system and is an important source of flexibility for the distribution system; The synchronous generator and the virtual synchronous machine (network-forming power source) mainly achieve the inertia response, frequency regulation, and voltage support of the system.

[0103] The fault scenario is set at t = 0 s when the connection point (node 1) between the distribution system and the upstream power grid suddenly disconnects, resulting in a significant power shortage in the entire system. To simulate the actual situation, considering the time delays in communication, calculation, and execution in the actual system, it is assumed that there is a 0.1 s action delay for the output adjustment of each control resource or the load shedding action after the fault is detected. The transient process lasts for 10 s, and the discrete step size is set to 0.02 s to ensure the accurate characterization of the transient dynamic characteristics.

[0104] In the solution of the optimization decision model, the discrete particle swarm optimization algorithm sets the number of particles to 100, and each particle represents a possible topological structure; the number of iterations is set to 100 to fully explore the solution space and approach the global optimal solution; the particle dimension is 31, that is, the on-off decisions are made for the remaining 31 lines except the line from node 1 to node 2.

[0105] The core task of the optimization decision is to comprehensively consider the system topological structure, the load demands of each node, the output of distributed resources, and the transient process, and perform active islanding division and frequency emergency control. Active islanding division divides the original system into several independently operating small islands by reasonably adjusting the line on-off states, making the power supply and demand within each island as balanced as possible, and at the same time reducing the impact of power deficits on the overall system; frequency emergency control utilizes the response capabilities of various resources to adjust the output and reasonably shed loads during the transient process, thereby preventing excessive frequency deviation and ensuring system stability.

[0106] Analysis of the results of flexible self-configuration division of islands The iterative results of the objective function obtained by the optimization decision are as Figure 7 shown. As the number of iterations increases, the objective function value shows a gradually decreasing trend, indicating that the optimization algorithm is gradually exploring a better solution space and making the optimization decision converge to a better result.

[0107] The results of the optimization decision show that after disconnecting from the upstream power grid, the system needs to form two independently operating islands to maintain the local power supply capacity, and their topologies are as Figure 8 shown. The decision result disconnects the line between node 2 and node 3, forming a small island 1 containing nodes 2, 19, 20, 21, and 22. A virtual synchronous machine power supply in this island serves as the main power supply for the entire island, and it has a certain inertia and frequency regulation ability to maintain the stability of voltage and frequency and ensure the stable operation of the island; the large island 2 includes the remaining nodes after disconnecting the line between node 14 and node 15, including most of the resources and important loads. Nodes 15, 16, 17, and 18 will not be included in any island because the load importance of these nodes is relatively low and they will all be powered off.

[0108] The overall load shedding situation of the system is as Figure 9As shown, the total load shedding of the system is 1.31 MW. It can be seen from the figure that no primary load is shed, fully guaranteeing its power supply demand; a small amount of secondary load is shed, with 0.210 MW shed, indicating that the optimization model moderately adjusts the less important loads on the premise of ensuring the power supply of the primary load. This partial shedding may be due to limited resources or system operating conditions, but the shedding amount is small, indicating that the secondary load still enjoys a high level of guarantee and minimizes the impact on its normal operation; for the tertiary load, a large amount of shedding occurs. The tertiary load is non-critical or interruptible, so in the case of resource shortage, the optimization model chooses to cut it on a large scale to ensure the power supply stability of higher-priority loads. This decision reflects that the optimization model makes a decision to ensure the power supply of important loads and cut unnecessary loads after weighing factors such as load importance and resource allocation.

[0109] A corresponding 33-node time-domain simulation model was built on the CloudPSS simulation platform. According to the decision results, the corresponding line disconnection, load shedding, and power output adjustment of the power source were set, and the frequency curve, voltage curve, and generator output curve during the system transient process were obtained through simulation as Figure 10 shown.

[0110] It can be seen from Figure a) that the lowest system frequencies of Island 1 and Island 2 do not drop below 49.8 Hz, indicating that the emergency control strategy has taken effect. After transient regulation, Island 1 operates at 49.95 Hz and Island 2 operates at 49.98 Hz, indicating that the island systems can still effectively maintain the frequency within the safe range after disconnecting from the main grid and the internal supply and demand are basically balanced.

[0111] Figure b) shows the voltages of the two island systems. The reference voltage of the 33-node distribution system is 12.66 kV. After forming islands by disconnecting from the grid, the voltage of Island 1 is maintained at 12.24 kV and the voltage of Island 2 is maintained at 12.91 kV.

[0112] In Figure c), there is a certain amount of frequency modulation reserve reserved in the initial output of the synchronous generators and virtual synchronous machines in the two islands, which is less than the maximum power. The transient output of the system dynamic response shows an instantaneous overshoot phenomenon at the initial stage of regulation. For the power supply with a power electronic interface, the maximum output during the transient regulation process is limited within 1.5 times of the maximum power, avoiding the failure risk caused by the equipment triggering overcurrent protection or burning out. For synchronous generators, the maximum output limit can be relaxed to within 2 times of the maximum power. After transient regulation, the output of each power source is gradually adjusted to the required steady-state value, and the steady-state output will not exceed its own maximum power, meeting the internal supply and demand balance of the islands.

[0113] Since there is no energy storage power supply in Island 1, the output curves of the two energy storage power supplies in Island 2 are shown in Figure d). It can be seen from the figure that after a 0.1s action delay, the energy storage power supply begins to adjust its output. Due to the PQ control adopted, the output of the energy storage power supply is quickly adjusted to the maximum output of 100kW.

[0114] Analysis of Passive Islanding Division Results In contrast, if instead of actively dividing into two islands, only the lines between Node 1 and Node 2 are passively disconnected, and the remaining nodes all form a large island as shown in Figure 11 In this case, the total load shedding situation of the system is as shown in Figure 12 as shown, and the transient process curve is as shown in Figure 13 as shown.

[0115] In this case, the total load shedding amount of the system is 1.38MW. It can be seen from Figure 12 that the primary load can also be fully powered, while 0.221MW of the secondary load is shed, which is an increase compared to the 0.210MW shed when actively dividing into two islands, indicating that a large passively formed island needs to shed more secondary load under various constraints. This shows that in the case of passively forming a large island, although the power supply demand of the primary load can be guaranteed, the guarantee ability for the secondary load is relatively weak.

[0116] Similarly, corresponding controls are set according to the decision results in the time-domain simulation model of CloudPSS. The simulation results show that during the transient process, when the system passively forms a large island, the frequency of the system is still within the safe range, not lower than 49.8Hz, the system voltage is also safe and stable, and the instantaneous maximum output of each power supply is also constrained, indicating that the power supply equipment is safe in this case. Whether actively dividing into two islands or passively forming a large island, the calculated maximum power angle does not exceed the set safety threshold, indicating that the power deficit disturbance caused by islanding will not lead to transient desynchronization of the system.

[0117] However, the calculation results of the critical clearing time after islanding show that the critical clearing time of the passively formed large island is 0.035 seconds, which fails to meet the constraint condition that the set critical clearing time needs to be greater than 0.1 seconds. This indicates that the passively formed large island has a high risk of transient desynchronization when suffering from large disturbances. In contrast, in the case of actively dividing into two islands, since Island 1 has only one network-forming power supply, there is no problem of transient desynchronization between power supplies; while the calculated critical clearing time of Island 2 is 0.115 seconds, which meets the constraint condition that the set critical clearing time is greater than 0.1 seconds. This result shows that in the case of actively dividing into two islands, when the island faces large disturbances, various protection measures have enough time to act, thus reducing the risk of transient desynchronization.

[0118] Therefore, by adopting the off-grid emergency control method for a distribution system considering flexible self-configuration division of islands in the present invention, an optimization model that comprehensively considers transient processes and steady-state operation constraint conditions can actively make decisions on island division areas, coordinate multiple resources to jointly execute emergency control during island switching, minimize load losses, preferentially ensure the power supply to important loads, and avoid situations such as transient instability of power sources, system frequency over-limitation, and large-scale power outages caused by unreasonable island division of the distribution system.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements do not enable the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A distribution system off-grid emergency control method considering flexible self-configuration partitioning of islands, characterized in that It includes the following steps: S1. Establish a frequency response model of a multi - resource power distribution system, and perform multi - resource frequency response modeling for synchronous generators, virtual synchronous machines, energy storage power supplies, photovoltaic power supplies, and load shedding. S2. With minimizing load loss and resource control amount as the objective function, construct an optimization decision - making model that integrates steady - state constraints and transient constraints. The transient constraints include the lowest frequency point constraint, frequency change rate constraint, transient power output constraint of power sources, maximum power angle constraint, and critical clearing time constraint. S3. Solve the optimization decision - making model based on an improved discrete particle swarm algorithm, and improve the global search ability by introducing the crossover and mutation operations of the genetic algorithm to obtain the optimal islanding division scheme and emergency control strategy. S4. Execute active islanding division according to the optimal islanding division scheme, coordinate the control of power output of power sources and shed non - critical loads to ensure the transient stability of the island and the power supply to important loads.

2. The off-grid emergency control method for a distribution system considering flexible self-configuration division in an islanding situation according to claim 1, characterized in that: In S1, the synchronous generator and the virtual synchronous machine include inertia response and primary frequency regulation modeling. The frequency response model of the inertia response is: ； In the formula, represents the generator inertia time constant, is the generator damping coefficient, is the mechanical power, is the electromagnetic power, is the frequency deviation; The frequency response model is transformed into a differential - algebraic model by the difference discretization method. The discretized frequency response model is: ； In the formula, represents the change amount of the frequency deviation value at the moment, the change amount of the frequency deviation value at the moment, represents the power change amount at the Primary frequency regulation is the process in which synchronous generators and virtual synchronous machines automatically adjust the active power output according to the frequency deviation. Its control strategy is based on the droop characteristics of the governor. After considering the time delay of control through a first - order inertia link, the droop characteristics of the governor are expressed as: ； wherein, is the output power, is the power reference value, is the droop coefficient of the governor, is the Laplace operator, is the control time constant; The discrete difference equation of the output power is: ； In the formula, represents the output power at time represents the output power at time 3. The off-grid emergency control method for a distribution system considering flexible self-configuration division in an islanding situation according to claim 2, wherein: In S1, after considering the outer - loop PI control characteristics and control time delay of the energy storage power supply, the discrete difference equation of the output power of the energy storage power supply is: ； Wherein, represents the battery output power at time represents the battery output power at time represents the PI control power at time represents the PI control power at time represents the PI control error at time represents the PI control error at time represents the power reference value, and are respectively the proportional and integral gain coefficients of the PI control, represents the differential time step, represents the control time constant, z is the index variable.

4. A method for off-grid emergency control of a distribution system considering flexible self-configuration division in an islanding situation, characterized in that: In S1, the actual PV output of the PV power source is as follows: ； In the formula, is the maximum photovoltaic output value, is the uncertainty coefficient.

5. A method for off-grid emergency control of a distribution system considering flexible self-configuration division of islands, as claimed in claim 4, wherein In S1, the frequency response model of the multi - resource power distribution system after aggregation, equivalence, and order reduction of similar resources is: ； wherein, is the frequency deviation of the system's inertial center, represents the power change of the system, is the inertia time constant of the whole system, is the damping coefficient of the whole system, t is time; The discrete - difference frequency response differential model of the multi - resource power distribution system is: ； In the formula, is the inertial center frequency deviation at time of the system, is the inertial center frequency deviation at time k of the system, represents the differential time step; ； In the formula, represents the capacity and control time constant of the overall system, , and represent the inertia time constant, damping coefficient, and capacity of the th synchronous generator, , and represent the inertia time constant, damping coefficient, and capacity of the th virtual synchronous machine.

6. The off-grid emergency control method for a distribution system considering flexible self-configuration division in an islanding situation according to claim 5, characterized in that: In S2, the steady - state constraint conditions include linear power flow constraint, power output constraint of power sources, node voltage constraint, line capacity constraint, and load shedding amount constraint.

7. A method for off-grid emergency control of a distribution system considering flexible self-configuration division in an islanding situation, characterized in that: In S2, the lowest frequency point constraint and the frequency change rate constraint are: ； wherein, represents the lowest safety value of the system frequency, and represent the minimum and maximum values of the frequency change rate respectively, represents the inertial center frequency of the system at time represents the inertial center frequency of the system at time The system frequency of the island in each step of the transient process at time must satisfy the frequency transient constraint.

8. A method for off-grid emergency control of a distribution system considering flexible self-configuration division in an islanding situation, characterized in that, In S2, the transient power output constraint of power sources is: ； In the formula, and respectively represent the maximum rates of the power output of the power source for upward and downward ramps, is the multiple of the maximum instantaneous amount of power that the power source can withstand exceeding the maximum power limit, represents the maximum power of the power source, represents the instantaneous value of the power of the power source at time represents the instantaneous value of the power of the power source at time During the transient process of the power output of the power source within the island, at each step the power transient constraint must be satisfied.

9. A method for off-grid emergency control of a distribution system considering flexible self-configuration division of islands, as claimed in claim 8, wherein: In S2, during the formation of islands, the disturbance caused by the power deficit causes the power angle characteristic curve to intersect with When there is an intersection point, the maximum power angle constraint does not exceed , ； In the formula, is the isolated island is the maximum power angle of the system during the transient process under disturbance, is the set of isolated islands, is the damping unbalanced power; When the disturbance caused by the power deficit makes the power angle characteristic curve and there is no intersection point, ； is an island The critical clearing time of the system during the transient process under disturbances.

10. A method for off-grid emergency control of a distribution system considering flexible self-configuration division in an islanding situation, characterized in that, In S2, the objective function is: ； In the formula, is the objective function, is the control cost weight coefficient of the battery, is the control cost weight coefficient of the synchronous generator, is the control cost weight coefficient of the virtual synchronous machine, is the control cost weight coefficient of the load shedding, is the battery control quantity cost, is the synchronous generator control quantity cost, is the virtual synchronous machine control quantity cost, is the load shedding control quantity cost, is the number of batteries, is the number of synchronous generators, is the number of virtual synchronous machines, is the number of load shedding, is the battery output power, is the synchronous generator output power, is the virtual synchronous machine output power, is the load shedding output power.

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