Off-grid emergency control method for distribution system considering flexible self-configuration partitioning of isolated islands

Abstract

The present invention discloses an off-grid emergency control method for a distribution system considering flexible self-configuration partitioning of islands, which belongs to the technical field of off-grid control of distribution networks. The off-grid emergency control method for a distribution system considering flexible self-configuration partitioning of islands comprises: establishing a frequency response model of a multi-resource distribution system; taking minimizing load loss and resource control quantity as the objective function, constructing an optimization decision model integrating steady-state constraints and transient constraints; solving the optimization decision model based on an improved discrete particle swarm algorithm; and executing active island partitioning according to the optimal island partitioning scheme. The present invention comprehensively considers the optimization model of transient processes and steady-state operation constraints, and coordinates multiple resources to jointly execute emergency control in island switching, minimize load losses, give priority to ensuring the power supply of important loads, and avoid situations such as transient instability of the power supply, system frequency exceeding the limit, and causing large-scale power outages caused by unreasonable island partitioning of the distribution system.

Description

Technical Field

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

[0002] In recent years, the frequency of extreme natural disasters has increased significantly worldwide, and their impact on power distribution systems has become increasingly severe. Such disasters can not only damage the physical infrastructure of distribution networks but also disrupt the electrical connection between local distribution networks and the main grid, leading to chain reactions that can trigger large-scale power outages and pose a significant threat to socioeconomic activities and the daily lives of residents. In this context, how to effectively respond to emergencies and ensure the security and continuity of power supply has become a key research topic. Islanding and frequency emergency control technologies are considered important strategies for improving the resilience and stability of modern distribution systems.

[0003] When a distribution system experiences a power shortage due to grid disconnection, the system frequency often drops rapidly. If timely action is not taken, the frequency drop could be so severe that it could lead to a system crash. Underfrequency load shedding, a classic emergency control method, relies on gradually shedding non-critical loads according to preset rules to maintain system frequency stability. This approach, which employs fixed frequency thresholds and a graded load shedding strategy, boasts high reliability and engineering practicality. However, this rigid control approach has significant drawbacks: its lack of dynamic adaptability often leads to unnecessary load loss and can even result in significant economic losses. For example, in certain situations, even if the system frequency slightly deviates from the safe range, underfrequency load shedding may still result in a significant amount of load shedding according to fixed rules, which clearly violates the principle of maximizing economic benefits. Consequently, recent research has shifted to making refined decisions about load shedding to achieve "precise control." Specifically, by incorporating mechanisms such as real-time status monitoring, dynamic optimization algorithms, and load priority assessment, load shedding strategies can be flexibly adjusted based on specific system operating conditions, minimizing load losses while ensuring system safety.

[0004] The counterpart to low-frequency load shedding is the high-frequency generator shedding strategy, primarily used to address high system frequency scenarios. This method rapidly removes some generator output power to prevent the frequency from exceeding the upper limit. High-frequency generator shedding can adversely affect the mechanical stability of the generator set, so its triggering conditions and action logic require careful design. While important in specific scenarios, high-frequency generator shedding is not suitable for typical distribution system off-grid scenarios, where the system is more likely to experience a frequency drop than an increase.

[0005] In contrast, automatic generation control (AGC) is a more advanced and flexible frequency control method. It monitors system frequency and load changes in real time and dynamically adjusts generator output to achieve rapid frequency recovery and stabilization. The core advantage of AGC lies in its ability to adaptively adjust based on current operating conditions, thus avoiding the limitations of traditional fixed threshold strategies. However, the effectiveness of AGC is highly dependent on the reliability of the communication system and the accuracy of the control algorithm. Especially in extreme scenarios such as island switching, communication delays or data loss can prevent AGC from responding in a timely manner, compromising overall control effectiveness.

[0006] As an important means of improving the reliability and resilience of power distribution systems, islanding technology has received widespread attention from academia and industry in recent years. From an implementation perspective, islanding technology can be divided into two categories: active islanding and passive islanding. Active islanding involves proactively selecting the optimal islanding solution and implementing it by monitoring the grid status in real time and utilizing advanced algorithms and optimization techniques when a possible fault or system failure or abnormality is foreseen. Passive islanding, on the other hand, involves adjusting the network structure in real time based on the system status after a fault occurs, relying on pre-set protection devices to form islands. Compared to passive islanding, active islanding emphasizes the rapid and reasonable partitioning of islands through active control strategies before or during a fault, to maximize power supply protection and improve system resilience.

[0007] In the problem of active islanding in 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, and modeling is complex and difficult, and is often difficult to apply to distribution systems with rapidly changing conditions. Summary of the Invention

[0008] The purpose of the present invention is to provide an off-grid emergency control method for a distribution system that takes into account the flexible self-configuration division of islands. The method comprehensively considers the optimization model of transient processes and steady-state operation constraints, can actively decide on the island division area, and coordinate multiple resources to jointly perform emergency control during island switching, minimize load losses, give priority to power supply to important loads, and avoid unreasonable island division of the distribution system leading to transient instability of the power supply, system frequency exceeding the limit, and causing large-scale power outages.

[0009] To achieve the above object, the present invention provides an off-grid emergency control method for a power distribution system considering flexible self-configuration partitioning of isolated islands, comprising the following steps:

[0010] S1. Establish a frequency response model for a multi-resource distribution system, and perform multi-resource frequency response modeling for synchronous generators, virtual synchronous generators, energy storage power sources, photovoltaic power sources, and load shedding;

[0011] S2. With minimizing load loss and resource control as the objective function, an optimization decision model is constructed that integrates steady-state constraints and transient constraints. Transient constraints include frequency minimum point constraint, frequency change rate constraint, power output transient constraint, maximum power angle constraint, and extreme removal time constraint.

[0012] S3. Based on the improved discrete particle swarm optimization algorithm, the optimization decision model is solved and the global search capability is improved by introducing the crossover and mutation operation of the genetic algorithm to obtain the optimal island partitioning scheme and emergency control strategy;

[0013] S4. Perform active islanding according to the optimal islanding plan, coordinate and control power output and cut off non-critical loads to ensure transient stability of the island and power supply to important loads.

[0014] The advantages and positive effects of the off-grid emergency control method for a power distribution system considering flexible self-configuration partitioning of isolated islands described in the present invention are:

[0015] 1. The present invention constructs a framework for an optimization decision-making model from a theoretical level. During the island 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. In addition, for distributed energy with increasing penetration rates in new distribution systems, it is also an important variable that needs to be considered in island division decisions. In order to avoid larger-scale power outages caused by transient instability of the power supply due to disturbances during off-grid operation and island operation, the model introduces transient stability constraints in the decision-making process. Emergency frequency control maintains the system frequency within a safe range by optimizing the cutting off of non-critical loads and adjusting the power output, thereby avoiding system crashes caused by frequency exceeding the limit.

[0016] 2. This invention separately models synchronous generators, virtual synchronous generators, energy storage batteries, photovoltaic power sources, electric vehicles, and removable loads to describe the dynamic characteristics of each resource during island switching, providing a solid theoretical foundation for subsequent optimization decisions. Furthermore, through aggregate equivalence and order reduction, the complex multi-resource system is transformed into a low-dimensional model that is easy to analyze, significantly reducing computational complexity while retaining the ability to characterize key dynamic characteristics.

[0017] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The frequency response model structure of the multi-resource system of the present invention;

[0019] Figure 2 The frequency response reduced-order model structure of the multi-resource system of the present invention;

[0020] Figure 3This is the structure of the two-machine parallel power supply system of the present invention;

[0021] Figure 4 Optimize the decision model structure diagram of the present invention;

[0022] Figure 5 Optimize the solution structure of the decision model of the present invention;

[0023] Figure 6 This is a 33-node power distribution system according to an embodiment of the present invention;

[0024] Figure 7 is the objective function iteration curve of the embodiment of the present invention;

[0025] Figure 8 This is the active island division result of an embodiment of the present invention;

[0026] Figure 9 The total load shedding condition of the system according to the embodiment of the present invention;

[0027] Figure 10 Transient process data curves of an embodiment of the present invention, a) is the frequency of the island system, b) is the voltage of the island system, c) the engine output curve, d) the energy storage output curve;

[0028] Figure 11 The results are divided into passive islands;

[0029] Figure 12 Divide the total load shedding of the system into passive islands;

[0030] Figure 13 Transient process data curve for passive islanding, a) islanding system frequency, b) islanding system voltage, c) engine output curve, d) energy storage output curve;

[0031] Figure 14 The power angle characteristic curve of large-scale disturbance in a single-machine infinite system;

[0032] Figure 15 The system angular frequency deviation and time relationship curve of large-scale disturbance in a single-machine infinite system;

[0033] Figure 16 This is the power angle characteristic curve of small-scale disturbances in a single-machine infinite system. DETAILED DESCRIPTION

[0034] 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 art to which this application belongs. In the event of any inconsistency, the meaning described in this specification or the meaning derived from the contents 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.

[0035] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0036] A method for off-grid emergency control of a power distribution system considering flexible self-configuration partitioning of isolated islands comprises the following steps:

[0037] S1. Establish a frequency response model for a multi-resource distribution system, and perform multi-resource frequency response modeling for synchronous generators, virtual synchronous machines, energy storage power sources, photovoltaic power sources, and load shedding.

[0038] As the core device in the island system, the frequency response characteristics of the synchronous machine are mainly composed of two parts: inertial response and primary frequency modulation. The frequency response model of inertial response is:

[0039] ; (1)

[0040] Where, represents the generator inertia time constant, is the generator damping coefficient, is the mechanical power, is the electromagnetic power, is the frequency deviation, .

[0041] By converting the frequency response model into a differential algebraic model through the differential discretization method, the relationship between the adjacent steps of the variables at each discrete moment can be obtained. The forward Euler method is used for differentiation, and the frequency response model of the differentiation is:

[0042] ; (2)

[0043] Where, express The frequency deviation value change at the moment, express The frequency deviation value change at the moment, represents the difference time step, express The power change at each moment.

[0044] Primary frequency regulation is the process of automatically adjusting the active power output of synchronous generators and virtual synchronous machines based on frequency deviation. Its control strategy is based on the droop characteristic of the speed regulator. After considering the control time delay through the first-order inertia link, the droop characteristic of the speed regulator is expressed as:

[0045] ; (3)

[0046] Where, is the output power, is the power reference value, is the droop coefficient of the speed regulator, is the Laplace operator, is the control time constant.

[0047] The same differential processing is performed, and the discrete differential equation of the output power of the synchronous machine during the primary frequency modulation process is:

[0048] ; (4)

[0049] Where, express The output power at the moment, express Output power at any moment.

[0050] The output power of energy storage batteries is highly controllable. The amount of active and reactive power injected can be directly varied by adjusting current or voltage commands, adapting to varying power demands. PQ control is a classic method designed to target the output of energy storage batteries at given active and reactive power levels, compensating for power shortfalls and ensuring overall system power balance. The outer-loop power control in PQ control typically takes the difference between the target and reference power values ​​and feeds this into the inner-loop current control via a PI controller. Because the inner-loop control has a much larger bandwidth than the outer-loop control, it can be ignored in this analysis.

[0051] After considering the outer loop PI control characteristics and control time delay of the energy storage power supply, the discrete difference equation of the energy storage power supply output power is:

[0052] ; (5)

[0053] Where, express The battery output power at the moment, express The battery output power at the moment, express PI control power at the moment, express PI control power at the moment, express The PI control error at time t, express The PI control error at time t, Indicates the power reference value, and are the proportional and integral gain coefficients of PI control respectively, represents the difference time step, represents the control time constant, z is the index variable.

[0054] The uncertainty of photovoltaic power output needs to be considered in island 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 ambient temperature. Generally, the maximum power point tracking strategy is adopted to ensure that the system operates in the best state. Since the impact of extreme disasters may occur at different times and is interfered 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 shortage, the photovoltaic output needs to be regarded as a random variable. This uncertainty can be described by probability distribution. Assuming the maximum photovoltaic output Normal distribution within a certain period of time:

[0055] ; (6)

[0056] in, Indicates the maximum output value predicted by photovoltaic power generation. It reflects the fluctuation range of its output. N is a normal distribution.

[0057] Taking into account the deviation in actual scenarios, we can introduce an uncertainty coefficient To characterize the upper and lower floating range of photovoltaic output. for:

[0058] ; (7)

[0059] Where, is the maximum photovoltaic output value. It is the uncertainty coefficient, and its value range can be determined according to the specific situation. It is usually in [-0.2, +0.2] and is used to indicate the possible deviation of photovoltaic output.

[0060] 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 its output can be considered to basically maintain the actual output in a shorter time scale during the island switching process. Therefore, in emergency control, the photovoltaic power supply only provides constant power support, and the output power in the transient process cannot be adjusted.

[0061] Distribution System Frequency Response Modeling

[0062] The system frequency response characteristic uses the widely used Center of Inertia (COI) to represent the system frequency, as shown in the following formula:

[0063] ; (8)

[0064] Where, is the system inertia center frequency, is the inertia time constant of the entire system, For generators The inertia time constant (unit types include synchronous generators and virtual synchronous machines, i.e. units that can provide inertia support), For generators The frequency of the node.

[0065] Disturbance moment The system frequency change rate (RoCoF) is:

[0066] ; (9)

[0067] Where, Indicates the power change of the system.

[0068] The control methods and control characteristics of various types of resources in the system are shown in Table 1. The frequency response model structure of the multi-resource system is shown in Figure 1 shown.

[0069] Table 1 Frequency modulation methods and control characteristics of control resources

[0070] ;

[0071] Reduced-Order Modeling of Distribution System Frequency Response

[0072] The frequency response model of the multi-resource system is obtained after aggregation and equivalence of similar resources and order reduction, such as Figure 2 shown.

[0073] The aggregation equivalent parameters are:

[0074] ; (10)

[0075] Where, and are the power equivalent aggregation of energy storage battery and load shedding, It is the equivalent aggregation of the rated power variation of photovoltaic power after considering the uncertainty. 、 and are the number of energy storage batteries, photovoltaic power sources, and load shedding respectively.

[0076] The control parameters of the power supply with inertia support capability are equivalently aggregated as follows:

[0077] ; (11)

[0078] Where, 、 、 and Represents the inertia time constant, damping coefficient, capacity and control time constant of the entire system. 、 and Indicates the The inertia time constant, damping coefficient and capacity of the synchronous generator, 、 and Indicates the Inertia time constant, damping coefficient and capacity of a virtual synchronous machine.

[0079] ; (12)

[0080] Where, and is the proportionality coefficient, indicating the Synchronous generator and The ratio of the rated capacity of the virtual synchronous machine to the total capacity of the system. and Indicates the Synchronous generator and The droop coefficient of a virtual synchronous machine, Indicates the droop coefficient of the entire system. For the The weighting coefficient of the feedback control branch. Indicates the The control time constant of the generator. and are the number of synchronous generators and virtual synchronous machines, respectively.

[0081] Finally, the established frequency response model of the multi-resource distribution system is:

[0082] ; (13)

[0083] Where, is the system inertia center frequency deviation, Indicates the power change of the system, is the inertia time constant of the entire system, is the damping coefficient of the entire system, t For time.

[0084] The frequency response differentiation model of the multi-resource distribution system after discrete differentiation is:

[0085] ; (14)

[0086] Where, For the system The inertial center frequency deviation at time , For the system The inertial center frequency deviation at time , represents the difference time step.

[0087] Based on this model, the transient state of system frequency can be constrained during emergency frequency control.

[0088] S2. With minimizing load loss and resource control as the objective function, an optimization decision model integrating steady-state constraints and transient constraints is constructed. Transient constraints include frequency minimum point constraint, frequency change rate constraint, power output transient constraint, maximum power angle constraint, and limit removal time constraint.

[0089] (1) Steady-state constraints

[0090] Steady-state constraints include linear power flow constraints, power output constraints, node voltage constraints, line capacity constraints, and load shedding constraints.

[0091] After a fault occurs, the distribution system will be divided into multiple island systems, and the node 01 state variable needs to be introduced. and line 01 state variables , to describe the topological structure inside the island system after a failure.

[0092] variable and Need to meet:

[0093] ; (15)

[0094] ; (16)

[0095] ; (17)

[0096] ; (18)

[0097] Where, is a collection of multiple isolated islands divided into For isolated islands The node set within For isolated islands The node set where the internal power supply is located, For isolated islands The collection of lines within Indicates an island Internal Node The parent node of . Indicates line status, Indicates line In disconnected state.

[0098] Formula 15 indicates that a node belongs to at most one island; Formula 16 indicates that a power node must belong to the island where the power is located; Formula 17 indicates that a node Belong to an island The premise is that the parent node It's also an isolated island Yes, and the line Not disconnected; Formula 18 shows that the line Belong to an island The premise is that the nodes at both ends of the line and All belong to this island.

[0099] The linear DistFlow model ignores the nonlinear terms in the traditional power flow model, making the solution easier. It is a simplified model suitable for power flow calculation of radial network structure of distribution system. The power flow constraints are as follows:

[0100] ; (19)

[0101] ; (20)

[0102] ;(twenty one)

[0103] ;(twenty two)

[0104] ;(twenty three)

[0105] Where, and From the parent node Flow to child nodes The active and reactive power flows on the line, and From the parent node Flow to child nodes Active and reactive power flows on the line. and Indicates that the node Power on g Output active and reactive power, and Indicates that the node The active and reactive power of the load on and Indicates that the node Active and reactive power of the load shed. M Indicates big M A large constant in the law. It means that it is the square of the grid node voltage amplitude before disconnection. Represents the square of the voltage amplitude of the power node, is the square of the rated voltage amplitude, and is a node and The square of the voltage amplitude. and is a node and The resistance and reactance of the line. and It is the active and reactive power flowing through the line at maximum operation.

[0106] Equation 19 represents the active and reactive power flow balance at each node; Equation 20 defines the voltage at the grid connection point and the power supply node as the reference value; Equation 21 describes the voltage drop between adjacent nodes on the line; Equation 22 constrains the node voltage deviation; and Equation 23 limits the amount of power flowing on the line.

[0107] Power output constraints include upper and lower limits on active and reactive power as well as reserve capacity limits. The constraints are as follows:

[0108] ;(twenty four)

[0109] Where, and It is a power supply g The lower limit of active and reactive power output, and It is the power supply g The upper limit of active and reactive power output, Indicates the reserve capacity factor, ranging from (0,1].

[0110] Load shedding constraints are used to limit the range and proportion of load shedding in an emergency. The constraints are as follows:

[0111] ; (25)

[0112] ; (26)

[0113] Where, and is a node i The lower limit of active and reactive load shedding, and is a node i The upper limit of active and reactive load shedding.

[0114] Formula 36 ensures that the node i The load is cut off in proportion to the active and reactive power of the original load.

[0115] (2) Transient constraints

[0116] After islanding, due to the radial network structure, the power deficit of each island can be expressed by the power flowing through the island boundary node line, that is, the difference between the power flowing into the island boundary node line and the power flowing out of the island boundary node line:

[0117] ; (27)

[0118] Where, Indicates flow into an island The power on the boundary node line, Indicates outflow from the island The power on the boundary node line.

[0119] After an island is disturbed, if the system frequency drops below the safety threshold or the frequency change rate is too large, underfrequency load shedding protection will be triggered, causing system instability. Therefore, it is necessary to constrain the frequency transient process:

[0120] ; (28)

[0121] Where, Indicates the minimum safe value of the system frequency, and Represent the minimum and maximum values ​​of the frequency change rate, Representation System The center frequency of inertia at time , Representation System The inertial center frequency at the moment, the island System frequency Each step in the transient process Frequency transient constraints must be met at all times.

[0122] During the frequency modulation process, the power regulation of the power supply must meet the output ramp speed constraint, limiting the maximum rate of power change between adjacent moments. In addition, considering the limited overcurrent tolerance of the power supply of the power electronic interface, excessive power overshoot will cause equipment burnout, so it is also necessary to limit the instantaneous maximum power. The power output transient constraint is:

[0123] ; (29)

[0124] Where, and Respectively represent the maximum rate of power output climbing up and down, It is the multiple of the maximum instantaneous power that the power supply can withstand exceeding the maximum power limit. Indicates the maximum power of the power supply. express The instantaneous value of power supply at the moment, express Instantaneous power value at any moment, island Internal power output Each step in the transient process Power transient constraints must be met at all times.

[0125] The transient synchronization stability constraint ensures that the generators in the islanded system will not lose synchronization during the transient process after the disturbance, thereby maintaining the overall stable operation of the system.

[0126] In the process of forming an island, the disturbance caused by the power shortage is a small disturbance, that is, the power angle characteristic curve is When there is an intersection, considering the calculation error and the conservative requirements in actual engineering applications, the maximum power angle constraint does not exceed ,

[0127] ; (30)

[0128] Where, It's an isolated island The maximum power angle of the system during transient state under disturbance, A collection of isolated islands, To damp unbalanced power;

[0129] Considering that the protection device takes 100ms to operate, if a subsequent secondary disaster strikes the isolated island system, and the island system's maximum clearing time under a large fault disturbance is less than the protection device's operating time, the protection may not be able to clear the fault in time, causing power outages within the island and ultimately causing the island system to crash. Therefore, the formed island must have a certain degree of resilience, meaning that the system's maximum clearing time must be greater than 100ms. The maximum clearing time constraints are as follows:

[0130] ; (31)

[0131] It's an isolated island The limit cut-off time of the system during transient process under disturbance.

[0132] The improved extended equal-area rule is used to calculate the maximum power angle and limit removal time in a multi-machine system.

[0133] When extending the equal-area rule from a single-machine infinite system to a multi-machine system, the rotor motion equations of each generator are coupled with the state variables of the other generators, requiring the resolution of the complexity introduced by the dynamic coupling and energy interactions of the multiple machines. Therefore, the system's dynamic behavior cannot be simply described by a single power angle characteristic curve; instead, the mutual influence of multiple power angles must be considered. Furthermore, in a multi-machine system, the damping characteristics between generators significantly affect the system's transient response, introducing stronger nonlinear characteristics that make direct analysis using the traditional equal-area rule difficult. For multi-machine systems, equivalent simplification can be used to approximate them to a two-machine system, allowing the improved and extended equal-area rule to be applied to analyze system stability.

[0134] Establish a two-machine parallel power supply system structure such as Figure 3 As shown, two power sources are connected to a common bus via lines, and a load is connected to the common bus. The type of power source is not limited and can be two SGs, two VSGs, or one SG and one VSG.

[0135] Figure 3 In the figure, the effective values ​​of the phase voltages of power source 1 and power source 2 are and , the voltage phase angles are and The effective value of the phase voltage at the load is , the phase angle is . is the line admittance of node 1-3, is the line admittance of node 2-3, is the load equivalent admittance.

[0136] According to the circuit model of the parallel power supply system, its current Norton equation can be expressed as:

[0137] ; (32)

[0138] Where, 、 and are the injected currents of node 1, node 2, and node 3 respectively.

[0139] Further deduction yields:

[0140] ; (33)

[0141] Easy to know , eliminating the intermediate variables Simplifying, we get:

[0142] ; (34)

[0143] Defining variables 、 and for:

[0144] ; (35)

[0145] Combining formula (2-30) and formula (2-31), we can get:

[0146] ; (36)

[0147] Where, and is the voltage amplitude, 、 and is the admittance amplitude, 、 and is the equivalent admittance angle.

[0148] The line dynamic characteristics are much faster than the response speed of the power supply speed regulator. After ignoring the line dynamic characteristics, the output power of the parallel system is:

[0149] ; (37)

[0150] Where, and are the complex powers of power source 1 and power source 2 respectively, and Current and The conjugate vector of .

[0151] Substituting Equation 34 into Equation 35 and taking the real part, we can obtain the active power output of the two power supplies as:

[0152] ; (38)

[0153] The rotor motion equations of the two power supplies are as follows:

[0154] ; (39)

[0155] In the formula, the relevant variables of power supply 1 are represented by subscript 1, and the relevant variables of power supply 2 are represented by subscript 2.

[0156] The phase angle difference between the two power sources is , then formula (2-35) can be changed to:

[0157] ; (40)

[0158] Reasonably set the parameters of VSG so that , the parallel power supply system can be converted into a single-machine infinite system, and the equivalent rotor motion equation is obtained:

[0159] ; (41)

[0160] Where, is the equivalent inertia, is the equivalent damping coefficient, is the equivalent rated power, is the equivalent electromagnetic power.

[0161] Finally, the equivalent rotor motion equation of the two-machine parallel power supply system is obtained as follows:

[0162] ; (42)

[0163] At this point, 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 scope of application of the equal-area rule and retains the simplicity of the equal-area rule. At the same time, it 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 quantitative indicators of the maximum power angle constraint and the limit removal time constraint required for the optimization decision simulation can be extracted.

[0164] Analytical calculation of CCA and CCT in a single-machine infinite system using the improved extended equal-area method

[0165] Within the research framework of a single-machine infinite-power system, when the system encounters a disturbance, the power angle trajectory of the synchronous generator (SG) or virtual synchronous generator (VSG) gradually deviates from its initial equilibrium position. This process begins with an acceleration phase, followed by a deceleration phase as the fault clearing action is implemented. Based on the principle of energy conservation, if the energy accumulated during the deceleration phase fully compensates for the energy consumed during the acceleration phase, the system will reach a new steady-state operating point. Conversely, if the two cannot reach equilibrium, the system will face the risk of losing synchronization.

[0166] For traditional synchronous machines, the dynamic characteristics of electromagnetic and mechanical power can be described by the rotor motion equations. During a fault, the electromagnetic power decreases due to a drop in grid voltage, while the mechanical power remains constant, causing the generator to accelerate. After the fault is cleared, the electromagnetic power gradually recovers, and the generator begins to decelerate.

[0167] For virtual synchronous machines, the control strategy simulates the mechanical and electromagnetic characteristics of synchronous generators. During a fault, although the physical structure of a VSG is different from that of a synchronous machine, the control strategy makes its dynamic characteristics during transients similar to those of a synchronous machine. Therefore, the equal-area rule is also applicable to the transient stability analysis of VSGs.

[0168] Active power transmitted from the power source to the grid and reactive power It can be expressed as follows:

[0169] (43)

[0170] Where, 、 is the resistance and reactance of the line, is the power supply output voltage, is the grid voltage, is the power angle.

[0171] In a single-machine infinite system, the rotor motion equations of SG and VSG can be described by simplified second-order nonlinear differential equations:

[0172] (44)

[0173] Where, 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.

[0174] The traditional equal-area method assumes that the mechanical power remains constant and that the damping can be ignored during transients. This is because the damping coefficient of the SG is usually small, and its impact on the unbalanced power during transients is limited, serving only as an attenuation factor after stabilization. However, for VSGs, their virtual damping is tightly coupled with the primary frequency modulation, and the virtual damping is generally set to be large. If the impact of virtual damping is ignored during the analysis and calculation of the acceleration and deceleration area, the calculated limit cut-off angle will often be too conservative, thus affecting the judgment of the transient stability of the system.

[88] .

[0175] In order to more accurately reflect the dynamic characteristics of VSG, it is necessary to include the damping term in the analysis and define the damping unbalanced power Then formula (44) becomes:

[0176] (45)

[0177] In the traditional equal-area method, it is also assumed that 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, where this coupling effect is more significant. When a three-phase symmetrical short-circuit fault occurs in the grid, the instantaneous drop in grid voltage will cause the reactive power output of small SGs and small VSGs to increase. Since reactive power and voltage amplitude have a drooping relationship, the drop in voltage amplitude will further lead to a decrease in the active power output of the power supply and an increase in the acceleration area. If this process is ignored, the risk of transient instability of the system may be underestimated. The relationship between reactive power and voltage can be expressed as follows:

[0178] (46)

[0179] Where, is the power supply output voltage, is the rated voltage, is the reactive-voltage droop coefficient, is the initial reactive power.

[0180] In summary, combining formula (43), formula (45) and formula (46) can establish the steady-state Power angle relationship:

[0181] (47)

[0182] When a fault occurs, the corresponding variable should take the value at the time of the fault, which is indicated by the subscript F. The power angle relationship is:

[0183] (48)

[0184] According to the degree 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 is There is no intersection; Category II: The disturbance is small, and the power angle characteristic curve is There is an intersection.

[0185] Based on the power angle characteristic curve, the constraints required for optimization decision-making can be extracted to guide the island partitioning scheme. It is worth noting that there are different focuses for these two types of faults.

[0186] (1) Calculation of CCT in case I

[0187] Category I usually corresponds to severe short-circuit grounding faults or other large-scale disturbances, and its power angle characteristic curve is as follows: Figure 14 The acceleration area represents the kinetic energy added by the generator during the disturbance, that is, the power angle curve and mechanical power of the system during the acceleration process after the disturbance. The area enclosed by the horizontal line The deceleration area represents the kinetic energy reduced by the generator during the deceleration process, that is, the power angle curve and mechanical power of the system during the deceleration process after the disturbance. The area enclosed by the horizontal line During the fault period, the power angle characteristic curve is Mutation , causing the rotor to undergo an acceleration process, and the system operating point changes from the initial equilibrium point Start to deviate; the fault is After removal, the power angle characteristic curve returns to , the system enters the deceleration stage.

[0188] In case of type I, the power angle characteristic curve under system fault is The absence of a stable equilibrium intersection between the two indicates that the system cannot recover to a steady state without clearing the fault after the disturbance. Due to the large magnitude of the disturbance, the system's critical clearance time (CCT) is typically short, meaning the fault may not be cleared in time, and the system will inevitably lose synchronous stability. Therefore, in such cases, research focuses more on the calculation of CCT. CCT directly reflects the system's critical stability time under extreme disturbances, providing a scientific basis for the operating time of protective devices, ensuring that they can quickly clear the fault before instability occurs, thereby minimizing the impact of the accident.

[0189] When calculating and solving CCA after considering damping, due to It is difficult to solve the problem directly by analyzing the dynamic changes over time. A simplified method is to calculate the area of ​​the curve generated by the damping. Approximately the area of ​​a triangle Go calculate.

[0190] The rotor motion equation of the power supply during the fault is:

[0191] ; (49)

[0192] Further we get:

[0193] ; (50)

[0194] Integrate both sides of formula (50):

[0195] ; (51)

[0196] Among them, the right side of the equation For curve graphics area, is a stable equilibrium point, since Not about The algebraic equation cannot be solved analytically, so we need to assume is the system limit cut-off angle, when the system is The fault is removed and the system is in a critical stable state. Corresponding Get the maximum value, defined as .

[0197] Depend on Figure 14 See, the line segment The length is , we can calculate the triangle The area is as follows:

[0198] ; (52)

[0199] The curve The area is approximately a triangle The area of ​​​​

[0200] ; (53)

[0201] Substituting formula (53) into formula (51) yields:

[0202] ; (54)

[0203] The left side of the equation shows that the system moves to The kinetic energy of the system increases when the equation is correct. The right side of the equation shows that the excess input power of the rotor is from Exercise to The increase in rotor kinetic energy.

[0204] Solving formula (54) yields about The analytical expression is:

[0205] ; (55)

[0206] The calculation of the acceleration and deceleration area of ​​a single-machine infinite system is as follows:

[0207] ; (56)

[0208] Where, is the acceleration area of ​​the VSG system when it is critically stable; is the deceleration area of ​​the VSG system when it is critically stable.

[0209] The scaling method is used again to convert the unbalanced energy of the transient damping (curve graph area) is reduced to a triangle Area, the final equal area formula is as follows:

[0210] ; (57)

[0211] The resection angle can be obtained by combining formula (55) and formula (57) , defined as the system limit resection angle .

[0212] The method for calculating CCA is scaled twice. The first scaling makes The calculated value is less than The actual value, the second scaling results in the actual acceleration area being smaller than the calculated value , and the actual deceleration area is greater than the calculated value This difference ultimately makes the calculated limit resection angle smaller than the actual limit resection angle. Nevertheless, compared with the traditional method that completely ignores the influence of damping, this method significantly reduces conservatism, and the calculation results are still conservative to a certain extent, which can meet the conservative requirements of actual engineering applications.

[0213] Get the limit resection angle The limit removal time can be solved .because and It is difficult to obtain the analytical expression between - Here, we can again use the triangle scaling method mentioned above to approximate the analytical expression. The scaling process is as follows: Figure 15 shown.

[0214] Figure 15 The relationship curve between the system angular frequency deviation and time is given. The point corresponds to the limit removal time. From the above analysis, it can be seen that the angular frequency deviation reaches its 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:

[0215] ; (58)

[0216] Will The area of ​​the curve graph is reduced to The area of ​​a triangle is:

[0217] ; (59)

[0218] Combining formula (55) and formula (59) yields The approximate solution is:

[0219] ; (60)

[0220] (2) Calculation of the maximum power angle in case II

[0221] The second type of situation usually corresponds to the disturbance caused by power shortage, and its power angle characteristic curve is as follows: Figure 16 shown.

[0222] In this case, the power angle characteristic curve under system fault is There is a stable equilibrium intersection between them, indicating that the system has the possibility of recovering to a new steady state even if the fault is not cleared after the disturbance. Due to the small disturbance amplitude, the transient process of the system is relatively gentle, and the limit clearance time CCT is usually longer, generally exceeding the typical value of the inherent action delay of the relay protection of 0.1-0.3 seconds. This means that the action time threshold of the protection device can usually meet the requirements and will not become a limiting factor. Therefore, in such cases, the focus of research is more 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 clearance, and also represents its maximum margin for withstanding disturbances.

[0223] During disturbance Power angle characteristic curve and There are two equilibrium intersections and , at this time the acceleration area should be the interval The curve area within the deceleration area should be the interval The area of ​​the curve inside, here It represents the maximum power angle that the rotor can reach after the disturbance. Its physical meaning is: after the disturbance, the electromagnetic power is less than , the rotor deviates from the steady-state power angle , after acceleration, it reaches the power angle ,Exceed The rear electromagnetic power is greater than , the rotor enters the deceleration process and reaches the maximum power angle After that, it no longer increases, but continues to decelerate and the power angle decreases until the oscillation decays and stabilizes at the equilibrium intersection. , or just critical deceleration stabilizes at the equilibrium intersection .like Greater than equilibrium intersection , it means that the system will continue to accelerate under this disturbance until it loses synchronization stability. At this time, it is necessary to increase the deceleration area by removing the fault or reducing the power shortage. In the interval Only by doing so can the synchronization stability of the system be guaranteed.

[0224] Similarly, when considering damping to calculate the acceleration and deceleration area, it is also necessary to use the triangle scaling approximation method. 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 Normally will not exceed the power angle by much , so when calculating the damping area, we only need to focus on the interval Internal area, negligible interval Internal area.

[0225] Correspondingly, the triangle The area calculation is modified as follows:

[0226] ; (61)

[0227] at this time Power angle Hegong Angle The angular frequency corresponding to the midpoint of is modified to:

[0228] ; (62)

[0229] The intermediate process derivation will not be repeated here, and the final equal area formula is modified to:

[0230] ; (63)

[0231] Combining formula (62) and formula (63) can obtain the maximum power angle .

[0232] Objective function

[0233] The objective function of the off-grid emergency control optimization decision model for the distribution system considering the flexible self-configuration partitioning of the island is to minimize the load loss and resource control amount, as shown in the following formula:

[0234] ; (64)

[0235] Where, 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 batteries Control cost, For synchronous generators Control cost, For virtual synchronization machines Control cost, To cut load The control cost, is the number of batteries, is the number of synchronous generators, is the number of virtual synchronous machines, is the amount of load shedding, For batteries The output power, For synchronous generators The output power, For virtual synchronization machines The output power, To cut load output power.

[0236] The weighting factor reflects the priority of different resources in emergency control. The smaller the weighting factor, the smaller the increment of the objective function, and the higher the control priority. Generally speaking, the control cost of power-side resources such as energy storage, SG, and VSG is much lower than the control cost of load shedding. During emergency load shedding, different control costs are set for primary, secondary, and tertiary loads to ensure that non-critical loads are removed first. In actual applications, the weighting factors and control costs of different control resources can be set based on safety requirements.

[0237] After comprehensively considering the steady-state constraints and transient constraints, the complete optimization decision model structure is as follows: Figure 4 、 Figure 5 shown.

[0238] In summary, the established off-grid emergency control optimization decision model for the distribution system considering the flexible self-configuration partitioning of the island is as follows:

[0239] . (65)

[0240] S3. Based on the improved discrete particle swarm algorithm to solve the optimization decision model, the global search capability is improved by introducing the crossover and mutation operation of the genetic algorithm to obtain the optimal island partitioning scheme and emergency control strategy.

[0241] Islanding decisions involve a large number of 01 variables related to line switching states. Traditional continuous optimization algorithms often face combinatorial explosion, local optimality traps, and low convergence efficiency due to the discretization of the search space, making them difficult to solve efficiently. Heuristic optimization algorithms have demonstrated excellent performance in solving optimization decision problems involving a large number of 01 variables.

[0242] The particle swarm optimization (PSO) algorithm draws inspiration from the information-sharing and collaborative collaboration of birds when foraging. Its design goal is to solve complex global optimization problems. Since its introduction, the PSO algorithm has been widely used in fields such as function optimization, neural network training, and data mining due to its simplicity, ease of implementation, and high efficiency. However, traditional PSO algorithms primarily optimize in continuous spaces and have limited effectiveness in discrete spaces (such as optimization problems with a large number of 01 variables). Therefore, the discrete particle swarm optimization (DPSO) algorithm was developed. Its basic idea is to discretize the position and velocity concepts used in the continuous PSO algorithm. DPSO has demonstrated unique advantages in solving optimization decision problems with a large number of 01 variables, making it an effective tool for solving discrete optimization problems.

[0243] 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 transfer probability or direction of the solution in the discrete space. Different particles give different topological structures. The mixed integer linear programming problem is solved according to the determined topological structure to obtain the objective function value of the optimization decision model, and the fitness value of the particle is returned. The DPSO algorithm will guide the particles to continuously move towards a better solution through information sharing and collaboration between particles, and finally find the optimal solution to the objective function. The island partition result in the optimal emergency control solution is the topological structure corresponding to the optimal particle.

[0244] The particle velocity and position update formula of DPSO is as follows:

[0245] ; (66)

[0246] ; (67)

[0247] Where, and Represent particles i In the t The velocity and position in the iteration. is the inertia weight, which controls the influence of the particle's historical motion on its current velocity. and is the acceleration constant, which adjusts the particles to their optimal positions and the global optimal position The tendency of the larger The value helps particles fully explore individual experiences, while larger The value enhances the information sharing ability between particles. and The value of will be set close to achieve a balance between individual exploration and group collaboration. and It is a random number in the interval [0,1], used to introduce randomness and enhance search capabilities. Sigmoid The function maps the velocity to the interval [0,1]. rand The function generates uniformly distributed random numbers in the interval [0,1], allowing particles to jump in the solution space in a probabilistic manner.

[0248] The inertia weight controls the influence of the particle's historical motion on its current velocity. The value helps particles to explore a wide range in the solution space, while a lower The value tends to be a fine search. In practical applications, A dynamic adjustment strategy is usually adopted to linearly reduce the inertia weight. The formula is:

[0249] ; (68)

[0250] Where, It is t The inertia weight in the iteration, and are the maximum and minimum values ​​of the inertia weight, is the maximum number of iterations.

[0251] DPSO may fall into a local optimal solution when solving. By introducing the crossover and mutation operations of the genetic algorithm, the diversity of the population can be increased and the probability of particles converging to the global optimal solution can be improved. The basic steps are:

[0252] (1) Randomly generate the initial positions and velocities of a group of particles, where the initial positions are represented by 01 variables and the initial velocities are randomly generated between [-1, 1].

[0253] (2) Calculate the fitness value of each particle according to the objective function, and record the individual optimal solution and the global optimal solution.

[0254] (3) Use the velocity update formula and position update formula to recalculate the velocity and position of particles in the population. Sigmoid Function that maps particle positions to 0 or 1.

[0255] (4) Calculate the fitness value of the newly generated particle, compare it with the previous individual optimal solution, and update the individual optimal solution and the group optimal solution.

[0256] (5) A roulette wheel strategy is used to select a certain number of particles from the particle swarm to form a sub-population. Then, two individuals are randomly selected from the sub-population for crossover operation to obtain a new individual and calculate its fitness. If the fitness of the new individual exceeds that of the original individual, it is replaced.

[0257] (6) In the updated particle swarm, some particles are mutated according to the pre-set mutation probability to generate new individuals and calculate their fitness. If the fitness of the new individual exceeds that of the original individual, the new individual is used to replace the old one.

[0258] (7) Check whether the termination condition is met, that is, the maximum number of iterations 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.

[0259] S4. Perform active islanding according to the optimal islanding plan, coordinate and control power output and cut off non-critical loads to ensure transient stability of the island and power supply to important loads.

[0260] Example

[0261] In order to better illustrate the control process of the present invention, a specific example test is given. The example system is modified based on the standard 33-node power distribution system. Figure 6 As shown, synchronous generators with a maximum power of 600kW are added at nodes 25 and 30, virtual synchronous machines with a maximum power of 450kW are added at nodes 14 and 21, photovoltaic power sources with a maximum power of 200kW are added at nodes 5 and 11, and energy storage power sources with a maximum power of 100kW are added at nodes 8 and 24. The power sources set up have different control parameters.

[0262] The 33-node distribution system originally had a total active load of 3,715 kW. After the transformation, the total installed capacity of distributed power sources reached 2,700 kW, with local self-balancing capabilities. The transformed system also coordinated the configuration of various types of power sources and energy storage devices: photovoltaic power sources provide stable power output but cannot flexibly respond to the dynamic needs of the system. They represent a type of resource that is uncontrollable or difficult to quickly adjust output, and are mainly used to provide constant power support; energy storage power sources (grid-following power sources) adopt a PQ control strategy, which can quickly adjust active power and reactive power output according to dispatch instructions. It is mainly used to quickly respond to system power shortages and is an important source of distribution system flexibility; synchronous generators and virtual synchronous machines (grid-forming power sources) mainly realize the system's inertia response, frequency regulation and voltage support.

[0263] The fault scenario is set at time t = 0, when the distribution system's connection point with the upper power grid (node ​​1) is suddenly disconnected, resulting in a significant power shortage across the entire system. To simulate actual conditions and taking into account the time delays in communication, computation, and execution in a real system, it is assumed that each control resource has a 0.1s delay in output adjustment or load shedding after fault detection. The transient process lasts for 10s, with a discrete step length of 0.02s to ensure accurate characterization of transient dynamic characteristics.

[0264] In solving the optimization decision model, the discrete particle swarm algorithm sets the number of particles to 100, with each particle representing 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, decisions are made on the on-off of the remaining 31 lines except the line from node 1 to node 2.

[0265] The core task of optimization decision-making is to comprehensively consider the system topology, the load demands of each node, the output of distributed resources, and transient processes, and implement active islanding and frequency emergency control. Active islanding divides the original system into several independently operating small islands by rationally adjusting the on-off status of lines. This ensures that the power supply and demand within each island is as balanced as possible, while also minimizing the impact of power shortages on the overall system. Frequency emergency control utilizes the responsiveness of various resources to adjust output and appropriately shed loads during transient processes, thereby preventing excessive frequency deviations and ensuring system stability.

[0266] Analysis of results of flexible self-configuration partitioning of isolated islands

[0267] The iterative result of the objective function obtained by optimizing the decision is as follows Figure 7 As shown in Figure 2, as the number of iterations increases, the objective function value shows a decreasing trend, which indicates that the optimization algorithm is gradually exploring a better solution space and making the optimization decision converge towards a better result.

[0268] The results of the optimization decision show that after being disconnected from the upper power grid, the system needs to form two independently operated islands to maintain local power supply capabilities. The respective topologies are as follows: Figure 8 As shown in the figure, the decision disconnects nodes 2 and 3, forming Small Island 1, which includes nodes 2, 19, 20, 21, and 22. This island is powered by a virtual synchronous generator as the primary power source. This generator has a certain level of inertia and frequency modulation capabilities, maintaining voltage and frequency stability and ensuring stable operation. Large Island 2 encompasses the remaining nodes after disconnecting nodes 14 and 15, encompassing most resources and critical loads. Nodes 15, 16, 17, and 18 are not included in any island because their loads are less important and will all be de-energized.

[0269] The total load shedding situation of the system is as follows: Figure 9 As shown, the total system load shedding was 1.31 MW. The figure shows that primary loads remained completely unshed, fully ensuring their power supply needs. Secondary loads experienced a small amount of shedding, amounting to 0.210 MW. This indicates that the optimization model, while ensuring power supply for primary loads, moderately adjusted less critical loads. This partial shedding may be due to limited resources or system operating conditions, but the small amount of shedding indicates that secondary loads were still highly guaranteed, minimizing the impact on their normal operation. Tertiary loads experienced significant shedding. Tertiary loads are non-critical or interruptible. Therefore, given resource constraints, the optimization model opted for significant shedding to ensure power supply stability for higher-priority loads. This decision demonstrates that, after weighing factors such as load importance and resource allocation, the optimization model prioritized power supply for critical loads while reducing unnecessary loads.

[0270] A corresponding 33-node time-domain simulation model was built on the CloudPSS simulation platform. Based on the decision results, the corresponding line disconnection, load shedding, and power output adjustment were set. The frequency curve, voltage curve, and generator output curve of the system transient process were obtained by simulation. Figure 10 shown.

[0271] As can be seen from Figure a), the lowest points of the system frequencies of Island 1 and Island 2 did not fall below 49.8 Hz, indicating that the emergency control strategy worked. After transient adjustment, Island 1 operated at 49.95 Hz and Island 2 operated at 49.98 Hz, indicating that the island system can still effectively maintain frequency within a safe range after being disconnected from the main grid, and the internal supply and demand are basically balanced.

[0272] Figure b) shows the voltages of the two island systems. The baseline voltage of the 33-node distribution system is 12.66 kV. After disconnection from the grid and forming islands, the voltage of island 1 remains at 12.24 kV, and the voltage of island 2 remains at 12.91 kV.

[0273] In Figure c), the initial output of the synchronous generators and virtual synchronous machines within the two islands reserves a certain amount of frequency regulation and is less than the maximum power. The transient output of the system's dynamic response exhibits a transient overshoot during the initial stages of regulation. For the power electronics interface power supply, the maximum output during transient regulation is limited to 1.5 times the maximum power, avoiding the risk of equipment failure due to overcurrent protection or burnout. For synchronous generators, the maximum output limit can be relaxed to within 2 times the maximum power. After transient regulation, the output of each power supply is gradually adjusted to the required steady-state value. Under steady-state conditions, the output of each power supply will not exceed its maximum power, ensuring a balanced supply and demand within the island.

[0274] Because island 1 lacks an energy storage unit, Figure d) shows the output curves of the two energy storage units in island 2. As can be seen, the energy storage units begin adjusting their output after a 0.1s delay. Thanks to the PQ control employed, the output of the energy storage units quickly adjusts to a maximum of 100kW.

[0275] Analysis of passive island division results

[0276] In contrast, if the network is not actively divided into two isolated islands, but only the lines between node 1 and node 2 are passively disconnected, the remaining nodes will all form a network as shown in the following example: Figure 11 In the case of a large isolated island as shown in the figure, the total load shedding of the system is as follows: Figure 12 As shown, the transient process curve is as follows Figure 13 shown.

[0277] In this case, the total load shedding capacity of the system is 1.38MW. Figure 12 As can be seen from the figure, the primary load is fully powered, while the secondary load is removed by 0.221 MW, an increase from the 0.210 MW removed when actively dividing the two islands. This indicates that a passively formed large island requires more secondary load removal to meet various constraints. This means that while the power supply needs of the primary load can be guaranteed when a large island is passively formed, the ability to guarantee the power supply needs of the secondary load is relatively weak.

[0278] Similarly, in the CloudPSS time-domain simulation model, appropriate controls were set based on the decision-making results. The simulation results show that during transient conditions, when the system passively forms a large island, the system frequency remains within a safe range, not falling below 49.8 Hz. The system voltage is also safe and stable, and the instantaneous maximum output of each power source is also constrained, indicating that the power supply equipment is safe in this situation. Whether actively dividing the two islands or passively forming a large island, the calculated maximum power angle does not exceed the set safety threshold, indicating that the power shortage disturbance caused by the grid disconnection will not cause the system to temporarily lose synchronization.

[0279] However, the calculation results of the limit removal time after the formation of the island show that the limit removal time of the passively formed large island is 0.035 seconds, which fails to meet the set limit removal time constraint of greater than 0.1 seconds. This shows that the passively formed large island has a higher risk of transient loss of synchronization when subjected to large disturbances. In contrast, when the two islands are actively divided, Island 1 has only one grid-forming power source, so there is no problem of transient loss of synchronization between power sources; and the limit removal time of Island 2 is calculated to be 0.115 seconds, which meets the set limit removal time constraint of greater than 0.1 seconds. This result shows that when the two islands are actively divided, when the island faces a large disturbance, various protection measures have enough time to act, thereby reducing the risk of transient loss of synchronization.

[0280] Therefore, the off-grid emergency control method for the distribution system considering the flexible self-configuration division of the island as described in the present invention is adopted, and the optimization model that comprehensively considers the transient process and steady-state operation constraints can actively decide the island division area, and coordinate multiple resources to jointly execute emergency control in the island switching, minimize load losses, give priority to the power supply of important loads, and avoid unreasonable island division of the distribution system leading to transient instability of the power supply, system frequency exceeding the limit, and causing large-scale power outages.

[0281] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for off-grid emergency control of a power distribution system considering flexible self-configuration partitioning of isolated islands, characterized in that: The following steps are involved: S1. Establish a frequency response model for a multi-resource distribution system, modeling the frequency response of synchronous generators, virtual synchronous generators, energy storage power sources, photovoltaic power sources, and load shedding; perform discrete differentiation on the frequency response model, and constrain the transient state of the system frequency during emergency frequency control based on the frequency response model after discrete differentiation; S2. With minimizing load loss and resource control as the objective function, an optimization decision model is constructed that integrates steady-state constraints and transient constraints. Transient constraints include frequency minimum point constraint, frequency change rate constraint, power output transient constraint, maximum power angle constraint, and extreme removal time constraint. S3. Based on the improved discrete particle swarm optimization algorithm, the optimization decision model is solved and the global search capability is improved by introducing the crossover and mutation operation of the genetic algorithm to obtain the optimal island partitioning scheme and emergency control strategy; S4. Execute active islanding according to the optimal islanding scheme, coordinate and control power output, and cut off non-critical loads to ensure transient stability of the island and power supply to important loads; In S1, the frequency response model of the multi-resource distribution system after aggregation and simplification of similar resources is: ； Where, is the system inertia center frequency deviation, Indicates the power change of the system, is the inertia time constant of the entire system, is the damping coefficient of the entire system, For time; The frequency response differentiation model of the multi-resource distribution system after discrete differentiation is: ； Where, For the system The inertial center frequency deviation at time , For the system The inertial center frequency deviation at time , represents the difference time step; ； Where, Indicates the overall system capacity and control time constant, 、 and Indicates the The inertia time constant, damping coefficient and capacity of the synchronous generator, 、 and Indicates the Inertia time constant, damping coefficient and capacity of the virtual synchronous machine; is the number of synchronous generators, is the number of virtual synchronous machines, is the index of the synchronous generator, The index of the virtual synchronization machine.

2. The off-grid emergency control method for a power distribution system considering flexible self-configuration partitioning of isolated islands according to claim 1, characterized in that: In S1, the synchronous generator and virtual synchronous machine include inertial response and primary frequency modulation modeling, and the frequency response model of the inertial response is: ； Where, 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 through the differential discretization method. The differential frequency response model is: ； Where, express The frequency deviation value change at the moment, express The frequency deviation value change at the moment, represents the difference time step, express Power change at each moment; Primary frequency regulation is the process of automatically adjusting the active power output of synchronous generators and virtual synchronous machines based on frequency deviation. Its control strategy is based on the droop characteristic of the speed regulator. After considering the control time delay through the first-order inertia link, the droop characteristic of the speed regulator is expressed as: ； Where, is the output power, is the power reference value, is the droop coefficient of the speed regulator, is the Laplace operator, To control the time constant; The discrete difference equation of output power is: ； Where, express The output power at the moment, express Output power at any moment.

3. The off-grid emergency control method for a power distribution system considering flexible self-configuration of islands according to claim 2, characterized in that: In S1, after the energy storage power supply considers the outer loop PI control characteristics and control time delay, the discrete difference equation of the energy storage power supply output power is: ； Where, express The battery output power at the moment, express The battery output power at the moment, express PI control power at the moment, express PI control power at the moment, express The PI control error at time t, express The PI control error at time t, Indicates the power reference value, and are the proportional and integral gain coefficients of PI control respectively, represents the difference time step, represents the control time constant, is the index variable.

4. The off-grid emergency control method for a power distribution system considering flexible island self-configuration partitioning according to claim 3, characterized in that: In S1, the actual photovoltaic output of the photovoltaic power source for: ； Where, is the maximum photovoltaic output value, is the uncertainty coefficient.

5. The off-grid emergency control method for a power distribution system considering flexible self-configuration of islands according to claim 4, characterized in that: In S2, the steady-state constraints include linear power flow constraints, power output constraints, node voltage constraints, line capacity constraints, and load shedding constraints.

6. The off-grid emergency control method for a power distribution system considering flexible self-configuration of islands according to claim 5, characterized in that: In S2, the frequency minimum point constraint and the frequency change rate constraint are: ； Where, Indicates the minimum safe value of the system frequency, and Represent the minimum and maximum values ​​of the frequency change rate, Representation System The center frequency of inertia at time , Representation System The inertial center frequency at the moment, the island System frequency Each step in the transient process Frequency transient constraints must be met at all times.

7. The off-grid emergency control method for a power distribution system considering flexible self-configuration partitioning of isolated islands according to claim 6, characterized in that: In S2, the transient power output constraint is: ； Where, and Respectively represent the maximum rate of power output climbing up and down, It is the multiple of the maximum instantaneous power that the power supply can withstand exceeding the maximum power limit. Indicates the maximum power of the power supply. express The instantaneous value of power supply at the moment, express Instantaneous power value at any moment, island Internal power output Each step in the transient process Power transient constraints must be met at all times.

8. The off-grid emergency control method for a power distribution system considering flexible self-configuration of islands according to claim 7, characterized in that: In the process of forming an island in S2, the disturbance caused by the power shortage makes the power angle characteristic curve When there is an intersection, the maximum power angle constraint does not exceed , ； Where, It's an isolated island The maximum power angle of the system during transient state under disturbance, A collection of isolated islands, To damp unbalanced power; When the disturbance caused by power shortage makes the power angle characteristic curve When there is no intersection, ； It's an isolated island The limit cut-off time of the system during transient process under disturbance.

9. The off-grid emergency control method for a power distribution system considering flexible self-configuration partitioning of isolated islands according to claim 8, characterized in that: In S2, the objective function is: ； Where, 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 batteries Control cost, For synchronous generators Control cost, For virtual synchronization machines Control cost, To cut load The control cost, is the number of batteries, is the number of synchronous generators, is the number of virtual synchronous machines, is the amount of load shedding, For batteries The output power, For synchronous generators The output power, For virtual synchronization machines The output power, To cut load output power.

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