Distribution network distributed photovoltaic plannable capacity interval evaluation method considering soft switching fault interference factors

Abstract

The invention discloses a power distribution network distributed photovoltaic plannable capacity interval evaluation method considering soft switching fault interference factors, and relates to the technical field of power distribution network planning and operation. According to the method, for an SOP structure integrating energy storage, an E-SOP model is established, and the uncertainty of unplanned off-network of the E-SOP model is described. And then, respectively depicting the most optimistic value and the most pessimistic value of the installable capacity through a deterministic model and a double-layer robust optimization model so as to form plannable capacity interval evaluation of the distributed PV. The deterministic model is a linear programming problem and can be directly solved by a solver; the double-layer robust optimization model is converted into a mixed integer linear programming problem through a KKT optimization condition so as to be solved. Compared with a traditional method, the method has the advantages that the applicability is higher, the dependence on the data quality and the uncertainty description accuracy degree is low, and a reliable evaluation result can be obtained.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning and operation technology, and in particular to a method for evaluating the planarable capacity range of distributed photovoltaic power in distribution networks that takes into account the interference factors of soft switching faults. Background Technology

[0002] To address climate change and promote a clean and low-carbon energy transition, the large-scale development and utilization of new energy sources such as distributed photovoltaic (PV) power in distribution networks has become an important trend. However, the high penetration rate of distributed PV also brings safety risks to traditional distribution networks, such as overvoltage and line overload. Therefore, accurately assessing the maximum capacity of distributed PV that the distribution network can accommodate (i.e., the planned capacity) is a crucial prerequisite for ensuring grid security and promoting the grid-friendly integration of new energy sources.

[0003] To enhance the capacity of distribution networks to accommodate distributed photovoltaic (PV) power, flexible distribution network (DP) technology has emerged. Among these technologies, smart soft switching (SOP) enables flexible adjustment of power flows across different feeders, while energy storage systems facilitate the spatiotemporal shift of electrical energy. Existing research has recognized the positive role of SOP and energy storage in improving the planarable capacity of distributed PV and has developed a series of evaluation methods. For example, the paper "Segmented Algorithm for Maximum Carrying Capacity of Multiple Distributed Sources Accessing Distribution Networks Considering Multiple Constraints" (Tan Xiao, Wang Zhuding, Li Qiang, et al.) proposes a segmented calculation method based on single-constraint and multi-constraint coordination using distributed PV capacity sensitivity indices; another example is "An Efficient Hybrid Particle Swarm and Gradient Descent Method for the Estimation of the Hosting Capacity of Photovoltaics by Distribution Networks" (Zulu E, Hara R, Kita H.), which proposes an efficient method for evaluating the planarable capacity of distributed PV power in distribution networks by combining particle swarm optimization and gradient descent algorithms. However, most of these methods are based on the assumption of continuously idealized operation of SOP and can only calculate a single, fixed maximum capacity value.

[0004] In reality, Standard Operating Procedures (SOPs), as complex power electronic devices, inherently carry the risk of unplanned outages due to faults or extreme conditions. Ignoring this uncertainty will lead to overly optimistic assessment results, and if some functions of the SOP fail, the power grid may face safety hazards. Furthermore, existing methods cannot provide a capacity range, failing to reflect the true range of system capacity under the influence of uncertainties. Therefore, there is an urgent need for a more realistic assessment method with richer results, which, considering the uncertainties of SOP operation, provides a planarable capacity range for power grid planning composed of both optimistic and pessimistic boundaries, thereby enhancing the practicality and robustness of the assessment results. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a method for assessing the planarable capacity range of distributed photovoltaic power generation in a distribution network that takes into account the interference factors of soft switching faults.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for evaluating the planarable capacity range of distributed photovoltaic power generation in a distribution network considering the interference factors of soft switching faults, comprising the following steps:

[0007] S1. Establish operational constraints for the power distribution network that include flexible power distribution equipment;

[0008] S2. Construct a planarable capacity interval assessment model, including a deterministic assessment model for determining the upper boundary of the planarable capacity interval, and an optimization model considering uncertainties for determining the lower boundary of the planarable capacity interval; wherein,

[0009] The deterministic evaluation model takes maximizing the capacity of distributed renewable energy access as the objective function and solves it under the constraints of the distribution network operation. The optimization model considering uncertainty takes into account the uncertainty of unplanned outages of the flexible distribution equipment and the timing uncertainty of distributed renewable energy output as factors, with the goal of minimizing the distributed renewable energy access capacity that the system can guarantee under uncertain conditions.

[0010] S3. Solve the deterministic evaluation model and the optimization model considering uncertainty to obtain the upper and lower boundary values ​​of the planarable capacity interval, thereby forming the planarable capacity interval.

[0011] Preferably, the flexible power distribution equipment is an intelligent soft switch E-SOP that integrates energy storage; the power distribution network operation constraints include at least one of the following: power flow equation constraints, branch current constraints, voltage deviation constraints, reactive power compensation equipment operation constraints, and reactive power regulation constraints of distributed new energy inverters.

[0012] More preferably, the distributed new energy source is distributed PV.

[0013] More preferably, the deterministic evaluation model includes an E-SOP operation model, a power flow equation model, a voltage and current constraint model, a reactive power compensation equipment model, and a photovoltaic reactive power regulation model, and the deterministic evaluation model takes the maximum distributed PV access capacity as the objective function.

[0014] More preferably, the optimization model considering uncertainty is a two-layer robust optimization model, which includes:

[0015] The outer model takes into account the impact of uncertainty factors on the planarable capacity of distributed PV through the E-SOP unplanned detachment uncertainty model and the distributed PV time series uncertainty model, thereby minimizing the planarable capacity of distributed PV.

[0016] The inner model maximizes the planarable capacity of distributed PV through flexible control methods in a flexible distribution network.

[0017] More preferably, the E-SOP unplanned churn uncertainty model is as follows:

[0018] (14);

[0019] (15);

[0020] (16);

[0021] (17);

[0022] In the formula, For off-grid state variables; This is the variable used to start the offline process; Maintenance time refers to the time required for an E-SOP to reconnect to the grid after being taken offline; For E-SOP The probability of a port being disconnected from the network unplanned; , They are respectively Time Port Active and reactive power flowing to E-SOP; and These are the upper and lower limits of the active power of E-SOP, respectively; and These are the upper and lower limits of the reactive power of E-SOP, respectively.

[0023] More preferably, the distributed PV time-series uncertainty model is:

[0024] (37);

[0025] In the formula, for The actual power value of the distributed PV at any given time; for The expected power of the distributed PV at any given time; and These represent the deviations between the expected power of distributed PV and the upper and lower boundaries of the power fluctuation range, respectively. and Let these represent the situations where the power fluctuation of distributed PV reaches the upper and lower boundaries, respectively;

[0026] (38);

[0027] (39);

[0028] In the formula, The scheduling period for distributed PVs; A robust budget is set to control the level of conservatism in the model.

[0029] More preferably, the two-layer robust optimization model is expressed as:

[0030] (40);

[0031] (42);

[0032] (43);

[0033] (44);

[0034] (45);

[0035] In the formula, and These are the decision variables for the two-level robust optimization model.

[0036] More preferably, the solution method for the two-layer robust optimization model includes: first, using the Karush-Kuhn-Tucker conditions to transform the inner model into KKT equations; then, transforming the two-layer robust optimization model into a mixed-integer linear programming problem and solving it.

[0037] More preferably, the process of transforming the inner model into KKT equations using Karush-Kuhn-Tucker conditions includes:

[0038] (46);

[0039] (47);

[0040] In the formula, In the objective function The coefficient matrix; , , and These are the coefficient matrices of inequality constraints and equality constraints related to the power distribution network, respectively. , , and These are the coefficient matrices of inequality constraints and equality constraints related to E-SOP, respectively. , , and These are the Lagrange multipliers corresponding to inequality constraints and equality constraints, respectively;

[0041] (48);

[0042] (49);

[0043] (50);

[0044] (51);

[0045] (52);

[0046] (53);

[0047] (54);

[0048] (55);

[0049] At this point, there is a nonlinear part in equation (52). Therefore, the Big M method is used to transform it into a linear complementary condition:

[0050] (56);

[0051] In the formula, It is a sufficiently large number; Let be a binary variable, which ensures that only one of the two expressions in the above formula always takes effect;

[0052] Similarly, equation (53) can be transformed into:

[0053] (57);

[0054] Therefore, the two-layer robust optimization model is equivalently transformed into the mixed-integer linear programming problem shown in equation (58), which can be directly solved using the Cplex solver:

[0055] (58)

[0056] Compared with existing technologies, this invention provides grid planners with unprecedented, comprehensive decision support by constructing a planarable capacity range defined by an upper boundary (most optimistic capacity) and a lower boundary (most pessimistic capacity). This range clearly demonstrates the potential fluctuation range of distributed renewable energy access capacity, enabling planners to better conduct risk assessments and formulate planning strategies, significantly improving the practicality of assessment results and the reliability of grid operation. The results of numerical examples demonstrate that the method of this invention has stronger applicability than traditional methods and is less dependent on data quality and the accuracy of uncertainty descriptions, thus obtaining reliable assessment results. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the framework structure of the evaluation method of the present invention;

[0058] Figure 2 This is a schematic diagram of the structure of an intelligent energy storage-soft switching device (E-SOP);

[0059] Figure 3 This is a diagram illustrating the offline state variables and the offline start variables.

[0060] Figure 4 This is a topology diagram of the IEEE 123 node distribution network.

[0061] Figure 5 A graph showing the active power curves for load and distributed PV;

[0062] Figure 6 The results of the planarable capacity range assessment and the box plot based on MCM;

[0063] Figure 7 The diagram shows the actual results of the planarable capacity of distributed PV under different E-SOP unplanned off-grid recovery times, as well as the planarable capacity range of the evaluation method in the examples and the numerical solution of the planarable capacity based on the traditional method.

[0064] Figure 8 This is a schematic diagram illustrating the impact of E-SOP on the planarable capacity range of distributed PV.

[0065] Figure 9 This diagram illustrates the impact of uncertainties on the planarable capacity of distributed PV. Detailed Implementation

[0066] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0067] like Figure 1 As shown in this embodiment, the method for assessing the planarable capacity range of distributed photovoltaic power grids, which considers the interference factors of soft switching faults, is based on two types of models: a deterministic assessment model and an optimization model that considers uncertainty (a two-layer robust optimization model). The main process steps are as follows:

[0068] S1. Establish operating constraints for the power distribution network that include flexible power distribution equipment.

[0069] The flexible power distribution equipment in this embodiment uses a SOP (SOP integrated with energy storage, E-SOP) structure. Compared to the traditional back-to-back SOP structure, E-SOP can better improve the distribution network's capacity to accommodate distributed PV systems, such as... Figure 2 In the E-SOP structure shown, the two ports of the E-SOP are connected to different nodes of the distribution network, and a battery energy storage system is installed on the DC bus. The E-SOP can be considered to consist of two parts: the SOP and the battery energy storage system. Figure 2 The dashed box shows the SOP main circuit topology, which consists of two voltage source converters based on IGBTs and generating voltage waveforms using pulse width modulation (PWM) technology, and two sets of inductors. Based on the E-SOP structure, a system is established containing... E-SOP model with multiple ports:

[0070] (1);

[0071] (2);

[0072] (3);

[0073] (4);

[0074] (5);

[0075] (6);

[0076] (7);

[0077] (8);

[0078] (9);

[0079] In the formula, and They are respectively The charging and discharging power of the energy storage battery at all times; and These are the maximum values ​​for the charging and discharging power of the energy storage battery, respectively. for The battery's charge level at all times; , They are respectively The lower and upper limits of the energy storage battery capacity at all times; and They are respectively Time Port Active and reactive power flowing to E-SOP; and These are the limits for active and reactive power that are allowed to flow through the E-SOP port, respectively. For the first The capacity of the converter at the port.

[0080] For the nonlinear constraint of equation (9), this embodiment uses the polygon approximation linearization method to transform it into a linear model, as follows:

[0081] (10);

[0082] (11);

[0083] (12);

[0084] (13);

[0085] It should be noted that the E-SOP model constructed in this step mainly focuses on the lower boundary of the planarable capacity range and does not consider the impact of E-SOP power loss. This is because E-SOP power loss will consume distributed PV generation, which will undoubtedly increase the capacity available for distributed PV. When calculating the lower boundary of the planarable capacity range, the calculation result should be the most pessimistic value. Therefore, E-SOP power loss is not considered when evaluating the lower boundary of the planarable capacity range. When evaluating the upper boundary, the E-SOP power loss model will be introduced.

[0086] The constraints on the operation of the distribution network include the power flow equation constraints, branch current constraints, voltage deviation constraints, reactive power compensation equipment operation constraints, and reactive power regulation constraints of distributed PV inverters.

[0087] The models for each constraint are as follows:

[0088] First, the power flow equations are used, employing the commonly used Distflow model:

[0089] (18);

[0090] (19);

[0091] (20);

[0092] (twenty one);

[0093] In the formula, It is the set of nodes in the distribution network; and They are nodes The active and reactive power are defined with the direction of outflow from the node as the positive direction. and They are nodes Active and reactive power of distributed PV; and They are nodes Flow to Node Active power and reactive power; and Branch roads Resistance and reactance; For nodes The square of the voltage amplitude; branch road The square of the current amplitude.

[0094] Since equation (21) contains a nonlinear part, the Distflow model is still a nonconvex model and cannot obtain the optimal solution. Therefore, this embodiment uses a first-order Taylor series expansion method to further linearize the nonlinear part of equation (21):

[0095] (twenty two);

[0096] (twenty three);

[0097] In the formula, and The and are set respectively in this embodiment and Related independent variable functions; and They are respectively and The initial value; and New variables introduced for ease of writing.

[0098] Equations (22) and (23) can transform equation (21) into a constraint without nonlinear components:

[0099] (twenty four).

[0100] Then there are branch current constraints:

[0101] (25);

[0102] In the formula, for Time Node and nodes The current values ​​between; This represents the maximum allowable current for a branch circuit.

[0103] Voltage deviation constraint:

[0104] (26);

[0105] In the formula, for Time Node The voltage amplitude; , These represent the upper and lower limits of the voltage amplitude allowed at the node, respectively.

[0106] Next are the operating constraints of the reactive power compensation equipment. The model of the Static Var Compensator (SVC) is represented as follows:

[0107] (27);

[0108] In the formula, , These are the minimum and maximum reactive power compensation power of the SVC, respectively. for Time Node The reactive power compensation of the SVC connected to the location.

[0109] Finally, there is the reactive power regulation constraint of distributed PV inverters. Distributed PV in the distribution network can use inverters to perform reactive power regulation. Its reactive power regulation capability is related to the inverter capacity, and the model can be expressed as:

[0110] (28);

[0111] (29);

[0112] (30);

[0113] In the formula, , These are the maximum and minimum capacities for distributed PV grid connection, respectively. For nodes Capacity of distributed PVs; , They are respectively Time Node Active and reactive power of distributed PV; For nodes Inverter capacity; and They are nodes The upper and lower limits of the power factor angle of a distributed PV.

[0114] For the nonlinear constraint of equation (29), the polygon approximation linearization method is used to transform it into a linear model, as follows:

[0115] (31);

[0116] (32);

[0117] (33);

[0118] (34).

[0119] S2. Construct a planarable capacity range assessment model, including a deterministic assessment model for determining the upper boundary of the planarable capacity range, and an optimization model considering uncertainties for determining the lower boundary of the planarable capacity range.

[0120] In this step, the deterministic evaluation model is a single-layer model, which solves the problem of maximizing distributed PV access capacity without violating operational constraints. This model serves as the upper boundary of the planarable capacity range. The deterministic evaluation model includes the aforementioned E-SOP operation model, power flow equation model, voltage and current constraint model, reactive power compensation equipment model, and photovoltaic reactive power regulation model, ultimately expressed as:

[0121] (35);

[0122] (36);

[0123] In the formula, This represents the set of nodes that a distributed PV may connect to. For the first The capacity of each node connected to the distributed PV.

[0124] In this step, the optimization model considering uncertainty incorporates the uncertainty of unplanned E-SOP outages and the timing uncertainty of distributed PV output as factors, aiming to minimize the distributed PV access capacity that the system can guarantee under uncertain conditions. The uncertainty of unplanned E-SOP outages can be described using the unplanned E-SOP disconnection uncertainty model:

[0125] (14);

[0126] (15);

[0127] (16);

[0128] (17);

[0129] In the formula, For off-grid state variables; This is the variable used to start the offline process; Maintenance time refers to the time required for an E-SOP to reconnect to the grid after being taken offline; For E-SOP The probability of a port being disconnected from the network unplanned; , They are respectively Time Port Active and reactive power flowing to E-SOP; and These are the upper and lower limits of the active power of E-SOP, respectively; and These are the upper and lower limits of the reactive power of E-SOP, respectively.

[0130] Equation (14) represents the off-grid status when the E-SOP fails. To facilitate characterization of the E-SOP's status, a binary variable is introduced. and . Figure 3 In order to be in After an unplanned disconnection occurs during E-SOP and The relationship between them Indicates the time it takes for the network to recover after being disconnected. This represents the time when the E-SOP begins to disconnect from the network. Its value is 1 when the E-SOP begins to disconnect, and 0 at other times. Figure 3 As shown . This indicates the E-SOP's grid-connected / off-grid status. Its value is 1 when the E-SOP is off-grid and 0 when it is grid-connected. This is because the E-SOP needs maintenance time after being off-grid. It can only be reconnected to the grid after that, so Moment Will be arrive All of the moments Calculation, such as Figure 3 As shown Equation (15) stipulates that any port of an E-SOP can experience at most one unplanned disconnection per day. Equation (16), based on Claude Shannon's information theory, uses disconnection probability to characterize the number of times an E-SOP disconnects, where... Uncertainty budgets set by humans.

[0131] The temporal uncertainty of distributed PV output can be understood as the random variation of distributed PV output within a certain range. This randomness is caused by numerous factors, such as changes in weather conditions (cloud cover, temperature, humidity), seasonal variations, different times of day (sunrise and sunset), and the performance degradation of the photovoltaic system itself. Therefore, to characterize the temporal uncertainty of distributed PV output, this embodiment introduces... and Let represent the situations where the distributed PV power fluctuation reaches the upper and lower boundaries, respectively. The resulting distributed PV time-series uncertainty model is shown in equation (37). (or When ) is 1, the power of distributed PV reaches the upper boundary (or lower boundary).

[0132] (37);

[0133] In the formula, for The actual power value of the distributed PV at any given time; for The expected power of the distributed PV at any given time; and These represent the deviations between the expected power of distributed PV and the upper and lower boundaries of the power fluctuation range.

[0134] For the time-series stochastic output of distributed PV, an uncertainty set consisting of equations (37) to (39) is established. Equation (38) specifies... and They cannot both be 1. Equation (39) specifies that during the scheduling cycle... The number of fluctuations in the internally distributed PV cannot exceed the robust budget. .

[0135] (38);

[0136] (39);

[0137] In the formula, The scheduling period for distributed PVs; The robust budget set for this paper is used to control the conservatism of the model.

[0138] After understanding the uncertainties of unplanned outages of E-SOPs and the timing uncertainties of distributed PV output, the planarable capacity of distributed PVs can be calculated using an optimization model that considers these uncertainties. In this embodiment, the optimization model considering uncertainties is a two-layer robust optimization model, which includes an outer model and an inner model. Specifically:

[0139] The outer model primarily considers the impact of uncertainties on the planarable capacity of distributed PV through the E-SOP unplanned off-grid uncertainty model and the distributed PV time-series uncertainty model, aiming to minimize the planarable capacity of distributed PV. The inner model, on the other hand, maximizes the planarable capacity of distributed PV through flexible control measures in the flexible distribution network (such as the power flow spatiotemporal adjustment and reactive power compensation actions of E-SOP). This two-layer robust optimization model is expressed as follows:

[0140] (40);

[0141] (42);

[0142] (43);

[0143] (44);

[0144] (45);

[0145] In the formula, and These are the decision variables for the two-level robust optimization model.

[0146] S3. Solve the deterministic evaluation model and the optimization model considering uncertainty to obtain the upper and lower boundary values ​​of the planarable capacity interval, thus forming the planarable capacity interval. Among them, the deterministic evaluation model of the upper boundary is a linear programming problem, so it can be solved directly using the Cplex solver. The lower boundary is a two-layer robust optimization model, which is a two-layer model and cannot be solved directly using a solver. Therefore, in this embodiment, the inner layer model in equation (40) is transformed into a KKT equation using the Karush-Kuhn-Tucker (KKT) condition. The inner layer problem of the two-layer robust optimization model can be written in the following compact form:

[0147] (46);

[0148] (47);

[0149] In the formula, In the objective function The coefficient matrix; , , and These are the coefficient matrices of inequality constraints and equality constraints related to the power distribution network, corresponding to equations (18)-(34); , , and These are the coefficient matrices of the inequality constraints and equality constraints related to E-SOP, respectively, corresponding to equations (1)-(13); , , and These are the Lagrange multipliers corresponding to inequality constraints and equality constraints, respectively.

[0150] Using the KKT conditions, the inner-layer primal problem of the two-layer robust optimization model is transformed into KKT equations, as follows:

[0151] (48);

[0152] (49);

[0153] (50);

[0154] (51);

[0155] (52);

[0156] (53);

[0157] (54);

[0158] (55);

[0159] At this point, there is a nonlinear part in equation (52). Therefore, the Big M method is used to transform it into a linear complementary condition, as follows:

[0160] (56);

[0161] In the formula, It is a sufficiently large number; Let be a binary variable, which ensures that only one of the two expressions in the above equation always takes effect.

[0162] Similarly, equation (53) can be transformed into:

[0163] (57);

[0164] Therefore, the two-layer robust optimization model is equivalently transformed into the mixed integer linear programming problem shown in equation (58), which can be solved directly using the Cplex solver.

[0165] (58)

[0166] Simulation test

[0167] The effectiveness of the evaluation method proposed in the above embodiments was verified using the IEEE 123-node flexible power distribution system.

[0168] The topology of the IEEE 123-node power distribution system is as follows: Figure 4 As shown, the line parameters and loads are based on existing technology. The base voltage is 4.16kV, and the peak loads are 4.49MW and 1.92Mvar. The node voltage safety range is 0.93pu-1.07pu. The transformer capacity is 10MVA. The flexible interconnection of E-SOPs transforms the original IEEE 123 node distribution system into a flexible distribution system. The AC / DC converter ports of E-SOPs are connected to nodes 2, 3, 44, and 49, respectively, each with a rated capacity of 1MVA. A 0.5MW / 2MWh energy storage battery is connected to the DC bus of E-SOPs. The basic example assumes a recovery time of 10 hours for the E-SOP AC / DC converter ports to return to normal operation after an unplanned off-grid event. The time-series curves for load and photovoltaics are shown below. Figure 5 The distribution network currently has 3MW of distributed photovoltaic (PV) installed, located at nodes 67, 96, and 111, with each node having a PV installed capacity of 1MW. Using the evaluation method proposed in the above embodiment, the maximum allowable PV capacity for candidate nodes 44, 49, 59, and 73 is evaluated, i.e., the planarable capacity of the distributed PV for the system is calculated.

[0169] The effectiveness and accuracy of the proposed evaluation method were verified using a randomized evaluation method based on the Monte Carlo method (MCM). If the planned capacity range result obtained by this method can cover the calculation result of the randomized evaluation method, the planned capacity range calculation result is considered to be valid. The verification process is as follows: First, 300 sets of uncertainties are randomly sampled from the uncertain sets of PV time-series output and E-SOP unplanned off-grid uncertainties using MCM; then, based on the known uncertainties, the planned capacity of distributed photovoltaic is calculated using equations (35)-(36), and a planned capacity value point can be calculated for each set of uncertainties; finally, a box plot is used to describe the planned capacity value point of distributed PV, and it is compared with the planned capacity range result obtained by the method in this paper. The comparison between the planned capacity range evaluation results and the MCM box plot under different E-SOP converter port capacities is shown in the figure. Figure 6 As shown.

[0170] Depend on Figure 6 As can be seen, the upper and lower boundaries of the planarable capacity range increase from 7.93-10.89MW to 9.32-11.34MW as the capacity of each port of E-SOP increases, while the range size (i.e. the difference between the upper and lower boundaries) decreases from 2.96MW to 2.02MW. Specific data are shown in Table 1.

[0171] Table 1. Upper and lower bounds of the planarable capacity interval and the size of the interval.

[0172] Port capacity 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Upper Realm 10.89 10.91 10.92 10.94 10.96 10.98 11.04 11.07 11.20 11.34 The Lower World 7.93 7.95 8.01 8.15 8.35 8.55 8.75 8.90 9.11 9.32 Interval size 2.96 2.96 2.91 2.79 2.61 2.43 2.29 2.17 2.09 2.02

[0173] Figure 6 Table 1 illustrates how the capacity of the E-SOP port affects the upper and lower boundaries (i.e., the size of the interval) and their difference (i.e., the range) of the planarable capacity interval. The variation in the size and range of the planarable capacity interval is attributed to the temporal and spatial flexibility of the E-SOP. The temporal and spatial flexibility of the E-SOP can improve system power flow distribution and alleviate node overvoltage. Therefore, the larger the capacity of the E-SOP port, the higher its temporal and spatial flexibility, and the better the effect of the E-SOP on improving the distributed PV absorption capacity. Furthermore, Figure 6 As can be seen, the planarable capacity range always encloses the MCM box plot, which verifies the effectiveness of the evaluation method provided in the above embodiments.

[0174] To verify the superiority of the evaluation method provided in the above embodiments, it was compared with the calculation results of the traditional method (HostingCapacity Assessment in Electrical Power Distribution Systems Using GeneticAlgorithm[J] , Hanjalić M, Melić E, Šarić M, et al. and Photovoltaic hostingcapacity of feeders with reactive power control and tap changers: 2017 IEEEPES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe)[C] , O. C, S. P, B. PB, et al.) under different E-SOP port off-grid recovery times. The traditional method uses the day with the highest PV output in a year to calculate the planarable capacity and does not consider the uncertainty of unplanned E-SOP off-grid. To verify the applicability of the calculation results from the two methods, 100 days of data from the photovoltaic and load dataset (An Efficient HybridParticle Swarm and Gradient Descent Method for the Estimation of the Hosting Capacity of Photovoltaics by Distribution Networks, Zulu E, Hara R, Kita H.) were randomly selected as test samples. Unplanned off-grid scenarios of E-SOPs were randomly included in each test sample. It was stipulated that unplanned off-grid disconnection of E-SOP ports could occur at most once per day, and at most two ports could simultaneously disconnect at any given time. The actual planarable capacity of distributed PV was calculated for the 100 test samples under different E-SOP unplanned off-grid recovery times, along with the planarable capacity interval (i.e., upper and lower bounds of the box type) based on the evaluation method provided in this embodiment and the numerical solution of the planarable capacity based on the traditional method. The results are as follows: Figure 7 As shown.

[0175] Depend on Figure 7It can be seen that as the E-SOP off-grid recovery time changes, both the actual results and the lower bound of the planarable capacity range change, but the results obtained by the traditional method remain constant. Regardless of the off-grid recovery time, the results obtained by the traditional method are always contained within the upper and lower bounds of the planarable capacity range. This is because the traditional method only calculates the planarable capacity of distributed PV on a typical day, while the evaluation method provided in this embodiment of the invention simultaneously considers both PV uncertainty and E-SOP unplanned off-grid uncertainty, resulting in a more comprehensive planarable capacity range that describes the fluctuation range of the planarable capacity of distributed PV. Furthermore, when the off-grid recovery time is greater than 3 hours, some actual results are smaller than the numerical solution of the traditional method, meaning that the traditional method yields overly optimistic calculation results. Following the traditional method to guide the planning and operation of distributed PV may lead to curtailment of newly installed distributed PV. In contrast, the absorption range of the evaluation method provided in this embodiment of the invention always encompasses the actual results. This indicates that the evaluation method provided in this embodiment of the invention can provide a more accurate basis for distribution network personnel to guide distributed PV access, and can avoid newly installed distributed PV failing to connect to the grid due to violations of safety constraints.

[0176] Based on the above analysis, it is evident that the capacity of each AC / DC converter port in the E-SOP has a significant impact on the planarable capacity of distributed PV. To further explore the impact of E-SOP port capacity and quantity on the planarable capacity range of the distribution network, the planarable capacity range was calculated by changing the E-SOP port capacity and quantity. The AC / DC converter capacity with E-SOPs was increased sequentially from 0.1MW to 0.8MW, and the number of ports was increased sequentially from 2 to 5. The calculation results for the upper bound of the planarable capacity range are shown below. Figure 8 (a), the calculation results for the upper bound are shown in [reference]. Figure 8 (b)

[0177] Depend on Figure 8 It is evident that the larger the E-SOP port capacity and the greater the number of ports, the higher the upper and lower bounds of the planarable capacity range. This is because increasing the number and capacity of E-SOPs enhances spatiotemporal flexibility, strengthens power flow control, and thus significantly improves the planarable capacity of distributed PV. However, the improvement in spatiotemporal flexibility of E-SOPs has a certain marginal effect. As the number and capacity of E-SOPs in the distribution network continue to increase, the effect on improving the planarable capacity range gradually weakens. Furthermore, when the E-SOP capacity is 1 p.u. and the number is 5, the upper bound of the planarable capacity range is increased by 5.69% compared to the upper bound of the planarable capacity range without E-SOPs, while the lower bound is increased by 18.82%.

[0178] To account for the impact of uncertainties, the influence of uncertainties on distributed PV power generation and carrying capacity is further analyzed. Four scenarios are set up: a) no uncertainty is considered; b) only the uncertainty of unplanned off-grid disconnection at E-SOP is considered; c) only the uncertainty of distributed PV is considered; d) both E-SOP and distributed PV uncertainties are considered. The calculation results of the planned capacity range of distributed PV for the four scenarios are shown below. Figure 9 (a) The calculation results of distributed PV power generation are shown in [reference]. Figure 9 (b)

[0179] from Figure 9 It can be seen that as the number of uncertainties considered increases, the lower bound of the planarable capacity range and its corresponding distributed PV power generation gradually decrease. In particular, when two uncertainties are considered simultaneously (i.e., case d), the carrying capacity and power generation decrease by 19.96% compared to when uncertainties are not considered. This is because the introduction of uncertainties makes it easier for the distribution network operating point to exceed the safe range. To avoid problems such as voltage overruns and backflow, the maximum allowable capacity of distributed PV under the most pessimistic scenario obtained by the planarable capacity range model will be relatively small. In addition, the upper bound of the planarable capacity range and its corresponding distributed PV power generation are equal in all four cases. This is because the upper bound model in the evaluation method provided in this embodiment is an optimistic model that does not consider uncertainties.

[0180] The above-described method for evaluating the planarable capacity range of distributed photovoltaic (PV) power grids, considering the interference factors of soft-switching faults, successfully assessed the maximum planarable capacity of flexible distribution networks for distributed PV. Furthermore, simulation tests yielded the following conclusions:

[0181] (1) The present invention can take into account the unplanned off-grid of E-SOP to obtain the fluctuation range of the maximum planarable capacity of distributed PV, which is more applicable than traditional methods; and it has a lower dependence on data quality and the accuracy of uncertainty description, and can obtain reliable evaluation results.

[0182] (2) E-SOP can alleviate voltage overrun and power flow overload problems, thereby improving the planarable capacity of distributed PV. The case study analysis on the IEEE 123 node distribution system shows that, compared with the absence of E-SOP, the upper limit of the planarable capacity range of distributed PV with E-SOP is increased by 5.69%, and the lower limit is increased by 18.82%.

[0183] To facilitate understanding by those skilled in the art of the improvements of this invention over the prior art, some of the accompanying drawings and descriptions have been simplified. The above embodiments are preferred implementations of this invention. In addition, this invention can be implemented in other ways. Any obvious substitutions without departing from the concept of this technical solution are within the protection scope of this invention.

Claims

1. A method for assessing the planarable capacity range of distributed photovoltaic power generation in a distribution network, considering the interference factors of soft switching faults, characterized in that: The power distribution network operation constraint condition containing the flexible power distribution equipment is established, and a deterministic evaluation model and an optimization model considering uncertainty are constructed, the deterministic evaluation model takes the maximum distributed new energy access capacity as an objective function, and the upper boundary value of the planned capacity interval is obtained under the power distribution network operation constraint condition, the optimization model considering uncertainty takes the non-planned outage uncertainty of the flexible power distribution equipment and the time sequence uncertainty of the distributed new energy output as factors, and takes the minimum distributed new energy access capacity that can be guaranteed by the system under the uncertainty environment as an objective, and the lower boundary value of the planned capacity interval is obtained, and then the planned capacity interval is obtained.

2. The method of claim 1, wherein the method further comprises: determining the maximum and minimum values of the distributed PV planning capacity interval based on the soft-switching fault interference factor. The flexible power distribution equipment is an intelligent soft switch E-SOP integrated with energy storage; the power distribution network operation constraint condition includes at least one of the power distribution system power flow equation constraint, the branch current constraint, the voltage deviation constraint, the reactive power compensation equipment operation constraint, and the distributed new energy inverter reactive power regulation constraint.

3. The method of claim 2, wherein the method further comprises: determining the maximum and minimum values of the soft-switching failure interference factor; and determining the maximum and minimum values of the soft-switching failure interference factor based on the maximum and minimum values of the soft-switching failure interference factor. The distributed new energy is distributed PV.

4. The method of claim 3, wherein the method further comprises: determining the maximum and minimum values of the soft-switching failure interference factor. The deterministic evaluation model includes an E-SOP operation model, a power flow equation model, a voltage and current constraint model, a reactive power compensation equipment model, and a photovoltaic reactive power regulation model, and the deterministic evaluation model takes the maximum distributed PV access capacity as an objective function.

5. The method of claim 4, wherein the method further comprises: determining the maximum and minimum values of the soft-switching failure interference factor; and determining the maximum and minimum values of the soft-switching failure interference factor based on the maximum and minimum values of the soft-switching failure interference factor. The optimization model considering uncertainty is a double-layer robust optimization model, the double-layer robust optimization model includes: An outer model, which takes into account the influence of uncertain factors on the distributed PV planned capacity through an E-SOP non-planned off-grid uncertainty model and a distributed PV time sequence uncertainty model, and minimizes the distributed PV planned capacity; An inner model, which maximizes the distributed PV planned capacity through flexible regulation means in the flexible power distribution network.

6. The method of claim 5, wherein the method further comprises: The E-SOP non-planned off-grid uncertainty model is: (14)； (15)； (16)； (17)； wherein, is the off-grid state variable; is the off-grid start variable; is the repair time, which represents the time required for the E-SOP to re-grid after off-grid; is the is the probability of unplanned off-grid of the port; , are the upper and lower limits of the active power of the E-SOP, respectively; is the time instant when the port are the active power and the reactive power flowing to the E-SOP, respectively; and are the upper and lower limits of the active power of the E-SOP, respectively; and are the upper and lower limits of the reactive power of the E-SOP, respectively.

7. The method of claim 6, wherein the method further comprises: The distributed PV time sequence uncertainty model is: (37)； wherein, is the real value of the distributed PV power at time instant t; is the expected value of the distributed PV power at time instant t; and respectively represent the deviation of the expected value of the distributed PV power from the upper and lower boundaries of the power fluctuation interval; and respectively represent the case that the distributed PV power fluctuation reaches the upper and lower boundaries. (38)； (39)； wherein is the scheduling period for distributed PVs; is the set robust budget to control the conservatism of the model.

8. The method of claim 7, wherein the method further comprises: The double-layer robust optimization model is represented as: (40)； (42)； (43)； (44)； (45)； wherein and are the decision variables of the double-layer robust optimization model.

9. The method of claim 8, wherein the method further comprises: determining the maximum and minimum values of the soft-switching failure interference factor. The solving method of the double-layer robust optimization model includes: first, the inner model is converted into a KKT equation by using the Karush-Kuhn-Tucker condition; then the double-layer robust optimization model is converted into a mixed integer linear programming problem and is solved.

10. The method of claim 9, wherein the method further comprises: The process of converting the inner model into a KKT equation by using the Karush-Kuhn-Tucker condition includes: (46)； (47)； In the formula, is a coefficient matrix in the objective function ; , , and are inequality constraint and equality constraint coefficient matrices related to the power distribution network, respectively; , , and are inequality constraint and equality constraint coefficient matrices related to the E-SOP, respectively; , , and are Lagrange multipliers corresponding to the inequality constraint and the equality constraint, respectively. (48)； (49)； (50)； (51)； (52)； (53)； (54)； (55)； At this time, there is a nonlinear part in formula (52), therefore, a large M method is used to convert it into a linear complementarity condition: (56)； wherein is a sufficiently large number; is a binary variable that makes only one of the two expressions in the above formula active at a time; Similarly, formula (53) can be converted into: (57)； Therefore, the double-layer robust optimization model is equivalent to the mixed integer linear programming problem shown in formula (58), which can be directly solved by using a Cplex solver: (58)。

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