Black-start method for active distribution network considering source load uncertainty and multi-type resources

Abstract

The application discloses a kind of active distribution network black-start method considering source load uncertainty and multiple types of resources, belong to distribution network resilience promotion field, this method is first based on Copula function establishes the joint distribution model of source load prediction data and prediction error, the prediction error uncertainty of DG and load is characterized intervalization;Second, with the minimum power failure loss and operation cost as target, establishes the active distribution network black-start optimization model considering gas turbine, DG, SESS, MESS multiple types of resources;Finally, according to source load prediction error interval random generation source load extreme disturbance scene, substitute into black-start optimization model and solve, obtain the black-start strategy that can respond to each source load extreme disturbance scene.This method can give full play to the black-start value of multiple types of resources, and effectively respond to the negative influence generated by source load bilateral uncertainty, guarantee system frequency and voltage stability, realize the robust recovery of active distribution network, reduce power failure loss.

Description

Technical Field

[0001] This invention belongs to the field of distribution network resilience enhancement, and more specifically, relates to an active distribution network black start method that considers source load uncertainty and multiple types of resources. Background Technology

[0002] In recent years, with the rapid development of the national economy and the gradual improvement of people's living standards, the scale and complexity of my country's power grid have been increasing. On the other hand, the large-scale integration of intermittent and uncertain renewable energy sources has also brought severe challenges to the safe and stable operation of the power grid. The intertwined emergence of potential risk factors such as extreme weather and cyberattacks has significantly increased the risk of system outages and their impact. Against this backdrop, research on black-start strategies for the power grid after major blackouts is of great significance for assessing the grid's recovery capacity, guiding resource optimization, accelerating system recovery, and reducing disaster losses. In the past, black-start recovery technologies have mostly focused on transmission networks, with less attention paid to distribution networks. This is mainly because traditional distribution networks have relatively scarce black-start resources and a low degree of automation, and can only wait for the upstream power grid to recover before initiating a black start. Currently, with the coordinated development of the main, distribution, and microgrids and the vigorous promotion of the policy of strengthening local power grids, various types of resources such as distributed generators (DGs), new energy storage, and electric vehicles are being continuously connected to the grid. The regulation and control capabilities of the distribution network have been greatly improved, and the grid structure has become increasingly flexible. It has completed the transformation from passive mode to active mode, and black start recovery after an accident is gradually becoming possible.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on the black start problem in distribution networks, fully exploring the coordinated regulation potential of black start resources such as gas turbines, stationary energy storage systems (SESSs), and mobile energy storage systems (MESSs). However, most studies directly use source load forecasts as input for scheduling without considering the potential negative impacts of their uncertainties. Some scholars have analyzed and modeled the source load uncertainties in the black start process of distribution networks, effectively improving the robustness and applicability of the resulting recovery strategies. However, most studies directly assume that the uncertainties follow a specific distribution, lacking consideration of the dependency relationship between predicted and actual values, thus losing some information that could be used to improve model accuracy. Furthermore, most studies are not comprehensive enough in their modeling and application of multiple resource types, including gas turbines, DGs, SESSs, and MESSs, only covering a few of them. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an active black start method for distribution networks that takes into account the uncertainty of source load and multiple types of resources, so that after a power outage, operators can make full use of existing resources to formulate a recovery plan and achieve a safe, stable and fast black start of the power grid.

[0005] To achieve the above objectives, according to a first aspect of the present invention, an active distribution network black start method considering source load uncertainty and multiple types of resources is provided, wherein the resources of the distribution network include gas turbines, distributed generators (DGs), serviceable energy storage systems (SESSs), and serviceable energy storage systems (MESSs), and the method includes:

[0006] S1. Construct a dataset that includes historical forecast data and historical forecast errors of the output of each DG in the distribution network and the load of the entire network, and divide the dataset into training samples and test samples.

[0007] S2, using training samples, calculate the marginal distributions of historical prediction data and historical prediction errors respectively, and use at least two Copula functions to establish joint distribution models of historical prediction data and historical prediction errors respectively; input the prediction data in the test samples into each of the joint distribution models respectively, obtain the uncertainty interval of the prediction error output by the model at at least one confidence level, and calculate the average reliability and sharpness of each of the joint distribution models in combination with the historical prediction errors in the test samples, and take the joint distribution model with the lowest absolute values ​​of average reliability and sharpness as the optimal model;

[0008] S3, input the predicted data of each DG output and the total network load during the black start period into the optimal model to obtain the uncertainty range of its prediction error, and generate multiple extreme disturbance scenarios based on the uncertainty range; wherein, the multiple extreme disturbance scenarios include power shortage scenario, power surplus scenario and source load fluctuation scenario, all of which are characterized by the prediction error of each DG output and the total network load during each period during the black start period.

[0009] S4. Taking the minimization of the load outage penalty cost, DG curtailment penalty cost, gas turbine fuel cost, energy storage device operating cost, and network loss cost of the distribution network as the objective function, a black start optimization model for the distribution network is established. The predicted data of each DG output and the entire network load under each extreme disturbance scenario are substituted one by one into the DG curtailment penalty cost and the node power balance constraint of the objective function to solve the objective function and obtain the black start strategy of the distribution network.

[0010] According to a second aspect of the present invention, an electronic device is provided, comprising: a computer-readable storage medium and a processor;

[0011] The computer-readable storage medium is used to store executable instructions;

[0012] The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0013] According to a third aspect of the invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to perform the method as described in the first aspect.

[0014] According to a fourth aspect of the invention, a computer program product is provided, comprising a computer program or instructions that, when executed by a processor, implement the method described in the first aspect.

[0015] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0016] This invention addresses the power grid recovery problem following a major power outage by proposing an active distribution network black-start strategy that considers uncertainties on both the source and load sides and multiple resource types. First, a joint distribution model of source and load prediction data and prediction errors is established based on the Copula function, and the uncertainty of prediction errors for DGs and loads is characterized in intervals. Second, with the objective of minimizing power outage losses and operating costs, an active distribution network black-start optimization model considering multiple resource types, including gas turbines, DGs, SESSs, and MESSs, is established. Finally, extreme source and load disturbance scenarios are randomly generated based on the source and load prediction error intervals, and substituted into the black-start optimization model for solution, yielding a black-start strategy capable of handling various extreme source and load disturbance scenarios. Based on the separate calculation of the marginal distribution of predicted output and prediction error, this invention further characterizes the nonlinear correlation between predicted output and prediction error, thus achieving better performance indicators and more effectively reflecting the actual error situation in the output interval results. Furthermore, this method considers the impact of source-load dual-sided uncertainty on the system recovery process and introduces it into the black-start optimization model in the form of confidence intervals. While fully leveraging the black-start value of DGs and energy storage devices, it can effectively ensure the stability of system frequency and voltage, and achieve robust recovery of active distribution networks.

[0017] Furthermore, to ensure that the final black-start scheme can effectively address uncertainties on both the source and load sides, this invention also uses randomly generated disturbance scenarios to verify the reliability of the distribution network black-start strategy obtained in step S4, which can simultaneously handle various extreme scenarios. If the strategy cannot handle a certain scenario, then based on the extreme disturbance scenario, combined with the predicted data of DGs output and total network load under that scenario, these data are substituted one by one into the DGs curtailment penalty cost and the node power balance constraint of the objective function, and the objective function is solved again until a black-start scheme that can effectively cope with the above-mentioned extreme disturbance scenarios and random disturbance scenarios is obtained. Since these scenarios cover various situations that may occur in real life, it can be ensured that the final black-start scheme can effectively address uncertainties on both the source and load sides. Attached Figure Description

[0018] Figure 1 A flowchart of an active distribution network black start method considering source load uncertainty and multiple types of resources provided in an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram illustrating the process of generating a random disturbance scenario of source loads, as provided in an embodiment of the present invention.

[0020] Figure 3 These are the sampled random numbers generated for the four extreme scenarios provided in the embodiments of the present invention.

[0021] Figure 4 The topology diagram for the improved IEEE 33-node system.

[0022] Figure 5 This is a power output prediction curve of DGs in an embodiment of the present invention.

[0023] Figure 6 This is a load power prediction curve diagram in an embodiment of the present invention.

[0024] Figure 7 (a) to (d) in the embodiments of the present invention are network status diagrams for time periods 1 to 5, 6 to 10, 11 to 15, and 16 to 20 during the overall system recovery process.

[0025] Figure 8 This is a schematic diagram comparing net load fluctuations and the system's primary frequency regulation capability in a typical scenario according to an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] As the "last mile" of public services, the distribution network is more closely connected to users. If the uncertainty of source load during its recovery process can be effectively characterized and properly handled, and multiple types of resources can be fully utilized to achieve a safe, stable, and rapid black start, it can not only ensure power supply to critical loads and reduce economic losses, but also provide auxiliary power and flexibility support for the startup of critical nodes in the transmission network, accelerating the overall system recovery process. Based on this, this invention provides an active distribution network black start method considering source load uncertainty and multiple types of resources. The resources of the distribution network include gas turbines, distributed generators (DGs), serviced energy storage systems (SESSs), and serviced energy storage systems (MESSs). The method includes:

[0028] S1. Construct a dataset that includes historical forecast data and historical forecast errors of the output of each DG in the distribution network and the load of the entire network, and divide the dataset into training samples and test samples.

[0029] Specifically, historical prediction data and historical prediction errors of DGs output and overall network load (i.e., network load) are collected, combined to form an input dataset, and further divided into two categories: training samples and test samples.

[0030] S2, using training samples, calculate the marginal distributions of historical prediction data and historical prediction errors respectively, and use at least two Copula functions to establish joint distribution models of historical prediction data and historical prediction errors respectively; input the prediction data in the test samples into each of the joint distribution models respectively, obtain the uncertainty interval of the prediction error output by the model at at least one confidence level, and calculate the average reliability and sharpness of each joint distribution model in combination with the historical prediction errors in the test samples, and take the joint distribution model with the lowest absolute values ​​of average reliability and sharpness as the optimal model.

[0031] Specifically, for each DG and the overall network load, the marginal distribution of historical prediction data and the marginal distribution of historical prediction errors are calculated using training samples. Existing methods are employed for these calculations, such as kernel density estimation, normal distribution fitting, and T-distribution fitting; this embodiment of the invention does not impose a unique limitation on these methods.

[0032] Those skilled in the art will know that Copula functions have various types, including Gaussian Copula, T Copula, Clayton Copula, and SJC Copula, etc., which will not be listed exhaustively here. The embodiments of the present invention do not impose a unique limitation on the specific type of Copula function used in S2.

[0033] As an example, if the Copula function used in S2 includes four types: Gaussian Copula, T Copula, Clayton Copula, and SJC Copula, then in S2, a joint distribution model of the prediction data and prediction error is established based on the Gaussian Copula, T Copula, Clayton Copula, and SJC Copula functions in turn, resulting in four joint distribution models.

[0034] Then, for each DG and the overall network load, the prediction data in the test sample is input into the four joint distribution models mentioned above to obtain the prediction error uncertainty range of each model output at at least one confidence level. This range is then compared with the actual prediction error in the test sample. The average reliability and sharpness index of the output results of the four sets of models are calculated to select the optimal model.

[0035] For example, taking nine confidence levels (0.98, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2) as an example, the prediction data from the test samples are input into the four joint distribution models mentioned above for each DG and the overall network load, respectively. The uncertainty interval of the prediction error output of each model at confidence levels of 0.98, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2 is obtained and compared with the actual prediction error in the samples. The average reliability index and sharpness index of the output results of each model at confidence levels of 0.98, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2 are calculated, and the optimal model is selected.

[0036] The formulas for calculating the reliability index and the sharpness index are as follows:

[0037]

[0038] In the above formula, Rel (ρ) and Shp (ρ) Here, ρ represents the reliability index and sharpness index of the model at confidence level ρ, respectively, and Num represents the total number of test samples. and χ represents the upper and lower bounds of the uncertainty interval of the prediction error of the k-th sample output by the model under confidence level ρ. kLet be the actual prediction error value corresponding to the k-th sample, and let Index(k) be the indicator function of the actual sample points enclosed in the model output interval. Thus, the reliability index characterizes the probability deviation between the model's ability to enclose the uncertainty interval and the selected confidence level, while the sharpness index reflects the redundancy of the model's output interval. Obviously, the lower the absolute values ​​of both, the better the model.

[0039] S3, input the predicted data of each DG output and the total network load during the black start period into the optimal model to obtain the uncertainty range of its prediction error, and generate multiple extreme disturbance scenarios based on the uncertainty range; wherein, the multiple extreme disturbance scenarios include power shortage scenario, power surplus scenario and source load fluctuation scenario, all of which are characterized by the prediction error of the predicted data of each DG output and the total network load during each period during the black start period.

[0040] Specifically, the predicted power data of each DG and the entire network load during the black start process are obtained, and the optimal model selected by S2 is input to calculate the uncertainty interval of its prediction error. Based on this uncertainty interval, multiple extreme disturbance scenarios are generated.

[0041] Understandably, multiple extreme disturbance scenarios include power shortage scenarios, power surplus scenarios, and source-load fluctuation scenarios, namely, extreme power shortage scenarios, extreme power surplus scenarios, and extreme source-load fluctuation scenarios ("source" refers to DGs, and "load" refers to the total network load), that is:

[0042] In the scenario of insufficient power supply, the prediction error of each DG output is taken as the lower bound of the uncertainty interval in S3, and the prediction error of the entire network load is taken as the upper bound of the uncertainty interval in S3.

[0043] In the scenario of power surplus, the prediction error of each DG output is taken as the upper bound of the uncertainty interval in S3, and the prediction error of the entire network load is taken as the lower bound of the uncertainty interval in S3.

[0044] The source load fluctuation scenario can be divided into a first source load fluctuation scenario and a second source load fluctuation scenario. In the first source load fluctuation scenario, the prediction errors of each DG fluctuate up and down with the same frequency over time (i.e., the upper limit of the interval is taken in the previous period, and the lower limit of the interval is taken in the next period, and the jumps are repeated), while the load prediction error does the opposite. The jumping process of the second source load fluctuation scenario is similar to that of the first source load fluctuation scenario, except that the upper and lower limits of the initial period are reversed, that is:

[0045] In the first source load fluctuation scenario, the prediction error of each DG output and the time frequency in the uncertainty interval of S3 repeatedly jump between the upper and lower bounds, and the prediction error of the entire network load and the time frequency in the uncertainty interval of S3 repeatedly jump between the lower and upper bounds.

[0046] In the second source-load fluctuation scenario, the prediction error of each DG output and the time frequency in the uncertainty interval of S3 repeatedly jump between the lower and upper bounds, and the prediction error of the entire network load and the time frequency in the uncertainty interval of S3 repeatedly jump between the upper and lower bounds.

[0047] S4. Taking the minimization of the load outage penalty cost, DG curtailment penalty cost, gas turbine fuel cost, energy storage device operating cost, and network loss cost of the distribution network as the objective function, a black start optimization model for the distribution network is established. The predicted output data of each DG under each extreme disturbance scenario is substituted into the DG curtailment penalty cost, and the predicted load data of the entire network under each extreme disturbance scenario is substituted into the node power balance constraint of the objective function. The objective function is then solved to obtain the black start strategy of the distribution network.

[0048] Specifically, an active distribution network black-start optimization model considering multiple resource types, including gas turbines, distributed generation (DGs), energy storage devices (SESSs), and mechanized energy storage devices (MESSs), is established. The optimization objective of this black-start model is to minimize the power outage losses and overall operating costs of the distribution network. Accordingly, the objective function includes the load outage penalty cost, DG curtailment penalty cost, gas turbine fuel cost, energy storage device operating cost, and network loss cost.

[0049]

[0050] In the above formula, T, N, J, I, M, S, and L are the sets of scheduling time periods, nodes, DGs, gas turbines, MESSs, SESSs, and lines, respectively; δ n The load outage penalty cost coefficient for node n is given. Considering that during the black start process, the primary goal should be to restore the load power supply safely, stably and quickly, while the economic dispatch of multiple types of resources is only an auxiliary option, the value of this coefficient is relatively large, so as to distinguish it from the subsequent power grid operation cost. and PL n,t denoted as the recovery state variables and active power load of node n in time period t; λ is the DGs curtailment penalty cost coefficient; and Let α be the schedulable power and the actual schedulable power of DGj during time period t; i Let be the fuel cost coefficient for gas turbine i; The active power output of gas turbine i during time period t; w m and w s The charge / discharge cost coefficients for MESSs and SESSs are respectively. and Let be the charging and discharging power of MESSm and SESSs respectively during time period t, γ be the mobility cost coefficient of MESSs, and v be the charging and discharging power of MESSm and SESSs respectively. m,tLet t be the mobility state variable of MESSsm during time period t; β be the network loss cost coefficient, and Pf be the network loss cost coefficient. l,t The active power on line l during time period t is the active power.

[0051] The constraints of the objective function include gas turbine operation constraints, DGs operation constraints, energy storage device charging and discharging constraints, MESSs mobility / access state constraints, node power balance constraints, power flow constraints, frequency and voltage security constraints, and network recovery constraints. Among these:

[0052] Gas turbine operating constraints: These constraints are used to ensure that the gas turbine meets the basic start-up and output requirements.

[0053] DGs operating constraints: These constraints are used to ensure that DGs meet basic output requirements.

[0054] Energy storage device charge and discharge constraints: These constraints are used to ensure that the energy storage device meets basic requirements such as power limits, SOC limits, and charge and discharge state limits.

[0055] MESSs Mobility / Access Status Constraints: These constraints are used to ensure that the access and mobility of MESSs meet the basic requirements of the power distribution network and transportation network.

[0056] Node power balance constraint: This constraint is used to ensure the real-time balance of power generation and consumption in the distribution network.

[0057] Power flow constraint: This constraint is used to ensure that the distribution network meets the basic power flow equations and that the lines are not overloaded.

[0058] Frequency and voltage safety constraints: These constraints are used to ensure that the frequency of the distribution network and the voltage of each node are within a reasonable range.

[0059] Network recovery constraint: This constraint is used to ensure that devices without black start capability are gradually restored by devices with black start capability, and that the grid structure is gradually expanded.

[0060] The mathematical expressions for the above constraints are described below.

[0061] Gas turbine operating constraints:

[0062] Generally, gas turbines have a fast ramp rate but relatively low start-up power. The process of switching from power absorption to power output can be completed within 1 minute, which is less than the time interval for resuming dispatch. Therefore, this conversion process can be simplified and considered to be instantaneous. The simplified operating constraints are as follows:

[0063]

[0064] In the above formula, T i STLet i be the startup time of unit i. and P represents the startup state variable and output state variable of unit i during time period t. i ST P is the starting power required for unit i. i G,max and These are the upper limits of active and reactive power output of unit i, respectively. Let t be the reactive power output of unit i during time period t. This is the active power output ramp-up limit for unit i.

[0065] DGs operational constraints:

[0066] DGs such as wind and solar power have low start-up power and fast start-up speed, requiring no ramp-up. Therefore, it can be approximated that they can start generating electricity as soon as their node recovers. Based on this, the operating constraints for DGs are:

[0067]

[0068] In the above formula, Let DGj be the output state variable during time period t. For the reactive power output of DGj during time period t, This is the upper limit of reactive power output of DGj.

[0069] Energy storage device charge and discharge constraints:

[0070]

[0071] In the above formula, and Let MESSm and SESSs be the charge / discharge state variables for time period t, respectively. and Let MESSm and SESSs be the startup state variables for time period t, respectively. and The active and reactive power output limits of MESSm and SESSs, respectively, are Q. m,t and Q s,t The reactive power outputs of MESSm and SESSs during time period t are E, respectively. m,t and E s,t Let ηm and ηs be the energy contained in MESSm and SESSs respectively during time period t, ηm and ηs be the charging and discharging efficiencies of MESSs and SESSs respectively, and Δt be the duration of a unit scheduling period. and The rated capacities and SOCs of MESSm and SESSs are respectively. max and SOC minThese represent the upper and lower limits of the State of Charge (SOC) of the energy storage device.

[0072] MESSs Mobile / Access State Constraints:

[0073]

[0074] In the above formula, N CM For the set of nodes that MESSs can access, u m,n,t Let MESSm be the connection state variable between node n and node n during time period t. Let MESSm be the required travel time. The constraints, from top to bottom, are as follows: ① The connection and travel states of MESSs are mutually exclusive, and a MESS can only connect to at most one accessible node at any given time; ② MESSs can only charge and discharge when connected; ③ Each accessible node can only connect to at most one MESS in each time period; ④ When MESSm connects to node n in time period t, it needs to travel at least... It can only be connected to the next node p after a certain time.

[0075] Node power balance constraints:

[0076]

[0077] In the above formula, and Let O(l) and D(l) be the sets of MESSs, SESSs, gas turbines, and DGs connected to node n, respectively, and let PL be the set of MESSs, SESSs, gas turbines, and DGs connected to node n. Let O(l) and D(l) be the first and last node numbers of line l, respectively. n,t and QL n,t Qf represents the active and reactive loads at node n during time period t. l,t The reactive power on line l during time period t is denoted as t.

[0078] Current constraints:

[0079]

[0080] In the above formula, Let G be the recovery state variable of line l during time period t. l and B l These are the conductance and susceptance of line l, respectively, V n,t and θ n,t Let Pf be the voltage amplitude and phase angle of node n during time period t, respectively, and let I(n) and E(n) be the incoming and outgoing lines of node n, respectively. l max and Qf l max These represent the upper limits of active and reactive power for line l, respectively.

[0081] Frequency and voltage safety constraints:

[0082]

[0083] In the above formula, Δf max The maximum allowable frequency deviation of the system is set to 0.5Hz as specified. and , where i, MESSm, and SESSs are the frequency response coefficients of the gas turbines, respectively, and ref is the reference node number. and These are the upper and lower limits of the voltage amplitude at node n, respectively. This represents the upper limit of the voltage phase angle deviation at node n.

[0084] Network recovery constraints:

[0085]

[0086] In the above formula, N root T represents the number of root nodes, initially calculated as the sum of the number of MESSs and SESSs, and gradually decreases as the network merges; l The required recovery time for line l is given. It should be noted that the merging process of the distribution network can be achieved by adjusting the output or load demand of gas turbines and energy storage devices. Compared to the transmission network, this process is shorter, therefore, this invention approximates it as the commissioning process of a tie line. Furthermore, the model assumes that MESSs and SESSs have black-start capability, and that DGs and gas turbines (excluding those powered by independent batteries) are units awaiting startup. This state is merely a typical example selected by the inventors and can be adjusted according to the actual situation of the power grid.

[0087] To ensure the robustness of the model and avoid the impact of excessive computation on timeliness, this invention utilizes the aforementioned four extreme scenarios to formulate a black-start scheduling strategy. Specifically, the predicted output data of each DG under each extreme disturbance scenario is substituted into the calculation formula for the DG curtailment penalty cost (i.e., Substitute the predicted data of the entire network load under the above extreme disturbance scenarios into the node power balance constraint (i.e., PL) of the objective function. n,t and QL n,t In the solution, the objective function is solved to obtain a black start strategy for the distribution network that can simultaneously cope with the above four extreme disturbance scenarios. Theoretically, this strategy can also cope with various source-load disturbance scenarios that may occur in real life.

[0088] To ensure that the final black-start scheme can effectively cope with uncertainties on both the source and load sides, a randomly generated disturbance scenario can be used to verify the reliability of the distribution network black-start strategy obtained in step S4, which can simultaneously cope with the above four extreme scenarios. If the strategy cannot handle any of the scenarios, then based on the extreme disturbance scenario, combined with the predicted data of DGs output and total network load under that scenario, these data are substituted one by one into the DGs curtailment penalty cost and the node power balance constraint of the objective function, and the objective function is solved again until a black-start scheme that can effectively cope with the above extreme disturbance scenarios and random disturbance scenarios is obtained. Since these scenarios cover various situations that may occur in real life, it is considered that the final black-start scheme can effectively cope with uncertainties on both the source and load sides, and it is output as the optimal result. That is, as a further preferred embodiment of the present invention, the method further includes:

[0089] S5. Verify whether the black start strategy of the distribution network can handle multiple random disturbance scenarios. If so, the current black start strategy is taken as the optimal strategy. Otherwise, substitute the predicted data of DGs output and total network load under each extreme disturbance scenario and the random disturbance scenario that cannot be handled into the DGs curtailment penalty cost and the node power balance constraint of the objective function, solve the objective function, obtain the black start strategy of the distribution network, and take it as the optimal strategy.

[0090] The multiple random disturbance scenarios are randomly generated based on the uncertainty interval in S3.

[0091] The number of random disturbance scenarios can be set according to the actual situation. For example, if the number of random disturbance scenarios is 200, then in step S5, the reliability of the black start strategy of the distribution network obtained by S4 is verified by using 200 randomly generated random disturbance scenarios. If the strategy obtained by S4 cannot handle a certain scenario (that is, the frequency and voltage of the power grid obtained by the black start strategy of the distribution network obtained by S4 under the random disturbance scenario do not meet the requirements of the frequency threshold and voltage threshold), then the objective function is re-solved in combination with the scenario until a black start scheme that can effectively cope with these 204 scenarios is obtained.

[0092] It is understandable that the uncertainty range of the prediction error of the predicted data of each DG output and the total network load during the black start period has been obtained through step S3. Based on this uncertainty range, multiple random disturbance scenarios can be obtained by random generation.

[0093] For example, random numbers can be generated and randomly selected within this uncertainty interval to characterize the source load prediction error of a random disturbance scenario. Figure 2 As shown, taking a binary random number (j) as an example, firstly, generate (j end +1) row, tend A matrix of positive and negative binary random numbers in column j, where j end t represents the number of DGs in the distribution network. end Let j be the number of time periods in the entire black start process; then, the first j... end The random number in each row corresponds one-to-one with each DG in the distribution network, and the (j)th row... end +1) The random numbers in the row correspond to the overall load of the power grid; if the random number corresponding to a certain DG (or the overall load of the power grid) in a certain period is positive, then the upper bound of the uncertainty interval is taken; if it is negative, then the lower bound of the uncertainty interval is taken, thus completing the source-load prediction error value under a certain random disturbance scenario. Similarly, the sampled random numbers corresponding to each extreme disturbance scenario are as follows: Figure 3 As shown.

[0094] It is understandable that the prediction errors of the DG output and total network load prediction data for each random disturbance scenario and each extreme disturbance scenario are used. Therefore, the prediction data of each DG output under a certain extreme disturbance scenario or random disturbance scenario is the sum of the prediction error of each DG output corresponding to that scenario and the prediction data of each DG output during the black start period in S3; the prediction data of the total network load under a certain extreme disturbance scenario or random disturbance scenario is the sum of the prediction error of the total network load corresponding to that scenario and the prediction data of the total network load during the black start period in S3.

[0095] The objective function described above can be solved using column constraint generation algorithms and software such as Gurobi, Cplex, and MOSEK.

[0096] The method provided by the present invention will be further illustrated below with a specific example.

[0097] Will as Figure 4 The improved IEEE 33-node system shown is the implementation object of the method provided by this invention. The system includes 6 gas turbines, 8 distributed gas turbines (DGs), 2 SESSs (Self-Electrical Storage Units), and 2 MESSs (Mechanical Storage Units), with parameters shown in Tables 1-3. The scheduling duration is 1 hour, and the time interval is 2 minutes. The upper limits of active and reactive power of the lines are 2000 kW and 1600 kVar, respectively, and the recovery time is set to 2 time periods. The initial and upper / lower limits of the State of Charge (SOC) of all energy storage devices are 0.5, 0.9, and 0.1, respectively, with a charge / discharge efficiency of 90%. Considering that the system voltage may fluctuate during black start, the upper and lower limits of the voltage at each node are set to 1.1 and 0.9 times the per-unit value, respectively.

[0098] The source-load power prediction curve during the scheduling process is as follows: Figure 5 and Figure 6As shown. The active and reactive power of the load at each bus can be proportionally calculated based on standard data. Furthermore, critical loads are connected at nodes 4, 8, 12, 15, 18, 29, 31, and 32. To ensure rapid recovery, MESSs charging and discharging stations are installed at these nodes, with a power outage penalty cost set at ¥30 / kWh, 10 times the penalty cost for ordinary loads. Simultaneously, the operating cost coefficients for SESSs and MESSs are set at ¥0.036 / kWh and ¥0.06 / kWh respectively, the moving cost coefficient for MESSs is set at ¥3 / time, and the network loss cost coefficient is ¥0.15 / kWh.

[0099] Table 1. Parameters of the gas turbine in the system

[0100]

[0101] Table 2 Parameters of DGs in the system

[0102]

[0103] Table 3 Parameters of the energy storage device in the system

[0104]

[0105] Based on the above parameters, this embodiment proceeds according to the following steps:

[0106] S1 collects historical prediction data and historical prediction errors of DGs and the overall network load, combines them to form the input dataset, and further divides it into two categories: training samples and test samples.

[0107] S2. For each DG and the overall network load, the marginal distribution of prediction data and prediction error is calculated using training samples and kernel density estimation. Then, joint distribution models of prediction data and prediction error are established based on Gaussian Copula, TCopula, Clayton Copula, and SJCCopula functions respectively. Further, for each DG and the overall network load, the prediction data in the test samples are input into the four joint distribution models to obtain the uncertainty interval of prediction error output by each model at confidence levels of 0.98, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2. The uncertainty intervals are compared with the actual prediction errors in the samples, and the average reliability and sharpness index of the four model output results are calculated to select the optimal model.

[0108] In this process, the reliability and sharpness indices of each model at different confidence levels are calculated according to equations (1)-(3), and the average values ​​are obtained, as shown in Table 4. As can be seen from the table, the optimal Copula function types corresponding to the 8 DGs and the total network load are SJC, SJC, Clayton, SJC, SJC, SJC, Clayton, Clayton, and Gaussian, respectively. The models corresponding to each optimal Copula function are the models used in the subsequent steps of this invention.

[0109] To verify the effectiveness of the model used in this invention, DG1 was used as an example, and its performance was compared with computational models based on the uncertain interval of source load prediction error obtained from Gaussian distribution, empirical distribution, overall kernel density estimation, and hierarchical kernel density estimation. Similarly, using the above training and test samples as input data, the uncertainty intervals of the four outputs were obtained respectively, and the average values ​​of their reliability and sharpness indices at different confidence levels were calculated, as shown in Table 5. As can be seen from the table, the indices corresponding to the empirical distribution and overall kernel density estimation models are similar and at a relatively high level. This is because they do not consider the correlation between predicted output and prediction error, and only model based on the frequency distribution results obtained statistically, thus the accuracy of the output interval is low. The Gaussian distribution also does not consider this correlation, but because its output interval is wider, it can achieve a partial improvement in model reliability at the expense of the sharpness index. In contrast, hierarchical kernel density estimation has significantly improved performance due to its consideration of the linear correlation between input data, but its reliability and sharpness are at a low level. The model of this invention, based on hierarchical kernel density estimation, further characterizes the nonlinear correlation between predicted output and prediction error, thus achieving better performance and the output interval results can more effectively reflect the actual error situation.

[0110] Table 4 Performance metrics of models corresponding to different Copula functions

[0111]

[0112] Table 5. Performance Indicators Comparison of the Invention Model and Common Models

[0113] type Average reliability index Average sharpness index The sum of the absolute values ​​of the two indicators Gaussian distribution 0.0111 0.0739 0.0850 Experience distribution -0.0678 0.0691 0.1369 Overall kernel density estimation -0.0639 0.0695 0.1334 Hierarchical kernel density estimation -0.0067 0.0708 0.0775 This invention model -0.0072 0.0638 0.0710

[0114] S3: Obtain the predicted power data of each DG and the entire network load during the black start process, input the corresponding optimal model selected by S2, calculate the uncertainty interval of its prediction error, and generate each extreme disturbance environment based on the uncertainty interval.

[0115] Each Figure 5 and Figure 6The source-load power prediction curve is input into the optimal model obtained in step S2 to obtain the uncertainty interval of the prediction error during the black start process. The interval results at a confidence level of 0.9 are selected to generate various extreme perturbation environments. It should be noted that the confidence level of 0.9 here is only a result randomly selected based on past research experience and can be adjusted according to the specific implementation environment.

[0116] S4. Taking the minimization of the load outage penalty cost, DG curtailment penalty cost, gas turbine fuel cost, energy storage device operating cost, and network loss cost of the distribution network as the objective function, a black start optimization model for the distribution network is established. The predicted data of each DG output and the entire network load under each extreme disturbance scenario are substituted one by one into the DG curtailment penalty cost and the node power balance constraint of the objective function to solve the objective function and obtain the black start strategy of the distribution network.

[0117] As a preferred option, in step S5, it is verified whether the black start strategy of the distribution network can handle multiple random disturbance scenarios. If so, the current black start strategy is taken as the optimal strategy. Otherwise, the predicted data of DG output and total network load under each extreme disturbance scenario and the random disturbance scenario that cannot be handled are substituted one by one into the DG curtailment penalty cost and the node power balance constraint of the objective function, and the objective function is solved again to obtain the black start strategy of the distribution network, which is then taken as the optimal strategy.

[0118] Figure 7Figures (a) to (d) illustrate the overall system recovery process corresponding to the obtained strategy, using different colors to distinguish the operational status of lines and nodes in different time periods. As shown in the figures, after the black start begins, the energy storage device will first restore nearby distributed gas turbines (DGs) to form a stable power source with flexible adjustment capabilities. This addresses frequency and voltage surges caused by uncertainties in load access and prediction errors. Subsequently, it gradually starts surrounding gas turbines and restores loads, forming a small, independently operating local power grid. As the local power grid continues to "grow," its boundaries become closer, and it will continue to merge into a larger power grid, providing mutual backup and emergency power support to further restore more loads. Furthermore, it can be seen that during periods 1-5, after completing the black start "ignition" task at node 18, MESS2 will continue to node 4 to supply power. This is because node 4 has important loads and a high proportion of nearby DGs are connected. In this context, MESS2 can fully utilize its spatial mobility to ensure power supply to important loads, reducing system outage losses, and through coordination with SESS1, provide greater flexibility for subsequent DG access. Throughout the recovery process, the system achieved a renewable energy absorption rate of 99.97%, with 56.94% of the load powered by renewable energy. The average power utilization rate of the energy storage device reached 67.36%, providing 86.47% positive reserve capacity and 91.89% negative reserve capacity. Furthermore, this invention employed a controlled variable method to conduct black-start capability tests on distribution networks without DGs, SESSs, and MESSs. The results showed that in these three scenarios, the system could not achieve black start due to either insufficient power supply capacity or a shortage of flexible adjustment resources. In summary, the black-start strategy proposed in this invention can fully leverage the recovery value of DGs and energy storage devices, enabling parallel system startup and effectively reducing power outage losses.

[0119] On the other hand, to illustrate the superiority of the proposed strategy over existing methods, the uncertainty intervals output by the model of this invention at a confidence level of 0.9 and the four common models mentioned in Table 5 were applied to the black start process of an active distribution network, and their economy and speed were compared, as shown in Table 6. As can be seen from the table, under the same confidence level, i.e., the same safety factor, compared with the four common models mentioned above, the overall operating cost of the model of this invention is reduced by 10.38%, 0.77%, 1.14%, and 0.23%, respectively, and the computation time is improved by 41.67%, 16.26%, 26.68%, and 4.78%, respectively, with a relatively earlier recovery time. Therefore, compared with existing methods, the model of this invention can provide a more economical and faster recovery scheme while taking safety into account. It should be noted that the analysis here only uses a confidence level of 0.9 as an example; if other confidence levels are used, the results are similar and will not affect the superior performance of this invention.

[0120] Table 6. Performance comparison of the present invention model and common models applied to the black start process.

[0121] type Overall system operating cost (¥) Recovery period Calculation time (min) Gaussian distribution <![CDATA[7.1696×10 3 ]]> 20 32.13 Experience distribution <![CDATA[6.4747×10 3 ]]> 19 22.38 Overall kernel density estimation <![CDATA[6.4991×10 3 ]]> 21 25.56 Hierarchical kernel density estimation <![CDATA[6.4398×10 3 ]]> 20 19.68 This invention model <![CDATA[6.4251×10 3 ]]> 19 18.74

[0122] Furthermore, to verify the effectiveness of the obtained strategy in handling uncertainties on both sides of the source load during black start, this invention also compared and analyzed the net load changes and the system's primary frequency regulation capability under four extreme scenarios and 200 sets of random scenarios (due to space limitations, Figure 8 (Only some typical scenarios were demonstrated). The results show that the net load fluctuations of the system in each scenario are within its primary frequency regulation capability range, and frequency safety issues will not arise due to uncertainties in source load prediction errors. Furthermore, the voltage at each node remains within the specified range throughout the entire recovery process. Therefore, the black-start strategy proposed in this invention can effectively address uncertainties on both the source and load sides, ensuring the stability of the system's frequency and voltage, and achieving robust recovery of the active distribution network.

[0123] In summary, the active distribution network black start method proposed in this invention, which considers source-load uncertainty and multiple types of resources, is effective and reasonable.

[0124] This invention provides an electronic device, including: a computer-readable storage medium and a processor;

[0125] The computer-readable storage medium is used to store executable instructions;

[0126] The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0127] This invention provides a computer-readable storage medium storing computer instructions that cause a processor to perform the method described in any of the above embodiments.

[0128] This invention provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the method described in any of the above embodiments.

[0129] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A black-start method for an active distribution network considering source-load uncertainty and multiple resource types, wherein the resources of the distribution network include gas turbines, distributed generators (DGs), serviceable energy storage systems (SESSs), and serviceable energy storage systems (MESSs), characterized in that, The method includes: S1. Construct a dataset that includes historical forecast data and historical forecast errors of the output of each DG in the distribution network and the load of the entire network, and divide the dataset into training samples and test samples. S2, using training samples, calculate the marginal distributions of historical prediction data and historical prediction errors respectively, and use at least two Copula functions to establish joint distribution models of historical prediction data and historical prediction errors respectively; input the prediction data in the test samples into each of the joint distribution models respectively, obtain the uncertainty interval of the prediction error output by the model at at least one confidence level, and calculate the average reliability and sharpness of each of the joint distribution models in combination with the historical prediction errors in the test samples, and take the joint distribution model with the lowest absolute values ​​of average reliability and sharpness as the optimal model; S3, input the predicted data of each DG output and the total network load during the black start period into the optimal model to obtain the uncertainty range of its prediction error, and generate multiple extreme disturbance scenarios based on the uncertainty range; wherein, the multiple extreme disturbance scenarios include power shortage scenario, power surplus scenario and source load fluctuation scenario, all of which are characterized by the prediction error of each DG output and the total network load during each period during the black start period. S4. Taking the minimum load outage penalty cost, DG curtailment penalty cost, gas turbine fuel cost, energy storage device operating cost, and network loss cost of the distribution network as the objective function, a black start optimization model for the distribution network is established. The predicted data of each DG output and the total network load under each extreme disturbance scenario are substituted one by one into the DG curtailment penalty cost and the node power balance constraint of the objective function to solve the objective function and obtain the black start strategy of the distribution network. The constraints of the objective function also include: gas turbine operation constraints, DGs operation constraints, energy storage device charging and discharging constraints, MESSs mobility / access state constraints, power flow constraints, frequency and voltage security constraints, and network recovery constraints.

2. The method as described in claim 1, characterized in that, In the scenario of insufficient power supply, the prediction error of each DG output is taken as the lower bound of the uncertainty interval in S3, and the prediction error of the entire network load is taken as the upper bound of the uncertainty interval in S3. In the scenario of power surplus, the prediction error of each DG output is taken as the upper bound of the uncertainty interval in S3, and the prediction error of the entire network load is taken as the lower bound of the uncertainty interval in S3. The source load fluctuation scenario includes the first source load fluctuation scenario and the second source load fluctuation scenario; In the first source load fluctuation scenario, the prediction error of each DG output and the time frequency in the uncertainty interval of S3 repeatedly jump between the upper and lower bounds, and the prediction error of the entire network load and the time frequency in the uncertainty interval of S3 repeatedly jump between the lower and upper bounds. In the second source-load fluctuation scenario, the prediction error of each DG output and the time frequency in the uncertainty interval of S3 repeatedly jump between the lower and upper bounds, and the prediction error of the entire network load and the time frequency in the uncertainty interval of S3 repeatedly jump between the upper and lower bounds.

3. The method as described in claim 1 or 2, characterized in that, The method further includes: S5. Verify whether the black start strategy of the distribution network can handle multiple random disturbance scenarios. If so, the current black start strategy is the optimal strategy. Otherwise, substitute the predicted data of DG output and total network load under each extreme disturbance scenario and the random disturbance scenario that cannot be handled into the DG curtailment penalty cost and the node power balance constraint of the objective function, and solve the objective function again to obtain the black start strategy of the distribution network until a black start scheme that can effectively cope with each extreme disturbance scenario and multiple random disturbance scenarios is obtained, and this scheme is taken as the optimal strategy. Among them, the multiple random disturbance scenarios are randomly generated according to the uncertainty interval in S3, and each random disturbance scenario is characterized by the prediction error of each DG output and the total network load in each time period during the black start period.

4. The method as described in claim 1, characterized in that, The objective function is: in, T , N , J , I , M , S , L These are sets of scheduling periods, nodes, DGs, gas turbines, MESSs, SESSs, and lines, respectively. For nodes n The load outage penalty cost coefficient is determined by taking into account that during the black start process, the primary goal should be to restore the load power supply safely, stably and quickly, while the economic dispatch of multiple types of resources is only an auxiliary option. Therefore, the value of this coefficient is relatively large, so as to distinguish it from the subsequent power grid operation cost. and They are respectively t Time period nodes n The restored state variables and active power load; The cost coefficient for DGs curtailment penalties; and They are respectively t DG Time Period j The schedulable power and the actual schedulable power; For gas turbine i Fuel cost coefficient; for t Time-of-use gas turbine i Those who have made meritorious contributions; and The charge / discharge cost coefficients for MESSs and SESSs, respectively. , , and They are respectively t Time period MESS m and SESS s The charging and discharging power, For the movement cost coefficient of MESSs, for t Time Periods MESSs m The movement state variable; This is the network loss cost coefficient. for t Time-of-day routes l The active power.

5. The method as described in claim 4, characterized in that, The operating constraints of the gas turbine are: in, For the unit i Startup time and They are respectively t Time-of-use units i The start-up state variables and output state variables, For the unit i Required startup power and The units i The upper limit of active and passive output, for t Time-of-use units i Unproductive efforts For the unit i The effective output climbing limit; The operational constraints of the DGs are: in, for t DG Time Period j The output state variable, for t DG Time Period j Unproductive efforts For DG j The upper limit of reactive power output; The charging and discharging constraints of the energy storage device are: in, , , and They are respectively t Time period MESS m SESS s The charge and discharge state variables, and They are respectively t Time period MESS m SESS s The startup state variables, , , and MESS m SESS s The upper limit of both active and passive effort output. and They are respectively t Time period MESS m SESS s Unproductive efforts and They are respectively t Time period MESS m SESS s The energy contained and The charge / discharge efficiencies of MESSs and SESSs are respectively. The duration of each scheduling period. and MESS m SESS s Rated capacity, and These are the upper and lower limits of the state of charge of the energy storage device, respectively. The MESSs mobile / access state constraints are as follows: in, This is the set of nodes that MESSs can access. for t Time period MESS m With nodes n The connection state variables, For MESS m Required travel time; The node power balance constraint is: in, , , and They are nodes n The upper-connected MESSs, SESSs, gas turbines and DGs collection, and The lines are respectively l The first and last node numbers, and They are respectively t Time period nodes n Active and reactive loads on the surface for t Time-of-day routes l reactive power; The power flow constraint is: in, for t Time-of-day routes l The recovery state variables, and The lines are respectively l The conductivity and susceptance, and They are respectively t Time period nodes n The voltage amplitude and phase angle, and They are nodes n The incoming and outgoing lines, and The lines are respectively l The upper limits of active and reactive power; The frequency and voltage safety constraints are as follows: in, The maximum allowable frequency deviation of the system is set to 0.5Hz as specified. , and Gas turbine i MESS m and SESS s The frequency response coefficient, where ref is the reference node number. and They are nodes n The upper and lower limits of voltage amplitude, For nodes n The upper limit of voltage phase angle deviation; The network recovery constraint is: in, The number of root nodes, For the line l Required recovery time.

6. An electronic device, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in any one of claims 1-5.

8. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method as described in any one of claims 1 to 5.

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