Active power distribution network black start method considering source load uncertainty and multi-type resources

Abstract

The invention discloses an active power distribution network black start method considering source load uncertainty and multi-type resources, and belongs to the field of power distribution network toughness improvement, and the method comprises the steps: firstly building a joint distribution model of source load prediction data and prediction errors based on a Copula function, and carrying out the interval representation of the prediction error uncertainty of DGs and loads; secondly, establishing an active power distribution network black-start optimization model considering multiple types of resources such as gas turbines, DGs, SESSs and MESSs by taking minimization of power failure loss and operation cost as targets; and finally, randomly generating source charge extreme disturbance scenes according to the source charge prediction error interval, substituting the source charge extreme disturbance scenes into the black-start optimization model for solving, and obtaining a black-start strategy capable of coping with each source charge extreme disturbance scene. The method can give full play to the black-start value of multiple types of resources, effectively deals with the negative influence caused by the uncertainty of the two sides of the source and the load, guarantees the stability of the system frequency and voltage, achieves the steady recovery of the active power distribution network, and reduces the power failure loss.

Description

Technical Field

[0001] The present invention belongs to the field of improving the resilience of distribution networks, and more specifically, relates to an active distribution network black start method that takes into account source-load uncertainty and multiple types of resources. Background Art

[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 access of intermittent and uncertain renewable energy has also brought severe challenges to the safe and stable operation of the power grid. The emergence of potential risk factors such as extreme weather and cyber attacks has significantly increased the risk of system power outages and its impact range. In this context, studying the black start strategy of the power grid after a major power outage is of great significance for evaluating the power grid's recovery capabilities, guiding the optimal allocation of resources, accelerating the system's recovery speed, and reducing disaster losses. In the past, most black start recovery technologies have focused on transmission networks, and less on distribution networks. This is mainly because traditional distribution networks are relatively short of black start resources and have a low degree of automation. They can only wait for the upper power grid to be restored before they can drive the black start. Nowadays, with the coordinated development of the main-distribution-micro network and the vigorous promotion of the policy of strengthening local power grids, various types of resources such as distributed generators (DGs), new energy storage, electric vehicles, etc. are continuously connected, the distribution network's control capacity has been greatly improved, the grid structure has become increasingly flexible, and the transition from passive mode to active mode has been completed. It is gradually becoming possible to achieve black start recovery after an accident.

[0003] At present, domestic and foreign scholars have carried out a lot of research on the black start problem of distribution network, and fully explored the coordinated regulation potential of black start resources such as DGs, stationary energy storage systems (SESSs), and mobile energy storage systems (MESSs). However, most of them only use the source-load prediction results as input for direct scheduling, without considering the possible negative impact of its uncertainty. Some scholars have analyzed and modeled the source-load uncertainty in the black start process of distribution network, effectively improving the robustness and applicability of the resulting recovery strategy, but most of them directly assume that it obeys a certain type of specific distribution, lack of consideration of the dependence relationship between the predicted value and the actual value, and lose some information that can be used to improve the accuracy of the model. In addition, most studies are not comprehensive enough in the modeling and application of multiple types of resources such as gas turbines, DGs, SESSs, and MESSs, and only involve a few of them. Summary of the invention

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

[0005] To achieve the above object, according to a first aspect of the present invention, there is provided an active distribution network black start method considering source-load uncertainty and multiple types of resources, wherein the resources of the distribution network include gas turbines, DGs, SESSs and MESSs, and the method comprises:

[0006] S1, constructing a data set including 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 dividing the data set into training samples and test samples;

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

[0008] S3, inputting the forecast data of each DG output and the whole network load in the black start period into the optimal model to obtain the uncertainty interval of its forecast error, and generating multiple extreme disturbance scenarios according to the uncertainty interval; 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 forecast error of each DG output and the whole network load in each period in the black start period;

[0009] S4, taking the minimization of the load power outage penalty cost, DGs power abandonment penalty cost, gas turbine fuel cost, energy storage device operation cost and network loss cost of the distribution network as the objective function, establish a black start optimization model for the distribution network, and substitute the predicted data of each DG output and the whole network load under each extreme disturbance scenario into the DGs power abandonment penalty cost and the node power balance constraint of the objective function one by one, solve the objective function, and obtain the black start strategy of the distribution network.

[0010] According to a second aspect of the present invention, there is provided an electronic device, 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 used to read the 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 present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to cause a processor to execute the method as described in the first aspect.

[0014] According to a fourth aspect of the present invention, there is provided a computer program product, comprising a computer program or instructions, wherein when the computer program or instructions are executed by a processor, the method according to the first aspect is implemented.

[0015] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0016] Aiming at the problem of power grid recovery after a major power outage, the present invention proposes an active distribution network black start strategy that considers uncertainty on both sides of the source and load and multiple types of resources. Firstly, a joint distribution model of source-load prediction data and prediction error is established based on the Copula function, and the uncertainty of the prediction error of DGs and load is characterized in intervals; secondly, with the goal of minimizing power outage losses and operating costs, an active distribution network black start optimization model considering multiple types of resources such as gas turbines, DGs, SESSs, and MESSs is established; finally, source-load extreme disturbance scenarios are randomly generated according to the source-load prediction error interval, and substituted into the black start optimization model for solution, and a black start strategy that can cope with each source-load extreme disturbance scenario is obtained. Based on the calculation of the marginal distribution of the predicted output and the predicted error, the present invention further characterizes the nonlinear correlation between the predicted output and the predicted error, so that the performance index is better, and the output interval result can more effectively reflect the actual error situation; in addition, the method takes into account the impact of uncertainty on both the source and load sides on the system recovery process, and introduces it into the black start optimization model in the form of confidence intervals. While giving full play to the black start value of DGs and energy storage devices, it can effectively ensure the frequency and voltage stability of the system and realize the robust recovery of the active distribution network.

[0017] Furthermore, in order to ensure that the black start solution finally obtained can properly deal with the uncertainty on both sides of the source and the load, the present invention also uses randomly generated disturbance scenarios to verify the reliability of the distribution network black start strategy obtained in step S4 that can simultaneously deal with various extreme scenarios. If the strategy cannot handle one of the scenarios, then on the basis of the extreme disturbance scenario, combined with the predicted data of the DGs output and the load of the entire network under the scenario, they are respectively substituted one by one into the DGs power abandonment penalty cost and the node power balance constraint of the objective function, and the objective function is re-solved until a black start solution that can effectively deal 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 ensure that the black start solution finally obtained can properly deal with the uncertainty on both sides of the source and the load. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A flow chart of a black start method for an active distribution network taking into account source-load uncertainty and multiple types of resources provided in an embodiment of the present invention.

[0019] Figure 2 A schematic diagram of a source-load random disturbance scenario generation process provided in an embodiment of the present invention.

[0020] Figure 3 The corresponding sampling random numbers when generating the four extreme scenarios provided in the embodiment of the present invention.

[0021] Figure 4 This is the improved IEEE 33-node system topology diagram.

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

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

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

[0025] Figure 8 It is a schematic diagram comparing the net load fluctuation and the primary frequency regulation capability of the system in a typical scenario in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0027] As the "last mile" serving the people's livelihood, the distribution network is more closely connected with users. If the uncertainty of source and load in the recovery process can be effectively characterized and properly handled, and multiple types of resources can be fully utilized to achieve black start safely, stably and quickly, it can not only ensure the power supply of key loads and reduce economic losses, but also provide auxiliary power supply and flexibility support for the startup of key nodes of the transmission network, and accelerate the overall recovery process of the system. Based on this, an embodiment of the present invention provides an active distribution network black start method considering source and load uncertainty and multiple types of resources, the resources of the distribution network include gas turbines, DGs, SESSs and MESSs, and the method includes:

[0028] S1, constructing a data set including historical prediction data and historical prediction errors of the output of each DG in the distribution network and the load of the entire network, and dividing the data set into training samples and test samples.

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

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

[0031] Specifically, for each DG and the overall load of the entire network, the marginal distribution of the historical forecast data of each DG and the overall load of the entire network and the marginal distribution of the historical forecast error are calculated using training samples. The calculation is performed using existing methods, such as kernel density estimation, normal distribution fitting method, T distribution fitting method, etc., and the embodiments of the present invention do not limit this to uniqueness.

[0032] Those skilled in the art know that there are many types of Copula functions, including Gaussian Copula, T Copula, Clayton Copula, SJC Copula, etc., which are not listed here. The embodiment of the present invention does not limit the specific type of Copula function used in S2 to be unique.

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

[0034] Then, for each DG and the overall load of the entire network, the predicted data in the test sample are input into the above four joint distribution models respectively to obtain the uncertainty interval of the prediction error output by each model under at least one confidence level, and compared with the actual prediction error in the test sample, and the average reliability and sharpness index of the output results of the four groups of models are calculated to select the optimal model.

[0035] For example, taking 9 confidence levels of 0.98, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3 and 0.2 as an example, the predicted data in the test sample are respectively input into the above four joint distribution models for each DG and the overall load of the whole network, and the uncertainty interval of the prediction error output by each model at the 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 sample, the average reliability index and sharpness index of the output results of each model at the 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 calculation formulas for the reliability index and sharpness index are:

[0037]

[0038] In the above formula, Rel (ρ) and Shp (ρ) are the reliability index and sharpness index of the model under the confidence level ρ, Num is the total number of test samples, and They are the upper and lower bounds of the uncertainty interval of the prediction error of the kth sample output by the model under the confidence level ρ, and χ kis the actual prediction error value corresponding to the kth sample, and Index(k) is the indicative function of the model output interval envelope of the actual sample point. It can be seen that the reliability index can characterize the probability deviation degree of the model output uncertainty interval envelope ability and the selected confidence level, while the sharpness index can reflect the redundancy of the model output interval. Obviously, the lower the absolute value of the two, the better the model.

[0039] S3, inputting the predicted data of the output of each DG and the load of the entire network during the black start period into the optimal model to obtain the uncertainty interval of its prediction error, and generating multiple extreme disturbance scenarios according to the uncertainty interval; wherein the multiple extreme disturbance scenarios include power shortage scenarios, power surplus scenarios and source-load fluctuation scenarios, all of which are characterized by the prediction error of the predicted data of the output of each DG and the load of the entire network in each period during the black start period.

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

[0041] It can be understood that multiple extreme disturbance scenarios include power shortage scenario, power surplus scenario and source-load fluctuation scenario, namely, extreme power shortage scenario, extreme power surplus scenario and source-load fluctuation scenario (“source” refers to DGs and “load” refers to the entire network load), that is:

[0042] In the power shortage scenario, 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 excess power supply, 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 the first and second source-load fluctuation scenarios. 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 bound of the interval is taken in the previous period, and the lower bound of the interval is taken in the next period, and the jump is repeated), while the load prediction error is the opposite. The jump 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 bounds of the initial period are opposite, that is:

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

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

[0047] S4, taking the minimization of the load power outage penalty cost, DGs power abandonment penalty cost, gas turbine fuel cost, energy storage device operation cost and network loss cost of the distribution network as the objective function, establish a black start optimization model for the distribution network, and substitute the predicted data of each DG output under each extreme disturbance scenario into the DGs power abandonment penalty cost, substitute the predicted data of the entire network load under each extreme disturbance scenario into the node power balance constraint of the objective function, solve the objective function, and obtain the black start strategy of the distribution network.

[0048] Specifically, an active distribution network black start optimization model considering multiple types of resources such as gas turbines, DGs, SESSs, and MESSs is established. The optimization objective of the black start optimization model is to minimize the power outage loss and overall operating cost of the distribution network. Accordingly, the objective function includes the load power outage penalty cost, DGs power abandonment 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 periods, nodes, DGs, gas turbines, MESSs, SESSs, and lines, respectively; δ n is the load outage penalty cost coefficient of node n. Considering that in the black start process, the primary goal should be to restore the load power supply safely, stably and quickly, and 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 grid operation cost; and PL n,t are the restored state variables and active load of node n in period t respectively; λ is the penalty cost coefficient of DGs power abandonment; and are the dispatchable power and actual dispatch power of DGj in period t respectively; α i is the fuel cost coefficient of gas turbine i; is the active power output of gas turbine i during period t; w m and w s are the charging and discharging cost coefficients of MESSs and SESSs, and are the charging and discharging power of MESSm and SESSs in period t, γ is the mobility cost coefficient of MESSs, v m,tis the mobile state variable of MESSsm in period t; β is the network loss cost coefficient, Pf l,t is the active power on line l during period t.

[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 safety constraints, and network recovery constraints.

[0052] Gas turbine operation constraints: These constraints are used to ensure that the gas turbine meets basic startup and output requirements.

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

[0054] Energy storage device charge and discharge constraints: This constraint is used to ensure that the energy storage device meets basic requirements such as power limit, SOC limit, and charge and discharge state limit.

[0055] MESSs mobility / access status constraints: This constraint is used to ensure that the access and mobility of MESSs meet the basic requirements of the distribution network and transportation network.

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

[0057] Power flow constraint: This constraint is used to ensure that the distribution network satisfies the basic power flow equation and the line is not overloaded.

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

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

[0060] The mathematical expressions of the above constraints are introduced below.

[0061] Gas turbine operating constraints:

[0062] Generally speaking, the ramp rate of a gas turbine is fast, while the starting power is relatively small. The process of converting power from absorption to output can be completed within 1 minute, which is shorter than the time interval for restoring scheduling. Therefore, the conversion process can be simplified and considered to be completed instantly. The simplified operation constraints are:

[0063]

[0064] In the above formula, T i STis the start-up time of unit i, and are the startup state variable and output state variable of unit i in period t, P i ST is the starting power required for unit i, P i G,max and are the upper limits of active and reactive output of unit i, is the reactive power output of unit i during period t, is the active output climbing limit of unit i.

[0065] DGs operation constraints:

[0066] DGs such as wind power and photovoltaic power have low startup power and fast startup speed, and do not need to climb. It can be approximately considered that they can start generating electricity after the node where they are located is restored. Based on this, the operation constraints of DGs are:

[0067]

[0068] In the above formula, is the output state variable of DGj in period t, is the reactive power output of DGj during period t, is the upper limit of reactive power output of DGj.

[0069] Energy storage device charging and discharging constraints:

[0070]

[0071] In the above formula, and are the charge and discharge state variables of MESSm and SESSs in period t, and are the startup state variables of MESSm and SESSs in period t, and are the upper limits of active and reactive output of MESSm and SESSs, respectively, Q m,t and Q s,t are the reactive power output of MESSm and SESSs in period t, E m,t and E s,t are the energies contained in MESSm and SESSs in period t, ηm and ηs are the charging and discharging efficiencies of MESSs and SESSs, Δt is the duration of the unit scheduling period, and are the rated capacities of MESSm and SESSs, SOC max and SOC minThey are respectively the upper and lower limits of the state of charge (SOC) of the energy storage device.

[0072] MESSs mobility / access status constraints:

[0073]

[0074] In the above formula, N CM is the set of nodes accessible to MESSs, u m,n,t is the connection state variable between MESSm and node n during period t, is the required moving time of MESSm. The constraints are expressed from top to bottom: ① The connection state and the moving state of MESSs are mutually exclusive, and a MESS can only access one accessible node at most in the same period; ② MESS can only be charged and discharged when it is connected; ③ Each accessible node can only access one MESS at most in each period; ④ When MESSm is connected to node n in period t, it needs to travel at least time before it can connect to the next node p.

[0075] Node power balance constraints:

[0076]

[0077] In the above formula, and are the sets of MESSs, SESSs, gas turbines and DGs connected to node n, O(l) and D(l) are the first and last node numbers of line l, respectively. n,t and QL n,t are the active and reactive loads on node n during period t, Qf l,t is the reactive power on line l during period t.

[0078] Power flow constraints:

[0079]

[0080] In the above formula, is the restored state variable of line l during period t, G l and B l are the conductance and susceptance of line l, V n,t and θ n,t are the voltage amplitude and phase angle of node n in period t, I(n) and E(n) are the input and output lines of node n, Pf l max and Qf l max are the upper limits of active and reactive power of line l respectively.

[0081] Frequency and voltage safety constraints:

[0082]

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

[0084] Network recovery constraints:

[0085]

[0086] In the above formula, N root is the number of root nodes, and its initial value is the sum of the number of MESSs and SESSs, which will gradually decrease as the network merges; T l is the required recovery time for line 1. It should be noted that the merging process of the distribution network can be carried out by adjusting the output or load demand of the gas turbine and the energy storage device. Compared with the transmission network, the time required is shorter, so the present invention approximately equates it to the commissioning process of the interconnection line. In addition, the model assumes that MESSs and SESSs have black start capabilities, and DGs and gas turbines (excluding independent battery power supply) are all waiting to be started. This state is only a typical example selected by the inventor and can be adjusted according to the actual situation of the power grid.

[0087] In order to ensure the robustness of the model and avoid the impact of a large amount of calculation on timeliness, the present invention uses the above four extreme scenarios to formulate black start scheduling strategies, that is, the predicted data of each DG output under the above extreme disturbance scenarios are substituted into the calculation formula of the DGs power abandonment penalty cost (i.e. ), substitute the predicted data of the whole network load under the above extreme disturbance scenarios into the node power balance constraint of the objective function (i.e. PL n,t and QL n,t ), the objective function is solved to obtain a distribution network black start strategy that can simultaneously cope with the above four extreme disturbance scenarios. From a theoretical analysis, this strategy can also cope with various source-load disturbance scenarios that may occur in real life.

[0088] In order to ensure that the black start solution finally obtained can properly deal with the uncertainty on both sides of the source and the load, a randomly generated disturbance scenario can be used to verify the reliability of the distribution network black start strategy obtained in step S4 that can simultaneously deal with the above four extreme scenarios. If the strategy cannot handle one of the scenarios, then on the basis of the extreme disturbance scenario, combined with the predicted data of the DGs output and the load of the entire network under the scenario, they are substituted one by one into the DGs power abandonment penalty cost and the node power balance constraint of the objective function, and the objective function is re-solved until a black start solution that can effectively deal 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 believed that the black start solution finally obtained can properly deal with the uncertainty on both sides of the source and the load, and output it as the optimal result. That is, as a further preference of the present invention, the method also 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 used as the optimal strategy. Otherwise, the predicted data of DGs output and the load of the entire network under each extreme disturbance scenario and the random disturbance scenario that cannot be handled are respectively substituted into the DGs power abandonment penalty cost and the node power balance constraint of the objective function one by one, and the objective function is solved to obtain the black start strategy of the distribution network, and use it as the optimal strategy;

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

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

[0092] It can be understood that the uncertainty interval of the prediction error of the prediction data of each DG output and the whole network load during the black start period has been obtained in step S3. According to the uncertainty interval, a plurality of random disturbance scenarios can be obtained by randomly generating.

[0093] For example, by generating random numbers, a random value is randomly selected in the uncertainty interval to characterize the source load prediction error of a random disturbance scenario. Figure 2 As shown, taking the random number as a positive and negative binary random number as an example, first, generate (j end +1) row, tend The columns are positive and negative binary random number matrices, where j end is the number of DGs in the distribution network, t end is the number of time periods in the entire black start process; then, the first j end The random numbers in each row correspond one by one to each DG in the distribution network. end +1) corresponds to the overall load of the power grid; if the random number corresponding to a DG (or the overall load of the power grid) in a certain period of time is a positive value, the upper bound of the uncertainty interval is taken; if it is a negative value, the lower bound of the uncertainty interval is taken, thereby completing the source load prediction error value under a certain random disturbance scenario. Similarly, the sampling random numbers corresponding to each extreme disturbance scenario are as follows Figure 3 shown.

[0094] It can be understood that each random disturbance scenario and each extreme disturbance scenario adopts the prediction error of the prediction data of each DG output and the whole network load in each period within the black start period. 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 the scenario and the prediction data of each DG output during the black start period in S3; the prediction data of the whole network load under a certain extreme disturbance scenario or random disturbance scenario is the sum of the prediction error of the whole network load corresponding to the scenario and the prediction data of the whole network load during the black start period in S3.

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

[0096] The method provided by the present invention is further illustrated by taking a specific example as follows.

[0097] Will be like Figure 4 The improved IEEE 33-node system shown is the implementation object of the method provided by the present invention. The system contains 6 gas turbines, 8 DGs, two SESSs and two MESSs, and their parameters are shown in Tables 1-3 respectively. The scheduling duration is 1 hour, and the time interval is set to 2 minutes. The upper and lower limits of the active and reactive power of the line are 2000kW and 1600kVar respectively, and the recovery time is set to 2 time periods. The initial value and upper and lower limits of the SOC of all energy storage devices are 0.5, 0.9 and 0.1, and the charging and discharging efficiency is 90%. Taking into account that the system voltage may fluctuate during the black start process, the upper and lower limits of each node voltage are taken as 1.1 and 0.9 times the standard value.

[0098] The source-load power prediction curve during the dispatch process is as follows: Figure 5 and Figure 6As shown. The active and reactive power of the load at each busbar can be obtained by proportional conversion based on standard data. In addition, important loads are connected at nodes 4, 8, 12, 15, 18, 29, 31 and 32. In order to ensure their rapid recovery, MESSs charging and discharging stations are installed at the above nodes, and their power outage penalty costs are set to 30￥ / kWh, which is 10 times the power outage penalty cost of ordinary loads. At the same time, the operating cost coefficients of SESSs and MESSs are set to 0.036￥ / kWh and 0.06￥ / kWh, the mobile cost coefficient of MESSs is set to 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 energy storage device in the system

[0104]

[0105] In combination with the above parameters, this embodiment is performed in the following steps:

[0106] S1, collects historical forecast data and historical forecast errors of DGs and the overall load of the whole network, combines them to form an input data set, and further divides them into two categories: training samples and test samples;

[0107] S2, for each DG and the overall load of the whole network, the marginal distribution of its prediction data and prediction error is calculated using training samples and kernel density estimation method, and then the joint distribution model of prediction data and prediction error is established based on Gaussian Copula, TCopula, Clayton Copula and SJCCopula functions in turn; further, for each DG and the overall load of the whole network, the prediction data in the test sample is input into the four sets of established joint distribution models to obtain the prediction error uncertainty intervals of each model output at 0.98, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3 and 0.2 confidence levels, and compared with the actual prediction errors in the samples, the average reliability and sharpness index of the output results of the four sets of models are calculated, so as to select the optimal model;

[0108] According to formulas (1)-(3), the reliability and sharpness indexes of each model at different confidence levels are calculated respectively, 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 whole network load are SJC, SJC, Clayton, SJC, SJC, SJC, Clayton, Clayton and Gaussian, respectively. The model corresponding to each optimal Copula function is the model used in the subsequent steps of the present invention.

[0109] In order to verify the effectiveness of the model adopted by the present invention, taking DG No. 1 as an example, its performance is compared with the calculation model of the uncertainty interval of the source load prediction error obtained based on Gaussian distribution, empirical distribution, overall kernel density estimation, and hierarchical kernel density estimation. Similarly, taking the above training samples and test samples as input data, the uncertainty intervals of the four outputs are obtained respectively, and the reliability and sharpness index average values ​​under different confidence levels are calculated, as shown in Table 5. It can be seen from the table that the indicators corresponding to the empirical distribution and the overall kernel density estimation model are similar and at a high level. This is because the two do not consider the correlation between the predicted output and the prediction error, and only model the output interval based on the frequency distribution results obtained by statistics, so the output interval accuracy is low; Gaussian distribution also does not consider the correlation, but because its output interval result is wider, it can sacrifice the sharpness index in exchange for a partial improvement in the reliability of the model. In contrast, the performance of the hierarchical kernel density estimation is significantly improved because it takes into account the linear correlation between the input data, and its reliability and sharpness indicators are also at a relatively low level; the model of the present invention further characterizes the nonlinear correlation between the predicted output and the predicted error on the basis of the hierarchical kernel density estimation, so the performance indicators are better, and the output interval results can more effectively reflect the actual error situation.

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

[0111]

[0112] Table 5 Comparison of performance indicators of the model of the present invention and common models

[0113] type Reliability index average value Average sharpness index The absolute value and 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 Model of the present invention -0.0072 0.0638 0.0710

[0114] S3, obtains the predicted power data of each DG and the whole network load during the black start process, inputs the corresponding optimal model screened by S2, calculates the uncertainty interval of its prediction error, and generates various extreme disturbance environments according to the uncertainty interval.

[0115] Respectively Figure 5 and Figure 6The source-load power prediction curve in is input into the optimal model obtained in step S2 to obtain the uncertainty interval of the prediction error during the black start process, and the interval results under the confidence level of 0.9 are selected to generate various extreme disturbance 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 power outage penalty cost, DGs power abandonment penalty cost, gas turbine fuel cost, energy storage device operation cost and network loss cost of the distribution network as the objective function, establish a black start optimization model for the distribution network, and substitute the predicted data of each DG output and the whole network load under each extreme disturbance scenario into the DGs power abandonment penalty cost and the node power balance constraint of the objective function one by one, solve the objective function, and obtain the black start strategy of the distribution network.

[0117] As a preferred solution, 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 used as the optimal strategy. Otherwise, the predicted data of DGs output and the load of the entire network under each extreme disturbance scenario and the random disturbance scenario that cannot be handled are respectively substituted into the DGs power abandonment penalty cost and the node power balance constraint of the objective function one by one, and the objective function is re-solved to obtain the black start strategy of the distribution network, and it is used as the optimal strategy.

[0118] Figure 7(a) to (d) in the figure show the overall system recovery process corresponding to the obtained strategy, and use different colors to distinguish the input status of lines and nodes in each period. As can be seen from the figure, after the black start begins, the energy storage device will first restore the nearby DGs, and form a stable power source with flexible adjustment capabilities to cope with the frequency and voltage shocks caused by the source load access and prediction error uncertainty, and then gradually start the surrounding gas turbines and restore the load, forming a local power grid that operates independently in a small range. As the local power grid continues to "grow and grow", its boundaries are getting closer and closer, and it will continue to merge into a larger power grid, thereby providing backup and emergency power support to each other to further restore more loads. In addition, it can be seen that in periods 1 to 5, after MESS2 completes the black start "ignition" task at node 18, it will continue to go to node 4 for power supply. This is because there are important loads at node 4 and a high proportion of DGs are connected nearby. In this context, MESS2 can give full play to its flexible mobility in space, ensure the power supply of important loads to reduce system power outage losses, and provide higher flexibility support for subsequent DGs access through coordination with SESS1. During the entire recovery process, the system's renewable energy consumption rate reached 99.97%, and 56.94% of the load was powered by renewable energy. The average power utilization rate of the energy storage device reached 67.36%, and it provided 86.47% of positive reserve capacity and 91.89% of negative reserve capacity. Furthermore, the present invention uses the control variable method to test the black start capability of the distribution network that does not contain DGs, SESSs and MESSs. The results show that in the above three cases, the system cannot achieve black start due to insufficient power supply capacity or shortage of flexible adjustment resources. Based on the above analysis, it can be seen that the black start strategy proposed in the present invention can fully tap the recovery value of DGs and energy storage devices, realize parallel startup of the system, and effectively reduce power outage losses.

[0119] On the other hand, in order to illustrate the superiority of the proposed strategy over the existing methods, the uncertainty intervals of the outputs of the model of the present invention and the four common models mentioned in Table 5 under the confidence level of 0.9 are respectively applied to the black start process of the active distribution network, and their economy and rapidity are compared, as shown in Table 6. It can be seen from the table that under the same confidence level, that is, the same safety factor, compared with the above four common models, the overall operating cost of the model of the present invention is reduced by 10.38%, 0.77%, 1.14% and 0.23% respectively, and the calculation time is also improved by 41.67%, 16.26%, 26.68% and 4.78% respectively, and the time period for completing the recovery is also relatively early. It can be seen that compared with the existing methods, the model of the present invention can provide a more economical and rapid recovery plan while taking into account safety. It should be noted that the analysis here only takes the 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 the present invention.

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

[0121] type Overall system operating cost (￥) Time period to complete recovery 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 Model of the present invention <![CDATA[6.4251×10 3 ]]> 19 18.74

[0122] In addition, in order to verify the processing ability of the obtained strategy for the uncertainty of both the source and the load during the black start process, the present invention also compares and analyzes the net load changes and the primary frequency regulation capability of the system under four extreme scenarios and 200 groups of random scenarios (due to space limitations, Figure 8 Only some typical scenarios are shown). The results show that the net load fluctuations of the system in each scenario are within the range of its primary frequency regulation capability, and there will be no frequency safety issues due to the uncertainty of the source-load prediction error. In addition, during the entire recovery process, the voltage of each node is also within the specified range. It can be seen that the black start strategy proposed in the present invention can effectively deal with the uncertainty on both sides of the source and load, ensure the stability of the system's frequency and voltage, and achieve the robust recovery of the active distribution network.

[0123] In summary, the active distribution network black start method proposed in the present invention that takes into account source-load uncertainty and multiple types of resources is effective and reasonable.

[0124] An embodiment of the present 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 used to read the executable instructions stored in the computer-readable storage medium and execute the method described in any of the above embodiments.

[0127] An embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method described in any of the above embodiments.

[0128] An embodiment of the present invention provides a computer program product, including a computer program or instructions, and when the computer program or instructions are executed by a processor, the method described in any of the above embodiments is implemented.

[0129] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. An active distribution network black start method considering source-load uncertainty and multi-type resources, wherein the resources of the distribution network include gas turbines, DGs, SESSs and MESSs, characterized in that: The method comprises: S1, constructing a data set including 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 dividing the data set into training samples and test samples; S2, using the training samples to respectively calculate the marginal distribution of the historical prediction data and the historical prediction errors, and using at least two Copula functions to respectively establish the joint distribution models of the historical prediction data and the historical prediction errors; inputting the prediction data in the test samples into each of the joint distribution models, obtaining the uncertainty interval of the prediction error output by the model under at least one confidence level, and calculating the average reliability and sharpness of each of the joint distribution models in combination with the historical prediction errors in the test samples, and taking the joint distribution model with the lowest absolute values ​​of the average reliability and sharpness as the optimal model; S3, inputting the forecast data of each DG output and the whole network load in the black start period into the optimal model to obtain the uncertainty interval of its forecast error, and generating multiple extreme disturbance scenarios according to the uncertainty interval; 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 forecast error of each DG output and the whole network load in each period in the black start period; S4, taking the minimization of the load power outage penalty cost, DGs power abandonment penalty cost, gas turbine fuel cost, energy storage device operation cost and network loss cost of the distribution network as the objective function, establish a black start optimization model for the distribution network, and substitute the predicted data of each DG output and the whole network load under each extreme disturbance scenario into the DGs power abandonment penalty cost and the node power balance constraint of the objective function one by one, solve the objective function, and obtain the black start strategy of the distribution network.

2. The method according to claim 1, characterized in that In the power shortage scenario, 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 excess power supply, 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 scenarios include first and second source-load fluctuation scenarios; Among them, in the first source load fluctuation scenario, the prediction error of each DG output and the time frequency repeatedly jump between the upper and lower bounds of the uncertainty interval in S3, and the prediction error of the entire network load and the time frequency repeatedly jump between the lower and upper bounds of the uncertainty interval in S3; In the second source-load fluctuation scenario, the prediction error of each DG output and the time frequency repeatedly jump between the lower and upper bounds of the uncertainty interval in S3, and the prediction error of the entire network load and the time frequency repeatedly jump between the upper and lower bounds of the uncertainty interval in S3.

3. The method according to claim 1 or 2, characterized in that The method further comprises: 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 used as the optimal strategy. Otherwise, the predicted data of DGs output and the load of the entire network under each extreme disturbance scenario and the random disturbance scenario that cannot be handled are respectively substituted into the DGs power abandonment penalty cost and the node power balance constraint of the objective function one by one, and the objective function is solved to obtain the black start strategy of the distribution network, and use it as the optimal strategy; 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 whole network load in each period during the black start period.

4. The method according to claim 1, characterized in that The objective function is: Among them, T, N, J, I, M, S, and L are the sets of scheduling periods, nodes, DGs, gas turbines, MESSs, SESSs, and lines, respectively; δ n is the load outage penalty cost coefficient of node n. Considering that in the black start process, the primary goal should be to restore the load power supply safely, stably and quickly, and 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 grid operation cost; and PL n,t are the restored state variables and active load of node n in period t respectively; λ is the penalty cost coefficient of DGs power abandonment; and are the dispatchable power and actual dispatch power of DGj in period t respectively; α i is the fuel cost coefficient of gas turbine i; is the active power output of gas turbine i during period t; w m and w s are the charging and discharging cost coefficients of MESSs and SESSs, and are the charging and discharging power of MESSm and SESSs in period t, γ is the mobility cost coefficient of MESSs, v m,t is the mobile state variable of MESSs m in period t; β is the network loss cost coefficient, Pf l,t is the active power on line l during period t.

5. The method according to claim 1, characterized in that 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 status constraints, power flow constraints, frequency and voltage safety constraints and network recovery constraints.

6. The method according to claim 5, characterized in that The gas turbine operating constraints are: Among them, T i ST is the start-up time of unit i, and are the startup state variable and output state variable of unit i in period t, P i ST is the starting power required for unit i, P i G,max and Q i G,max are the upper limits of active and reactive output of unit i, is the reactive power output of unit i during period t, is the active output ramp limit of unit i; The DGs operation constraints are: in, is the output state variable of DGj in period t, is the reactive power output of DGj during period t, is the upper limit of reactive power output of DGj; The energy storage device charging and discharging constraints are: in, and are the charge and discharge state variables of MESSm and SESSs in period t, and are the startup state variables of MESSm and SESS s in period t, and are the upper limits of active and reactive output of MESS m and SESS s, respectively, Q m,t and Q s,t are the reactive power outputs of MESS m and SESS s in period t, E m,t and E s,t are the energies contained in MESS m and SESS s in period t, ηm and ηs are the charge and discharge efficiencies of MESSs and SESSs, Δt is the duration of the unit scheduling period, and are the rated capacities of MESS m and SESS s, respectively, and SOC max and SOC min are the upper and lower limits of the state of charge of the energy storage device respectively; The MESSs mobility / access state constraints are: Among them, N CM is the set of nodes accessible to MESSs, u m,n,t is the connection state variable between MESS m and node n during period t, The moving time required for MESSm; The node power balance constraint is: in, and are the sets of MESSs, SESSs, gas turbines and DGs connected to node n, O(l) and D(l) are the first and last node numbers of line l, PL n,t and QL n,t are the active and reactive loads on node n during period t, Qf l,t is the reactive power on line l during period t; The power flow constraint is: in, is the restored state variable of line l during period t, G l and B l are the conductance and susceptance of line l, V n,t and θ n,t are the voltage amplitude and phase angle of node n in period t, I(n) and E(n) are the input and output lines of node n, Pf l max and Qf l max are respectively the upper limits of active and reactive power of line l; The frequency and voltage safety constraints are: Where Δf max The maximum frequency deviation allowed by the system is set to 0.5 Hz. and are the frequency response coefficients of gas turbine i, MESSm and SESS s, ref is the reference node number, V n max and V n min are the upper and lower limits of the voltage amplitude at node n, is the upper limit of the voltage phase angle deviation at node n; The network recovery constraints are: Among them, N root is the number of root nodes, T l is the required recovery time of line l.

7. An electronic device, characterized in that: include: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method according to any one of claims 1 to 6.

9. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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