Autonomous region division method based on stochastic model predictive control under chance constraint

Abstract

This paper proposes an autonomous region (AGR) partitioning method based on stochastic model predictive control under opportunity constraints. It uses a differential autoregressive moving average model to predict wind and solar power output. Considering the uncertainty of wind and solar power output, an opportunity constraint system for AGR partitioning is established with the objective of minimizing the load shedding risk rate of the AGR. Combining the prediction error probability models of solar and wind turbines, a scenario analysis method is used to generate a distributed power output scenario set within a specified reasonable output range. Stochastic simulation technology is then used to solve the opportunity constraints. A novel AGR partitioning optimization model for distribution systems based on stochastic model predictive control is constructed, continuously optimizing through rolling optimization and feedback correction. This method addresses the problem of excessively high control dimensions caused by distributed energy access to the distribution network in existing technologies. It can maintain a low load shedding risk probability at a certain confidence level, improving the absorption of distributed renewable energy and the stability of the AGR while ensuring power supply reliability.

Description

Technical Field

[0001] This invention relates to the field of distribution network optimization partitioning, and in particular to an autonomous region partitioning method based on stochastic model predictive control under chance constraints. Background Technology

[0002] Under the "dual carbon" target, distributed energy generation has gradually shifted from the previous free grid connection mode to a model that combines centralized and decentralized photovoltaic grid connection, resulting in an excessively high proportion of distributed energy grid connection in some regions. Due to the uncertainty of distributed power output and the shortcomings of previous centralized voltage control methods, the problems brought about by large-scale distributed energy grid connection to the distribution network are increasing. Transforming the high-dimensional optimization problem of a distribution network with distributed energy grid connection into the optimization problem of several sub-autonomous regions, with each autonomous region being regulated as a whole, effectively improves the distribution network's ability to manage distributed energy and facilitates hierarchical and zonal control of the distribution network. Therefore, it is necessary to study a dynamic division method of autonomous regions based on stochastic model predictive control under chance constraints, considering system uncertainties, to effectively reduce the difficulty and dimensionality of distribution network control, and enable more stable system operation, regulation, and management.

[0003] Experts and scholars in the field of power systems have also conducted extensive research on the delineation of autonomous regions in distribution networks, but it is still in its initial stage, and a universal delineation system and method have not yet been established. Existing research on the delineation of autonomous regions in distribution networks often uses indicators such as improved modularity functions and autonomous region power balance as the basis for delineation, and employs intelligent algorithms for solving these problems. However, it does not adequately consider the impact of the intermittency and volatility of distributed resource output, and static delineation methods are prone to making the results difficult to adapt to changes in system operating conditions. Existing delineation methods are mostly based on intelligent algorithms, which easily lead to local optima, and they do not adequately consider the impact of the intermittency and volatility of distributed resource output. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this application discloses an autonomous region partitioning method based on stochastic model predictive control under chance constraints. This method is used to solve the problem of excessively high control dimensions caused by distributed energy access to the distribution network in existing technologies. The proposed partitioning method can ensure that the probability of load shedding risk remains at a low level under a certain confidence level, effectively and reasonably matching distributed renewable energy with autonomous regions, ensuring the power balance and power supply reliability of autonomous regions, improving the absorption of distributed renewable energy, and enhancing the stability of autonomous regions.

[0005] The technical solution to achieve the objective of this invention is:

[0006] An autonomous region delineation method based on stochastic model predictive control under chance constraints, specifically including the following steps:

[0007] Step 1: After obtaining all possible autonomous region division schemes by the branch cut enumeration method, the Autoregressive Integrated Moving Average Model (ARIMA) is used to predict the output of wind and solar power, generating the output power of photovoltaic, wind turbine and load in the prediction time domain;

[0008] Step 2: Considering the uncertainty of wind and solar power output, with the objective function of minimizing the load loss risk rate of the autonomous region, construct a partition constraint that covers the opportunity constraints of the power supply rate of the autonomous region, the opportunity constraints of the power balance of the autonomous region, and the system safety operation constraints.

[0009] Step 3: Combining the predicted output and prediction error probability models of photovoltaic and wind turbines, the scenario analysis method is used to generate a set of distributed output scenarios representing uncertainties within the specified reasonable output range, and the average output of distributed energy is obtained. Stochastic simulation technology is used to solve the chance constraints considering the uncertainty of wind and solar output.

[0010] Step 4: Construct a novel autonomous region partitioning optimization model for the power distribution system based on Stochastic Model Predictive Control (SMPC). In the rolling optimization part, a breadth-first search algorithm is used to collect information on all partitioning schemes, calculate the objective function that satisfies the constraints under a certain confidence level for all schemes, and determine the autonomous region partitioning scheme for the first rolling optimization time period. During feedback correction, the predicted values ​​of wind turbines, photovoltaics, and loads are updated based on the latest real-time measurements.

[0011] Step 5: Repeat steps 2 to 4 to complete the division of autonomous regions for subsequent time periods.

[0012] Furthermore, in step 1, the prediction module is used to generate the output power of photovoltaic, wind turbine, and load in the prediction time domain, as follows:

[0013] The prediction model uses the ARIMA model. Its core idea is to stationary the time series through differencing, and then use a moving average regression model for prediction after stationarization. The ARIMA model is represented as ARIMA(p, d, q). This model consists of two parts: an autoregressive (AR) model and a moving average (MA) model. p is the order of the autoregressive model, q is the order of the moving average, and d is the difference degree. ARIMA stationaries the data through differencing. Generally, one differencing operation is sufficient to stabilize the data; therefore, the value of d is typically 0, 1, or 2.

[0014] The mathematical formula for ARIMA(p, d, q) can be described as follows:

[0015]

[0016] In the formula: Y(t) is the value of the time series, t is the time point, and c is a constant term. It is the autoregressive coefficient, ε t These are the interference terms θ1, θ2, ..., θ q q is the moving average coefficient, p is the number of autoregressive terms in the AR model, and q is the number of moving average terms in the MA model.

[0017] The process of building an ARIMA model consists of the following three steps:

[0018] Step 1.1: Stationarity test. This step checks whether the time series meets the stationarity requirement. For non-stationary time series, it is necessary to first perform d-order differencing to transform it into a stationary time series.

[0019] Step 1.2: Calculate the autocorrelation coefficient (ACF) and partial autocorrelation coefficient (PACF) of the stationary time series, and perform parameter estimation by searching using the Akaikes Information Criterion (AIC) or Bayesian Information Criterion (BIC) to obtain the optimal order p and q;

[0020] Step 1.3: Obtain the ARIMA model using the above d, p, and q parameters. Perform model validation on the obtained model, specifically on the residual ε. t Perform analysis and checks to determine the applicability of the time series ARIMA model and to determine E(ε) t If the value is zero, it means that the obtained model has passed the test.

[0021] Furthermore, the objective function and constraints in step 2 are as follows:

[0022] (1) Objective function

[0023] Distributed renewable energy sources offer flexible operation modes, allowing for both grid-connected and off-grid operation. In the event of a major grid failure causing widespread power outages, autonomous regions can leverage their distributed renewable energy resources to provide power support for isolated operations, rapidly restoring power to critical loads and mitigating economic losses from large-scale power outages. This enables autonomous regions to operate independently. This paper aims to minimize the load loss risk rate of the autonomous region, establishing a chance-constrained objective function as follows:

[0024]

[0025] In the formula, F psr It is the target value for the risk rate of load loss in the autonomous region, F psrThe smaller the value, the better the power supply reliability of the autonomous region. str.j (t) is the power supply rate of autonomous region j at time t; P DG.i (t) is the output power of the i-th distributed power source in the autonomous region, P str.i (t) is the charging and discharging power of the i-th energy storage device in the autonomous region, P l.i (t) is the load power of node i in the autonomous region, N clu.j.DG N clu.j.str N clu.j.l N clu.j.g These represent the number of distributed power sources, energy storage devices, load nodes, and adjustable conventional units in autonomous region j, respectively, and T is the optimization period.

[0026] (2) Constraints:

[0027] 1) Probabilistic constraints on the power supply rate of autonomous regions, i.e.

[0028]

[0029] In the formula, F min ξ represents the minimum load power supply rate; x represents the decision variable, i.e., the division scheme of each autonomous region; ξ represents the distributed energy output scenario; n represents the number of distributed energy output scenarios. Let P be the sum of the probabilities of the events being true. ξ To contribute to a specific scenario within the set of scenarios that contribute to distributed resources; F(x,P) ξ For an output force of P ξ The load supply rate of the downstream system; β is the confidence level value satisfied by the objective function;

[0030] 2) Power balance indices and constraints for autonomous regions

[0031] The dynamic power balance of the autonomous region is constrained by the partitioning scheme to fully ensure power stability within the autonomous region. As load and DG power change in real time, certain risks are introduced to the safe and stable operation within the autonomous region. Based on this, a power balance index and constraint R for the autonomous region are proposed. p The definition is as follows:

[0032]

[0033] R p ≥β p (6)

[0034] In the formula: The total active power demand of the load within the autonomous region; Contributing to distributed energy resources; α represents the maximum active power output of distributed energy storage within the autonomous region; α represents the load power supply rate that needs to be satisfied within the autonomous region; β p The confidence level that the power balance constraint must satisfy;

[0035] Autonomous Region Power Balance Constraint R p This reflects the probability that the total output of DG within an autonomous region can meet the load demand to a certain extent under the condition of maximum energy storage. The higher the index, the higher the safety of the autonomous region and the more reasonable the division scheme.

[0036] 3) System safety operation constraints

[0037] U i,min ≤u i (t)≤U i,max (7)

[0038] |I ij (t)|≤I ij.max (8)

[0039] In the formula: u i (t) represents the voltage amplitude at node i at time t; U i,max and U i,min These are the upper and lower limits allowed for node i, respectively; I ij (t) represents the current amplitude of line ij at time t; I ij.max It is the maximum allowable current to flow through branch ij;

[0040] Furthermore, step 3 is as follows: The prediction errors for photovoltaic and wind turbine output and load are generally considered to follow a normal distribution, and the prediction error probability density function is:

[0041]

[0042] Where ΔP is the distributed energy output prediction error; μ and σ are the expected value and standard deviation of the prediction error, respectively, with μ set to 0; e i The value for each data point; n is the number of data points;

[0043] Latin hypercube sampling can avoid the problem of over-clustering of samples. The specific sampling steps are as follows:

[0044] Step 3.1: Divide the interval from 0 to 1 into l equal parts, and randomly generate a number P in each part according to a uniform distribution. i ;

[0045] Step 3.2: Shuffle the order of these l random numbers in any way, and these random numbers are the probability values ​​of each random sample;

[0046] Step 3.3: From the inverse function f of the probability distribution function-1 (P i )=x i Calculate the sample value corresponding to the probability value l of each sample;

[0047] Generally, there are analytical methods and stochastic simulation methods for handling chance constraints. This paper uses the stochastic simulation method to verify whether the division of autonomous regions satisfies the chance constraints. The steps to verify whether the division scheme can meet the confidence level of the chance constraints at time t are as follows:

[0048] 1) Based on the probability distribution characteristics of load and uncontrollable DG power output within the autonomous region, randomly select power curves based on the scenario generation technology in step 2;

[0049] 2) Count the total number of times the autonomous region satisfies power balance in M ​​samplings. p The total number of times M satisfies the probability constraint of the objective function for the rate of load loss in the autonomous region. v ;

[0050] 3) If If the autonomous region partitioning scheme at that moment is considered to satisfy the chance constraint, then the next autonomous region partitioning scheme is solved until the optimal autonomous region partitioning scheme that satisfies the objective function and the chance constraint at the confidence level is found.

[0051] Due to the randomness of wind and solar power output, prediction errors are prevalent in current wind and solar power forecasts. Most current forecasting methods have a wind speed prediction error of 25% to 40%. Although the ARIMA forecasting method proposed in this patent can effectively ensure the prediction accuracy of distributed power output, prediction errors still exist. Therefore, if the division of autonomous regions is carried out entirely according to the predicted output, there will be a large deviation, and the power quality and stability of the system after division will also be affected. However, if the prediction of distributed power output is not considered at all, and the output is calculated by randomly generating the prediction error of distributed power output according to the Weibull distribution function, it will be highly arbitrary and cannot guarantee the rationality of the division results. Therefore, if randomness and prediction regularity are combined, both arbitraryness and rationality of the division results can be avoided. This paper introduces the interval random simulation method to combine the two considerations.

[0052] For the power prediction curve of wind and solar power, considering the prediction error and its volatility, the output deviation is set at ±20%. It is assumed that the output level of wind and solar power at each moment fluctuates within the range of the upper and lower deviations, which is the range of random number generation for the output of wind and solar power at each moment.

[0053] Compared with the prior art, the present invention, employing the above technical solution, has the following beneficial effects:

[0054] 1. The autonomous region division method based on stochastic model predictive control under chance constraints proposed in this invention is used to solve the problem of excessive control dimension caused by distributed energy access to the distribution network in the prior art. It can ensure that the probability of load failure risk is kept at a low level under a certain confidence level, effectively and reasonably match distributed new energy with autonomous regions, and ensure the power balance and power supply reliability of autonomous regions.

[0055] 2. The autonomous region partitioning method based on stochastic model predictive control under chance constraints proposed in this invention includes all sampling scenarios in the chance constraint solution process and performs partitioning solution at a certain confidence level, thereby effectively balancing the impact of the randomness and volatility of distributed energy output on the partitioning results.

[0056] 3. The autonomous region partitioning method based on stochastic model predictive control under chance constraints proposed in this invention not only improves the absorption of distributed renewable energy and the stability of autonomous regions, but also provides data support and theoretical basis for the independent operation, regional coordination and islanding control of microgrids. Attached Figure Description

[0057] Figure 1 This is a flowchart of the autonomous region partitioning method based on stochastic model predictive control under chance constraints, according to a specific embodiment of the present invention.

[0058] Figure 2 This is a modified IEEE 33-node structure diagram of a specific embodiment of the present invention;

[0059] Figure 3 These are photovoltaic prediction values ​​under the ARIMA prediction model of a specific embodiment of the present invention;

[0060] Figure 4 This is the photovoltaic power output range of a specific embodiment of the present invention;

[0061] Figure 5 This is a partition map of the autonomous region of the No. 3 cutting line according to a specific embodiment of the present invention;

[0062] Figure 6 This is a partition map of the autonomous region of the cutting line No. 6 in a specific embodiment of the present invention;

[0063] Figure 7 This is a partition map of the autonomous region of cutting lines 4 and 8 in a specific embodiment of the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] To verify the effectiveness of the proposed method for dividing autonomous distribution networks, a case study is conducted using an improved IEEE 33-node power grid. The system has a total base capacity of 1 MVA, a voltage level of 12.66 kV, a voltage range of 0.95–1.05 pu, a total active load of 3715 kW, and a total reactive load of 2300 kvar. The system includes 2 wind turbines, 2 photovoltaic units, and 3 energy storage units, with their installation locations as follows: Figure 2 As shown, Figure 2 The black nodes in the table represent nodes with DG (Distributed Generation) capabilities. The DG installation nodes and their capacities are shown in Table 1. The minimum allowable power supply rate is set to 0.35. Simulation verification was performed on the Matlab 2016b platform. An autonomous region partitioning model was constructed using the Yalmip optimization toolbox, and the optimization solution software Cplex was used for solving the model.

[0066] Table 1 DG Installation Capacity

[0067]

[0068] Among them, nodes 13, 24, and 30 are equipped with energy storage devices, and their active and reactive power outputs are controllable; nodes 9 and 14 are equipped with photovoltaics, and nodes 25 and 27 are equipped with wind turbines. The active power of the photovoltaics and wind turbines is uncontrollable, but their reactive power is controllable.

[0069] Step 1: Use the prediction module to generate the output power of photovoltaic, wind turbine and load in the prediction time domain.

[0070] The prediction model uses the ARIMA model. Its core idea is to stationary the time series through differencing, and then use a regression-moving average model for prediction after stationarization. The ARIMA model is represented as ARIMA(p, d, q), which consists of two parts: an autoregressive model AR(p) and a moving average MA(q). p is the order of the autoregressive model, q is the order of the moving average, and d is the degree of differencing. ARIMA stationaries the data through differencing; generally, one differencing operation is sufficient for stabilization, therefore, the value of d is typically 0, 1, or 2.

[0071] The mathematical formula for ARIMA(p, d, q) can be described as follows:

[0072]

[0073] In the formula: Y(t) is the value of the time series, t is the time point, and c is a constant term. It is the autoregressive coefficient, ε t These are the interference terms θ1, θ2, ..., θ q q is the moving average coefficient, p is the number of autoregressive terms in the AR model, and q is the number of moving average terms in the MA model.

[0074] The process of building an ARIMA model consists of the following three steps:

[0075] Step 1.1: Stationarity test. This step checks whether the time series meets the stationarity requirement. For non-stationary time series, it is necessary to first perform d-order differencing to transform it into a stationary time series.

[0076] Step 1.2: Calculate the autocorrelation coefficient (ACF) and partial autocorrelation coefficient (PACF) of the stationary time series, and perform parameter estimation by searching using the Akaikes Information Criterion (AIC) or Bayesian Information Criterion (BIC) to obtain the optimal order p and q;

[0077] Step 1.3: Obtain the ARIMA model using the above d, p, and q parameters. Perform model validation on the obtained model, specifically on the residual ε. t Perform analysis and checks to determine the applicability of the time series ARIMA model and to determine E(ε) t If the value is zero, it means that the obtained model has passed the test.

[0078] After obtaining all possible autonomous region partitioning schemes using the branch-and-cut enumeration method, the differential autoregressive moving average model is used to predict wind and solar power output, generating the output power of solar, wind turbines, and loads within the predicted time domain. Taking 720 solar samples from a certain day as an example, 432 training data sets are extracted, and the ARIMA prediction module is used to generate node 9 to predict the solar output power of 288 samples within the predicted time domain, as shown below. Figure 3 As shown.

[0079] Step 2: Considering the uncertainty of wind and solar power output, with the objective function of minimizing the load loss risk rate of the autonomous region, construct a partition constraint that covers the opportunity constraints of the power supply rate of the autonomous region, the opportunity constraints of the power balance of the autonomous region, and the system safety operation constraints.

[0080] (1) Objective function

[0081] Distributed renewable energy sources offer flexible operation modes, allowing for both grid-connected and off-grid operation. In the event of a major grid failure causing widespread power outages, autonomous regions can leverage their distributed renewable energy resources to provide power support for isolated operations, rapidly restoring power to critical loads and mitigating economic losses from large-scale power outages. This enables autonomous regions to operate independently. This paper aims to minimize the load loss risk rate of the autonomous region, establishing a chance-constrained objective function as follows:

[0082]

[0083] In the formula, F psr It is the target value for the risk rate of load loss in the autonomous region, F psr The smaller the value, the better the power supply reliability of the autonomous region. str.j (t) represents the power supply rate of autonomous region j at time t. DG.i (t) is the output power of the i-th distributed power source in the autonomous region, P str.i (t) is the charging and discharging power of the i-th energy storage device in the autonomous region, P l.i (t) is the load power of node i in the autonomous region, N clu.j.DG N clu.j.str N clu.j.l N clu.j.g These represent the number of distributed power sources, energy storage devices, load nodes, and adjustable conventional units in autonomous region j, respectively, with T being the optimization period.

[0084] (2) Constraints:

[0085] 1) Probabilistic constraints on the power supply rate of autonomous regions, i.e.

[0086]

[0087] In the formula, F min ξ represents the minimum load power supply rate; x represents the decision variable, i.e., the division scheme of each autonomous region; ξ represents the distributed energy output scenario; n represents the number of distributed energy output scenarios. Let P be the sum of the probabilities of the events being true. ξ To contribute to a specific scenario within the set of scenarios that contribute to distributed resources; F(x,P) ξ For an output force of P ξ The load supply rate of the system is β; β is the confidence level value that the objective function satisfies.

[0088] 2) Power balance indices and constraints for autonomous regions

[0089] The dynamic power balance of the autonomous region is constrained by the partitioning scheme to fully ensure power stability within the autonomous region. As load and DG power change in real time, certain risks are introduced to the safe and stable operation within the autonomous region. Based on this, a power balance index and constraint R for the autonomous region are proposed. p The definition is as follows:

[0090]

[0091] In the formula: The total active power demand of the load within the autonomous region; Contributing to distributed energy resources; α represents the maximum active power output of distributed energy storage within the autonomous region; α represents the load power supply rate that needs to be satisfied within the autonomous region; β p This represents the confidence level that the power balance constraint must satisfy.

[0092] Autonomous Region Power Balance Constraint R p This reflects the probability that the total output of DG within an autonomous region can meet the load demand to a certain extent under maximum energy storage conditions. The higher the value of this indicator, the higher the safety of the autonomous region and the more reasonable the division scheme.

[0093] 3) System safety operation constraints

[0094] U i,min ≤u i (t)≤U i,max (18)

[0095] |I ij (t)|≤I ij.max (19)

[0096] In the formula: u i (t) represents the voltage amplitude at node i at time t; U i,max and U i,min These are the upper and lower limits allowed for node i, respectively; I ij (t) represents the current amplitude of line ij at time t; I ij.max It is the maximum allowable current to flow through branch ij.

[0097] Step 3: Combining the predicted output and prediction error probability models of photovoltaic and wind turbines, the scenario analysis method is used to generate a set of distributed output scenarios representing uncertainties within the specified reasonable output range, and the average output of distributed energy is obtained. Stochastic simulation technology is used to solve the chance constraints considering the uncertainty of wind and solar output.

[0098] For the prediction errors of photovoltaic and wind turbine output and load, it is generally assumed that they follow a normal distribution, and the prediction error probability density function is:

[0099]

[0100] Where ΔP is the distributed energy output prediction error; μ and σ are the expected value and standard deviation of the prediction error, respectively, with μ set to 0; e i The value for each data point; n is the number of data points.

[0101] Latin hypercube sampling can avoid the problem of over-clustering of samples. The specific sampling steps are as follows:

[0102] Step 3.1: Divide the interval from 0 to 1 into l equal parts, and randomly generate a number P in each part according to a uniform distribution. i .

[0103] Step 3.2: Shuffle the order of these l random numbers in any way, and these random numbers are the probability values ​​of each random sample.

[0104] Step 3.3: From the inverse function f of the probability distribution function -1 (P i )=x i Calculate the sample value corresponding to the probability value l of each sample.

[0105] Common methods for handling chance constraints include analytical methods and stochastic simulation methods. This paper uses the stochastic simulation method to verify whether the division of autonomous regions satisfies the chance constraints. The steps to verify whether the division scheme can meet the confidence level of the chance constraints at time t are as follows:

[0106] 1) Based on the probability distribution characteristics of load and uncontrollable DG power output within the autonomous region, randomly select power curves based on the scenario generation technology in step 2;

[0107] 2) Count the total number of times the autonomous region satisfies power balance in M ​​samplings. p The total number of times M satisfies the probability constraint of the objective function for the rate of load loss in the autonomous region. v ;

[0108] 3) If If the autonomous region division scheme at that moment is considered to satisfy the chance constraint, then the next autonomous region division scheme is solved until the optimal autonomous region division scheme under the confidence level that satisfies the objective function and the chance constraint is found.

[0109] Due to the randomness of wind and solar power output, prediction errors are prevalent in current wind and solar power forecasts, with current prediction methods showing a deviation of 25% to 40% in wind speed forecasts. While the ARIMA prediction method proposed in this patent can effectively guarantee the prediction accuracy of distributed power output, prediction errors still exist. Therefore, if the division of autonomous regions is carried out entirely based on the predicted output, there will be significant deviations, affecting the power quality and stability of the system after division. However, if the prediction of distributed power output is completely disregarded, and the output is calculated by randomly generating the prediction error according to the Weibull distribution function, it will be highly arbitrary and cannot guarantee the rationality of the division results. Therefore, combining randomness and predictive regularity can avoid arbitrariness while ensuring the rationality of the division results. This paper introduces an interval random simulation method to combine these two considerations.

[0110] Considering the prediction errors and fluctuations of wind and solar power, assuming that the power output level of wind and solar power fluctuates within ±20% at each moment, taking solar power as an example, its predicted power output range is as follows: Figure 4 As shown. Combining the predicted output and prediction error probability models of photovoltaic and wind turbines, stochastic simulation technology is used to solve the chance constraints. The 6-hour period from 12:00 to 18:00 is selected as the autonomous region's time segment. The rolling optimization cycle is 1 hour, the feedback correction cycle is 20 minutes, and the confidence level of the chance constraints is set to 80%. Stochastic simulation scenarios are generated for the photovoltaic and wind turbines within this time segment, considering the predicted output interval. When the sampling number is 1000, the photovoltaic samples for this time segment are as follows. Figure 5 As shown.

[0111] Step 4: Construct a novel autonomous region partitioning optimization model for the power distribution system based on SMPC. In the rolling optimization part, a breadth-first search algorithm is used to collect information on all partitioning schemes, calculate the objective function that satisfies the constraints under a certain confidence level for all schemes, and determine the autonomous region partitioning scheme for the first rolling optimization time period. During feedback correction, the predicted values ​​of wind turbines, photovoltaics, and loads are updated based on the latest real-time measurements.

[0112] The results of the dynamic autonomous region partitioning optimization based on chance constraints are shown in Table 2.

[0113] Table 2 Results of dynamic autonomous region delineation based on chance-constrained stochastic model prediction control

[0114]

[0115] Table 2 shows the results of the dynamic autonomous region division based on the chance-constrained stochastic model prediction control. The division results for each time period are as follows: Figure 5-7 As shown in Table 3, the average load loss risk rate of the autonomous region corresponding to the time period division results is shown in Table 3.

[0116] Depend on Figure 5 It can be seen that from 12:00 to 15:00, due to the large installed capacity of photovoltaic power, the output of photovoltaic power, together with wind turbines and energy storage, serves as the main active power support for the autonomous distribution network during this period. At this time, the autonomous distribution network is divided into two parts by the No. 3 cutting line. The average load shedding risk rate in each autonomous distribution network is 36.2%, which is relatively low, and the load in each autonomous distribution network can be effectively supported. The results of the autonomous distribution network division for the periods of 15:00-15:20 and 15:20-16:00 are as follows: Figure 6-7 As shown, as the output of photovoltaic power gradually weakens in the evening, wind turbines and energy storage gradually replace photovoltaic power as active power support to ensure the power supply rate in each autonomous region.

[0117] Table 3 shows the average risk rate of load failure in the autonomous regions based on the division results.

[0118]

[0119] By dividing the region, the control dimensions and difficulty of the distribution network are effectively reduced. Furthermore, the nodes in each autonomous region are relatively reasonable, and each autonomous region contains distributed energy nodes, which can meet the power supply rate requirements of each autonomous region and facilitate participation in regulation. Therefore, the division of autonomous regions is relatively reasonable.

Claims

1. A method for dividing autonomous regions based on stochastic model predictive control under chance constraints, characterized in that, The method includes: Step 1: After obtaining all possible autonomous region division schemes by the branch-cut enumeration method, the Autoregressive Integrated Moving Average Model (ARIMA) is used to predict the output of wind and solar power, generating the power of solar, wind turbines and loads in the prediction time domain; Step 2: Considering the uncertainty of wind and solar power output, with the objective function of minimizing the load loss risk rate of the autonomous region, construct a partition constraint that covers the opportunity constraints of the power supply rate of the autonomous region, the opportunity constraints of the power balance of the autonomous region, and the system safety operation constraints. Step 3: Combining the predicted output and prediction error probability models of photovoltaic and wind turbines, the scenario analysis method is used to generate a set of distributed output scenarios representing uncertainties within the specified reasonable output range, and the average output of distributed energy is obtained. Stochastic simulation technology is used to solve the chance constraints considering the uncertainty of wind and solar output. Step 4: Construct an optimization model for the autonomous region partitioning of the power distribution system based on Stochastic Model Predictive Control (SMPC). In the rolling optimization part, a breadth-first search algorithm is used to collect information on all partitioning schemes, calculate the objective function that satisfies the constraints under a certain confidence level for all schemes, and determine the autonomous region partitioning scheme in the first rolling optimization time period. During feedback correction, the predicted values ​​of wind turbines, photovoltaics, and loads are updated based on the latest real-time measurement values. Step 5: Repeat steps 2 to 4 to complete the division of autonomous regions for subsequent time periods.

2. The method for dividing autonomous regions under chance constraints based on stochastic model predictive control according to claim 1, characterized in that, In step 1, the prediction module is used to generate the power of photovoltaic, wind turbine, and load within the predicted time domain, as detailed below: The prediction model uses the ARIMA model. The core idea is to stationary the series through differencing. The stationary time series is then predicted using a regression moving average model. The ARIMA model is represented as ARIMA(p, d, q). This model consists of two parts: an autoregressive (AR) model and a moving average (MA) model. p is the order of the autoregressive model, q is the order of the moving average, and d is the degree of differencing. ARIMA makes the data stationary through differencing. The mathematical formula for ARIMA(p, d, q) can be described as follows: In the formula: Y(t) is the value of the time series, t is the time point, and c is a constant term. It is the autoregressive coefficient, ε t These are residuals, θ1, θ2, ..., θ q q is the moving average coefficient, p is the number of autoregressive terms in the AR model, and q is the number of moving average terms in the MA model. The process of building an ARIMA model consists of the following three steps: Step 1.1: Stationarity test. This test checks whether the time series meets the stationarity requirement. For non-stationary time series, it is necessary to perform d-order differencing to transform it into a stationary time series. Step 1.2: Calculate the autocorrelation coefficient (ACF) and partial autocorrelation coefficient (PACF) of the stationary time series, and perform parameter estimation by searching using the Akaikes Information Criterion (AIC) or Bayesian Information Criterion (BIC) to obtain the optimal order p and q; Step 1.3: Obtain the ARIMA model using the above d, p, and q parameters. Then, validate the model by verifying the residual ε. t Perform analysis and checks to determine the applicability of the time series ARIMA model and to determine E(ε) t If the value is zero, it means that the obtained model has passed the test.

3. The method for dividing autonomous regions under chance constraints based on stochastic model predictive control according to claim 1, characterized in that, The objective function and constraints in step 2 are as follows: (1) Objective function Distributed renewable energy operates flexibly, capable of both grid-connected and off-grid operation. In the event of a major grid failure causing widespread power outages, autonomous regions can rely on their distributed renewable energy resources to provide power support for isolated operations, rapidly restoring power to critical loads and mitigating economic losses from large-scale power outages. This empowers autonomous regions with independent operational capabilities. With the goal of minimizing the load loss risk rate of the autonomous region, a chance-constrained objective function is established as follows: In the formula, F psr It is the target value for the risk rate of load loss in the autonomous region, F psr The smaller the value, the better the power supply reliability of the autonomous region. str.j (t) is the power supply rate of autonomous region j at time t; P DG.i (t) is the output power of the i-th distributed power source in the autonomous region, P str.i (t) is the charging and discharging power of the i-th energy storage device in the autonomous region, P l.i (t) is the load power of node i in the autonomous region, N clu.j.DG N clu.j.str N clu.j.l N clu.j.g These represent the number of distributed power sources, energy storage devices, load nodes, and adjustable conventional units in autonomous region j, respectively, and T is the optimization period. (2) Constraints: 1) Opportunity constraint on the power supply rate of autonomous regions, i.e. In the formula, F min ξ represents the minimum load power supply rate; x is the decision variable, i.e., the division scheme of each autonomous region; ξ represents the distributed power output scenario; n is the number of distributed power output scenarios. Let P be the sum of the probabilities of the events being true. ξ Provide power to a specific scenario within a distributed power output scenario set; F(x,P) ξ For an output force of P ξ The load supply rate of the downstream system; β is the confidence level value satisfied by the objective function; 2) Power balance indices and constraints for autonomous regions To constrain the dynamic power balance of autonomous regions under the partitioning scheme and fully ensure power stability within these regions, it is necessary to address the risks posed by real-time changes in load and distributed generation (DG) power to the safe and stable operation of these regions. Based on this, a power balance index R for autonomous regions is proposed. p The constraints are defined as follows: R p ≥β p (6) In the formula: The total active power demand of the load within the autonomous region; Contributing to distributed energy resources; α represents the maximum active power output of distributed energy storage within the autonomous region; α represents the load power supply rate that needs to be satisfied within the autonomous region; β p The confidence level that the power balance constraint must satisfy; The power balance constraint of an autonomous region reflects the probability that the total output of DG within the autonomous region can meet the load demand to a certain extent under the condition of maximum energy storage. The higher the index, the higher the safety of the autonomous region and the more reasonable the division scheme. 3) System safety operation constraints U i,min ≤u i (t)≤U i,max (7) |I ij (t)|≤I ij.max (8) In the formula: u i (t) represents the voltage amplitude at node i at time t; U i,max and U i,min These are the upper and lower limits of the allowed voltage at node i, respectively; I ij (t) represents the current amplitude of line ij at time t; I ij.max It is the maximum allowable current to flow through branch ij.

4. The method for dividing autonomous regions under chance constraints based on stochastic model predictive control according to claim 1, characterized in that, Step 3 is as follows: Regarding the prediction errors of photovoltaic and wind turbine output and load, it is assumed that they follow a normal distribution, and the prediction error probability density function is: Where ΔP is the distributed energy output prediction error; μ and σ are the expected value and standard deviation of the prediction error, respectively, with μ set to 0; e i The value for each data point; n is the number of data points; Latin hypercube sampling can avoid the problem of over-clustering of samples. The specific sampling steps are as follows: Step 3.1: Divide the interval from 0 to 1 into l equal parts, and randomly generate a number P in each part according to a uniform distribution. i ; Step 3.2: Shuffle the order of these l random numbers in any way, and these random numbers are the probability values ​​of each random sample; Step 3.3: From the inverse function f of the probability distribution function -1 (P i )=x i Calculate the sample value corresponding to the probability value l of each sample, where x i For the corresponding probability P i The sample values ​​obtained from the mapping; To address the opportunity constraint, a stochastic simulation method is used to verify whether the division of autonomous regions satisfies the opportunity constraint. The steps to verify whether the division scheme can meet the confidence level of the opportunity constraint at time t are as follows: 1) Based on the probability distribution characteristics of load and uncontrollable DG power output within the autonomous region, M power curves are randomly selected based on the scenario generation technology in step 2; 2) Count the total number of times M in M ​​samplings that the autonomous region meets the power balance constraint. p The total number of times M satisfies the probability constraint of the objective function for the rate of load loss in the autonomous region. v ; 3) If If the autonomous region partitioning scheme at that moment is deemed to satisfy the chance constraint, then the next autonomous region partitioning scheme is solved, until the optimal autonomous region partitioning scheme that satisfies the objective function and the chance constraint at the given confidence level is found, where β p The confidence level that the power balance constraint must satisfy; If we combine randomness and predictive regularity, we can avoid blindness and ensure the rationality of the division results. We can combine the two by introducing the interval random simulation method. For the power prediction curve of wind and solar power, considering the prediction error and its volatility, the output deviation is set at ±20%. It is assumed that the output level of wind and solar power at each moment fluctuates within the range of the upper and lower deviations, which is the range of random number generation for the output of wind and solar power at each moment.

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