A power distribution network distributed photovoltaic dynamic bearing capacity probability evaluation method

Abstract

The application discloses a kind of distribution network distributed photovoltaic dynamic bearing capacity probability evaluation methods, comprising: obtaining multi-source data, and according to the set time scale, the evaluation period is divided into multiple continuous operation periods;For each operation period, establish power flow security constraint model of distribution network;According to the historical output data of distributed photovoltaic, establish photovoltaic output probability model of each operation period, according to the historical data of node load, establish load power probability model of each operation period;Generate multiple groups of source and load random operation scenarios using probability sampling method, form bearing capacity sample set arranged by time;The bearing capacity samples of each operation period are statistically analyzed, and the distributed photovoltaic dynamic bearing capacity probability evaluation result is formed;The application can realize the transformation from deterministic single-point bearing capacity evaluation to dynamic probability bearing capacity evaluation, and provide basis for distributed photovoltaic access planning, openable capacity calculation and distribution network operation risk analysis.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic carrying capacity technology, and in particular to a method for dynamic carrying capacity probability assessment of distributed photovoltaic power grids. Background Technology

[0002] As the scale of distributed photovoltaic (PV) grid integration in distribution networks continues to increase, these networks are gradually transforming from traditional unidirectional power supply networks into active distribution networks with bidirectional interaction between power sources and loads. Distributed PV integration can improve the utilization of clean energy and reduce electricity costs for users, but its output is significantly affected by sunlight conditions, weather changes, and operating times, exhibiting considerable randomness and volatility. When the integrated capacity of distributed PV is too high, it may cause problems such as node voltage exceeding limits, line overload, and increased reverse power flow in transformers, thereby affecting the safe and stable operation of the distribution network. Therefore, in the planning and management of distributed PV integration, it is necessary to conduct a capacity assessment of the distributed PV capacity that the distribution network can accommodate, providing a basis for determining the location, scale, and available capacity for distributed PV integration.

[0003] Currently, most methods for assessing the distributed photovoltaic (PV) carrying capacity of distribution networks are based on deterministic scenarios. This involves calculating the maximum PV access capacity that satisfies node voltage, line current carrying capacity, transformer capacity, and reverse power flow constraints, given load levels, PV output levels, and network operation modes. While these methods offer relatively clear calculations and can reflect the PV acceptance capacity of the distribution network under specific operating scenarios, they struggle to describe the carrying capacity fluctuations caused by changes in PV output and load power over time. In actual operation, PV output varies significantly across different time periods during the day, and load power continuously changes with user electricity consumption behavior. Furthermore, the voltage levels, line load rates, and transformer reverse power flow states differ across operating periods. Therefore, carrying capacity results obtained from a single scenario or typical section cannot comprehensively reflect the dynamic acceptance capacity of the distribution network throughout the entire assessment period.

[0004] Furthermore, both distributed photovoltaic (PV) output and load power are uncertain, and there may be a correlation between them. For example, periods of high PV output may correspond to lower or higher load levels, and different source-load combinations can lead to different risk states in the distribution network's carrying capacity. Existing deterministic carrying capacity assessments typically present a single capacity value, making it difficult to provide the probability distribution, confidence interval, and time-series variation range of carrying capacity under uncertain source-load conditions. This fails to effectively support the analysis of distribution network operation risks and the refined assessment of the available capacity for distributed PV.

[0005] Therefore, it is urgent to propose a probabilistic assessment method for the dynamic carrying capacity of distributed photovoltaic power in distribution networks. By establishing a probabilistic model of photovoltaic output and load power, and combining probabilistic sampling and multi-time period power flow safety constraint calculation, the probability distribution and upper and lower limit time series curves of distributed photovoltaic carrying capacity in different time periods can be obtained, thereby realizing the transformation from deterministic single-point assessment to dynamic probabilistic assessment. Summary of the Invention

[0006] The purpose of this invention is to provide a probabilistic assessment method for the dynamic carrying capacity of distributed photovoltaic (PV) power in distribution networks, addressing the problem that existing PV carrying capacity assessments are mostly based on deterministic scenarios and fail to reflect the uncertainties in PV output and load power. This method establishes a probabilistic model of PV output and load power, combining probabilistic sampling and multi-time period power flow safety constraint calculations to obtain the probability distribution, confidence interval, and upper and lower limit time-series curves of PV carrying capacity at different time periods. This transforms the assessment of PV carrying capacity in distribution networks from a single-point deterministic assessment to a dynamic probabilistic assessment.

[0007] The above-mentioned objective of this invention is achieved through the following technical solution: a method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids, comprising:

[0008] Step 1: Obtain the distribution network topology, line impedance parameters, transformer capacity parameters, node load time sequence curves, existing distributed power generation capacity, locations of distributed photovoltaic power to be connected, and historical output data of distributed photovoltaic power. Divide the evaluation period into multiple continuous operating segments according to the set time scale.

[0009] Step 2: Establish a power flow security constraint model for each operating period to describe the node power balance, node voltage, line current carrying capacity, transformer load rate and reverse power flow constraint relationship during that period;

[0010] Step 3: Establish a photovoltaic output probability model for each operating period based on the historical output data of distributed photovoltaic power, establish a load power probability model for each operating period based on the historical load data of nodes, and use a correlation function to describe the correlation between photovoltaic output and load power.

[0011] Step 4: Use a probabilistic sampling method to generate multiple sets of source-load random operation scenarios, and calculate the maximum accessible capacity of distributed photovoltaic power that meets the safety operation constraints of the distribution network in each set of scenarios, forming a carrying capacity sample set arranged in time;

[0012] Step 5: Perform probability statistics on the carrying capacity samples of each operating period to obtain the time-varying probability distribution, confidence interval, and time series curves of the upper and lower limits of the distributed photovoltaic carrying capacity, thereby forming the probability assessment results of the dynamic carrying capacity of distributed photovoltaic.

[0013] In a preferred embodiment of the present invention, in step 1, the multi-source data includes the distribution network topology, line impedance parameters, transformer capacity parameters, node load time-series curves, existing distributed power generation capacity, locations of distributed photovoltaic (PV) systems to be connected, and historical output data of distributed PV systems. This data is used to determine the network structure, equipment operating boundaries, source-load time-series characteristics, and PV connection locations for the distribution network capacity assessment. The assessment period is divided into multiple continuous operating segments according to a set time scale, so that each operating segment corresponds to the corresponding load level, PV output characteristics, and distribution network operating status, providing basic data for the subsequent establishment of a power flow security constraint model and the implementation of dynamic capacity probability assessment.

[0014] In a preferred embodiment of the present invention, step 2, which involves establishing a power flow security constraint model for each operating period, includes:

[0015] Based on the distribution network topology, line impedance parameters, node load power, and distributed photovoltaic access location, node active power balance constraints and node reactive power balance constraints are established for each operating period to describe the balance relationship between the injected power, load power, and network power flow of each node after distributed photovoltaic access.

[0016] Establish node voltage constraints to keep the voltage amplitude of distribution network nodes within the allowable upper and lower limits during each operating period, which is used to determine whether the addition of distributed photovoltaic power will cause the node voltage to exceed the limit.

[0017] Establish line current carrying capacity constraints to ensure that the line current or line transmission power does not exceed the corresponding line's safe operating limit during each operating period, which is used to determine whether distributed photovoltaic access causes line overload.

[0018] Establish transformer load rate constraints and reverse power flow constraints to ensure that the power transmitted by the transformer does not exceed its capacity limit during each operating period, and that the reverse power transmission under the high output and low load scenario of distributed photovoltaic power generation does not exceed the allowable range.

[0019] In a preferred embodiment of the present invention, step 3 involves establishing a source-load uncertainty probability model based on historical distributed photovoltaic power output data and historical node load data, and describing the correlation between photovoltaic power output and load power, including:

[0020] The historical output data of distributed photovoltaic power is divided into time periods according to the set time scale. Photovoltaic output samples corresponding to each operating period are extracted, and the probability density function of photovoltaic output for each operating period is established by kernel density estimation method to describe the random fluctuation characteristics of distributed photovoltaic output in different time periods.

[0021] The historical data of node load is divided into time periods according to the set time scale. Load power samples corresponding to each operating period are extracted, and the kernel density estimation method is used to establish the load power probability density function of each operating period to describe the random variation characteristics of node load power in different time periods.

[0022] Based on the probability density function of photovoltaic output and the probability density function of load power for each operating period, a joint probability distribution model of photovoltaic output and load power is constructed using the Copula function to describe the correlation between photovoltaic output and load power within the same operating period.

[0023] The joint probability distribution model is used to obtain the joint probability density function of the source load random variables for each runtime segment, providing a probability distribution basis for generating random runtime scenarios of source loads using probability sampling methods.

[0024] In a preferred embodiment of the present invention, step 4 involves generating multiple sets of source-load random operation scenarios using a probability sampling method, and calculating the maximum grid-connectable capacity of distributed photovoltaic power in each scenario, including:

[0025] Based on the joint probability distribution model of photovoltaic output and load power for each operating period obtained in step 3, the slice sampling Markov chain Monte Carlo method is used to perform random sampling to generate multiple sets of photovoltaic output and load power samples, forming the source-load random operation scenario corresponding to each operating period.

[0026] For each set of source-load random operation scenarios, the photovoltaic output sample and load power sample under the scenario are substituted into the distribution network power flow safety constraint model established in step 2 to calculate the maximum connectable capacity of distributed photovoltaic under the condition that the node voltage, line current carrying capacity, transformer load rate and reverse power flow all meet the safety operation requirements.

[0027] The carrying capacity of multiple source-load random operation scenarios in each operating segment is calculated sequentially to obtain multiple samples of the maximum accessible capacity of distributed photovoltaic power for each operating segment.

[0028] The maximum grid-accessible capacity samples of distributed photovoltaic power obtained from each operating period are arranged in chronological order to form a time-arranged carrying capacity sample set, which is used to characterize the dynamic characteristics of the carrying capacity of distributed photovoltaic power under the influence of source load uncertainty.

[0029] As a preferred embodiment of the present invention, for each operating period, the multiple maximum accessible capacity samples of distributed photovoltaic power obtained in step 4 are used as the carrying capacity sample set for that period, and the kernel density estimation method is used to fit the probability density function of the carrying capacity of distributed photovoltaic power in that period, which is used to describe the probability distribution characteristics of the carrying capacity in that period under the influence of source load uncertainty.

[0030] The cumulative distribution function is calculated based on the carrying capacity probability density function, and the probability assessment interval of the distributed photovoltaic carrying capacity during the operating period is determined according to the preset confidence level. The probability assessment interval includes the lower limit of carrying capacity and the upper limit of carrying capacity.

[0031] Probability statistics were performed on the bearing capacity samples of each operating segment within the evaluation period to obtain the bearing capacity probability distribution and confidence interval corresponding to each operating segment;

[0032] The lower and upper limits of the carrying capacity of each operating segment are connected in chronological order to form a time-series curve of the upper and lower limits of the carrying capacity of distributed photovoltaic power generation, which is used to characterize the dynamic range of the carrying capacity of distributed photovoltaic power generation over time.

[0033] Based on the time-varying probability distribution, confidence interval, and time series curves of upper and lower limits of carrying capacity for each operating period, a dynamic carrying capacity probability assessment result for distributed photovoltaic power is formed, which is used to reflect the impact of photovoltaic output and load fluctuations on the photovoltaic acceptance capacity of the distribution network at different times.

[0034] As a preferred embodiment of the present invention, in step 1, the evaluation period is divided into multiple continuous operating segments according to a set time scale, so that the load-bearing capacity evaluation is no longer limited to a single typical section, but can combine the time changes of load level, photovoltaic output characteristics and network operating status to carry out dynamic load-bearing capacity evaluation of distributed photovoltaics.

[0035] In step 2, a power flow safety constraint model for the distribution network is established for each operating period. The node power balance, node voltage, line current carrying capacity, transformer load rate and reverse power flow constraint are incorporated into the carrying capacity calculation process to determine whether the distribution network meets the safe operation requirements after the distributed photovoltaic access.

[0036] In step 3, the kernel density estimation method is used to establish the probability models of distributed photovoltaic power output and node load power for each operating period, and the Copula function is used to construct the joint probability distribution model of photovoltaic power output and load power to describe the correlation between source and load random variables, and to provide a probability distribution basis for the subsequent generation of source and load random operating scenarios.

[0037] In step 4, based on the source-load joint probability distribution model, multiple sets of random operation scenarios of photovoltaic output and load power are generated using the probability sampling method. In each set of scenarios, the maximum accessible capacity of distributed photovoltaic power that meets the safety operation constraints of the distribution network is calculated, thereby forming a carrying capacity sample set corresponding to each operating period.

[0038] In step 5, probability statistics are performed on the carrying capacity samples of each operating period to obtain the probability density function, cumulative distribution function and probability evaluation interval of the distributed photovoltaic carrying capacity under the preset confidence level. The upper and lower limits of the carrying capacity intervals of each time period are connected in chronological order to form the time series curve of the upper and lower limits of the distributed photovoltaic carrying capacity.

[0039] The beneficial effects of this invention are as follows: Compared with the traditional distributed photovoltaic carrying capacity assessment method based on deterministic scenarios, this invention can consider the impact of random fluctuations in distributed photovoltaic output and load power on the photovoltaic acceptance capacity of the distribution network, and avoid the problem that the assessment results of a single typical section are difficult to reflect the actual operation fluctuations.

[0040] Secondly, this invention obtains the dynamic characteristics of distributed photovoltaic carrying capacity over time through a multi-period evaluation method, which can more intuitively reflect the differences in photovoltaic acceptance capacity of the distribution network at different times.

[0041] Finally, this invention obtains the probability distribution, confidence interval, and upper and lower limit time series curves of carrying capacity through probabilistic statistics, which can provide a more reliable probabilistic assessment basis for distributed photovoltaic access planning, open capacity calculation, and distribution network operation risk analysis. Attached Figure Description

[0042] Figure 1 This is a flowchart of the algorithm for a dynamic carrying capacity probability assessment method for distributed photovoltaic power grids proposed in this invention.

[0043] Figure 2 An improved IEEE 33-node topology diagram as one of the embodiments;

[0044] Figure 3 This is the probability assessment result of the distributed photovoltaic dynamic carrying capacity of this embodiment in one scheduling cycle. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0046] like Figure 1 As shown in the figure, the dynamic carrying capacity probabilistic assessment method for distributed photovoltaic power grids proposed in this embodiment is implemented according to the following steps:

[0047] Step 1: First, obtain the topology of the distribution network to be evaluated, determine the electrical connection relationships between each node, line, transformer, existing distributed power source and distributed photovoltaic to be connected in the distribution network, and form the network structure foundation for power flow calculation and carrying capacity assessment.

[0048] Then, the impedance parameters of the distribution network lines, the current carrying capacity limit of the lines, the transformer capacity parameters, the allowable load rate, and the reverse power flow limit are obtained to determine the safe operating boundaries of key equipment such as lines and transformers in the distribution network, and to provide a parameter basis for the subsequent establishment of node voltage, line power flow, transformer load rate, and reverse power flow constraints.

[0049] Further, the load time-series curves of each node within the evaluation period are obtained. The load time-series curves include the active and reactive loads of each node at different time periods, which are used to describe the operating characteristics of the distribution network load level changing over time. At the same time, the existing distributed power generation capacity and the location of distributed photovoltaic power to be connected are obtained to determine the current initial connection status of the distribution network and the carrying capacity evaluation object.

[0050] Finally, historical output data of distributed photovoltaic power is obtained, which includes photovoltaic output samples for each time period within multiple historical days, used to characterize the random fluctuation characteristics of distributed photovoltaic output at different times; and the evaluation period is divided into multiple continuous operating segments according to a set time scale, so that each operating segment corresponds to the corresponding load level, photovoltaic output characteristics and distribution network operating status, providing basic data for subsequent dynamic carrying capacity probability assessment.

[0051] Step 2: For each operating segment obtained in Step 1, establish a power flow security constraint model for the distribution network. Let the set of distribution network nodes be... The route set is The runtime segment set is For any given time period ,node The active and reactive loads are respectively ,node The active power output of the connected distributed photovoltaic system is The node voltage amplitude is The above variables describe the operating status of the distribution network at different times after the distributed photovoltaic system is connected.

[0052] For each operating segment, establish node power balance constraints. Assume the line... Indicates that by node Pointing to node The power distribution lines, the lines The active power and reactive power are respectively Then the node power balance relationship can be expressed as:

[0053]

[0054]

[0055] In the formula, Indicates from node Flowing to downstream nodes Sum the line power. Indicates from the upstream node Inflow node Sum the line power.

[0056] Further establish the relationship between line power flow and node voltage. Assume the line... The resistance and reactance are respectively , The voltages at the nodes at both ends of the line can satisfy the following relationship:

[0057]

[0058] In the formula, and Time periods node and nodes voltage amplitude, For time period line The current amplitude. The line current and line power satisfy the following relationship:

[0059]

[0060] This allows us to describe the power flow relationship between line power, current, and node voltage after distributed photovoltaic (PV) grid integration.

[0061] Then, establish node voltage safety constraints. Let the lower and upper limits of the node voltage be respectively... , Then for any node and any time period It should satisfy:

[0062]

[0063] This constraint is used to determine whether the integration of distributed photovoltaic (PV) systems causes node voltage to exceed limits, especially to constrain voltage rise issues that may occur when PV output is high and load is low.

[0064] Establish line current carrying capacity constraints. Assume the line... The maximum allowable current is Then the line current carrying capacity constraint is:

[0065]

[0066] Establish transformer load rate constraints. Assume the transformer... During the period The active power and reactive power transmitted are respectively , The rated capacity of the transformer is Then the transformer capacity constraint is:

[0067]

[0068] This constraint is used to ensure that the transformer does not operate under overload after distributed photovoltaic power is connected.

[0069] Simultaneously, reverse power flow constraints are established for the transformer. Assume the transformer... During the period Active transmission power Taking the flow from the upstream power grid to the distribution network as the positive direction, the upper limit of the allowed reverse power transmission is: Then the reverse power flow constraint is:

[0070]

[0071] This constraint is used to limit the amount of power that distributed photovoltaic power can feed back to the upstream grid during periods of high photovoltaic output and low load.

[0072] Based on the above constraints, a set of power flow security constraints for each operating segment is formed:

[0073]

[0074] In the formula, For time period The feasible region for safe operation of the distribution network. Subsequently, when calculating the maximum connectable capacity of distributed photovoltaic power, it will only be considered if the power flow result in the corresponding scenario falls within this region. Only then is it considered that the photovoltaic access capacity meets the requirements for safe operation of the distribution network.

[0075] Step 3: For any runtime segment Extract the distributed photovoltaic power output samples and load power samples corresponding to this time period from multiple historical days, and denot them as follows:

[0076]

[0077]

[0078] In the formula, For the first Historical sample days during runtime Distributed photovoltaic power output, For the first Historical sample days during runtime The load power, This represents the number of historical samples.

[0079] A distributed photovoltaic (PV) output probability model for each operating period is established using the kernel density estimation method. For each time period... The probability density function of distributed photovoltaic power output can be expressed as:

[0080]

[0081] In the formula, runtime segment The output value of distributed photovoltaic power is The probability density function at time , For distributed photovoltaic power output variables, For kernel function, runtime segment The corresponding window width for estimating photovoltaic output kernel density. A Gaussian kernel function is typically chosen.

[0082]

[0083] In the formula, The input variables for the kernel function are used. The probability density function described above can describe the random fluctuation characteristics of distributed photovoltaic (PV) output at different times. For nighttime periods, if all historical PV output samples are zero, the PV output probability model for that period is directly degraded to a zero output state, i.e. .

[0084] Furthermore, a kernel density estimation method is used to establish a load power probability model for each operating period. For each time period... The load power probability density function can be expressed as:

[0085]

[0086] In the formula, runtime segment The load power is taken as The probability density function at time , For load power variables, runtime segment The corresponding load power kernel density estimation window width. If it is necessary to consider nodal reactive loads simultaneously, the reactive load can be estimated from the active load based on historical power factors or typical power factors, i.e.:

[0087]

[0088] In the formula, For the first Historical sample midday nodes During the period reactive load, For nodes The power factor.

[0089] After obtaining the edge probability models for photovoltaic power output and load power respectively, their cumulative distribution functions are calculated. The cumulative distribution functions for distributed photovoltaic power output and load power in time period ttt are expressed as follows:

[0090]

[0091]

[0092] In the formula, For time period Distributed photovoltaic output not greater than The cumulative probability, For time period Load power not greater than The cumulative probability, and These are the integral variables. The cumulative distribution function described above is used to map the photovoltaic power output and load power samples to a unified probability space.

[0093] Subsequently, the Copula function is used to describe the correlation between distributed photovoltaic power output and load power within the same operating period. For the operating period ,set up:

[0094]

[0095] Construct a joint distribution function for photovoltaic power output and load power based on the Copula function:

[0096]

[0097] In the formula, For time period The joint cumulative distribution function of photovoltaic power output and load power. For time period The selected Copula function, The correlation parameter of the Copula function is used to characterize the degree of correlation between photovoltaic output and load power during this period.

[0098] If Gaussian Copula is used, its joint distribution function can be expressed as:

[0099]

[0100] In the formula, The correlation coefficient is The two-dimensional standard normal distribution function, It is the inverse function of the one-dimensional standard normal distribution function. runtime segment The correlation coefficient between photovoltaic output and load power. It can be calculated from historical photovoltaic power output samples and load power samples, using the Spearman rank correlation coefficient:

[0101]

[0102] In the formula, For the sample Rank in the historical photovoltaic output sample For the sample Rank in the historical load sample The average value of the sample rank of photovoltaic power output. This is the average rank of the load power samples. This correlation coefficient allows the statistical correlation between photovoltaic output and load power to be incorporated into the joint probability model.

[0103] The runtime segment can be further obtained from the joint distribution function. The joint probability density function of the source and charge:

[0104]

[0105] In the formula, For time period The joint probability density function of photovoltaic power output and load power. For Copula density function, and These are the previously established photovoltaic power output probability density function and load power probability density function, respectively. This joint probability density function describes the probability that photovoltaic power output and load power will simultaneously take different values ​​within the same time period, providing a probability distribution basis for generating multiple sets of source-load random operation scenarios in step 4.

[0106] Finally, the source-load joint probability model obtained in step 3 is connected with the power flow security constraint model in step 2. For the model generated in subsequent step 4... In a scenario where the source and load operate in a random manner, photovoltaic output samples can be obtained using a joint probability model. and load power samples And further mapped to the node variables in step 2. , and This is used to calculate the maximum connectable capacity of distributed photovoltaic power that meets the safety operation constraints of the distribution network under this random scenario.

[0107] Step 4: Let the first... The joint probability density function of the source and load for each runtime segment is: ,in Represents the output variable of distributed photovoltaic power. This represents the load power variable. A probability sampling method is used to extract values ​​from this joint probability density function. Group samples, obtained:

[0108]

[0109] In the formula, runtime segment Next Distributed photovoltaic power output samples in a group of random scenarios runtime segment Next A set of randomized load power samples. These random samples correspond to the joint probability model in step 3 and are used to characterize the possible operating states in which photovoltaic output and load power fluctuate simultaneously within the same time period.

[0110] Specifically, if the source-load joint probability model is constructed using the Copula function in step 3, then pairs of random variables that satisfy the correlation can be generated first in the unified probability space:

[0111]

[0112] In the formula, and Runtime segment Next The cumulative probability variables corresponding to photovoltaic output and load power in the group scenario, and Then, the cumulative distribution function of photovoltaic output obtained in step 3 is used. and load power cumulative distribution function The inverse function maps the probability space samples to actual source-load power samples:

[0113]

[0114]

[0115] In the formula, runtime segment The inverse function of the cumulative distribution function of photovoltaic power output. runtime segment The inverse function of the cumulative load power distribution function. Through the above mapping, a stochastic operating scenario consistent with the historical source-load probability characteristics and correlations can be obtained.

[0116] For the In the random operation scenario of source and load, the photovoltaic output samples and load power samples are further mapped to the node variables in step 2. Let the set of distributed photovoltaic nodes to be connected be... ,node The photovoltaic capacity allocation factor is And satisfy:

[0117]

[0118] Runtime segment Scene The total grid connection capacity of distributed photovoltaic power to be determined is as follows: Then the node The actual output of distributed photovoltaic power can be expressed as:

[0119]

[0120] In the formula, Contribute to distributed photovoltaic power generation. This represents the total distributed photovoltaic (PV) grid connection capacity to be evaluated in this scenario. For the reason The normalized photovoltaic output coefficient is used to represent the power generation level per unit capacity of photovoltaic power during that period. If Then we have:

[0121]

[0122] For load power, the scenario load samples can be mapped to each node based on the baseline load or node load allocation ratio obtained in step 1. Let the nodes... The baseline active and reactive loads are respectively , runtime segment Scene The load factor is Then the node load can be expressed as:

[0123]

[0124]

[0125] In the formula, and These are active load and reactive load, respectively. Therefore, the random load sample in step 3 can be linked to the node power balance constraints in step 2.

[0126] For each set of random scenarios, with the goal of maximizing the total grid-connected capacity of distributed photovoltaic power, a carrying capacity calculation model is established for that scenario:

[0127]

[0128] satisfy:

[0129]

[0130] Runtime segments in sequence All inside The above bearing capacity calculations were performed on a group of random scenarios to obtain a bearing capacity sample set for that time period:

[0131]

[0132] In the formula, runtime segment The distributed photovoltaic (PV) carrying capacity sample set reflects the maximum grid-connectable PV capacity under different source-load random operation scenarios during this period. The above process is further repeated for all operating periods to obtain a carrying capacity sample set arranged by time:

[0133]

[0134] In the formula, This serves as a sample set of dynamic carrying capacity for distributed photovoltaic power throughout the entire evaluation period. This represents the total number of runtime segments.

[0135] Step 5: Use kernel density estimation method to evaluate the runtime segment. By fitting the probability distribution of the carrying capacity samples, the probability density function of the distributed photovoltaic carrying capacity for that period is obtained:

[0136]

[0137] In the formula, runtime segment The carrying capacity of distributed photovoltaic power is taken as: The probability density function at time , For bearing capacity variables, runtime segment The kernel density estimation window width for the load-bearing capacity sample.

[0138] Furthermore, the corresponding cumulative distribution function is calculated based on the bearing capacity probability density function:

[0139]

[0140] In the formula, runtime segment Distributed photovoltaic carrying capacity not greater than The cumulative probability, This is the integral variable. The cumulative distribution function is used to determine the probability assessment interval of the distributed photovoltaic carrying capacity at a given confidence level during this period.

[0141] Assume the preset information level is ,in Then the runtime segment The probability assessment interval for the carrying capacity of distributed photovoltaic power can be expressed as:

[0142]

[0143] In the formula, runtime segment Lower bound of distributed photovoltaic carrying capacity probability assessment runtime segment Upper bound of distributed photovoltaic carrying capacity probability assessment It is the inverse function of the cumulative distribution function of bearing capacity. This represents the confidence level. This interval indicates the runtime performance at a given confidence level. The distributed photovoltaic carrying capacity is likely to fall within this range.

[0144] At the same time, determine the runtime segment. The most likely value of the distributed photovoltaic carrying capacity. This most likely value can be obtained from the carrying capacity value corresponding to the maximum of the probability density function:

[0145]

[0146] In the formula, runtime segment The most probable value of distributed photovoltaic (PV) carrying capacity represents the PV carrying capacity level with the highest probability of occurrence during a given period under the influence of source-load uncertainty. Compared to simply using the sample mean, the most probable value can more intuitively reflect the peak position of the carrying capacity probability distribution.

[0147] For nighttime hours, since distributed photovoltaic power generation does not occur, it is not included in the assessment of new photovoltaic grid connection capacity. Therefore, the carrying capacity assessment result for this period can be:

[0148]

[0149] This approach is used to ensure that the dynamic load-bearing capacity assessment results are consistent with the day-night output characteristics of distributed photovoltaic power.

[0150] The above probability statistics process is repeated for all operating segments within the evaluation period to obtain the lower bound, most likely value, and upper bound sequence of bearing capacity for each operating segment:

[0151]

[0152]

[0153]

[0154] In the formula, This is the lower bound sequence for the probability assessment of distributed photovoltaic carrying capacity throughout the entire assessment period. This is the sequence of most likely values ​​for bearing capacity. This is the upper bound sequence for bearing capacity probability assessment.

[0155] Finally, the lower bound, most likely value, and upper bound of the carrying capacity for each operating segment are connected in chronological order to form a probability assessment curve for the dynamic carrying capacity of distributed photovoltaic power. and The upper and lower limit time series curves constitute the carrying capacity of distributed photovoltaic power, and the region between the two represents the dynamic carrying capacity probability interval under a given confidence level. This represents the most likely carrying capacity level during each operating period. This results in a dynamic carrying capacity probability assessment of distributed photovoltaic (PV) systems, reflecting the probabilistic range of changes in the distributed PV acceptance capacity of the distribution network over time under the influence of source-load uncertainty.

[0156] To verify the effectiveness of the present invention, Figure 2 The improved IEEE 33-node system shown is used as an example for simulation analysis. The system connects distributed photovoltaics at nodes 3, 8, 14, 20, and 30. Figure 3The results of the dynamic carrying capacity probability assessment of distributed photovoltaic (PV) power are presented. As shown in the figure, the carrying capacity is treated as 0 during the nighttime period because distributed PV does not generate electricity; the carrying capacity during the daytime period shows obvious dynamic change characteristics. The upper bound, most likely value, and lower bound of the probability assessment fluctuate continuously over time, indicating that the PV acceptance capacity of the distribution network is affected by PV output, load level, and network operation status, and is not a fixed single value.

[0157] Between 7:00 and 8:30 and between 16:00 and 17:30, the upper bound of the system's carrying capacity is relatively high, indicating that the distribution network still has a large margin for photovoltaic (PV) grid connection under certain favorable source-load scenarios. Between 10:00 and 14:00, the most likely carrying capacity is at a relatively low level, indicating that the capacity for new PV grid connection is limited during this period due to constraints such as voltage rise, line power flow, and reverse power transmission. Therefore, this invention can obtain the probability range and most likely level of distributed PV carrying capacity at different time periods. Compared with traditional deterministic assessment methods, it can more intuitively reflect the dynamic range of changes in the distribution network's PV carrying capacity under source-load uncertainty.

[0158] Although the present invention has been disclosed above with reference to preferred embodiments, the embodiments and accompanying drawings are not intended to limit the invention. Any person skilled in the art can make various changes or modifications without departing from the spirit and scope of the invention, and these changes will also be within the protection scope of the invention. Therefore, the protection scope of the present invention should be defined by the scope of the claims of this application.

Claims

1. A method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power in a distribution network, characterized in that, Includes the following steps: Step 1: Acquire multi-source data and divide the evaluation period into multiple consecutive running segments according to the set time scale; Step 2: Establish a power flow security constraint model for each operating period to describe the node power balance, node voltage, line current carrying capacity, transformer load rate and reverse power flow constraint relationship during that period; Step 3: Establish a photovoltaic output probability model for each operating period based on the historical output data of distributed photovoltaic power, establish a load power probability model for each operating period based on the historical load data of nodes, and use a correlation function to describe the correlation between photovoltaic output and load power. Step 4: Use a probabilistic sampling method to generate multiple sets of source-load random operation scenarios, and calculate the maximum accessible capacity of distributed photovoltaic power that meets the safety operation constraints of the distribution network in each set of scenarios, forming a carrying capacity sample set arranged in time; Step 5: Perform probability statistics on the carrying capacity samples of each operating period to obtain the time-varying probability distribution, confidence interval, and time series curves of the upper and lower limits of the distributed photovoltaic carrying capacity, thereby forming the probability assessment results of the dynamic carrying capacity of distributed photovoltaic.

2. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 1, characterized in that: In step 1, the multi-source data includes the distribution network topology, line impedance parameters, transformer capacity parameters, node load time-series curves, existing distributed power generation capacity, locations of distributed photovoltaic (PV) systems to be connected, and historical output data of distributed PV systems. This data is used to determine the network structure, equipment operating boundaries, source-load time-series characteristics, and PV connection locations for the distribution network carrying capacity assessment. The assessment period is divided into multiple continuous operating segments according to a set time scale, so that each operating segment corresponds to the corresponding load level, PV output characteristics, and distribution network operating status, providing basic data for the subsequent establishment of a power flow security constraint model and the development of dynamic carrying capacity probability assessment.

3. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Obtain the topology of the distribution network to be evaluated, determine the electrical connection relationships between nodes, lines, transformers, existing distributed power sources and distributed photovoltaics to be connected in the distribution network, and form the network structure foundation for power flow calculation and carrying capacity assessment; Step 1.2: Obtain the impedance parameters of the distribution network lines, the current carrying capacity limit of the lines, the transformer capacity parameters, the allowable load rate, and the reverse power flow limit. These parameters are used to determine the safe operating boundaries of key equipment such as lines and transformers in the distribution network, and to provide a parameter basis for the subsequent establishment of node voltage, line power flow, transformer load rate, and reverse power flow constraints. Step 1.3: Obtain the load time-series curves of each node within the evaluation period. The load time-series curves include the active and reactive loads of each node at different time periods, which are used to describe the operating characteristics of the distribution network load level changing over time. At the same time, obtain the existing distributed power generation capacity and the location of distributed photovoltaics to be connected, which are used to determine the current initial connection status of the distribution network and the carrying capacity evaluation object. Step 1.4: Obtain historical output data of distributed photovoltaic power. The historical output data of distributed photovoltaic power includes photovoltaic output samples of various time periods within multiple historical days, which are used to characterize the random fluctuation characteristics of distributed photovoltaic power output in different time periods. The evaluation period is divided into multiple continuous operating segments according to a set time scale, so that each operating segment corresponds to the corresponding load level, photovoltaic power output characteristics and distribution network operating status, providing basic data for subsequent dynamic carrying capacity probability assessment.

4. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 3, characterized in that: Step 2 specifically includes: Step 2.1: Let the set of distribution network nodes be... The route set is The runtime segment set is For any given time period ,node The active and reactive loads are respectively ,node The active power output of the connected distributed photovoltaic system is The node voltage amplitude is The above variables describe the operating status of the distribution network at different times after the distributed photovoltaic system is connected. Step 2.2: For each operating segment, establish node power balance constraints; assume the line Indicates that by node Pointing to node The power distribution lines, the lines The active power and reactive power are respectively The node power balance relationship can be expressed as: ； ； In the formula, Indicates from node Flowing to downstream nodes Sum the line power. Indicates from the upstream node Inflow node Sum the line power; Step 2.3: Establish the relationship between line power flow and node voltage; assume the line... The resistance and reactance are respectively , The voltages at the nodes at both ends of the line satisfy the following relationship: ； In the formula, and Time periods node and nodes voltage amplitude, For time period line The current amplitude; the relationship between line current and line power satisfies: ； This describes the power flow relationship between line power, current and node voltage after distributed photovoltaic (PV) grid integration. Step 2.4: Establish node voltage safety constraints; let the lower and upper limits of the node voltage be respectively... , Then for any node and any time period It should satisfy: ； This constraint is used to determine whether the integration of distributed photovoltaic systems causes node voltage to exceed limits. Step 2.5: Establish line current carrying capacity constraints; set the line... The maximum allowable current is Then the line current carrying capacity constraint is: ； Establish transformer load rate constraints; assume transformer... During the period The active power and reactive power transmitted are respectively , The rated capacity of the transformer is Then the transformer capacity constraint is: ； This constraint is used to ensure that the transformer does not operate under overload after distributed photovoltaic power is connected; Step 2.6: Establish reverse power flow constraints for the transformer; assuming the transformer... During the period Active transmission power Taking the flow from the upstream power grid to the distribution network as the positive direction, the upper limit of the allowed reverse power transmission is: Then the reverse power flow constraint is: ； This constraint is used to limit the amount of power that distributed photovoltaic power can feed back to the upstream grid during periods of high photovoltaic output and low load.

5. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 4, characterized in that: Based on multiple constraints, a set of power flow security constraints for each operating segment is formed: ； In the formula, For time period The feasible domain for safe operation of the distribution network; subsequently, when calculating the maximum connectable capacity of distributed photovoltaic power, it will only be considered if the power flow result in the corresponding scenario belongs to the feasible domain. Only then is it considered that the photovoltaic access capacity meets the requirements for safe operation of the distribution network.

6. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 5, characterized in that: Step 3 specifically includes: Step 3.1: For any runtime segment Extract the distributed photovoltaic power output samples and load power samples corresponding to this time period from multiple historical days, and denot them as follows: ； ； In the formula, For the first Historical sample days during runtime Distributed photovoltaic power output, For the first Historical sample days during runtime The load power, This represents the number of historical samples. Step 3.2: Establish a distributed photovoltaic power output probability model for each operating period using the kernel density estimation method; for each time period... The probability density function of distributed photovoltaic power output is expressed as: ； In the formula, runtime segment The output value of distributed photovoltaic power is The probability density function at time , For distributed photovoltaic power output variables, For kernel function, runtime segment The corresponding window width for estimating photovoltaic output kernel density; Choose the Gaussian kernel function: ； In the formula, The input variables for the kernel function are used to describe the random fluctuation characteristics of distributed photovoltaic (PV) output at different times. For nighttime periods, if all historical PV output samples are zero, the PV output probability model for that period is directly degraded to a zero output state. ; Step 3.3: Establish the load power probability model for each operating period using the kernel density estimation method; for each time period... The load power probability density function is expressed as: ； In the formula, runtime segment The load power is taken as The probability density function at time , For load power variables, runtime segment The corresponding load power kernel density estimation window width; if it is necessary to consider the nodal reactive load at the same time, the reactive load is estimated from the active load based on the historical power factor or typical power factor, that is: ； In the formula, For the first Historical sample midday nodes During the period reactive load, For nodes The power factor; Step 3.4: After obtaining the edge probability models for photovoltaic power output and load power respectively, calculate their cumulative distribution functions; distributed photovoltaic power output and load power in time period The cumulative distribution functions are expressed as follows: ； ； In the formula, For time period Distributed photovoltaic output not greater than The cumulative probability, For time period Load power not greater than The cumulative probability, and These are the integral variables; the cumulative distribution function is used to map the photovoltaic output and load power samples to a unified probability space. Step 3.5: Use the Copula function to describe the correlation between distributed photovoltaic power output and load power within the same operating period. For the operating period... ,set up: ； Construct a joint distribution function for photovoltaic power output and load power based on the Copula function: ； In the formula, For time period The joint cumulative distribution function of photovoltaic power output and load power. For time period The selected Copula function, The correlation parameter of the Copula function is used to characterize the degree of correlation between photovoltaic output and load power during this period. If Gaussian Copula is used, its joint distribution function is expressed as: ； In the formula, The correlation coefficient is The two-dimensional standard normal distribution function, It is the inverse function of the one-dimensional standard normal distribution function. runtime segment The correlation coefficient between photovoltaic output and load power; It can be calculated from historical photovoltaic power output samples and load power samples, using the Spearman rank correlation coefficient: ； In the formula, For the sample Rank in the historical photovoltaic output sample For the sample Rank in the historical load sample The average value of the sample rank of photovoltaic power output. The average value of the load power sample rank is given; the statistical correlation between photovoltaic output and load power is introduced into the joint probability model through the correlation coefficient. Step 3.6: Obtain the runtime segment from the joint distribution function. The joint probability density function of the source and charge: ； In the formula, For time period The joint probability density function of photovoltaic power output and load power. For Copula density function, and These are the photovoltaic output probability density function and the load power probability density function established above; the joint probability density function is used to describe the probability that photovoltaic output and load power take different values ​​at the same time period, providing a probability distribution basis for generating multiple sets of source-load random operation scenarios in step 4; Step 3.7: Connect the source-load joint probability model obtained in Step 3 with the power flow security constraint model in Step 2; for the subsequent Step 4, the generated first... In a scenario where the source and load operate in a random manner, photovoltaic output samples can be obtained using a joint probability model. and load power samples And further mapped to the node variables in step 2. , and This is used to calculate the maximum connectable capacity of distributed photovoltaic power that meets the safety operation constraints of the distribution network under this random scenario.

7. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 6, characterized in that: Step 4 specifically includes: Step 4.1: Let the first... The joint probability density function of the source and load for each runtime segment is: ,in Represents the output variable of distributed photovoltaic power. The load power variable is represented; it is extracted from the joint probability density function using a probability sampling method. Group samples, obtained: ； In the formula, runtime segment Next Distributed photovoltaic power output samples in a group of random scenarios runtime segment Next Load power samples in a set of random scenarios; Step 4.2: For the first In a random operation scenario involving both source and load, photovoltaic output samples and load power samples are mapped to node variables in step 2; let the set of distributed photovoltaic nodes to be connected be... ,node The photovoltaic capacity allocation factor is And satisfy: ； Runtime segment Scene The total grid connection capacity of distributed photovoltaic power to be determined is as follows: Then the node The actual output of distributed photovoltaic power is expressed as follows: ； In the formula, Contribute to distributed photovoltaic power generation. This represents the total distributed photovoltaic (PV) grid connection capacity to be evaluated in this scenario. For the reason The normalized photovoltaic output coefficient is used to represent the power generation level per unit capacity of photovoltaic power during that period; if Then we have: ； Step 4.3: For load power, based on the baseline load or node load allocation ratio obtained in Step 1, map the scenario load sample to each node; assuming the nodes... The baseline active and reactive loads are respectively , runtime segment Scene The load factor is Then the node load is expressed as: ； ； In the formula, and These are active load and reactive load, respectively; thus, the random load sample in step 3 can be connected with the node power balance constraint in step 2. Step 4.4: Under each set of random scenarios, with the goal of maximizing the total grid-connected capacity of distributed photovoltaic power, establish a carrying capacity calculation model for that scenario: ； satisfy: ； Runtime segments in sequence All inside The above bearing capacity calculations were performed on a group of random scenarios to obtain a bearing capacity sample set for that time period: ； In the formula, runtime segment The distributed photovoltaic carrying capacity sample set reflects the maximum grid-connectable photovoltaic capacity under different source-load random operation scenarios during this period; the above process is repeated for all operating periods to obtain the carrying capacity sample set arranged by time: ； In the formula, This serves as a sample set of dynamic carrying capacity for distributed photovoltaic power throughout the entire evaluation period. This represents the total number of runtime segments.

8. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 7, characterized in that: In step 4.1: The random samples correspond to the joint probability model in step 3, and are used to characterize the possible operating states where photovoltaic power output and load power fluctuate simultaneously within the same time period; if the source-load joint probability model is constructed using a Copula function in step 3, then pairs of random variables that satisfy the correlation are first generated in a unified probability space: ； In the formula, and Runtime segment Next The cumulative probability variables corresponding to photovoltaic output and load power in the group scenario, and Then, the cumulative distribution function of photovoltaic output obtained in step 3 is used. and load power cumulative distribution function The inverse function maps the probability space samples to actual source-load power samples: ； ； In the formula, runtime segment The inverse function of the cumulative distribution function of photovoltaic power output. runtime segment The inverse function of the cumulative load power distribution function; through the above mapping, a stochastic operating scenario consistent with the historical source load probability characteristics and correlation can be obtained.

9. The method for probabilistic assessment of the dynamic carrying capacity of distributed photovoltaic power grids according to claim 7, characterized in that: Step 5 specifically includes: Step 5.1: Use the kernel density estimation method to evaluate the runtime segment. By fitting the probability distribution of the carrying capacity samples, the probability density function of the distributed photovoltaic carrying capacity for that period is obtained: ； In the formula, runtime segment The carrying capacity of distributed photovoltaic power is taken as: The probability density function at time , For bearing capacity variables, runtime segment The kernel density estimation window width for the load-bearing capacity samples; Step 5.1: Calculate the corresponding cumulative distribution function based on the bearing capacity probability density function: ； In the formula, runtime segment Distributed photovoltaic carrying capacity not greater than The cumulative probability, The variable is the integral variable; the cumulative distribution function is used to determine the probability assessment interval of the distributed photovoltaic carrying capacity at a given confidence level during this period. Step 5.3: Set the preset signal level as follows: ,in Then the runtime segment The probability assessment interval for distributed photovoltaic carrying capacity is expressed as follows: ； In the formula, runtime segment Lower bound of distributed photovoltaic carrying capacity probability assessment runtime segment Upper bound of distributed photovoltaic carrying capacity probability assessment It is the inverse function of the cumulative distribution function of bearing capacity. The confidence level; the evaluation interval represents the runtime at a given confidence level. The distributed photovoltaic carrying capacity is likely to fall within this range; Step 5.4: Colleagues determine the runtime segment The most likely value of the distributed photovoltaic carrying capacity is obtained from the carrying capacity value corresponding to the maximum of the probability density function: ； In the formula, runtime segment The most probable value of distributed photovoltaic carrying capacity represents the photovoltaic carrying capacity level with the highest probability of occurring during this period under the influence of source-load uncertainty; For nighttime hours, since distributed photovoltaic power generation does not occur, it is not included in the assessment of new photovoltaic grid connection capacity. Therefore, the carrying capacity assessment result for this period is: ； Step 5.5: Repeat the above probability statistics process for all operating segments within the evaluation period to obtain the lower bound, most likely value, and upper bound sequence of bearing capacity for each operating segment: ； ； ； In the formula, This is the lower bound sequence for the probability assessment of distributed photovoltaic carrying capacity throughout the entire assessment period. This is the sequence of most likely values ​​for bearing capacity. This is the upper bound sequence for bearing capacity probability assessment; Step 5.6: Connect the lower bound, most likely value, and upper bound of the carrying capacity for each operating segment in chronological order to form a probability assessment curve for the dynamic carrying capacity of distributed photovoltaic power generation; where, and The upper and lower limit time series curves constitute the carrying capacity of distributed photovoltaic power, and the region between the two represents the dynamic carrying capacity probability interval under a given confidence level. This represents the most likely carrying capacity level during each operating period; thus forming the distributed photovoltaic dynamic carrying capacity probability assessment result, which is used to reflect the probability range of the distribution network's distributed photovoltaic acceptance capacity changing over time under the influence of source load uncertainty.

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