A power system stochastic power flow analytical method considering unit frequency modulation capacity segmentation constraints

Abstract

The application discloses a kind of power system stochastic power flow analytic method considering unit frequency modulation capacity segmentation constraint, it is related to power system operation analysis technical field, including the following steps: based on the frequency modulation capacity segmentation boundary of each frequency modulation unit, deviation breakpoint corresponding to random net power deviation is determined, and deviation segmentation interval is divided;According to the interval state corresponding to each deviation segmentation interval, the conditional mapping relationship between random net power deviation and node injection power correction amount is established;Based on the conditional mapping relationship, the random net power deviation falling into each deviation segmentation interval is respectively carried out power flow analysis, and the corresponding node voltage, branch power flow and unit output condition distribution are obtained;According to the occurrence probability of each deviation segmentation interval, the conditional distribution is synthesized, and the stochastic power flow analysis result is obtained.The application is analyzed by random power flow segmentation according to frequency modulation capacity segmentation boundary, to solve the problem that power flow distribution and out-of-limit probability are distorted due to fixed participation factor.

Description

Technical Field

[0001] This invention relates to the field of power system operation analysis technology, and more specifically, to a stochastic power flow analysis method for power systems that takes into account the segmented constraints of unit frequency regulation capacity. Background Technology

[0002] With the increasing impact of renewable energy output fluctuations and load forecasting errors on power system operation, stochastic power flow analysis methods are widely used to assess the uncertainty distribution of node voltage, line power flow, and generator output. Existing stochastic power flow analysis methods typically first establish a stochastic power deviation model, then allocate the system's net stochastic power deviation to the corresponding generators through fixed balancing machines, fixed frequency regulation participation factors, or multi-machine balancing methods, and further calculate the impact of stochastic disturbances on node injected power, line power flow, and voltage distribution. This type of method has good applicability when the response capability of frequency regulation units remains unchanged and can reflect the probabilistic impact of stochastic source fluctuations on power flow results.

[0003] However, in actual operation, the adjustability of frequency regulation units is not continuously and uniformly available across the entire random deviation range. Instead, it is constrained by the current baseline output, upward and downward capacity, ramp-up capability, and frequency regulation capacity segment boundaries. When the random net power deviation increases and causes some units to reach capacity segment boundaries, exhaust capacity segments, or exit frequency regulation, these units should not continue to bear subsequent deviations according to their original participation factors. If existing stochastic power flow analysis methods still use a unified participation relationship to handle all random deviations, units that have lost their subsequent regulation capability will still be included in the deviation sharing process, causing the unit output distribution, line power flow distribution, and over-limit probability calculations to deviate from the actual frequency regulation response state.

[0004] The aforementioned disclosed technical solutions have at least the following technical problems: Existing stochastic power flow analysis methods typically use fixed balancing machines or fixed frequency regulation participation factors to allocate stochastic power deviations. However, in actual operation, the frequency regulation capacity of generating units has segmented available boundaries. When some generating units reach the capacity segment boundary, the capacity segment is exhausted, or they exit frequency regulation, the subsequent stochastic deviations are still shared according to the original participation factors, which leads to distortions in the calculation of unit output distribution, line power flow distribution, and over-limit probability.

[0005] To address the above problems, this invention proposes a solution. Summary of the Invention

[0006] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a power system stochastic power flow analysis method that takes into account the unit frequency regulation capacity segmentation constraints. By dividing the stochastic net power deviation interval based on the frequency regulation capacity segmentation boundary and establishing node injection condition mapping relationships in each interval, the method solves the problem that the fixed participation factor in the existing stochastic power flow analysis cannot reflect the unit capacity segmentation switching, resulting in the distortion of the calculation of unit output, line power flow and over-limit probability.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A stochastic power flow analysis method for power systems considering unit frequency regulation capacity segmentation constraints includes the following steps: determining deviation breakpoints corresponding to stochastic net power deviations based on the frequency regulation capacity segmentation boundaries of each frequency regulation unit, and dividing deviation segmentation intervals by deviation breakpoints; establishing a conditional mapping relationship between stochastic net power deviations and node injection power corrections based on the interval states corresponding to each deviation segmentation interval; performing power flow analysis on stochastic net power deviations falling into each deviation segmentation interval based on the conditional mapping relationship to obtain the corresponding node voltage, branch power flow, and unit output condition distributions; obtaining the stochastic power flow analysis results according to the probability distribution of occurrence of each deviation segmentation interval, and outputting the frequency regulation capacity segmentation occupancy probability and the deviation breakpoints corresponding to branch overruns.

[0008] In a preferred embodiment, determining the deviation breakpoint corresponding to the random net power deviation includes: selecting the corresponding frequency modulation capacity segment boundary according to the frequency modulation direction of the random net power deviation; at the starting point of the current deviation segment interval, determining the current capacity segment and remaining frequency modulation amount based on the frequency modulation output occupancy already formed by each frequency modulation unit; converting each remaining frequency modulation amount into a random net power deviation increment according to the segment participation relationship within the current capacity segment, and determining the deviation value corresponding to the smallest positive deviation increment as the next deviation breakpoint; after updating the state of the frequency modulation unit that has reached the capacity segment boundary, continuing to determine subsequent deviation breakpoints.

[0009] In a preferred embodiment, the step of dividing the deviation segment interval by deviation breakpoints includes: sorting the points where the random net power deviation is zero and each deviation breakpoint according to the deviation amplitude in the corresponding frequency modulation direction, and forming deviation segment intervals by using adjacent breakpoints as interval boundaries; for each deviation segment interval, determining the frequency modulation output, occupied capacity segments, frequency modulation participation status, and segment participation relationships of each frequency modulation unit at its starting breakpoint as the interval state of that deviation segment interval; when the random net power deviation crosses a deviation breakpoint, updating the interval state of the next deviation segment interval according to the capacity segment boundary of the frequency modulation unit that triggered the deviation breakpoint, so that the frequency modulation response relationship within the same deviation segment interval remains unchanged.

[0010] In a preferred embodiment, establishing the conditional mapping relationship between random net power deviation and node injected power correction includes: reading the interval state corresponding to the current deviation segment interval; splitting the random net power deviation falling into the current deviation segment interval into the interval starting deviation breakpoint and the interval deviation increment; determining the starting injection offset of the corresponding node based on the frequency modulation output already formed by each frequency modulation unit at the interval starting point, and determining the incremental injection correction of the corresponding node based on the set of frequency modulation units currently participating in the deviation increment response and their sharing ratio; and superimposing the starting injection offset and the incremental injection correction to obtain the conditional mapping relationship between the random net power deviation within the current deviation segment interval and the node injected power correction.

[0011] In a preferred embodiment, determining the starting point injection offset of the corresponding node based on the frequency modulation output already formed by each frequency modulation unit at the start of the interval includes: determining the frequency modulation output occupancy of each frequency modulation unit at the start of the current deviation segment interval and its connected nodes; determining the correction direction of the frequency modulation output occupancy to the node injection power based on the frequency modulation direction corresponding to the random net power deviation; summarizing the frequency modulation output occupancy of the frequency modulation units connected to the same node according to the correction direction to obtain the starting point injection offset of the node at the start of the current deviation segment interval.

[0012] In a preferred embodiment, the step of performing power flow analysis on the random net power deviations falling into each deviation segment interval based on the conditional mapping relationship includes: for each deviation segment interval, calling the conditional mapping relationship corresponding to the deviation segment interval to convert the random net power deviations falling into the deviation segment interval into node injection power correction amounts; superimposing the node injection power correction amounts with the basic power flow state to form a conditional power flow input that is only applicable to the deviation segment interval; obtaining the node voltage, branch power flow, and unit output results based on the conditional power flow input, and associating the results with the interval state of the deviation segment interval to form conditional power flow results; and distributing the conditional power flow results according to the range of random net power deviation values ​​to obtain the conditional distribution of node voltage, branch power flow, and unit output.

[0013] In a preferred embodiment, the step of obtaining the node voltage, branch power flow, and unit output results based on the conditional power flow input includes: superimposing the node injection power correction and the injection change of the corresponding random disturbance source node onto the basic power flow state to form the conditional power flow input corresponding to the current deviation segment interval; under the condition that the capacity occupancy state and segment participation relationship of the current deviation segment interval remain unchanged, performing power flow solution on the conditional power flow input to obtain the node voltage result and branch power flow result; determining the frequency regulation unit output result based on the frequency regulation output already formed at the starting point of the current deviation segment interval and the sharing amount corresponding to the newly added deviation increment within the interval; and associating the node voltage result, branch power flow result, and frequency regulation unit output result with the interval state of the current deviation segment interval to form the conditional power flow result.

[0014] In a preferred embodiment, the step of synthesizing the conditional distribution according to the occurrence probability of each deviation segment interval includes: determining the occurrence probability of a random net power deviation falling into each deviation segment interval based on the random net power deviation distribution; weighting and synthesizing the node voltage condition distribution, branch power flow condition distribution, and unit output condition distribution corresponding to each deviation segment interval according to the occurrence probability to obtain the overall node voltage distribution, the overall branch power flow distribution, and the overall unit output distribution; statistically analyzing the occupancy probability of each frequency regulation unit capacity segment based on the occurrence probability and interval status of each deviation segment interval, and determining the deviation segment interval corresponding to the branch over-limit probability; and outputting the starting deviation breakpoint, ending deviation breakpoint, and corresponding frequency regulation unit capacity occupancy status of the deviation segment interval as deviation breakpoint information corresponding to the branch over-limit.

[0015] In a preferred embodiment, determining the probability of a random net power deviation falling into each deviation segment interval based on the random net power deviation distribution includes: converting the random net power deviation into a deviation amplitude according to the corresponding frequency modulation direction, and reading the deviation segment intervals formed by adjacent deviation breakpoints; when the deviation amplitude has a probability distribution function, calculating the probability of the deviation amplitude falling into each deviation segment interval based on the probability distribution function; when the deviation amplitude is represented by historical samples, prediction error samples, or scene samples, determining the occurrence probability of each deviation segment interval based on the proportion of the number of samples falling into each deviation segment interval to the total number of samples; and associating each deviation segment interval with its corresponding occurrence probability for weighted synthesis of the conditional distribution of each deviation segment interval.

[0016] In a preferred embodiment, the output frequency modulation capacity segment occupancy probability and the deviation breakpoint corresponding to branch over-limit include: calculating the probability that each frequency modulation unit capacity segment is occupied or participating in the deviation increment response state based on the occurrence probability and interval state of each deviation segment interval; calculating the contribution of each deviation segment interval to the branch over-limit probability based on the branch power flow condition distribution corresponding to each deviation segment interval; determining the deviation segment interval that contributes to the branch over-limit probability as the over-limit associated interval, and outputting the starting deviation breakpoint, ending deviation breakpoint, frequency modulation unit capacity occupancy state, and over-limit probability contribution corresponding to the over-limit associated interval; when the same branch corresponds to multiple over-limit associated intervals, determining the over-limit associated interval with the largest over-limit probability contribution as the dominant over-limit interval, and using the deviation breakpoint corresponding to the dominant over-limit interval as the main deviation breakpoint corresponding to the branch over-limit.

[0017] The technical effects and advantages of the present invention regarding a stochastic power flow analysis method for power systems that takes into account the segmented constraints of unit frequency regulation capacity are as follows: This invention determines the deviation breakpoints of random net power deviations by defining the frequency regulation capacity segment boundaries, and establishes node injection power condition mapping relationships within each deviation segment interval. This allows the stochastic power flow analysis process to switch according to changes in the capacity status of frequency regulation units, preventing units that have reached capacity limits or exited frequency regulation from continuing to bear subsequent deviations based on their original participation factors. This improves the accuracy of unit output distribution, branch power flow distribution, and over-limit probability calculations, and enables the output of frequency regulation capacity segment occupancy probabilities and deviation breakpoints corresponding to branch over-limits, facilitating the location of over-limit risk sources. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a stochastic power flow analysis method for a power system that takes into account the segmented constraints of unit frequency regulation capacity, according to the present invention. Figure 2 A graph showing the relationship between the frequency regulation output occupancy of each generating unit and the random net power deviation. Figure 3 A comparison chart of the analytical results for the power flow of the key branch. Detailed Implementation

[0019] 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] Example 1, Figure 1This invention presents a stochastic power flow analysis method for power systems that takes into account segmented constraints on unit frequency regulation capacity, comprising the following steps: S1. Based on the frequency regulation capacity segment boundary of each frequency regulation unit, determine the deviation breakpoint corresponding to the random net power deviation, and divide the deviation segment interval by the deviation breakpoint. In this embodiment, the frequency modulation capacity segment boundary refers to the capacity boundary value at which the frequency modulation unit can continue to bear frequency modulation power in the upward or downward adjustment direction under the current reference output. Each capacity segment boundary is used to indicate the position of the unit from one frequency modulation response state to another, such as from the first frequency modulation capacity segment to the second frequency modulation capacity segment, or exiting the subsequent deviation sharing after reaching the upper limit of adjustable capacity.

[0021] The deviation breakpoint refers to the random net power deviation value that causes at least one frequency regulation unit to reach the corresponding frequency regulation capacity segment boundary when the random net power deviation increases to a certain value.

[0022] Specifically, if the random net power deviation is shared proportionally by units G1 and G2, and G1 bears 40% of the system deviation, G1's first-stage capacity increase is 20MW. Then, when the system random net power deviation reaches 50MW, G1 bears 20MW and reaches the first-stage boundary. At this point, 50MW is a deviation breakpoint.

[0023] The determination of the deviation breakpoint corresponding to the random net power deviation based on the frequency regulation capacity segmentation boundary of each frequency regulation unit includes: Based on the direction of the random net power deviation, select the upper or lower capacity segment boundary for each frequency regulation unit, and take the unit's benchmark output when the random net power deviation is zero as the initial state. At the starting point of the current deviation segment interval, determine the frequency modulation output occupancy of each frequency modulation unit, and determine the current capacity segment of each frequency modulation unit based on the frequency modulation output occupancy. For frequency-regulating units that are still participating in frequency regulation within the current capacity segment, calculate the remaining frequency regulation amount they need to undertake from the current frequency regulation output occupancy to the boundary of the next capacity segment; Based on the segment participation relationship of each frequency modulation unit in the current capacity segment, the remaining frequency modulation amount is converted into the corresponding random net power deviation increment, and the smallest positive deviation increment is determined as the termination increment of the current deviation segment interval. Add the random net power deviation value corresponding to the starting point of the current deviation segment interval to the termination increment to obtain the next deviation breakpoint, and update the frequency modulation unit that has reached the capacity segment boundary to the next capacity segment participation state, capacity segment exhaustion state, or frequency modulation exit state. Repeat the above process until the target analytical range of the random net power deviation distribution is covered, and obtain multiple deviation breakpoints corresponding to the random net power deviation.

[0024] The remaining frequency modulation amount is calculated using the following formula:

[0025] The specific formula for calculating the random net power deviation increment is as follows:

[0026]

[0027] in, Let i be the remaining frequency regulation capacity that frequency regulating unit i needs to undertake to reach the current capacity segment boundary within the k-th deviation segment interval. This represents the termination boundary of the capacity segment currently occupied by frequency regulation unit i. This represents the frequency regulation output occupancy already formed by frequency regulation unit i at the starting point of the k-th deviation segment interval. Let i be the capacity segment number of frequency regulation unit i within the k-th deviation segment interval. This represents the random net power deviation increment required for frequency regulation unit i to reach the current capacity segment boundary from its current frequency regulation output occupancy. Let i be the proportion of the random net power deviation increment shared by the frequency regulation unit i in the k-th deviation segment interval. This represents the segment participation factor for frequency regulation unit i within the current capacity segment. Let K be the set of generating units that still participate in frequency regulation within the k-th deviation segment interval. When this occurs, it indicates that the frequency regulation unit does not bear the random net power deviation increment within the current deviation segment interval and does not participate in the deviation breakpoint calculation.

[0028] The segmented participation relationship is determined in the following manner: At the starting point of the k-th deviation segment interval, the units that have not yet reached the frequency regulation capacity boundary are identified as candidate frequency regulation units; For each candidate frequency modulation unit, calculate its achievable frequency modulation amount within the current capacity segment. The achievable frequency modulation amount is the smaller value between the remaining capacity of the current capacity segment and the ramp-up adjustment amount within the target response time. Units that can withstand frequency regulation values ​​greater than zero are identified as units participating in frequency regulation within the current deviation segment interval; If the scheduling system has given an AGC participation factor, the sharing ratio of each participating frequency regulation unit is determined according to the AGC participation factor; if no AGC participation factor is given, the sharing ratio is determined according to the proportion of frequency regulation that each participating frequency regulation unit can handle.

[0029] Furthermore, the step of dividing the deviation segment interval by the deviation breakpoint includes: The point where the random net power deviation is zero is taken as the initial breakpoint, and the calculated deviation breakpoints are sorted in ascending order of the absolute value of the deviation in the corresponding frequency modulation direction. Using two adjacent deviation breakpoints as interval boundaries, deviation segment intervals are formed in the corresponding frequency regulation direction; each deviation segment interval is used to characterize that when the random net power deviation changes within the interval, no new capacity segment switching, capacity segment exhaustion, or frequency regulation exit occurs for each frequency regulation unit. For each deviation segment interval, the frequency modulation output, occupied capacity segment, and still available capacity segment of each frequency modulation unit at its initial deviation breakpoint are taken as the interval state of that deviation segment interval. When a certain deviation breakpoint is formed by at least one frequency modulation unit reaching the capacity segment boundary, the interval state is updated according to the state after the frequency modulation unit enters the next capacity segment, the capacity segment is exhausted, or the frequency modulation is exited within the deviation segment interval after the deviation breakpoint. Each deviation segment interval is associated with and stored with the corresponding interval status. The interval status includes the frequency modulation output, occupied capacity segment, frequency modulation status and segment participation relationship of each frequency modulation unit at the starting point of the corresponding interval. This is used to establish a conditional mapping relationship in the future without reallocating the previous frequency modulation output.

[0030] Figure 2 The figure illustrates the relationship between the frequency regulation output occupancy of each frequency regulation unit and the magnitude of the random net power deviation. The horizontal axis represents the magnitude of the random net power deviation, and the vertical axis represents the frequency regulation output occupancy of the unit. The three curves correspond to the frequency regulation output undertaken by frequency regulation units G1, G2, and G3 under different deviation magnitudes. The vertical dashed lines in the figure represent deviation breakpoints triggered by the frequency regulation capacity segment boundaries. When the random net power deviation crosses the corresponding deviation breakpoint, at least one frequency regulation unit reaches the current capacity segment boundary, and the subsequent deviation allocation relationship switches accordingly. As can be seen from the figure, the frequency regulation output of different units does not always increase continuously at the same fixed ratio, but exhibits different growth slopes in different deviation intervals. This demonstrates that the present invention, by dividing the deviation segment intervals through deviation breakpoints, can reflect the impact of unit capacity segment switching on the frequency regulation output allocation relationship.

[0031] This diagram visually illustrates that the present invention does not allocate random net power deviations to each unit according to a fixed participation factor. Instead, after a unit reaches its capacity segment boundary, the previously established frequency regulation output is retained as the starting state of the interval, and a new segment response relationship is established only for subsequent new deviations. This avoids units that have reached their capacity boundary or have exited frequency regulation from continuing to participate in subsequent deviation sharing, thus improving the accuracy of the unit output distribution calculation.

[0032] S2, based on the interval state corresponding to each deviation segment interval, establish a conditional mapping relationship between random net power deviation and node injection power correction. In this embodiment, establishing the conditional mapping relationship between the random net power deviation and the node injection power correction includes: Within the current deviation segment interval, read the interval status corresponding to the deviation segment interval. The interval status includes the interval starting point deviation breakpoint, frequency modulation direction, frequency modulation output occupancy of each frequency modulation unit at the interval starting point, the node where each frequency modulation unit is located, the set of frequency modulation units still participating in the deviation increment response, and the corresponding sharing ratio. The random net power deviation falling into the current deviation segment interval is represented as the sum of the deviation breakpoint at the starting point of the interval and the deviation increment within the interval, so that the frequency modulation output already formed before the starting point of the interval no longer participates in the redistribution. Based on the frequency modulation output occupancy already formed by each frequency modulation unit at the start of the interval, the frequency modulation output formed before the start of the interval is converted into the start injection offset of the corresponding node. Based on the set of frequency regulation units still participating in the deviation increment response and their corresponding sharing ratio, the deviation increment within the interval is converted into the incremental injection correction amount of the corresponding node; The starting point injection offset and the incremental injection correction are superimposed to obtain the conditional mapping relationship between the random net power deviation and the node injection power correction within the current deviation segment interval.

[0033] The conditional mapping relationship is as follows:

[0034] in, Let n be the injection power correction amount for node n within the k-th deviation segment interval. Inject an offset into the starting point of node n at the beginning of the k-th deviation segment interval. The random net power deviation falling within the k-th deviation segment interval, Let the starting point of the k-th deviation segment interval be the deviation breakpoint. It represents the injection correction ratio of node n for the random net power deviation increment within the k-th deviation segment interval.

[0035] The starting point injection offset is determined according to the following formula:

[0036] The injection correction ratio is determined according to the following formula:

[0037] in, Let n be the set of frequency regulation units connected to node n. Let be the frequency modulation direction coefficient of frequency modulation unit i. It takes a positive value when the frequency modulation unit increases its output and a negative value when the frequency modulation unit decreases its output. This represents the frequency regulation output occupancy already formed by frequency regulation unit i at the starting point of the k-th deviation segment interval. This refers to the set of frequency regulation units that still participate in the deviation increment response within the k-th deviation segment interval. This represents the proportion of the random net power deviation increment shared by frequency regulation unit i in the k-th deviation segment interval.

[0038] Furthermore, the step of converting the frequency modulation output already formed before the start of the interval into the start-point injection offset of the corresponding node based on the frequency modulation output occupancy already formed by each frequency modulation unit at the start of the interval includes: Determine the frequency regulation output occupancy of each frequency regulation unit at the starting point of the current deviation segment interval, and the access node of each frequency regulation unit in the power grid; Based on the frequency modulation direction corresponding to the random net power deviation, determine the direction of the effect of the frequency modulation output of each frequency modulation unit on the injected power of the node; when the random net power deviation requires the frequency modulation unit to increase its output, the frequency modulation output already formed is used as the positive injection correction amount of the corresponding node; when the random net power deviation requires the frequency modulation unit to decrease its output, the frequency modulation output already formed is used as the negative injection correction amount of the corresponding node. The frequency modulation output occupancy already formed at the starting point of the current deviation segment interval by the frequency modulation units connected to the same node is summarized according to the direction of action to obtain the starting point injection offset of the node at the starting point of the current deviation segment interval. The starting point injection offset is used to characterize the node injection change that has been fixed due to the previous frequency modulation capacity segment response before the random net power deviation enters the current deviation segment interval; within the current deviation segment interval, the starting point injection offset is retained as an established state and is no longer redistributed with the addition of new deviation increments within the interval.

[0039] S3, based on the condition mapping relationship, perform power flow analysis on the random net power deviation falling into each deviation segment interval to obtain the corresponding node voltage, branch power flow and unit output condition distribution. In this embodiment, the power flow analysis of the random net power deviation falling into each deviation segment interval based on the conditional mapping relationship includes: For each deviation segment interval, the conditional mapping relationship corresponding to that deviation segment interval is called, and the interval state of that deviation segment interval is used as the power flow analysis state. The frequency modulation capacity occupancy state of other deviation segment intervals is no longer incorporated into the current power flow analysis process. The random net power deviation falling into the current deviation segment interval is limited to the condition input within the deviation segment interval, and the corresponding node injection power correction is generated according to the condition mapping relationship, so that the current power flow analysis only reflects the impact of the new deviation within the deviation segment interval on the node injection power. The node injected power correction is superimposed with the basic power flow state to form the conditional power flow input corresponding to the current deviation segment interval, and the node voltage, branch power flow and unit output are obtained under this conditional power flow input. The node voltage, branch power flow, and unit output results are correlated with the current deviation segment interval boundary, the starting frequency regulation output occupancy, the set of units still participating in frequency regulation, and the segment participation relationship to form the conditional power flow result corresponding to the deviation segment interval. Based on the range of random net power deviation within the current deviation segment interval, the conditional power flow results are distributed to obtain the node voltage condition distribution, branch power flow condition distribution, and unit output condition distribution corresponding to the deviation segment interval.

[0040] Through the above processing, the power flow analysis process no longer uses a unified input relationship covering the entire range of random net power deviations. Instead, it maintains consistency in the frequency regulation capacity occupancy status, participating unit set, and node injection mapping relationship within each deviation segment interval. This avoids the mixing and analysis of different frequency regulation response states after crossing the frequency regulation capacity segment boundary. The resulting conditional distribution can reflect the differences in branch power flow and node voltage under different frequency regulation capacity segment states, and provides a basis for subsequent identification of deviation breakpoints and frequency regulation unit capacity segments corresponding to branch over-limits.

[0041] Furthermore, the step of superimposing the node injected power correction amount with the basic power flow state to form the conditional power flow input corresponding to the current deviation segment interval, and obtaining the node voltage, branch power flow, and unit output results under this conditional power flow input, includes: Read the baseline active power injection, baseline reactive power injection, initial node voltage, initial branch power flow, and baseline output of each frequency regulation unit in the basic power flow status. For the current deviation segment interval, the node injection power correction obtained from the conditional mapping relationship is superimposed on the reference active power injection of the corresponding node to form the node active power injection amount that varies with the random net power deviation within the deviation segment interval. When the random net power deviation originates from the output deviation of new energy sources or the load forecast deviation, the random injection changes of the corresponding new energy access node or load node are synchronously superimposed on the corresponding node, so that the injection correction amount of the frequency regulation unit node and the injection change of the random disturbance source node maintain a power balance relationship within the same deviation segment interval. Using the active power injection at the node, the baseline reactive power injection, and the basic power flow state as inputs for power flow calculation, and under the condition that the frequency regulation capacity occupancy status corresponding to the current deviation segment interval remains unchanged, the power flow solution is performed to obtain the node voltage and branch power flow results within the deviation segment interval. Based on the frequency modulation output occupancy of each frequency modulation unit at the starting point of the current deviation segment interval, and the sharing amount corresponding to the new deviation increment in the deviation segment interval, determine the unit output result of each frequency modulation unit in the deviation segment interval. The obtained node voltage, branch power flow, and unit output results are correlated with the interval boundary, capacity occupancy status, and segment participation relationship of the current deviation segment interval to serve as the conditional power flow result corresponding to that deviation segment interval.

[0042] The specific calculation formula for the conditional power flow input is as follows:

[0043] The branch power flow can be written as:

[0044] The node voltage can be written as:

[0045] in, Let n be the conditional active power injection amount for node n within the k-th deviation segment interval. The baseline active power injection for node n under the basic power flow state. This refers to the random injection of changes at node n caused by deviations in new energy output or load forecasting. The power flow results for branch l within the k-th deviation segment interval are as follows: The power flow of branch l under the basic power flow condition. Let n be the coefficient representing the impact of changes in active power injection at node n on the power flow of branch l. This represents the voltage result at node m within the k-th deviation segment interval. This represents the voltage result at node m within the k-th deviation segment interval. The effect coefficient of the change in active power injection at node n on the voltage at node m.

[0046] The influence coefficient is obtained by linearizing the power flow equations under the basic power flow state, specifically: Using the basic power flow state as the linearization reference point, the voltage amplitude, voltage phase angle, branch parameters, and admittance matrix of each node under the basic power flow state are obtained. Based on the aforementioned basic power flow state, a Jacobian matrix is ​​established for the power flow equation. The Jacobian matrix is ​​used to characterize the local response relationship between changes in active power injection, changes in reactive power injection, changes in node voltage phase angle, and changes in node voltage magnitude. Under the condition of keeping the reactive power injection change zero or determining the reactive power injection change according to the preset reactive power control method, the node voltage amplitude change and node phase angle change caused by the unit node active power injection change are obtained according to the Jacobian matrix. Based on the changes in node phase angle and node voltage amplitude caused by the change in active power injection at a unit node, and combined with the branch power flow equation, the influence of the change in active power injection at a unit node on the power flow of each branch is calculated, and it is determined as the influence coefficient of the change in active power injection at a unit node on the power flow of the branch. The change in voltage amplitude at each node caused by the change in active power injection at a unit node is determined as the influence coefficient of the change in active power injection on the node voltage.

[0047] The unit's output is specifically as follows:

[0048] in, Let x be the output of frequency regulating unit i in the k-th deviation segment interval. The reference output of frequency modulation unit i, This represents the frequency modulation output occupancy already formed by frequency modulation unit i at the starting point of this deviation segment interval. Let i be the proportion of the frequency modulation unit i that shares the incremental deviation within this deviation segment interval. This is the frequency regulation direction coefficient, which takes a positive value when the unit increases its output and a negative value when the unit decreases its output. x is the random net power deviation amplitude after processing according to the current frequency regulation direction. The starting point of the k-th deviation segment interval is the deviation breakpoint.

[0049] S4, according to the probability distribution of occurrence of each deviation segment interval, obtains the random power flow analysis result, and outputs the frequency modulation capacity segment occupancy probability and the deviation breakpoint corresponding to branch over-limit.

[0050] In this embodiment, the step of combining the probability distribution of occurrence of each deviation segment interval includes: Based on the random net power deviation distribution, determine the probability of the random net power deviation falling into each deviation segment interval; The node voltage condition distribution, branch power flow condition distribution, and unit output condition distribution corresponding to each deviation segment interval are multiplied by the occurrence probability of that deviation segment interval to obtain the probability contribution of the corresponding deviation segment interval to the overall stochastic power flow result. According to the order of the deviation segment intervals, the probability contributions corresponding to each deviation segment interval are accumulated to obtain the overall distribution of node voltage, the overall distribution of branch power flow, and the overall distribution of unit output. Based on the interval status corresponding to each deviation segment interval, the probability of each frequency regulation unit capacity segment being occupied in different deviation segment intervals is calculated to obtain the frequency regulation capacity segment occupancy probability. For branches that exceed limits, determine which deviation segment intervals the probability of exceeding limits originates from, and output the starting deviation breakpoint, ending deviation breakpoint, and frequency modulation unit capacity occupancy status within the corresponding deviation segment interval as the deviation breakpoint information corresponding to the branch exceeding limits.

[0051] The step of determining the probability of a random net power deviation falling into each deviation segment interval based on the random net power deviation distribution includes: Determine the magnitude of the random net power deviation in the corresponding frequency modulation direction, and use the magnitude of the deviation as the object of probability calculation; Read the deviation segment interval formed by the deviation breakpoints, where the deviation segment interval is the value range between two adjacent deviation breakpoints; When the random net power deviation has a known probability distribution function, the probability of the random net power deviation falling into each deviation segment interval is calculated according to the probability distribution function. When the random net power deviation is represented by historical samples, prediction error samples, or scenario samples, the number of samples falling into each deviation segment interval is counted, and the proportion of the sample number to the total number of samples is determined as the probability of occurrence of the corresponding deviation segment interval. Each deviation segment interval is associated with its corresponding occurrence probability, which is used to synthesize the probability distribution of node voltage conditions, branch power flow conditions, and unit output conditions for each deviation segment interval.

[0052] If the probability distribution function of the random net power deviation magnitude x is... The probability of the occurrence of the k-th deviation segment interval is:

[0053] If the random net power deviation is represented by a sample set, the sample set is: The probability of the occurrence of the k-th deviation segment interval is:

[0054] in, Let $\mathbf{k}$ be the probability that the random net power deviation falls into the $k$-th deviation segment interval. This represents the number of samples falling into the k-th deviation segment interval. This represents the total number of random net power deviation samples.

[0055] Furthermore, the output frequency modulation capacity segment occupancy probability and the deviation breakpoint corresponding to branch over-limit include: Read the occurrence probability and interval status corresponding to each deviation segment interval. The interval status includes the capacity segment that each frequency regulation unit has occupied in the deviation segment interval, the capacity segment that is participating in the deviation increment response, and the capacity status that has withdrawn from frequency regulation. For each frequency regulation unit, each capacity segment is taken as a statistical object, and it is determined whether the interval status corresponding to each deviation segment interval contains the occupancy status of that capacity segment; if it does, the occurrence probability of that deviation segment interval is included in the occupancy probability of the corresponding capacity segment. For the same capacity segment of the same frequency modulation unit, the probability of occurrence of all deviation segment intervals that include the occupancy status of that capacity segment is accumulated to obtain the occupancy probability of the corresponding capacity segment of the frequency modulation unit. For each branch, based on the branch power flow condition distribution in each deviation segment interval, determine whether the branch power flow exceeds the corresponding branch power flow upper limit or is lower than the corresponding branch power flow lower limit, and calculate the contribution of each deviation segment interval to the probability of exceeding the limit for the branch. The deviation segment interval that contributes to the probability of branch exceeding the limit is determined as the limit exceeding associated interval of the branch, and the starting deviation breakpoint, ending deviation breakpoint, frequency regulation unit capacity occupancy status and limit exceeding probability contribution corresponding to the limit exceeding associated interval are output. When there are multiple over-limit associated intervals for the same branch, the deviation segment interval with the largest contribution to the over-limit probability is determined as the dominant over-limit interval of the branch, and the starting deviation breakpoint corresponding to the dominant over-limit interval is taken as the main deviation breakpoint corresponding to the over-limit of the branch.

[0056] The deviation breakpoint corresponding to the branch exceeding the limit does not mean that the branch power flow will definitely exceed the limit at that breakpoint. Rather, it means that the probability of the branch exceeding the limit comes from the frequency modulation capacity occupancy state formed after the deviation breakpoint. If it is necessary to further locate the starting position of the limit exceeding the limit, the critical deviation value when the branch power flow reaches the limit can be solved within the corresponding deviation segment interval.

[0057] The occupancy probability of the corresponding capacity segment of the frequency modulation unit is as follows:

[0058] If the m-th capacity segment of frequency regulation unit i is in an occupied or participating response state within the k-th deviation segment interval, then let Otherwise .

[0059] in, Let m be the probability that the m-th capacity segment of frequency regulation unit i is occupied. Let be the probability of the occurrence of the k-th deviation segment interval.

[0060] For branch exceeding the limit, let the power flow conditional random quantity of branch l in the k-th deviation segment interval be: The upper limit of the branch flow is The lower limit of the branch power flow is Then the contribution of the k-th deviation segment interval to the probability of branch l exceeding the limit is:

[0061] when The k-th deviation segment interval is determined as the over-limit correlation interval of branch l, and the corresponding deviation breakpoint is output. .

[0062] Figure 3 The results show a comparison between the existing fixed participation factor analysis method and the piecewise conditional analysis method of this invention, illustrating the variation of critical branch power flow with random net power deviation. The horizontal axis represents the magnitude of random net power deviation, the vertical axis represents the power flow of critical branches, the dashed curve represents the results of the existing fixed participation factor analysis, the solid curve represents the results of the piecewise conditional analysis method of this invention, the horizontal dashed line represents the branch thermal stability limit, and the vertical dashed line represents the location of the deviation breakpoint identified by this invention.

[0063] As can be seen from the figure, when the random net power deviation is small, the branch power flow results obtained by the two methods are similar; however, when the deviation amplitude crosses some deviation breakpoints, due to the change in the segmented state of the frequency modulation unit capacity, the segmented condition analytical curve of the present invention and the fixed participation factor analytical curve gradually become different, and can show the interval where the power flow of the key branch exceeds the thermal stability limit.

[0064] This figure illustrates that existing fixed participation factor methods tend to mix power flow responses under different frequency modulation capacity states into a single analytical curve, making it difficult to accurately reflect branch power flow changes after capacity segmentation switching. This invention, by establishing node injection power condition mapping relationships within different deviation segment intervals and performing power flow analysis, can identify deviation breakpoints and deviation intervals corresponding to branch overruns, thereby improving the accuracy of line power flow distribution and overrun probability calculation, and providing a basis for subsequently locating the sources of overrun risk.

[0065] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0066] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0067] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0068] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0069] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0070] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A stochastic power flow analysis method for a power system considering segmented constraints on unit frequency regulation capacity, characterized in that, Includes the following steps: Based on the frequency regulation capacity segmentation boundary of each frequency regulation unit, the deviation breakpoint corresponding to the random net power deviation is determined, and the deviation segmentation interval is divided by the deviation breakpoint. Based on the interval state corresponding to each deviation segment interval, establish a conditional mapping relationship between random net power deviation and node injection power correction. Based on the conditional mapping relationship, the random net power deviation falling into each deviation segment interval is analyzed to obtain the corresponding node voltage, branch power flow and unit output condition distribution. Based on the probability distribution of occurrence of each deviation segment interval, the random power flow analysis results are obtained, and the frequency modulation capacity segment occupancy probability and the deviation breakpoints corresponding to branch over-limit are output.

2. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 1, characterized in that, The determination of the deviation breakpoint corresponding to the random net power deviation includes: Select the corresponding frequency modulation capacity segment boundary according to the frequency modulation direction of the random net power deviation; At the starting point of the current deviation segment interval, the current capacity segment and remaining frequency regulation amount are determined based on the frequency regulation output occupancy of each frequency regulation unit; Based on the segment participation relationship within the current capacity segment, each remaining frequency modulation quantity is converted into a random net power deviation increment, and the deviation value corresponding to the minimum positive deviation increment is determined as the next deviation breakpoint. After updating the status of the frequency regulation unit that has reached the capacity segment boundary, continue to determine the subsequent deviation breakpoints.

3. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 2, characterized in that, The process of dividing the deviation segment interval by the deviation breakpoint includes: The points where the random net power deviation is zero and each deviation breakpoint are sorted according to the deviation amplitude in the corresponding frequency modulation direction, and the adjacent breakpoints are used as interval boundaries to form deviation segment intervals. For each deviation segment interval, the frequency modulation output, occupied capacity segment, frequency modulation participation status, and segment participation relationship of each frequency modulation unit at its starting break point are determined as the interval status of that deviation segment interval. When the random net power deviation crosses the deviation breakpoint, the interval state of the next deviation segment interval is updated according to the frequency regulation unit capacity segment boundary that triggered the deviation breakpoint, so that the frequency regulation response relationship within the same deviation segment interval remains unchanged.

4. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 3, characterized in that, The establishment of the conditional mapping relationship between the random net power deviation and the node injection power correction includes: Read the interval status corresponding to the current deviation segment interval; The random net power deviation falling into the current deviation segment interval is divided into the interval start deviation breakpoint and the deviation increment within the interval; Based on the frequency modulation output already formed by each frequency modulation unit at the starting point of the interval, determine the starting point injection offset of the corresponding node, and based on the set of frequency modulation units currently participating in the deviation increment response and their sharing ratio, determine the increment injection correction of the corresponding node. The starting point injection offset and the incremental injection correction are superimposed to obtain the conditional mapping relationship between the random net power deviation and the node injection power correction within the current deviation segment interval.

5. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 4, characterized in that, The step of determining the starting point injection offset of the corresponding node based on the frequency modulation output already formed by each frequency modulation unit at the starting point of the interval includes: Determine the frequency modulation output occupancy of each frequency modulation unit at the starting point of the current deviation segment interval and its connection node; Based on the frequency modulation direction corresponding to the random net power deviation, determine the correction direction of the frequency modulation output occupancy on the node injected power; The frequency modulation output occupancy of the frequency modulation units connected to the same node is summarized according to the correction direction to obtain the starting point injection offset of the node at the starting point of the current deviation segment interval.

6. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 5, characterized in that, The power flow analysis based on the conditional mapping relationship for the random net power deviation falling into each deviation segment interval includes: For each deviation segment interval, the conditional mapping relationship corresponding to that deviation segment interval is called to convert the random net power deviation falling into that deviation segment interval into the node injection power correction amount. The node-injected power correction is superimposed on the basic power flow state to form a conditional power flow input that is only applicable to the deviation segment interval; Based on the conditional power flow input, the node voltage, branch power flow and unit output are obtained, and the results are correlated with the interval state of the deviation segment interval to form the conditional power flow result; Based on the range of random net power deviation, the conditional power flow results are distributed to obtain the distribution of node voltage, branch power flow, and unit output conditions.

7. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 6, characterized in that, The results of obtaining node voltage, branch power flow, and unit output based on conditional power flow input include: The node injection power correction and the injection change of the corresponding random disturbance source node are superimposed on the basic power flow state to form the conditional power flow input corresponding to the current deviation segment interval; Under the condition that the capacity occupancy status and segment participation relationship of the current deviation segment interval remain unchanged, the power flow input of the condition is solved to obtain the node voltage result and the branch power flow result. The output of the frequency modulation unit is determined based on the frequency modulation output already formed at the starting point of the current deviation segment interval and the sharing amount corresponding to the new deviation increment within the interval. The node voltage results, branch power flow results, and frequency regulation unit output results are correlated with the interval state of the current deviation segment interval to form conditional power flow results.

8. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 7, characterized in that, The conditional distribution based on the probability of occurrence of each deviation segment interval includes: Based on the random net power deviation distribution, determine the probability of the random net power deviation falling into each deviation segment interval; Based on the occurrence probability, the distribution of node voltage conditions, branch power flow conditions, and unit output conditions corresponding to each deviation segment interval are weighted and synthesized to obtain the overall distribution of node voltage, the overall distribution of branch power flow, and the overall distribution of unit output. Based on the occurrence probability and interval status of each deviation segment interval, the occupancy probability of each frequency regulation unit capacity segment is calculated, and the deviation segment interval corresponding to the branch over-limit probability is determined. The starting deviation breakpoint, ending deviation breakpoint, and corresponding frequency modulation unit capacity occupancy status of the deviation segment interval are output as deviation breakpoint information corresponding to branch over-limit.

9. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 8, characterized in that, The step of determining the probability of a random net power deviation falling into each deviation segment interval based on the random net power deviation distribution includes: The random net power deviation is converted into deviation amplitude according to the corresponding frequency modulation direction, and the deviation segment interval formed by adjacent deviation breakpoints is read. When the deviation amplitude has a probability distribution function, the probability that the deviation amplitude falls into each deviation segment interval is calculated according to the probability distribution function; When the deviation amplitude is represented by historical samples, prediction error samples, or scenario samples, the probability of occurrence of each deviation segment interval is determined based on the proportion of the number of samples falling into each deviation segment interval to the total number of samples. Each deviation segment interval is associated with its corresponding occurrence probability, which is used to perform weighted synthesis of the conditional distribution of each deviation segment interval.

10. The method for analyzing stochastic power flow in a power system considering segmented constraints of unit frequency regulation capacity according to claim 9, characterized in that, The output frequency modulation capacity segment occupancy probability and the deviation breakpoints corresponding to branch over-limit include: Based on the occurrence probability and interval status of each deviation segment, the probability that each frequency regulation unit capacity segment is occupied or participating in the deviation increment response state is calculated to obtain the frequency regulation capacity segment occupancy probability. Based on the branch power flow condition distribution corresponding to each deviation segment interval, calculate the contribution of each deviation segment interval to the branch over-limit probability. The deviation segment interval that contributes to the probability of branch exceeding the limit is determined as the limit-related interval, and the starting deviation breakpoint, ending deviation breakpoint, frequency regulation unit capacity occupancy status and limit-related probability contribution corresponding to the limit-related interval are output. When the same branch corresponds to multiple over-limit associated intervals, the over-limit associated interval with the largest contribution to the over-limit probability is determined as the dominant over-limit interval, and the deviation breakpoint corresponding to the dominant over-limit interval is taken as the main deviation breakpoint corresponding to the over-limit of the branch.

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