A method for quantifying reserve demand considering the joint probability of random load fluctuation and equipment failure outage

Abstract

The application discloses a kind of reserve demand quantification method considering net load random fluctuation and equipment failure outage joint occurrence probability, comprising the following steps: step 1) considering that prediction error offsets each other, the total prediction error distribution of system is modeled;Step 2) the discrete fault loss distribution is modeled;Step 3) the cumulative distribution function of total gap random quantity is constructed;Step 4) based on the cumulative distribution function of total gap random quantity, reserve capacity demand target function is constructed;Step 5) the reserve capacity demand target function is standardized, and the reserve capacity demand standardized target function is obtained;Step 6) the reserve capacity demand standardized target function is solved, and the reserve capacity demand of system caused by prediction error is obtained.The application can more accurately depict the correlation and aggregation effect of prediction error, effectively balance the reliability and economy of reserve capacity configuration, especially suitable for system operation and market decision under the condition of high proportion of renewable energy grid connection.

Description

Technical Field

[0001] This invention relates to the field of power systems and their automation, specifically a method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages. Background Technology

[0002] With the continuous increase in the proportion of renewable energy installed capacity in the power system, the uncertainty of system operation has increased significantly. Renewable energy sources such as wind power and photovoltaics are greatly affected by meteorological conditions, and the prediction error of their output power varies with time, space, and climate conditions, posing a significant challenge to the system's power balance and safe and stable operation. To ensure that the system can maintain supply and demand balance under various operating conditions, the power system needs to be equipped with a certain amount of reserve capacity. The determination of reserve capacity is directly related to the system's reliability, economy, and market operating efficiency. Therefore, industry and academia have conducted extensive research on determining the system's reserve capacity requirements.

[0003] Existing methods for determining system reserve capacity mainly include the "maximum method," the "summation method," and the discrete event method based on the N-1 criterion. The "maximum method" typically takes the sum of the maximum values ​​of various uncertainties (such as prediction errors and unit failures) as the reserve capacity requirement; the "summation method" directly adds up the reserve requirements of each entity. While these methods are simple to calculate and easy to implement, they ignore the correlation and probabilistic characteristics between uncertainties, leading to results that are often overly conservative or unreliable, making it difficult to accurately reflect reserve demand in systems with a high proportion of renewable energy penetration. Furthermore, traditional discrete event assumptions (such as maximum single-unit failure) are insufficient to characterize the continuous random fluctuations in renewable energy output, while continuous models that only consider probabilistic prediction errors cannot cover the discrete impact of sudden events, resulting in biases in reserve capacity setting. Summary of the Invention

[0004] The purpose of this invention is to provide a method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, comprising the following steps:

[0005] Step 1) Consider the mutual cancellation of prediction errors and model the distribution of the total prediction error of the system;

[0006] Step 2) Model the discrete fault loss distribution;

[0007] Step 3) Based on the total prediction error and discrete fault loss of the system, construct the expression for the total gap random quantity, and construct the cumulative distribution function of the total gap random quantity;

[0008] Step 4) Construct the objective function for reserve capacity demand based on the cumulative distribution function of the total gap random quantity;

[0009] Step 5) Standardize the objective function of reserve capacity demand to obtain the standardized objective function of reserve capacity demand;

[0010] Step 6) Solve the standardized objective function of reserve capacity demand to obtain the reserve capacity demand of the system due to prediction errors.

[0011] Furthermore, when modeling the distribution of the total prediction error of the system, the prediction errors of wind power, photovoltaics and load are set as normal disturbances with a mean of zero and a standard deviation proportional to the predicted value.

[0012] Furthermore, the total prediction error of the system follows a normal distribution;

[0013] The mean of the total prediction error distribution of the system is 0, and the standard deviation is shown below:

[0014] (1)

[0015] In the formula, , The standard deviation indicates that the error in new energy and load forecasting follows a normal distribution.

[0016] Furthermore, the discrete fault loss Y follows a two-point distribution, i.e., capacity loss occurs. The probability is The probability of no capacity loss is ; .

[0017] Furthermore, the total gap stochastic quantity is as follows:

[0018] (2)

[0019] In the formula, X is the total prediction error of the system, and Z is the total gap random quantity.

[0020] Furthermore, the cumulative distribution function of the total gap random variable is shown below:

[0021] (3)

[0022] in, The standard normal CDF; Let be the cumulative distribution function of the total gap random quantity; This represents the total probability of capacity loss occurring. This represents the mean of the total prediction error of the system. Reserve capacity level; The standard deviation of the total prediction error of the system; This refers to the additional power deficit caused by equipment failure and downtime.

[0023] Furthermore, the objective function for reserve capacity requirements is as follows:

[0024] (4)

[0025] In the formula, R represents the reserve capacity requirement; It is the inverse function of the cumulative distribution function of the total gap random quantity.

[0026] Furthermore, step 5) involves standardizing the objective function for reserve capacity demand, which includes:

[0027] Step 5.1) Rewrite the objective function for reserve capacity demand into the formula to be solved, i.e.:

[0028] (5)

[0029] In the formula, This represents the total probability of capacity loss occurring. This represents the mean of the total prediction error of the system. Reserve capacity level; The standard deviation of the total prediction error of the system; Additional power loss due to equipment failure and downtime;

[0030] Step 5.2) Let the iteration parameters Update the formula to be solved to obtain the standardized objective function of reserve capacity requirement, that is:

[0031] (6)

[0032] (7)

[0033] Furthermore, in step 6), the standardized objective function of reserve capacity demand is solved using Newton's iteration method to obtain the iteration parameters. ;

[0034] Wherein, the iteration parameters at the (k+1)th iteration As shown below:

[0035] (8)

[0036] In the formula, Given the standard normal density, the initial value is... .

[0037] Furthermore, in step 6), the system reserve capacity requirement R is as follows:

[0038] (9)

[0039] In the formula, These are the parameters for the final iteration.

[0040] The technical advantage of this invention is undeniable. It assumes that the prediction errors of each power generation entity and load entity follow a normal distribution, constructs their mean vector and covariance matrix, and analytically derives the mean and variance of the total system prediction error, thereby obtaining the system prediction error distribution. Based on this, at a given confidence level, considering both the system prediction error and the maximum single-unit failure, the required system reserve capacity can be calculated. Compared with existing methods, this method can more accurately characterize the correlation and aggregation effect of prediction errors, effectively balancing the reliability and economy of reserve capacity configuration, and is particularly suitable for system operation and market decision-making under conditions of high proportion of renewable energy grid connection. Attached Figure Description

[0041] Figure 1 The distribution of the total prediction error of the system after the prediction errors of market participants cancel each other out. Detailed Implementation

[0042] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0043] Example 1:

[0044] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages includes the following steps:

[0045] Step 1) Consider the mutual cancellation of prediction errors and model the distribution of the total prediction error of the system;

[0046] Step 2) Model the discrete fault loss distribution;

[0047] Step 3) Based on the total prediction error and discrete fault loss of the system, construct the expression for the total gap random quantity, and construct the cumulative distribution function of the total gap random quantity;

[0048] Step 4) Construct the objective function for reserve capacity demand based on the cumulative distribution function of the total gap random quantity;

[0049] Step 5) Standardize the objective function of reserve capacity demand to obtain the standardized objective function of reserve capacity demand;

[0050] Step 6) Solve the standardized objective function of reserve capacity demand to obtain the reserve capacity demand of the system due to prediction errors.

[0051] Example 2:

[0052] See Figure 1A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages is provided. The technical content is the same as in Example 1. Furthermore, when modeling the total prediction error distribution of the system, the prediction errors of wind power, photovoltaic power and load are set as normal disturbances with a mean of zero and a standard deviation proportional to the predicted value.

[0053] Example 3:

[0054] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with the same technical content as any one of Examples 1-2, further wherein the total prediction error of the system follows a normal distribution;

[0055] The mean of the total prediction error distribution of the system is 0, and the standard deviation is shown below:

[0056] (1)

[0057] In the formula, , The standard deviation indicates that the error in new energy and load forecasting follows a normal distribution.

[0058] Example 4:

[0059] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with technical content identical to any one of embodiments 1-3, further wherein the discrete failure loss Y follows a two-point distribution, i.e., capacity loss occurs. The probability is The probability of no capacity loss is ; .

[0060] Example 5:

[0061] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with the same technical content as any one of embodiments 1-4, further wherein the total gap random quantity is as follows:

[0062] (2)

[0063] In the formula, X is the total prediction error of the system, and Z is the total gap random quantity.

[0064] Example 6:

[0065] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with the same technical content as any one of embodiments 1-5, further wherein the cumulative distribution function of the total gap random quantity is as follows:

[0066] (3)

[0067] in, The standard normal CDF; Let be the cumulative distribution function of the total gap random quantity; This represents the total probability of capacity loss occurring. This represents the mean of the total prediction error of the system. Reserve capacity level; The standard deviation of the total prediction error of the system; This refers to the additional power deficit caused by equipment failure and downtime.

[0068] Example 7:

[0069] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with the same technical content as any one of Examples 1-6, further wherein the objective function for reserve capacity demand is as follows:

[0070] (4)

[0071] In the formula, R represents the reserve capacity requirement; It is the inverse function of the cumulative distribution function of the total gap random quantity.

[0072] Example 8:

[0073] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with technical content identical to any one of embodiments 1-7, further comprising, in step 5), the step of standardizing the objective function of reserve capacity demand, including:

[0074] Step 5.1) Rewrite the objective function for reserve capacity demand into the formula to be solved, i.e.:

[0075] (5)

[0076] In the formula, This represents the total probability of capacity loss occurring. This represents the mean of the total prediction error of the system. Reserve capacity level; The standard deviation of the total prediction error of the system; Additional power loss due to equipment failure and downtime;

[0077] Step 5.2) Let the iteration parameters Update the formula to be solved to obtain the standardized objective function of reserve capacity requirement, that is:

[0078] (6)

[0079] (7)

[0080] Example 9:

[0081] See Figure 1 A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, with technical content identical to any one of embodiments 1-8, further comprising, in step 6), solving the standardized objective function of reserve capacity demand using the Newton-Raphson iteration method to obtain the iteration parameters. ;

[0082] Wherein, the iteration parameters at the (k+1)th iteration As shown below:

[0083] (8)

[0084] In the formula, Given the standard normal density, the initial value is... .

[0085] Example 10:

[0086] See Figure 1 A method for quantifying reserve requirements that considers the combined probability of random fluctuations in net load and equipment failure outages, with technical content identical to any one of embodiments 1-9, further wherein, in step 6), the system reserve capacity requirement R is as follows:

[0087] (9)

[0088] In the formula, These are the parameters for the final iteration.

[0089] Example 11:

[0090] See Figure 1This invention presents a method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages. Based on the statistical characteristics of renewable energy output and load forecasting errors, as well as the maximum single-unit failure rate, this method assumes that the forecasting error distributions of each entity follow a normal distribution. Using this as a theoretical foundation, a mathematical model describing the overall uncertainty of the system is constructed. By parametrically describing the forecasting error distributions of each power generation and load entity (including mean and variance), this invention first performs linear combination processing on the random forecasting errors of each entity, analytically deriving the comprehensive forecasting error distribution at the system level, thereby transforming multi-source uncertainty into total system uncertainty. This distribution accurately characterizes the central tendency and dispersion of the overall system forecasting deviation, providing a solid probabilistic foundation for further reserve capacity calculations at a given confidence level.

[0091] The specific steps include:

[0092] (1) Modeling the total prediction error distribution of the system considering the mutual cancellation of prediction errors

[0093] Considering that the prediction errors of renewable energy output and load are not always in the same direction over time and often cancel each other out, the total prediction error at the system level should not be simply the sum of the standard deviations of each component. Since this invention treats the prediction errors of wind power, photovoltaic power, and load as normal disturbances with a mean of zero and a standard deviation proportional to the predicted value, under this assumption, the prediction error of the system's net load can also be approximated as a normal distribution with a mean of zero. Its overall uncertainty (standard deviation) is synthesized from the errors of each component according to statistical rules. Accordingly, the upper and lower reserve capacity requirements caused by prediction deviations can be determined at a 95% confidence level: the upper and lower reserve capacities are each taken as 1.96 times the overall system standard deviation, such as... Figure 1 As shown.

[0094] Therefore, under the assumptions of this invention, the system prediction error also follows a normal distribution with a mean of 0 and a standard deviation as shown in equation (1).

[0095] (1)

[0096] In the formula, The standard deviation of the prediction error of new energy / load indicates that it follows a normal distribution. After the standard deviation of the system prediction error distribution, the upper / lower reserve capacity demand caused by the prediction error can be determined (at a 95% confidence level, the upper / lower reserve capacity demand is 1.96 times the standard deviation).

[0097] (2) A method for determining the system reserve capacity under the mixed normal chance constraint of continuous prediction error and discrete faults

[0098] This paper assumes that the prediction error X follows a mean of 0 and a standard deviation of . The normal distribution. Let the discrete failure loss Y be a two-point distribution; the capacity loss S occurs with probability p, and the probability... It is 0. Multiple faults can also be extended: ,satisfy Adding the two together gives the total gap random quantity:

[0099] (2)

[0100] Since Y is discrete, X is normal, and the cumulative distribution function (CDF) of Z is a normal mixture distribution.

[0101] (3)

[0102] in, It is a standard normal CDF.

[0103] To ensure that the backup capacity requirement meets the system requirements, the backup capacity must meet the following formula.

[0104] (4)

[0105] The required reserve capacity R is shown in the following formula.

[0106] (5)

[0107] Therefore, the above equation (3) can be written as a solvable formula, as shown in the following equation.

[0108] (6)

[0109] The standardization is shown in the following formula.

[0110] (7)

[0111] Therefore, equation (6) is transformed into the following equation.

[0112] (8)

[0113] (9)

[0114] Since the above equation is strictly monotonically increasing with respect to 'a', this invention uses Newton's iteration method to solve it.

[0115] (10)

[0116] In the formula, Given the standard normal density, the initial value is... After convergence, the system's reserve capacity requirement R is shown in the following formula.

[0117] (11)

[0118] In the formula, This is the final solution value obtained through iteration.

[0119] Example 12:

[0120] See Figure 1 The verification of a method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages is as follows:

[0121] (1) Data collection

[0122] To verify the effectiveness of the reserve demand quantification method proposed in this invention, which considers the combined probability of random fluctuations in net load and equipment failure outages, this invention collects grid load and actual operation data of renewable energy in a certain province of China from January 2024 to December 2024. In this study, net load data with high renewable energy penetration rate is obtained by proportionally scaling up the renewable energy data.

[0123] (2) Modeling of the total prediction error distribution of the system

[0124] Within a given time period, the prediction errors of each entity are aggregated according to their direction and contribution relationship to obtain the total prediction error at the system level. Considering that the prediction errors of renewable energy output and load are not always in the same direction over time, there is a mutual cancellation phenomenon between system-level errors. Based on this, a normal distribution assumption is used to statistically model the total prediction error of the system, giving its mean and dispersion, which is used as the continuous random component for subsequent backup calculations.

[0125] (3) Joint modeling of continuous error and discrete fault

[0126] Based on the total prediction error of the system, capacity loss caused by equipment failure and its probability of occurrence are introduced to form a joint description of continuous random error and discrete sudden events. By combining the two into the same overall random quantity, the composite distribution of the system within a given time period is obtained, which reflects the supply and demand uncertainty under the combined effect of "prediction error fluctuation" and "failure outage".

[0127] (4) Standardization and numerical solution

[0128] The process of solving the composite distribution is standardized to separate the variables to be solved from the key parameters. The monotonicity of the objective equation is used to solve it iteratively, and the initial value of the iteration is taken from the commonly used standard normal quantile.

[0129] (5) A method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages.

[0130] This project, based on actual load, renewable energy, and meteorological data from a provincial power grid in my country, uses a real 661-node system to verify the effectiveness of the proposed reserve capacity demand quantification. The real 661-node system, constructed from actual data from a provincial power grid in my country, includes 1047 lines and 48 generator units. In the simulation, the collected actual data was scaled for different example systems to ensure that the data used for simulation matched the parameters of the example systems.

[0131] The simulation will compare the following methods for quantifying reserve capacity requirements:

[0132] M1: The standby demand quantification method proposed in this patent that takes into account the probability of joint occurrence of random fluctuations in net load and equipment failure outages;

[0133] M2: The system standby capacity requirement is the greater of the random fluctuation of net load and the equipment failure outage;

[0134] M3: The system standby capacity requirement is the sum of net load random fluctuations and equipment failure downtime.

[0135] This invention compares and analyzes the system reserve capacity requirements calculated by different methods under different failure rates and reserve capacity requirements caused by prediction errors. First, under the condition that the new energy penetration rate is 18.4%, the variance of the system prediction error is statistically analyzed through historical data. The comparison results of different reserve capacity requirement data-driven quantification methods are shown in Table 1.

[0136] Table 1. Results of different quantification methods when the new energy penetration rate is 18.4%

[0137] As shown in Table 1, M1 directly reflects changes in the failure rate in reserve requirements: when the failure rate increases from 2% to 100%, the average reserve of M1 smoothly rises from 539.8MW to 1003.8MW. In contrast, M2 and M3 remain constant across the entire range (approximately 523.7MW and 1003.8MW respectively), failing to reflect the increase in risk. In the low-to-medium failure rate range (approximately 2%–26%), M1 is slightly higher than M2 but significantly lower than M3. As the failure rate continues to rise (approximately 37%–71%), M1 falls between M2 and M3 and continues to increase. At the high-risk end (50%–100%), M1 further approaches M3, indicating that while meeting the given constraints, M1, considering the mutual offsetting between prediction errors and failure rates, has a lower reserve capacity requirement and relative cost compared to M3, while its relative reserve requirement increases with the failure rate compared to M2, better achieving "risk matching and cost controllability".

[0138] To verify that the method proposed in this invention still performs well under the condition of a renewable energy penetration rate of 36.8%, the error variance was predicted by statistically analyzing historical data. Table 2 shows the comparison results of different reserve capacity demand data-driven quantification methods under the condition of a renewable energy penetration rate of 36.8%.

[0139] Table 2 Results of different quantification methods when the new energy penetration rate is 36.8%

[0140]

[0141]

[0142] As shown in Table 2, the M1 method still demonstrates superior performance even with a renewable energy penetration rate of 36.8%. As the failure rate increases from 2% to 100%, the reserve capacity of M1 gradually increases from 1032MW to 1507.8MW, maintaining flexible adjustments throughout and effectively addressing system uncertainties. In contrast, the reserve capacities of M2 and M3 remain unchanged at 1007.7MW and 1507.8MW respectively, failing to effectively respond to changes in the failure rate. This results in excessively high reserve requirements at high failure rates, increasing system costs. M1, while ensuring system reliability, demonstrates its advantages under high renewable energy penetration with its lower reserve capacity requirements and relatively lower cost, proving that the M1 method has better adaptability and economic efficiency.

Claims

1. A method for quantifying reserve demand that considers the combined probability of random fluctuations in net load and equipment failure outages, characterized in that, Includes the following steps: Step 1) Consider the mutual cancellation of prediction errors and model the distribution of the total prediction error of the system; Step 2) Model the discrete fault loss distribution; Step 3) Based on the total prediction error and discrete fault loss of the system, construct the expression for the total gap random quantity, and construct the cumulative distribution function of the total gap random quantity; Step 4) Construct the objective function for reserve capacity demand based on the cumulative distribution function of the total gap random quantity; Step 5) Standardize the objective function of reserve capacity demand to obtain the standardized objective function of reserve capacity demand; Step 6) Solve the standardized objective function of reserve capacity demand to obtain the reserve capacity demand of the system due to prediction errors.

2. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 1, characterized in that, When modeling the distribution of the total prediction error of the system, the prediction errors of wind power, photovoltaics and load are set as normal disturbances with a mean of zero and a standard deviation proportional to the predicted value.

3. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 1, characterized in that, The total prediction error of the system follows a normal distribution; The mean of the total prediction error distribution of the system is 0, and the standard deviation is shown below: （1） In the formula, , The standard deviation indicates that the error in new energy and load forecasting follows a normal distribution.

4. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 1, characterized in that, Discrete fault loss Y follows a two-point distribution, i.e., capacity loss occurs. The probability is The probability of no capacity loss is ; .

5. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 1, characterized in that, The total gap random quantity is shown below: （2） In the formula, X is the total prediction error of the system, Z is the total gap random quantity, and Y is the discrete fault loss.

6. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 5, characterized in that, The cumulative distribution function of the total gap random variable is shown below: （3） in, The standard normal CDF; Let be the cumulative distribution function of the total gap random quantity; This represents the total probability of capacity loss occurring. This represents the mean of the total prediction error of the system. Reserve capacity level; The standard deviation of the total prediction error of the system; This refers to the additional power deficit caused by equipment failure and downtime.

7. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 1, characterized in that, The objective function for reserve capacity requirements is shown below: （4） In the formula, R represents the reserve capacity requirement; It is the inverse function of the cumulative distribution function of the total gap random quantity.

8. The method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages as described in claim 1, characterized in that, Step 5) involves standardizing the objective function for reserve capacity demand, including the following steps: Step 5.1) Rewrite the objective function for reserve capacity demand into the formula to be solved, i.e.: （5） In the formula, This represents the total probability of capacity loss occurring. This represents the mean of the total prediction error of the system. Reserve capacity level; The standard deviation of the total prediction error of the system; Additional power loss due to equipment failure and downtime; Step 5.2) Let the iteration parameters Update the formula to be solved to obtain the standardized objective function of reserve capacity requirement, that is: （6） （7） In the formula, It is a standard normal CDF.

9. A method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages, as described in claim 8, is characterized in that... In step 6), the standardized objective function of reserve capacity demand is solved using Newton's iteration method to obtain the iteration parameters. ; Wherein, the iteration parameters at the (k+1)th iteration As shown below: （8） In the formula, It represents the standard normal density.

10. A method for quantifying reserve demand considering the combined probability of random fluctuations in net load and equipment failure outages, as described in claim 8, is characterized in that... In step 6), the system reserve capacity requirement R is as follows: （9） In the formula, These are the final iteration parameters.

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