A probabilistic model quantification method for the flexibility potential of building air conditioning

Abstract

This invention discloses a probabilistic model quantification method for the flexibility potential of building air conditioning systems. The method includes: extracting upper and lower bound cumulative distribution functions using the probability box method to describe the flexibility fluctuation range of the air conditioning system in interval probability form; introducing the Wasserstein distance index to quantify the difference in load probability distribution before and after regulation, and using this to characterize the expected value of the flexibility potential. This invention can accurately characterize the adjustable load range of a building under multi-source disturbance conditions, providing reliable support for flexible resource scheduling and response strategy formulation.

Description

Technical Field

[0001] This invention belongs to the field of building operation and control technology, and in particular relates to a probabilistic model quantification method for the flexibility potential of building air conditioning. Background Technology

[0002] As the global energy system accelerates its transition to clean and low-carbon energy, the flexibility of building resources, especially the flexibility of air conditioning, urgently needs to be fully explored and utilized to absorb the increasingly volatile renewable energy generation. As a significant energy consumer, buildings can proactively respond to grid demands and adjust energy usage through load regulation of their air conditioning and other equipment, without compromising user comfort. This allows for load shifting and peak shaving, providing the grid with more flexible regulation capabilities and ensuring a balance and match between supply and demand.

[0003] While the flexibility potential of air conditioning systems in building demand response is widely recognized, the high degree of uncertainty in building loads makes it difficult to accurately quantify this potential in practical applications. Unlike traditional load forecasting methods that focus on design loads or specific operating times, quantifying the flexibility potential of building air conditioning systems requires evaluating the differences in load scenarios before and after control measures are implemented. However, the high degree of uncertainty in external weather and internal loads during building operation directly affects the magnitude of cooling load and response effectiveness, causing air conditioning systems to exhibit different load reduction results under the same control strategy, thus resulting in a significant uncertainty characteristic in the flexibility potential.

[0004] In practical quantification, the inherent uncertainty of load scenarios becomes a key factor restricting the accurate assessment of flexibility potential. When load scenario uncertainties are not considered, power reductions or changes in electricity consumption typically only reflect a portion of the flexibility potential already utilized, failing to fully represent the true flexibility potential of a building's air conditioning system. Most current flexibility assessment methods are still based on typical operating conditions, failing to fully consider the impact of random disturbances in load scenarios. Flexibility indicators often rely on fixed formula derivations, making it difficult to accurately characterize the actual adjustable load range. Therefore, current flexibility assessment methods are prone to misjudging the flexible adjustability of air conditioning systems, thereby reducing their application value in energy dispatch and electricity market transactions. Summary of the Invention

[0005] To address the aforementioned technical issues, this invention proposes a probabilistic model quantification method for the flexible potential of building air conditioning, which can accurately characterize the adjustable load range of a building under multi-source disturbance conditions, providing reliable support for flexible resource scheduling and response strategy formulation.

[0006] To achieve the above objectives, this invention provides a probabilistic model quantification method for the flexibility potential of building air conditioning, comprising:

[0007] The probability box method is used to extract the upper and lower bound cumulative distribution functions, which describe the flexible fluctuation range of the air conditioning system in the form of interval probability.

[0008] The Wasserstein distance index is introduced to quantify the difference in load probability distribution before and after regulation, and to characterize the expected value of flexibility potential. The process of introducing the Wasserstein distance index includes:

[0009] Define the cumulative distribution function of the baseline load probability density distribution and the cumulative distribution function of the regulation load probability density distribution; calculate the first-order Wasserstein distance formula and correlate the integral results with the expected value of the flexibility potential.

[0010] Optionally, the process of using the probability box method includes:

[0011] Based on a combination of random load disturbance scenarios and demand response strategies, a flexible potential sample set is obtained through joint simulation. The process of obtaining the flexible potential sample set includes:

[0012] Based on six types of disturbance parameters—outdoor dry-bulb temperature, relative humidity, solar radiation, occupancy rate, lighting activation rate, and equipment activation rate—a random disturbance scenario is generated using Monte Carlo sampling.

[0013] Parameter estimation and distribution function fitting were performed on the samples. The fitting accuracy was evaluated and the optimal distribution model was selected through testing. The Kolmogorov-Smirnov test was used to evaluate the distribution fitting accuracy, and the sample size was set to 100 groups to achieve statistical convergence.

[0014] Output the optimal probability model of baseline load and regulated load, and construct the upper and lower boundary functions of the probability box.

[0015] Optionally, the process of constructing the upper and lower boundary functions of the probability box includes:

[0016] The cumulative distribution function of the controlled load is defined as the lower bound function, and the cumulative distribution function of the baseline load is defined as the upper bound function.

[0017] The combination forms an interval probability envelope model that covers the uncertainty range of the true distribution.

[0018] Technical effects of the invention:

[0019] (1) This invention proposes an uncertainty expression framework based on P-box. By extracting the upper and lower bound distribution functions and setting the non-guarantee rate, an interval expression model of flexible potential is established, which provides theoretical support for the credible expression and risk perception of flexible resources under multi-source disturbance conditions.

[0020] (2) This invention focuses on the probabilistic quantification of the flexibility potential in the demand response process of air conditioning systems. It proposes a probabilistic model quantification method for flexibility potential based on Wasserstein distance, and provides a comparison of the quantification results of flexibility potential under different flexibility control strategies, laying the foundation for the efficient allocation and utilization of flexibility resources in air conditioning systems. Attached Figure Description

[0021] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0022] Figure 1 This is a flowchart illustrating the probabilistic model quantification method for the flexibility potential of building air conditioning according to an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of a P-box according to an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of scalars, intervals, random variables, and P-boxes in an embodiment of the present invention;

[0025] Figure 4 This is a schematic diagram of the Wasserstein distance for the flexibility potential of an embodiment of the present invention;

[0026] Figure 5 This is a schematic diagram of the cumulative distribution function of the baseline load and the controlled load in an embodiment of the present invention;

[0027] Figure 6 This is a flowchart of batch co-simulation according to an embodiment of the present invention;

[0028] Figure 7 This is a flowchart illustrating the generation process of random load scenarios in an embodiment of the present invention.

[0029] Figure 8 This is a graph showing the variation of KS statistical results of load reduction distribution fitting with the number of samplings in an embodiment of the present invention;

[0030] Figure 9 This is a probability box representation of the flexible potential of the temperature reset strategy in an embodiment of the present invention.

[0031] Figure 10 This is a probability box representation of the flexible potential of the precooling strategy in an embodiment of the present invention.

[0032] Figure 11 This is a comparison chart of the absolute errors of load reduction amounts under different control strategies in embodiments of the present invention;

[0033] Figure 12 This is a comparison chart of the relative errors of load reduction amounts under different control strategies in embodiments of the present invention;

[0034] Figure 13 This is a comparison chart of the results of quantifying flexible potential under deterministic and probabilistic scenarios according to an embodiment of the present invention;

[0035] Figure 14 This is a relative error diagram for predicting flexible potential under deterministic and probabilistic scenarios, based on an embodiment of the present invention. Detailed Implementation

[0036] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0038] like Figure 1 As shown, this embodiment provides a probabilistic model quantification method for the flexibility potential of building air conditioning, including:

[0039] Step 1: Input data preparation: Based on random load disturbance scenarios and combinations of various demand response strategies, EnergyPlus and Python are used for joint simulation to obtain a sample set of flexibility potential of each strategy under uncertain disturbance conditions;

[0040] Step 2: Probability distribution fitting: For the flexible potential samples corresponding to each strategy, perform parameter estimation and distribution function fitting, and evaluate the fitting accuracy through the Kolmogorov-Smirnov test to select the optimal distribution model;

[0041] Step 3: Output the fitting results: Output the optimal probability model of the baseline load and regulation load distribution under each strategy, and plot the corresponding cumulative distribution function (CDF) curve;

[0042] Step 4: Constructing the P-box model: Baseline load and regulation load are selected as the upper and lower boundaries of the P-box model, respectively, thus forming a flexible potential P-box model with interval probability representation capabilities. The upper and lower boundaries of the flexible potential P-box model can be represented as the regulation load CDF and the baseline load CDF, respectively, specifically defined as:

[0043]

[0044] Among them, F L (x) is the lower bound CDF function of variable X, representing the minimum acceptable probability; F U(x) is the upper bound CDF function of variable X, representing the maximum acceptable probability; together, they constitute the uncertainty envelope of the true distribution function; thus, the flexible potential P-box model is constructed as follows:

[0045]

[0046] Among them, the flexible potential P-box model. A P-box is a probabilistic modeling tool used to describe random variables under conditions of incomplete or uncertain distribution information. Its basic form consists of an envelope interval formed by a pair of upper and lower bounds (CDFs). Its representation is as follows: Figure 2 As shown. The P-box is a flexible representation; it can represent intervals, probability distributions, and scalars. A coordinate system is established with the horizontal axis representing information content and the vertical axis representing determinism, listing intervals, probability distributions, scalars, and P-boxes. Figure 3 In the middle. For example Figure 3 As shown, the P-box can be viewed as a hybrid model of intervals and probabilities.

[0047] Based on this, the probabilistic model quantification method for the building air conditioning flexibility potential based on Wasserstein distance in this invention is as follows:

[0048] For any two probability distributions, the p-order Wasserstein distance is defined as follows:

[0049]

[0050] Among them, W p (u, v) represents the Wasserstein distance between two probability distributions; d(x, y) represents the distance metric between X and Y, such as Euclidean distance, L1 distance, etc.; π(x, y) is the joint probability distribution of u and v; Π(u, v) represents the set of all possible joint distributions; p represents the order of the Wasserstein distance; u(x) and v(y) represent the marginal distributions of the two probability distributions.

[0051] Within any demand response time period, the probability density distribution of the baseline load is f(x), and the probability density distribution of the controlled load after applying the demand response control strategy is g(x), where x represents the building load, such as... Figure 4 As shown; to compare the differences between two probability density functions (PDFs), the first-order Wasserstein distance is defined as:

[0052]

[0053] Where F(x) is the cumulative distribution function (CDF) of the baseline load probability density distribution f(x):

[0054]

[0055] G(x) is the CDF of the probability density distribution g(x) after regulation:

[0056]

[0057] The physical meaning of the first-order Wasserstein distance is: the minimum transmission cost required to transform the baseline load probability distribution f(x) into the regulated load probability distribution g(x); based on this, the energy flexibility index F is defined. s To characterize the total load reduction before and after demand response adjustment, such as Figure 5 As shown, the calculation formula is as follows:

[0058] F s =W1(f,g) (9);

[0059] Among them, F s F represents the cumulative power reduction of the air conditioning system within a demand response period. s The larger the value, the greater the impact on the distribution of air conditioning load after using the control strategy, the stronger the adjustment force, and the greater the flexibility potential; F s The smaller the value, the smaller the impact of the control strategy on the distribution of air conditioning load, the weaker the adjustment force, and the smaller the flexibility potential.

[0060] Construct a process for generating stochastic load scenarios for batch simulation of building energy consumption, such as... Figure 6 The process mainly includes the following four steps: disturbance modeling, random sampling, parameter generation and time-series filtering, which are used to generate simulation inputs with uncertain characteristics to drive subsequent flexible response simulations.

[0061] Furthermore, based on the co-simulation platform of Python and EnergyPlus, a batch load simulation workflow suitable for flexibility potential assessment was constructed. This workflow is as follows: Figure 7 This demonstrates the ability to perform batch simulations of building loads under multiple disturbance sample conditions. For each disturbance sample, baseline load simulations before the implementation of the demand response strategy and response load simulations after the strategy implementation are conducted, and hourly building cooling load data are extracted.

[0062] This invention selects six uncertainty parameters affecting the flexibility potential of building air conditioning systems as disturbance inputs considered in the construction of stochastic scenarios. These parameters include: outdoor dry-bulb temperature, relative humidity, solar radiation, occupancy rate, lighting activation rate, and equipment activation rate. The specific value ranges and distribution patterns of each disturbance parameter are statistically shown in Table 1. A set of stochastic load scenarios with uncertainty characteristics is constructed for the assessment and strategy analysis of the flexibility potential of building air conditioning systems.

[0063] Table 1

[0064]

[0065] In the uncertainty modeling of flexibility potential, an insufficient sample size may fail to adequately cover the fluctuation range of external disturbances, leading to biases in the flexibility potential estimation results and making it difficult to accurately characterize its uncertainty features. Conversely, an excessive sample size significantly increases the computational load of simulations and reduces simulation efficiency. Therefore, this invention performs batch simulations of random disturbance scenarios generated under various sampling numbers and statistically analyzes the load reduction during demand response control in each scenario. Based on this, the distribution of the obtained reduction samples is fitted, and the Kolmogorov-Smirnov (KS) test is used to evaluate the fitting effect. Figure 8 This demonstrates the trend of the KS statistic variation for the flexible potential distribution under different sampling numbers, from... Figure 8 As can be seen, with the increase of the sample size, the KS value gradually decreases while the P-value gradually increases, showing a good convergence trend overall. When the sample size is small (e.g., 10), the KS value is large (>0.2) and the P-value is small, indicating that the fitting effect of the load reduction sample is poor, the fitted distribution differs significantly from the real sample, and it is difficult to accurately characterize the statistical properties of the flexibility potential. When the sample size increases to 100, the KS value drops below 0.05 and the P-value reaches about 0.99, indicating that the fitting effect is very good, and further increasing the sample size does not significantly improve the accuracy of the distribution fitting, demonstrating good marginal convergence. Therefore, this invention ultimately selects 100 random disturbance scenarios as the number of disturbance inputs for the uncertainty quantification stage of flexibility potential.

[0066] Based on this, and using the case building simulation model, two typical demand response control strategy scenarios were designed and implemented: a temperature reset strategy scenario and a pre-cooling strategy scenario. In the temperature reset strategy scenario, considering the case building's baseline air conditioning setpoint temperature of 26℃, to avoid significant impact on indoor thermal comfort, the upper limit of the setpoint temperature was limited to 28℃. The control method selected was the direct temperature regulation method, which has the greatest flexibility potential. For the pre-cooling strategy, the setting condition with the greatest flexibility potential was selected, namely, a pre-cooling setpoint temperature of 22℃ and a uniform pre-cooling duration of 5 hours to ensure sufficient cooling capacity during the control period. The demand response period was uniformly set from 16:00 to 20:00, with a response duration of 4 hours. This setting is based on the characteristic of a significant increase in load level after noon in the typical summer electricity load curve of Tianjin, and combined with the peak-valley time-of-use pricing policy shown in Table 2 (where 16:00-20:00 is the peak electricity price period), aiming to ensure that demand response events have practical load regulation value and an economic incentive basis. Furthermore, to avoid interference from time-of-use factors on strategy performance, the above settings were kept consistent across all simulation strategies.

[0067] Table 2

[0068]

[0069] After setting the strategy scenarios, a set of random load scenarios reflecting the uncertainty of key input variables was constructed according to typical prediction error levels. Monte Carlo sampling combined with Savitzky-Golay time-series filtering was used to generate multiple sets of time-continuous building operation scenario input data. Based on this, batch simulation calculations were conducted for baseline operating conditions, temperature reset, and pre-cooling control strategies, respectively, to obtain hourly air conditioning system electrical load data for each strategy under multiple disturbance conditions.

[0070] After acquiring load data under various control strategies, a P-box modeling method was further employed to construct a flexibility potential uncertainty expression model for each strategy. Specifically, for the temperature reset strategy and the precooling strategy, adaptive distribution fitting and Kolmogorov-Smirnov tests were performed using baseline loads and control loads obtained from multiple perturbation samples to determine the optimal cumulative distribution model. Load upper and lower bound CDF curves for each strategy were constructed to form a flexibility potential P-box expression model.

[0071] To verify the applicability and predictive accuracy of the proposed method for quantifying the uncertainty of the flexibility potential of building air conditioning systems in the assessment of actual building demand response strategies. Figure 9 and Figure 10 The P-box expression results of the flexibility potential of the temperature reset strategy and the precooling strategy under the selected control parameter settings are presented respectively. Figure 9 The baseline load CDF represents the upper bound distribution function of the flexibility potential, and the control load CDF represents the lower bound distribution function of the flexibility potential. The region enclosed between the two is the probability interval of the flexibility potential that the air conditioning system may achieve under the current strategy setting, considering uncertain disturbances. Figure 9 and Figure 10It can be observed that the load CDF curve under the control strategy shifts to the left overall, indicating that under the same disturbance conditions, temperature setting or pre-cooling adjustment can significantly reduce the electrical load of the building air conditioning system, thereby releasing flexibility potential. Specifically, the horizontal distance between the CDF curve of the controlled load under the pre-cooling strategy and the baseline load CDF is significantly greater than that under the temperature reset strategy, indicating that it achieves a greater load reduction under the same disturbance conditions, and the corresponding flexibility potential is also higher. This phenomenon reflects that the pre-cooling strategy has a stronger load transfer capability, and can "store cold" in advance before the demand response period, thereby effectively reducing the operating power of the air conditioning system during the response period. Further observation reveals that as the cumulative probability value increases, the horizontal distance between the two CDF curves also gradually increases, and the difference between the baseline load and the controlled load is larger, that is, the flexibility potential is greater. This difference is not a single value, but fluctuates within a certain range with the disturbance uncertainty; therefore, the flexibility potential should be characterized in the form of an interval.

[0072] To further quantify the flexibility potential information expressed by the P-box model, based on Figure 7 and Figure 8 The flexible potential P-box corresponding to each strategy was calculated, and the upper and lower limits of the flexible potential interval, Wasserstein distance, interval width, etc. were obtained, as shown in Table 3.

[0073] Table 3

[0074]

[0075] Table 3 shows significant differences in the quantification results of the two strategies regarding flexibility potential. The pre-cooling strategy is significantly superior to the temperature reset strategy in terms of the upper and lower limits of the flexibility potential range, the Wasserstein distance, and the actual load reduction, indicating that it has a stronger load regulation capability within the same response period. Specifically, the flexibility potential range of the pre-cooling strategy is [137.16 kWh, 178.54 kWh], and the actual load reduction is 151.22 kWh, both significantly higher than the [93.96 kWh, 131.84 kWh] and 100.22 kWh of the temperature reset strategy, respectively, verifying its higher flexibility potential. Furthermore, the Wasserstein distance of the pre-cooling strategy is 158.15 kWh, much higher than the 109.47 kWh of the temperature reset strategy, further reflecting the significant difference between the two strategies in terms of baseline and regulated load distribution. Additionally, it can be observed that the actual load reduction is effectively encompassed within the flexibility potential range. These quantitative data allow for further analysis of the flexibility response capability of each strategy under typical regulation parameter settings and the accuracy of the prediction model.

[0076] After verifying the effective envelope capability of the P-box model for the flexible potential range under different policy scenarios, the accuracy and applicability of the proposed Wasserstein distance index in characterizing the deviation of the control policy are further evaluated from a quantitative perspective. Compared with the interval expression provided by the P-box model, the Wasserstein distance can characterize the overall deviation between the policy flexible response and the baseline load at the probability distribution level, thereby quantifying the flexible potential value under the influence of uncertainty. To this end, the Wasserstein distance value (flexible potential) predicted based on uncertainty disturbance simulation is compared with the actual flexible potential value obtained through simulation to verify the accuracy and robustness of the index in the process of flexible potential quantification.

[0077] To quantify the difference between predicted and actual values ​​of flexibility potential, relative error (RE) is used as an evaluation metric to reflect both the numerical and percentage deviations of the predicted values. The formula is as follows:

[0078]

[0079] In the formula, W i This represents the actual value of the flexibility potential of the i-th strategy obtained through simulation under measured input conditions. The predicted value of the i-th strategy flexibility potential after considering uncertainty parameters; RE i The relative error for predicting the flexibility potential of the i-th strategy.

[0080] After clarifying the evaluation index system for the quantification error of flexibility potential, a bar chart is used to visually display the differences between the upper and lower boundary values ​​of the flexibility potential range under various control strategies, the flexibility potential value predicted based on Wasserstein distance, and the actual load reduction. For example... Figure 11 As shown in the figure, this comparison presents the degree of deviation in absolute value of various flexible potential quantification results under different strategies.

[0081] like Figure 11As shown, the dotted lines on the left and right represent the upper and lower limits of the flexibility potential range obtained based on P-box quantization under the temperature reset strategy and the pre-cooling strategy, respectively. The left bar chart represents the actual load reduction value, and the right bar chart represents the flexibility potential value based on Wasserstein distance quantization. The Wasserstein distance prediction value is close to the actual load reduction value under both control strategies, demonstrating good prediction accuracy. Specifically, under the temperature reset strategy, the actual load reduction is 100.22 kWh, and the Wasserstein distance prediction value is 109.47 kWh, with an absolute error of 9.25 kWh. Under the pre-cooling strategy, the actual value is 151.22 kWh, and the Wasserstein distance prediction value is 158.15 kWh, with an absolute error of 6.93 kWh. Comparatively, the prediction accuracy of the pre-cooling strategy is slightly better than that of the temperature reset strategy. Meanwhile, from the perspective of the upper and lower boundaries of the probability interval for flexible potential, the upper boundary of the flexible potential is higher than the actual value, while the lower boundary is lower than the actual value, but the difference from the actual value is relatively large. This indicates that although the upper and lower boundaries can provide the range of load changes, they have a larger error when used as single-point estimates. Therefore, the Wasserstein distance is more suitable as an estimation indicator of flexible potential than the interval boundaries, and can more accurately reflect the quantitative level of the control effect under uncertainty conditions.

[0082] After analyzing the numerical differences between the predicted and actual values ​​of flexibility potential, relative error is further introduced as an evaluation index to measure the proportion of prediction deviation relative to the actual value under each strategy. For example... Figure 12 As shown, the relative errors of the flexibility potential prediction results under different temperature reset and precooling strategies are presented, which are used to further analyze the prediction stability and adaptability of the flexibility potential interval boundary and Wasserstein distance under different control intensities and response mechanisms.

[0083] like Figure 12As shown, the flexibility potential prediction based on Wasserstein distance exhibits good accuracy under both strategies. The relative error is 9.22% under the temperature reset strategy and even lower at 4.58% under the pre-cooling strategy, verifying the applicability and accuracy of the method in different flexibility response scenarios. Looking at the P-box upper and lower boundary prediction results, the relative error at the lower boundary of the flexibility potential is smaller, at 6.25% for the temperature reset strategy and 9.3% for the pre-cooling strategy. However, the relative error at the upper boundary is larger, at 31.55% for the temperature reset strategy and 18.07% for the pre-cooling strategy. This difference is because the lower boundary corresponds to the most conservative non-guarantee rate level, representing the minimum flexibility potential that can be guaranteed under high confidence, while the upper boundary represents the maximum flexibility potential prediction under the highest non-guarantee rate. The upper boundary often deviates significantly from the actual value and is more prone to overestimating flexibility, especially in load scenarios with low actual weather forecast errors and internal disturbance prediction errors.

[0084] To further verify the advantages of the proposed flexible potential quantification method based on uncertainty perturbation modeling, this invention compares it with the flexible potential results based on traditional single deterministic scenario prediction. Specifically, deterministic scenario prediction refers to the flexible potential estimation result obtained from a single simulation using weather forecast values ​​and predicted internal perturbation schedules as inputs, without considering the volatility of external weather and internal perturbations. In contrast, the probabilistic scenario method constructs a flexible potential P-box based on multiple perturbation samples and uses Wasserstein distance to measure the expected flexible potential under uncertain scenarios, or different flexible potential values ​​can be obtained based on different confidence levels. Figure 13 and Figure 14 The comparison of the predicted load reduction values ​​under the two strategies and their corresponding relative errors are presented, which intuitively reflects the difference between the two methods in terms of the accuracy of quantifying flexibility potential.

[0085] like Figure 13 and Figure 14As shown, under both temperature reset and pre-cooling strategies, the Wasserstein distance prediction based on probabilistic scenarios outperforms the deterministic scenario prediction in terms of flexibility potential quantification accuracy. Specifically, in the temperature reset strategy, the flexibility potential corresponding to the Wasserstein distance is 109.47 kWh, with a relative error of 9.22% compared to the actual reduction of 100.22 kWh; while the flexibility potential predicted based on the deterministic scenario is 117.24 kWh, with the error increasing to 16.98%. Under the pre-cooling strategy, the Wasserstein distance prediction result is 158.15 kWh, with only a 4.58% relative error compared to the actual value of 151.22 kWh, while the deterministic prediction result of 163.18 kWh has a high error of 7.9%. This result fully demonstrates that the probabilistic scenario method exhibits stronger adaptability and predictive stability under different control strategies.

[0086] Essentially, predictions based on deterministic scenarios ignore the volatile impact of key input variables in building operation (such as external weather and internal load disturbances). Results obtained relying solely on a single set of inputs cannot effectively reflect the stochastic characteristics of flexibility potential, and are highly susceptible to prediction bias when internal and external disturbances have large prediction errors or when the control boundary conditions approach system limits. In contrast, the flexible potential P-box modeling method proposed in this invention constructs load distribution boundaries through a large number of disturbance samples and combines Wasserstein distance to capture the global probability distribution difference between the baseline and the control load, resulting in higher prediction accuracy and robustness of the obtained flexible potential.

[0087] In addition, from Figure 13 and Figure 14 It can be observed that the probabilistic representation method has a more significant error advantage under the pre-cooling strategy, indicating that the method can still maintain good predictive performance in scenarios with high control intensity, long response time, and amplified input uncertainty. This provides a more practical quantitative tool and theoretical support for assessing the adjustability of flexible resources and implementing demand response strategies.

[0088] The above are merely preferred embodiments 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.

Claims

1. A probabilistic model quantification method for the flexibility potential of building air conditioning, characterized in that, include: The probability box method is used to extract the upper and lower bound cumulative distribution functions, which describe the flexible fluctuation range of the air conditioning system in the form of interval probability. The Wasserstein distance index is introduced to quantify the difference in load probability distribution before and after regulation, and to characterize the expected value of flexibility potential. The process of introducing the Wasserstein distance index includes: Define the cumulative distribution function of the baseline load probability density distribution and the cumulative distribution function of the regulation load probability density distribution; calculate the first-order Wasserstein distance formula and associate the integral result with the expected value of the flexibility potential, and the first-order Wasserstein distance represents the cumulative power reduction of the air conditioning system within a demand response period. The process of using the probability box method includes: Based on a combination of random load disturbance scenarios and demand response strategies, a flexible potential sample set is obtained using EnergyPlus and Python co-simulation. The process of obtaining the flexible potential sample set includes: Based on six types of disturbance parameters—outdoor dry-bulb temperature, relative humidity, solar radiation, occupancy rate, lighting activation rate, and equipment activation rate—a random disturbance scenario is generated using Monte Carlo sampling. Parameter estimation and distribution function fitting were performed on the samples. The fitting accuracy was evaluated and the optimal distribution model was selected through testing. The Kolmogorov-Smirnov test was used to evaluate the distribution fitting accuracy, and the sample size was set to 100 groups to achieve statistical convergence. Output the optimal probability model of baseline load and regulated load, and construct the upper and lower boundary functions of the probability box; The process of constructing the upper and lower boundary functions of the probability box includes: The cumulative distribution function of the controlled load is defined as the lower bound function, and the cumulative distribution function of the baseline load is defined as the upper bound function. The combination forms an interval probability envelope model that covers the uncertainty range of the true distribution.

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