Method and system for predicting regional distributed photovoltaic installed capacity based on time sequence weighting

Abstract

The present application relates to a kind of region distributed photovoltaic installed capacity prediction method and system based on timing weighting, method includes the following steps: obtaining photovoltaic benefit data under current region, and the historical time series data of investment return rate, comprehensive return rate are obtained by calculation to prospective saturated photovoltaic capacity, according to the historical time series data extrapolation prediction, obtain future year investment return rate time series variation data;According to the dynamic weighting of investment return rate and comprehensive return rate to time series, the independent variable of the Logistic growth model is obtained as weighted time series;Parameter optimization is carried out to the Logistic growth model;Using the Logistic growth model after parameter optimization obtains each year photovoltaic installed capacity growth prediction data.Compared with prior art, the present application further improves the prediction accuracy, and can adapt to the prediction demand under a variety of photovoltaic development scenarios.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic capacity prediction technology, and in particular to a method and system for predicting regional distributed photovoltaic installed capacity based on time-weighted calculation. Background Technology

[0002] With the rapid development of the photovoltaic industry in recent years, the installed capacity of photovoltaic systems in various regions has expanded rapidly. The forecasting of this scale is of great guiding significance for the development planning of the power system and the analysis of the sufficiency and reliability of new energy sources. Distributed photovoltaic systems, due to their ability to fully utilize the rooftop space of various types of buildings, will become the main form of photovoltaic installation for some time to come.

[0003] Currently, methods for predicting photovoltaic (PV) capacity can be mainly divided into system dynamics and time series analysis. System dynamics methods primarily focus on the mechanistic factors influencing PV capacity growth, such as green trade mechanisms, PV investment returns, and herd mentality in investment, using these as the main driving factors for dynamic model calculations. This type of method is characterized by complex system structures and strong coupling between factor coefficients and regional spatiotemporal characteristics, making model application and generalization difficult, but it exhibits good predictive performance in the short to medium term. Time series analysis methods are based on statistical principles, combining reference factors to analyze the development direction, trends, and characteristics of time series data, thereby constructing mathematical models describing the spatiotemporal correlation between variables and generalizing predictions based on time series data. For example, using a Logistic model to directly fit the cumulative PV capacity of a region over time, or fitting the total PV capacity using an "S" growth curve under spatial saturation capacity constraints, both methods fail to consider the significant impact of investment returns and PV policy effects on PV capacity growth. If this condition is not considered and time series data is directly used for model fitting, the model fitting error is large, and there is a serious problem of cumulative error effects. The second-order adaptive method can automatically update the smoothing coefficient to adjust the predicted capacity. This method has high short-term prediction accuracy but has obvious time lag problems. Its medium- and long-term prediction accuracy is low, making it difficult to apply to the prediction of photovoltaic capacity under the current environment. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology, which has high short-term prediction accuracy but obvious time lag, low medium- and long-term prediction accuracy, and is difficult to apply to the prediction of photovoltaic capacity in the current environment, and to provide a time-weighted regional distributed photovoltaic installed capacity prediction method and system.

[0005] The objective of this invention can be achieved through the following technical solutions: A time-weighted regional distributed photovoltaic (PV) installed capacity prediction method includes the following steps: Obtain photovoltaic benefit data for the current region, calculate historical time series data of prospective saturated photovoltaic capacity, return on investment, and overall return on investment, and extrapolate and predict future annual return on investment data based on this historical time series data; The time series is dynamically weighted based on the aforementioned rate of return on investment and overall rate of return, and the resulting weighted time series is used as the independent variable of the Logistic growth model. The parameters of the Logistic growth model are optimized; the predicted growth data of photovoltaic installed capacity for each year are obtained by using the optimized Logistic growth model.

[0006] Furthermore, the formula for calculating the rate of return on investment is as follows: In the formula, The initial unit installation investment cost, Annual operating and management cost per unit of installed capacity Financial cost per unit of installed capacity The unit's annual revenue from grid-connected electricity sales. For the regional photovoltaic grid-connected electricity sales price, The proportion of grid-connected electricity to total annual power generation. Annual electricity revenue per unit of installed capacity This refers to the unit price of electricity. The unit's installed capacity subsidy income, This represents the initial annual return on investment for the project. In the formula, For the region in h Maximum annual power generation per unit installed capacity for photovoltaic modules for h Photovoltaic module self-generated power loss rate for h The annual utilization hours of photovoltaic modules in this region.

[0007] Furthermore, the formula for calculating the overall rate of return is as follows: In the formula, For the region in h Maximum annual power generation per unit installed capacity for photovoltaic modules This indicates the carbon dioxide emissions per kilowatt-hour of photovoltaic power generation. , , These represent the emission reduction benefits per kilowatt-hour and treatment costs for carbon dioxide and other pollutants, respectively. A This indicates the number of pollutant types considered. This refers to the environmental benefits of distributed generation, including emission treatment costs and actual emission reduction benefits. This represents the revenue from thermal power generation under the same power generation capacity. Indicates the overall benefits of photovoltaic power generation. This indicates the cost of thermal power generation during the same period of operation. The overall return on photovoltaic investment; In the formula, This refers to the carbon dioxide emissions per kilowatt-hour from regional thermal power generation. J The generator sets are classified into levels according to boiler pressure rating. For the region j Standard coal consumption per kilowatt-hour for a Class A boiler pressure thermal power unit This represents the carbon dioxide emission coefficient based on standard coal consumption. For the region j The power generation ratio of a boiler pressure thermal power unit within a statistical period. For the region j Power generation of a Class A boiler pressure thermal power unit within a statistical period; In the formula, for a The per-unit-of-electricity emissions of pollutants of this type for a The amount of each kilowatt-hour of the pollutant type, In standard coal a The ratio of the emission coefficient of pollutants to carbon dioxide. For the region a Treatment coefficients for pollutants.

[0008] Furthermore, a triple exponential smoothing algorithm is used to extrapolate and predict the historical time series data.

[0009] Furthermore, the calculation expression for the weighted timing sequence is: In the formula, for The weighted coefficient of the investment return rate at a given time point, with a value between [0,1]; This represents a correlation index indicating the rate of return on investment; its value is greater than 0. This indicates the time point at which the emission reduction benefits affect capacity growth in the model; K This represents the slope of the weighting coefficients as they change over time. express Weighted time series values ​​at specific time points For return on investment, This refers to the overall rate of return.

[0010] Furthermore, the calculation expression for the Logistic growth model with weighted time series as the independent variable is as follows: In the formula, This indicates the model capacity for the weighted time series. T The cumulative value, For regional distributed photovoltaic in h Maximum installed capacity of photovoltaic modules This is the initial installed capacity. The representation model for weighted time series T The intrinsic growth rate; the weighted time series is fitted to the model using the least squares method to obtain the regional photovoltaic capacity growth rate for the weighted time series. T The best model intrinsic growth rate .

[0011] Furthermore, the regional distributed photovoltaic in h Maximum installed capacity of photovoltaic modules The calculation expression is: In the formula, m The number of building types in the region. for h The installed capacity per unit area of ​​photovoltaic modules, for h Photovoltaic modules are limited by their module characteristics. h Corrected utilization factor when installing on the roof of similar buildings. For the region l Maximum available roof installation area for this type of building for l Total floor area of ​​buildings of this type for l The development coefficient of similar buildings participating in distributed photovoltaic installations. for lAverage number of floors in areas with similar buildings for l The roof area utilization coefficient of this type of building.

[0012] Furthermore, in the process of parameter optimization for the Logistic growth model, the optimal K value is first determined, and then the optimal K value is searched. Secondary smoothing of the trend in time series data; changing the step size. The model is then fitted again, and the parameters of the fitting curve change accordingly until the model fit R is achieved. 2 It has reached its maximum value.

[0013] Furthermore, the parameter optimization process for the aforementioned Logistic growth model is as follows: S101: Setting K and The initial value; S102: The investment return rate and the overall return rate are weighted over time according to the K value, and the model data are fitted with Logistic regression based on the least squares method; S103: Determine the curve fit R 2 If the maximum value has been reached, proceed to step 104; otherwise, modify the K value according to the preset step size. S104: Based on the determined K value, according to the mapping correlation index The weighted time-series trend is smoothed twice, and then Logistic fitting is performed again. S105: Determine the curve fit R 2 Has the maximum value been reached? If so, proceed to step 106; otherwise, modify according to the preset step size. value; S106: Obtain the final K. and model variable values; S107: According to K, The values ​​are calculated on the original time series data to obtain the weighted time series sequence; S108: Substitute the weighted time series into the Logistic growth model for calculation.

[0014] The present invention also provides a time-weighted regional distributed photovoltaic installed capacity prediction system, including a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of the method described above.

[0015] Compared with the prior art, the present invention has the following advantages: (1) This invention transforms the driving force of photovoltaic emission reduction into comprehensive emission reduction benefits. Combining the rate of return on investment and the upper limit of the potential capacity of distributed photovoltaic, it proposes a photovoltaic capacity prediction model that uses the rate of return on investment and the comprehensive rate of return to dynamically weight the original time series and then fits it with a Logistic regression. The model quantifies the maximum potential installed capacity of distributed photovoltaic in a region, the specific costs of photovoltaic development, and the benefits generated, which greatly increases the practical application feasibility of the method and further improves the prediction accuracy. It can also adapt to the prediction needs under various photovoltaic development scenarios.

[0016] (2) The present invention introduces a mapping correlation index, which enhances the correlation between the rate of return on investment and capacity growth, and makes the model more adaptable to the photovoltaic growth characteristics of different regions. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a Logistic growth curve provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of distributed photovoltaic logistic fitting in Shanghai from 2016 to 2021, provided in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the principle of time-weighted model fitting provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the impact of photovoltaic emission reduction benefits on model predictions provided in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the effect of overweighting and underweighting on fitting, provided in an embodiment of the present invention. Figure 6 This is a schematic diagram of the original data calculation process for a model provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of a model solving and prediction process provided in an embodiment of the present invention; Figure 8 This is a schematic diagram illustrating the trend of photovoltaic investment return rate in Shanghai from 2014 to 2030, provided in an embodiment of the present invention. Figure 9 This is a schematic diagram of a model fitting result provided in an embodiment of the present invention; Figure 10 This is a schematic diagram illustrating the projected photovoltaic installed capacity in Shanghai from 2016 to 2030, provided in an embodiment of the present invention. Figure 11 This is a schematic diagram comparing model values ​​and actual values ​​of several prediction methods provided in this embodiment of the invention from 2016 to 2021. Figure 12This is a schematic diagram comparing the predicted values ​​of Shanghai from 2019 to 2021 using several methods provided in an embodiment of the present invention. Figure 13 This is a flowchart illustrating a time-weighted regional distributed photovoltaic installed capacity prediction method provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0021] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed during use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0022] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0023] Furthermore, terms such as "horizontal" and "vertical" do not imply that components must be absolutely horizontal or suspended, but rather that they can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0024] Example 1 This embodiment provides a method for predicting regional distributed photovoltaic installed capacity based on time-series weighted average, including the following steps: Obtain photovoltaic benefit data for the current region, calculate historical time series data of prospective saturated photovoltaic capacity, return on investment, and overall return on investment, and extrapolate and predict future annual return on investment data based on this historical time series data; The time series is dynamically weighted based on the aforementioned rate of return on investment and overall rate of return, and the resulting weighted time series is used as the independent variable of the Logistic growth model. The parameters of the Logistic growth model are optimized; the predicted growth data of photovoltaic installed capacity for each year are obtained by using the optimized Logistic growth model.

[0025] The following is a detailed description.

[0026] I. Application of the Logistic Model in Photovoltaic Capacity Growth 1.1 Regional Distributed Photovoltaic Installed Capacity Growth Model The Logistic growth model is a self-inhibiting growth model that can be used to represent the population growth process of a species after it migrates to a new, spatially limited ecological environment. Its general basic form can be expressed as: (1) In the formula, This represents the total number of people in the group at time t. This represents the intrinsic growth rate of a population, and is usually taken as a constant. N This represents the maximum environmental capacity of a population in a new ecological environment, where The initial total number of the population is represented by the function curve shown below. Figure 1 As shown.

[0027] The changes and growth rate of distributed photovoltaic power generation can be described by the Logistic function, which is divided into the initial stage, acceleration stage, turning point stage, deceleration stage and saturation stage, as shown in Table 1.

[0028] 1.2 Research on Multi-Factor Time-Weighted Logistic Model Taking Shanghai's distributed photovoltaic installation data from 2016 to 2021 as an example, if we directly use the historical cumulative capacity and time to fit the data based on the least squares method, the existing data trend and the predetermined fitting function trend will be considered.

[0029] Table 1. Five stages and characteristics of distributed photovoltaic development When the difference is large, the fitting error is large and it cannot reflect the true trend of the time series data. For example... Figure 2 As shown, the overall actual capacity growth trend is non-linear, with a large fitting deviation and a tendency for error divergence.

[0030] The reason is that when the Logistic growth model is applied to species population growth, one of its assumptions is that the intrinsic growth rate remains constant. When applied to predicting regional photovoltaic capacity growth, in addition to time, the independent variables affecting the total installed capacity include the return on investment in photovoltaics, the development of new energy sources, and the promotion of emission reduction policies. Under ideal conditions (i.e., when the annual return on investment and the policy impact remain constant), the Logistic fit between the photovoltaic capacity curve and time is optimal.

[0031] Based on the Logistic mapping relationship between installation capacity and time under ideal conditions, this is generalized, with the annual rate of return on investment as the weight of time. Since the rate of return on investment remains constant under ideal conditions, the growth of the independent variable time can be rewritten as follows: (2) In the formula n The time series number, express The corresponding rate of return on investment at a given time point. n The time series number, This indicates the interval length of the original time series. express The weighted time series value of the investment return rate at each point in time. The time span length of the mapped values ​​at each weighted point in time can then be expressed as: (3) when As it changes over time, the following is true. Figure 3 As shown, taking five time periods with different investment returns as an example, when directly fitting the time series, the mapped time spans represented by each time point are equal; however, after weighting them using investment returns, for t0+3 with a larger investment return... t、t0+5 t, its mapping time span , The larger the value, the larger the cumulative capacity growth rate (P3-P2, P5-P4) of the model. This means mapping the relationship between photovoltaic capacity and the original time series to the relationship with the weighted time series, thereby reflecting the positive correlation between the return on investment and the growth of photovoltaic capacity.

[0032] When weighting the original time-series data using only the rate of return on investment, a comparative study of existing data reveals that the predicted trend line is lower than the actual trend line, and this prediction error tends to increase over time, as illustrated in the diagram below. Figure 4 As shown. The reason is that the driving effect of photovoltaic emission reduction benefits on photovoltaic capacity growth at the current stage was not considered. my country is currently in the period of industrial and social energy structure reform and carbon emission reduction. With the implementation of the "carbon peaking" target and related policies, the impact of photovoltaic emission reduction benefits on photovoltaic capacity growth will gradually increase. Moreover, the overall promoting effect on capacity growth in the current period is approximately linear. Therefore, this embodiment uses linear weight changes to simulate this trend.

[0033] To incorporate the emission reduction benefits of photovoltaic power into the model's reference variables, the emission reduction benefits of distributed photovoltaic power are quantitatively calculated using the marginal emission reduction costs and benefits of regional thermal power plants, and combined with the return on investment. Achieve overall return Influenced by policy objectives such as carbon peaking and new energy development, the driving factors for actual photovoltaic capacity growth are beginning to shift towards considering emission reduction benefits. Offset. In view of this, this embodiment proposes a method to simulate this trend by dynamically weighting the time series using the rate of return on investment and the overall rate of return, as shown in the following formula: (4) (5) In the formula, for The weighted coefficient of the investment return rate at a given time point, with a value between [0,1]; This represents a mapping-related index of investment returns, with a value greater than 0. It is based on the index calculation of investment returns, thereby altering its weighted time series. T The relative span is used to perform secondary smoothing on the trend of the weighted time series data; This indicates the time point at which the emission reduction benefits affect capacity growth in the model; K This represents the slope of the weighting coefficients as they change over time. express Weighted time series values ​​at specific time points.

[0034] Weighted time series TAs the independent variable in the Logistic model, the original model is modified as follows: (6) in, This indicates the model capacity for the weighted time series. T The cumulative value is determined by the region's projected saturated installed capacity. Compared with initial installed capacity Calculations show that The representation model for weighted time series T The intrinsic growth rate. The weighted time series is fitted to the model using the least squares method to obtain the regional photovoltaic capacity growth rate with respect to the weighted time series. T The best model intrinsic growth rate .

[0035] Further discussion on the mapping correlation index is needed if the mapping correlation index is not considered. The time series trend is smoothed twice, i.e., the default. A value of 1 may indicate that data points are either excessively overweighted or excessively underweighted. For example... Figure 5 As shown.

[0036] Analyzing two typical points T1 and T2 (T1 corresponds to a higher rate of return on investment, and T2 corresponds to a lower rate of return on investment), we can find that the T1' corresponding to the isopleth of the P1 value on the fitted curve for point T1 is further to the right than the original T1, resulting in a lower predicted value. Similarly, for the T2 corresponding to the P2 value on the fitted curve, the T2' is further to the left, resulting in a higher predicted value. This is because the time-series weighting value for point T1 is relatively small, and the time-series weighting value for T2 is relatively large. Increasing the mapping correlation index... When the overall time-series weighted values ​​decrease (both the rate of return on investment and the rate of return on total return are less than 1), the time-series weighted value at point T1 increases relatively, while the time-series weighted value at point T2 decreases relatively, which increases the model fit.

[0037] For mapping correlation index The optimization process is dynamic; changing the step size leads to changes in the weighted time series, and also alters the dynamic relationship between the rate of return on investment and the overall rate of return under the original scale. Therefore, this embodiment first determines the optimal [missing information]. K Value, then search for the optimal one. Secondary smoothing is applied to the trend of the time series data. The smoothing is changed according to the step size. The model needs to be refitted, and the parameters of the fitting curve will change accordingly until the model fit R is achieved. 2 It has reached its maximum value.

[0038] 1.3 Prediction Model Flow Given the characteristics of the Logistic growth model for distributed photovoltaic applications, in order to improve the model fit and prediction accuracy while simplifying the calculation process and steps when using this method for predictive analysis, as follows: Figure 13 As shown, the prediction model flow in this embodiment is as follows: S1: Cluster the available roof area of ​​each type in the region and calculate the potential value of the region's future distributed photovoltaic installed capacity.

[0039] S2: Calculate the basic installation cost and power generation benefits of regional distributed photovoltaic power, photovoltaic installation cost, grid-connected power sales mode and revenue, policy subsidies, etc., to obtain the return on investment for each year.

[0040] S3: Calculate the emission reduction benefits of regional distributed photovoltaic power generation. This involves statistically calculating the emission of pollution factors per kilowatt-hour from regional thermal power units and the marginal emission reduction cost, and combining this with the rate of return on investment to obtain the overall investment benefits.

[0041] The purpose of the above process is to obtain time-series data on the changes in parameters such as projected saturated photovoltaic capacity, return on investment, and overall return on investment, which affect the accuracy of model predictions. The relationships and processes are as follows: Figure 6 As shown.

[0042] S4: Extrapolate existing historical time series data based on the triple exponential smoothing algorithm to predict the time series changes in investment returns in future years.

[0043] S5: Based on the obtained time-series change data, the model calculation, model parameter solution, and prediction process are as follows: Figure 7 As shown, it specifically includes: S101: Setting K and The initial value; S102: The investment return rate and the overall return rate are weighted over time according to the K value, and the model data are fitted with Logistic regression based on the least squares method; S103: Determine the curve fit R 2 If the maximum value has been reached, proceed to step 104; otherwise, modify the K value according to the preset step size. S104: Based on the determined K value, according to the mapping correlation index The weighted time-series trend is smoothed twice, and then Logistic fitting is performed again. S105: Determine the curve fit R 2 Has the maximum value been reached? If so, proceed to step 106; otherwise, modify according to the preset step size. value; S106: Obtain the final K. and model variable values; S107: According to K, The values ​​are calculated on the original time series data to obtain the weighted time series sequence; S108: Substitute the weighted time series into the Logistic growth model for calculation.

[0044] 2. Model parameter calculation 2.1 Calculation of Maximum Installation Capacity in the Region 2.1.1 Calculation of the maximum usable installation area based on the roof area Currently, distributed photovoltaic (PV) installations are primarily rooftop installations, therefore, it is necessary to calculate the available rooftop installation area for a given region. The available rooftop area can be obtained from the area data of various buildings obtained from the local statistics bureau, combined with the region's average number of floors and rooftop development coefficient, as shown in the following formula: (7) For the region l Maximum available roof installation area for this type of building for l Total floor area of ​​buildings of this type for l The development coefficient of similar buildings participating in distributed photovoltaic installations. for l Average number of floors in areas with similar buildings for l The roof area utilization coefficient of this type of building.

[0045] 2.1.2 Calculation of Maximum Installed Capacity Based on Utilization Factor The installed capacity per unit area of ​​a building is affected by factors such as building type characteristics and photovoltaic cell performance. In actual calculations, the process can be simplified by selecting representative photovoltaic modules. The calculation process is as follows: (8) For regional distributed photovoltaic in h Maximum installed capacity of photovoltaic modules m The number of building types in the region. for h The installed capacity per unit area of ​​photovoltaic modules, for h Photovoltaic modules are limited by their module characteristics. h The corrected utilization factor for installation on the roof of similar buildings is obtained by empirically calculating based on existing installation data.

[0046] 2.1.3 Calculation of Maximum Annual Power Generation Capacity per Unit Installed Capacity The maximum annual power generation of photovoltaic modules can be used to further calculate their unit power generation efficiency; the actual power output of the system needs to be reduced by its own module losses. (9) For the region in h Maximum annual power generation per unit installed capacity for photovoltaic modules for h Photovoltaic module self-generated power loss rate for h The annual utilization hours of photovoltaic modules in this region can be obtained through simulation using PVsyst software.

[0047] 2.2 Calculation of Regional Photovoltaic Emission Reduction and Comprehensive Benefits 2.2.1 Calculation of Photovoltaic Emission Reduction Since the environmental benefits of photovoltaic (PV) emission reduction cannot be directly assessed and calculated, this embodiment proposes a method of equivalent substitution of regional thermal power generation with PV power generation. By calculating the unit pollution emission cost and pollution treatment cost of regional thermal power generation, the emission reduction benefits of PV can be calculated equivalently. Because the coal consumption per kilowatt-hour varies among thermal power generating units in different regions and with different boiler pressure levels, calculations should be performed separately, and the average value should be used as the benchmark for regional PV emission reduction. Since the proportion coefficients of pollutants such as carbon, sulfur dioxide, and nitrogen oxides in standard coal are fixed, the carbon dioxide emission per kilowatt-hour can be calculated first, and then the emission amounts of various pollutants per kilowatt-hour can be calculated based on the ratio of carbon dioxide to the coefficients of other pollutants, thus simplifying the calculation.

[0048] (1) Carbon dioxide emissions per kilowatt-hour from regional thermal power generation: (10) (11) In the formula: This refers to the carbon dioxide emissions per kilowatt-hour from regional thermal power generation. J The generator sets are classified into levels according to boiler pressure rating. For the region j Standard coal consumption per kilowatt-hour for a Class A boiler pressure thermal power unit This represents the carbon dioxide emission coefficient based on standard coal consumption. For the region j The power generation ratio of a boiler pressure thermal power unit within a statistical period. For the region j The power generation of a Class A boiler pressure thermal power unit within a statistical period.

[0049] (2) Other pollutants emitted per kilowatt-hour: (12) (13) In the formula, for a The per-unit-of-electricity emissions of pollutants of this type for a The amount of each kilowatt-hour of the pollutant type, In standard coal a The ratio of the emission coefficient of pollutants to carbon dioxide. For the region a Treatment coefficients for pollutants.

[0050] 2.2.2 Investment Return Model for Traditional Photovoltaic Power Generation Projects The traditional investment return (ROI) calculation model for photovoltaic (PV) power generation projects mainly consists of considering project costs and power generation revenue. Project costs can be primarily divided into the fixed initial total investment cost of PV modules, operating costs, and project investment financial costs. Project revenue sources can be categorized as PV power generation revenue for self-consumption, grid-connected electricity sales revenue, and local government PV subsidies. The calculation is as follows: (14) (15) (16) in, The initial unit installation investment cost, Annual operating and management cost per unit of installed capacity The unit installation cost is the financial cost. The unit's annual revenue from grid-connected electricity sales. For the regional photovoltaic grid-connected electricity sales price, This refers to the proportion of grid-connected electricity to total annual power generation. Annual electricity revenue per unit of installed capacity The unit price of electricity can be calculated by taking into account the proportion of different types of users such as households, commercial users, and factories in the region, and then obtaining the average value. The unit's installed capacity subsidy income, This represents the initial annual return on investment for the project.

[0051] 2.2.3 Comprehensive Rate of Return Model Considering Emission Reduction Benefits To quantify the emission reduction benefits of photovoltaic power into concrete returns, the overall return on investment (ROI) is calculated by combining the emission and treatment costs of various pollutants from regional thermal power plants per unit of electricity generated with traditional ROI rates. The calculation is as follows: (17) (18) (19) in, This indicates the carbon dioxide emissions per kilowatt-hour of photovoltaic power generation. , , These represent the emission reduction benefits per kilowatt-hour and treatment costs for carbon dioxide and other pollutants, respectively. A This indicates the number of pollutant types considered. This refers to the environmental benefits of distributed generation, including emission treatment costs and actual emission reduction benefits. This represents the revenue from thermal power generation under the same power generation capacity. Indicates the overall benefits of photovoltaic power generation. This indicates the cost of thermal power generation during the same period of operation. This refers to the overall return on photovoltaic investment.

[0052] 2.2.4 Time Series Data Prediction Based on Triple Exponential Smoothing In this embodiment, the method predicts future years based on changes in the rate of return on investment (ROI). Since factors influencing ROI, such as component prices, electricity sales revenue, and electricity consumption revenue, exhibit clear and converging trends, a triple exponential smoothing algorithm is employed for time-series data prediction.

[0053] Where the smoothing constant Since the selection is subjective, its value will affect the weight of the predicted data. In this example, the data fluctuations such as roof area changes and photovoltaic module price changes are relatively stable and have obvious long-term trends, so they can be selected. The value is between [0.1, 0.3].

[0054] 3. Regional Case Analysis 3.1 Example Data Taking the development of distributed photovoltaic (PV) systems in Shanghai, my country, as an example, this study statistically analyzed the area of ​​various types of buildings in the city from 2011 to 2020 and calculated the potential roof area based on an exponential smoothing algorithm. The average number of floors was selected according to the method used by Qiu Xilan et al. The roof area utilization coefficient was determined according to the requirements of the Shanghai Municipal Development and Reform Commission: 0.2 for residential buildings, 0.4 for public buildings, and 0.3 for industrial and commercial buildings, with a modified utilization coefficient of 0.8. Considering the further development of PV technology in the future, the unit installed capacity was simulated using a Longi-LR 5-72HIH 540M high-performance monocrystalline silicon PVsyst software. The average installed capacity of residential and public building rooftops was 0.172 kW / m². 2 The power consumption for industrial and commercial plants is 0.193 kW / m². 2The results are shown in Table 2 below: Table 2 Calculation of Saturated Installed Capacity in Shanghai Based on statistical data from local thermal power plants in Shanghai, and with a standard coal consumption of 0.3 kg / kWh and a standard coal price of 900 yuan / ton, the emission coefficient per kilowatt-hour was calculated according to IPCC standards. The emission reduction benefits per ton of carbon dioxide, sulfur dioxide, and nitrogen oxides from thermal power generation were 298 yuan, 1260 yuan, and 2000 yuan, respectively. When the sulfur dioxide removal rate reached 99% and the nitrogen oxide removal rate reached 95%, the removal cost per ton was 2500 yuan and 9000 yuan, respectively. The results are shown in Table 3 below. Table 3. Conversion Factors and Processing Costs for Thermal Power Units The photovoltaic (PV) module loss rate is 83%, with an annual utilization of 1123 hours. The PV grid connection mode is calculated based on 80% self-consumption for industrial and commercial use and 40% for residential use. Electricity consumption at different times is statistically analyzed based on regional time-of-use pricing. The comprehensive electricity price for residential use is RMB 0.617 / kWh, and for industrial and commercial use, it is RMB 0.866 / kWh. The grid connection price will consider national and municipal subsidies before 2021, and will be at parity after that. The trends in the initial total investment cost and annual operation and maintenance costs of the power plant are based on data from the China Photovoltaic Industry Association, and further extrapolated using a triple exponential smoothing algorithm. The calculated annual return on investment and comprehensive return rate under the total investment are as follows: Figure 8 As shown.

[0055] 3.2 Solving for Model Parameters In SPSS software, the return on investment and the overall return are dynamically weighted, and a Logistic model is fitted based on the least squares method. The K value is searched with a step size of 0.001, and the model fit coefficient R0.018 is determined. 2 The maximum value is 0.974577. Taking K=0.018, the correlation index is mapped with a step size of 0.01. Perform a search, in When the coefficient of determination R is 2.92, the model fit is determined by the following factor. 2 The maximum value was 0.992022, the F-test value increased by more than two times, and the significance levels were all far less than 0.05, indicating that the overall fit was quite ideal. The model fitting parameters and corresponding test indices are shown in Table 4. Table 4 Model Summary and Parameter Estimates The error between the model's fitted result and the actual capacity is as follows: Figure 9 As shown.

[0056] 3.3 Comparative Analysis of Prediction Results Using the method in this embodiment, based on the distributed photovoltaic installation capacity data of Shanghai from 2016 to 2021, and taking the optimal model fit K=0.018, =2.92, substituting the projected annual rate of return and overall rate of return into the calculation, the prediction results are as follows. Figure 10 As shown, it can be observed that the remapped years are relatively concentrated between 2020 and 2022, indicating a slower development speed. The main reason for this is that during this period, regional photovoltaic subsidies continued to decline and grid parity policies were implemented, leading to a rapid decline in the rate of return on investment. This resulted in a shorter time span after model mapping, and a decrease in the relative growth between corresponding years.

[0057] After fitting the growth curve using the text prediction method, three other fitting methods are used for fitting: (1) Using the original time series to fit the trend of the Logistic curve, and without considering the method in the text to calculate the maximum photovoltaic installation capacity in the future. (2) Using the method of this embodiment to calculate the optimal fit K of the model, but without considering the mapping correlation index. (3) The second-order adaptive trend analysis method can use the previous year's forecast error data to update the smoothing coefficient for the following year. The forecast data is shown in Table 5 below: Table 5. Comparison of Capacity Prediction Data from Several Different Methods in Shanghai Compared with existing data, the method in this embodiment has an average relative error of 3.31% and an average absolute error of 29,100 kW in fitting the historical values ​​of photovoltaic capacity in Shanghai from 2016 to 2021, showing a high degree of matching with historical values. The model predicts that distributed photovoltaic capacity will increase by 297,000 kWh in 2022, reaching a total capacity of 1,722,000 kWh, which is basically consistent with the construction plan announced by the Shanghai Municipal Government in early 2022 (adding 300,000 kWh, bringing the total capacity to 1,742,000 kWh).

[0058] as follows Figure 11As shown, compared to directly fitting the Logistic growth trend using the original time series, this method suffers from a larger average relative error (11.07%) and an average absolute error (92.8 MW) because it does not consider the impact of the key factor of return on investment (ROI) on the capacity growth rate. Due to the exponential growth characteristic of the Logistic growth curve during the acceleration phase, this error will rapidly amplify. Furthermore, since it does not quantitatively assess the projected saturated photovoltaic capacity, the reliability of its projected values ​​will continuously decrease, with predicted values ​​for 2029 and beyond already exceeding the theoretical saturation capacity limit. The second-order adaptive method can adjust the model's quadratic smoothing exponent for the following year based on the previous year's prediction deviation. However, due to significant policy changes in Shanghai between 2016 and 2021, the ROI fluctuated greatly, resulting in uneven changes in photovoltaic capacity growth across years. Consequently, the model's predictions will fluctuate around the actual values. Moreover, the extrapolation trend of this method exhibits a significant time lag, failing to reflect the impact of rapid changes in ROI on photovoltaic development, leading to poor prediction performance in the medium to long term.

[0059] For the method in this embodiment, without considering the mapping correlation index At that time, the average relative error reached 6.90%, and the average absolute error reached 57,100 kilowatts, indicating that the model fit was lower than expected after considering the mapping correlation index. The main reason is that the relationship between the rate of change of the rate of return on investment and the change in the mapping time T affecting model growth is not a simple linear one. Analysis of the error between the fitted value and the actual value in this case reveals that in 2018-2019, when the rate of return on investment was high, the fitted value was lower than the actual value, and the medium capacity point of the fitted curve was shifted to the right on the mapped time axis; in 2020-2021, when the rate of return on investment fell rapidly, the fitted value was higher than the actual value, and the medium capacity point of the fitted curve was shifted to the left on the mapped time axis. Therefore, this embodiment incorporates a mapping correlation index. A secondary correction was made to the magnitude of the impact of the rate of return on investment on the time axis of the mapping, which reduced the relative error of the model fitting by 3.59 percentage points, a reduction of more than 50%.

[0060] 3.4 Comparison of Three-Year Forecasts To verify the sensitivity of the model in this embodiment to the scenario of rapid changes in the rate of return on investment, based on distributed photovoltaic (PV) data in Shanghai from 2014 to 2018, the model was used to predict the growth data of distributed PV during the period of rapid decline in the rate of return on investment from 2019 to 2021. The results were compared with several other methods and a dynamic prediction method considering the impact of incentive policies. The results are as follows. Figure 12 As shown.

[0061] Comparing the actual data, the predicted values ​​of all methods for the three years were higher than the actual values. Analysis suggests that the sharp drop in investment returns caused by changes in Shanghai's photovoltaic policy had a significant impact on the progress of photovoltaic capacity growth. The prediction errors of different methods are related to their degree of consideration of the policy impact. The method in this embodiment had an average relative prediction error of 12.14% for the three years from 2019 to 2021, which is better than the 19.41% of the prediction method that incorporates the dynamics of incentive effects. The prediction deviation for 2021 was 10.07%, indicating good overall prediction accuracy. The original time-series fitting method, due to its failure to consider the impact of policy changes, had a large prediction deviation in this scenario, with a deviation of 84.39% for the predicted value in 2021. The second-order adaptive method, due to its time-lag limitation, lacked a deviation adjustment benchmark for subsequent predictions, resulting in a prediction deviation of 39.60% for the predicted value in 2021.

[0062] Compared to other forecasting methods, the method in this embodiment has better forecasting accuracy when regional photovoltaic policies change rapidly. However, it requires reasonable calculation and forecasting analysis of the trend of return on investment. Furthermore, this method can adjust relevant indices based on the relationship between the growth rate of photovoltaic capacity and the change rate of return on investment in different regions. Adjustments will be made to adapt to the different characteristics of photovoltaic capacity growth in various regions. As photovoltaic policies and photovoltaic module prices gradually stabilize in the coming years, and with the further enrichment of existing reference data, the predictive accuracy of the methods described in this paper will be further improved.

[0063] 4. Conclusion This embodiment addresses the driving effects of photovoltaic (PV) investment return rate and PV emission reduction benefits on PV capacity growth. It proposes a Logistic regional PV capacity growth model considering multiple factors and time-series dynamic weighting, and conducts simulation predictions for a case study of Shanghai, drawing the following conclusions: 1) The method in this embodiment comprehensively considers the impact of return on investment and emission reduction benefits on photovoltaic capacity growth, thereby enhancing the prediction accuracy of the model during periods of rapid changes in the current photovoltaic return on investment; 2) The introduction of a mapping correlation index enhances the correlation between return on investment and capacity growth, thereby improving the model's adaptability to the photovoltaic growth characteristics of different regions; 3) As the model can incorporate new time-series data and continuously roll over, the prediction accuracy will continue to improve as existing data becomes richer and photovoltaic policies and module prices gradually stabilize.

[0064] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for predicting regional distributed photovoltaic installed capacity based on time-series weighted average, characterized in that, Includes the following steps: Obtain photovoltaic benefit data for the current region, calculate historical time series data of prospective saturated photovoltaic capacity, return on investment, and overall return on investment, and extrapolate and predict future annual return on investment data based on this historical time series data; The time series is dynamically weighted based on the aforementioned rate of return on investment and overall rate of return, and the resulting weighted time series is used as the independent variable of the Logistic growth model. The parameters of the Logistic growth model are optimized; the predicted growth data of photovoltaic installed capacity for each year are obtained using the optimized Logistic growth model. The calculation expression for the weighted time series is: In the formula, for The weighted coefficient of the investment return rate at a given time point, with a value between [0,1]; This represents a correlation index indicating the rate of return on investment; its value is greater than 0. This indicates the time point at which the emission reduction benefits affect capacity growth in the model; K This represents the slope of the weighting coefficients as they change over time. express Weighted time series values ​​at specific time points For return on investment, The overall rate of return; The calculation expression for the Logistic growth model with weighted time series as the independent variable is as follows: In the formula, This indicates the model capacity for the weighted time series. T The cumulative value, For regional distributed photovoltaic in h Maximum installed capacity of photovoltaic modules This is the initial installed capacity. The representation model for weighted time series T The intrinsic growth rate; the weighted time series is fitted to the model using the least squares method to obtain the regional photovoltaic capacity growth rate for the weighted time series. T The optimal intrinsic growth rate of the model; Distributed photovoltaic power in the region h Maximum installed capacity of photovoltaic modules The calculation expression is: In the formula, m The number of building types in the region. for h The installed capacity per unit area of ​​photovoltaic modules, for h Photovoltaic modules are limited by their module characteristics. h Corrected utilization factor when installing on the roof of similar buildings. For the region l Maximum available roof installation area for this type of building for l Total floor area of ​​buildings of this type for l The development coefficient of similar buildings participating in distributed photovoltaic installations. for l Average number of floors in areas with similar buildings for l The roof area utilization coefficient of this type of building.

2. The method for predicting regional distributed photovoltaic installed capacity based on time-series weighting according to claim 1, characterized in that, The formula for calculating the rate of return on investment is as follows: In the formula, The initial unit installation investment cost, Annual operating and management cost per unit of installed capacity The unit installed financial cost The unit's annual revenue from grid-connected electricity sales. For the regional photovoltaic grid-connected electricity sales price, The proportion of grid-connected electricity to total annual power generation, Annual electricity revenue per unit of installed capacity This refers to the unit price of electricity. The unit's installed capacity government subsidy income; In the formula, For the region in h Maximum annual power generation per unit installed capacity for photovoltaic modules for h Photovoltaic module self-generated power loss rate for h The annual utilization hours of photovoltaic modules in this region.

3. The method for predicting regional distributed photovoltaic installed capacity based on time-series weighting according to claim 2, characterized in that, The formula for calculating the overall rate of return is as follows: In the formula, This indicates the carbon dioxide emissions per kilowatt-hour of photovoltaic power generation. , , The values ​​represent the emission reduction benefits per kilowatt-hour and treatment costs for carbon dioxide and other pollutants, respectively. A This indicates the number of pollutant types considered. This refers to the environmental benefits of distributed generation, including emission treatment costs and actual emission reduction benefits. This represents the revenue from thermal power generation under the same power generation capacity. Indicates the overall revenue from photovoltaic power generation. This indicates the cost of thermal power generation during the same electricity output period. In the formula, This refers to the carbon dioxide emissions per kilowatt-hour from regional thermal power generation. J The generator sets are classified into levels according to boiler pressure rating. For the region j Standard coal consumption per kilowatt-hour for a Class A boiler pressure thermal power unit This represents the carbon dioxide emission coefficient based on standard coal consumption. For the region j The power generation ratio of a boiler pressure thermal power unit within a statistical period. For the region j Power generation of a Class A boiler pressure thermal power unit within a statistical period; In the formula, for a The per-unit-of-electricity emissions of pollutants of this type for a The amount of each kilowatt-hour of the pollutant type, In standard coal a The ratio of the emission coefficient of pollutants to carbon dioxide. For the region a Treatment coefficients for pollutants.

4. The method for predicting regional distributed photovoltaic installed capacity based on time-series weighting according to claim 1, characterized in that, The historical time series data are extrapolated and predicted using a triple exponential smoothing algorithm.

5. The method for predicting regional distributed photovoltaic installed capacity based on time-series weighting according to claim 1, characterized in that, In the process of parameter optimization for the Logistic growth model, the optimal K value is first determined, and then the optimal K value is searched. Secondary smoothing of the trend in time series data; changing the step size. The model is then fitted again, and the parameters of the fitting curve change accordingly until the model fit R is achieved. 2 It has reached its maximum value.

6. The method for predicting regional distributed photovoltaic installed capacity based on time-series weighting according to claim 1, characterized in that, The parameter optimization process for the aforementioned Logistic growth model is as follows: S101: Setting K and The initial value; S102: The investment return rate and the overall return rate are weighted over time according to the K value, and the model data are fitted with Logistic regression based on the least squares method; S103: Determine the curve fit R 2 If the maximum value has been reached, proceed to step 104; otherwise, modify the K value according to the preset step size. S104: Based on the determined K value, according to the mapping correlation index The weighted time-series trend is smoothed twice, and then Logistic fitting is performed again. S105: Determine the curve fit R 2 Has the maximum value been reached? If so, proceed to step 106; otherwise, modify according to the preset step size. value; S106: Obtain the final K. and model variable values; S107: According to K, The values ​​are calculated on the original time series data to obtain the weighted time series sequence; S108: Substitute the weighted time series into the Logistic growth model for calculation.

7. A regional distributed photovoltaic installed capacity prediction system based on time-series weighting, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor invokes the computer program to perform the steps of the method as described in any one of claims 1 to 6.

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