A Method for Evaluating the Credibility of Photovoltaic Power Generation Capacity Based on Joint Probability Modeling and Stochastic Processes

Abstract

The present invention discloses a method for evaluating the capacity credibility of photovoltaic power generation based on joint probability modeling and stochastic processes, including: collecting historical irradiance and temperature data of the target area, extracting their hourly means and standard deviations, and dividing seasonal data sets; constructing a joint probability distribution model of irradiance and temperature using the Copula function, where the Gumbel Copula function is selected for summer and the Clayton Copula function is selected for winter; generating stochastic fluctuation sequences of irradiance and temperature based on stochastic differential equations, and calculating the real-time photovoltaic output in combination with the characteristic equation of the photovoltaic cell; simulating the faults of traditional units and load fluctuations using a two-state Markov model, and quantifying the loss-of-load expectation (LOLE) of the system through Monte Carlo simulation; dynamically iterating using the equivalent conventional capacity method (ECP) to calculate the capacity credibility of photovoltaic power generation; the present invention provides a basis for reliability evaluation for high-proportion photovoltaic grid connection planning.

Description

Technical Field

[0001] The present invention relates to the technical field of power system planning and photovoltaic reliability assessment, and particularly relates to a method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic processes. Background Art

[0002] As one of the most abundant and easily accessible renewable energy sources, photovoltaic power generation has low power generation costs, is environmentally friendly, and has the potential to replace fossil fuels and meet global energy demands. Accurately and objectively evaluating the reliability of photovoltaic power generation capacity is of great significance for the operation and planning of power systems. However, photovoltaic power generation has the characteristics of intermittency and volatility, and its output is affected by multiple factors such as weather and seasonal changes, resulting in uncertainty in photovoltaic power generation power, which poses a major challenge to the stability of high-penetration power systems. Traditional methods for evaluating reliability usually adopt univariate probability distributions and do not fully consider the dynamic correlation between irradiance and temperature, resulting in large deviations in evaluation results. In addition, traditional methods do not consider high-precision stochastic process models to simulate the time-series characteristics of photovoltaic output, and cannot obtain the impact of short-term fluctuations in photovoltaic power on system reliability. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide a method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic processes, which solves the problems of ignoring the correlation between irradiance and temperature and time-series fluctuations in traditional methods.

[0004] Technical Solution: A method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic processes according to the present invention includes the following steps:

[0005] S1. Collect historical irradiance data of the target area G t and ambient temperature data , and extract their hourly averages G trend,t , and standard deviations σ G,t , σ T,t ;

[0006] S2. Divide the data according to seasons. In summer, use the Gumbel Copula function to establish the joint probability distribution model of irradiance G t and temperature , and in winter, use the Clayton Copula function to establish the joint probability distribution model of irradiance G t and temperature ;

[0007] S3. Generate a random fluctuation sequence of irradiance and temperature using the Stochastic Differential Equation (SDE);

[0008] S4. Calculate the real-time PV output according to the PV cell characteristic equation P pv,t , and use a two-state Markov model to simulate the faults of traditional units and load fluctuations;

[0009] S5. Generate time series data of PV output, traditional unit status, and load based on Monte Carlo simulation, and calculate the Expected Load Shedding (ELS) of the system;

[0010] S6. Determine the PV capacity creditability using the Equivalent Conventional Capacity Method (ECP) CC pv.

[0011] Furthermore, in step S2, the joint probability distribution model is specifically as follows:

[0012] ;

[0013] where H( ) represents the joint cumulative distribution function; G t is the historical irradiance data of the target area; C θ is the Copula function; Z G is a standard normal distribution random number related to Z T , Z T is a standard normal distribution random number related to Z G , Z T and Z G consider their correlation through the joint probability distribution model; G trend,t is the hourly average irradiance; the hourly average of the ambient temperature data; is the ambient temperature data of the target area; σ G,t is the variance of the historical hourly solar irradiance; σ T,t is the variance of the historical hourly ambient temperature; Φ( Z G ) is Z G 's standard normal distribution; Φ( Z T ) is Z T 's standard normal distribution.

[0014] Further, in step S2, the Gumbel Copula function is used in summer as follows:

[0015] ;

[0016] where, θ reflects the correlation strength, θ the closer it is to 1, the more independent it is, θ and it represents complete correlation when approaching infinity.

[0017] Further, in step S2, the Clayton Copula function is used in winter as follows:

[0018] ;

[0019] where, θ the closer it is to 0, the more independent it is, θ and it represents complete correlation when approaching infinity.

[0020] Further, in step S3, the specific process of generating the random fluctuation sequences of irradiance and temperature using the stochastic differential equation SDE is as follows:

[0021] ;

[0022] where, G n,t is the random irradiance variable modeled by the SDE; is the random ambient temperature variable modeled by the SDE; dW t represents the differential form of the Wiener process.

[0023] Further, in step S4, the real-time PV output is calculated according to the PV cell characteristic equation P pv,t The specific process is as follows:

[0024] ;

[0025] is t the solar PV output power at time is the rated power of solar PV generation (W); T cell,t is the temperature of the solar cell (°C); G STC = 1000 W / m 2 is the standard test irradiance; T STC is the standard test temperature; T STC= 25 °C; γ is the temperature coefficient, -0.05 < γ<- 0.003; T NOC is the nominal operating temperature; T NOC = 46 °C; is the actual electric power of solar photovoltaic power generation at time t; is the conversion efficiency of solar photovoltaic electric power;

[0026] The formula for simulating the faults of traditional units and load fluctuations using a two-state Markov model is as follows:

[0027] ;

[0028] where, TTF is the fault time or the duration of the availability of the power generation equipment; TTR is the repair time or the time when the power generation equipment is unavailable; λ is the failure rate of each power generation unit in the two-state Markov model; r is the average repair time of each power generation unit, equal to ; is the repair rate of each power generation unit in the two-state Markov model; U is a random value uniformly distributed in [0,1], Z is a random value from a standard normal distribution; is the variance of the repair time of each generator, represented by 0.1 r ; L t is t the load size at time is t the predicted value of the load size at time α is the load prediction error coefficient; Z is a random number conforming to a standard normal distribution, Z ~ N (0,1).

[0029] Furthermore, step S5 is specifically as follows:

[0030] ;

[0031] where, LOLE is the system load shedding expectation; d ( P t < L t ) is the duration when the total system output is less than the load; T is the total simulation duration.

[0032] Further, step S6 is specifically as follows: First, calculate the benchmark LOLE , keep the photovoltaic installed capacity C pv and the original traditional unit capacity C conv,initial unchanged, generate photovoltaic output time series data based on steps S1 - S5; based on step S4, simulate the traditional unit random failure states TTF and TTR, and generate the unit available capacity sequence P conv,t ; Then, superimpose the actual electric power of solar photovoltaic power generation at time t, and calculate the total system output P t , where: P t =P conv,t + P e,pv,t ; Finally, calculate the benchmark LOLE value LOLE base ;

[0033] Then, perform iterative calculation on the equivalent traditional capacity, remove the photovoltaic system, set the step size ΔC = 1 MW, and gradually increase the traditional unit capacity; in the k - th iteration, the traditional unit capacity is updated to C conv,k , ; Calculate the new LOLE value LOLE new,k based on step S5, when the condition ∣ LOLE new,k − LOLE base ∣≤ϵ is satisfied, terminate the iteration, where is the tolerance threshold, = 0.09 h / year; finally record the final equivalent traditional capacity C conv，end ;

[0034] Finally, calculate the photovoltaic power generation capacity credibility CC pv , and its formula is:

[0035] .

[0036] An electronic device according to the present invention includes a memory, a processor, and a computer program stored on the memory. When the processor executes the program, it implements the steps of any one of the above - described methods.

[0037] A computer-readable storage medium according to the present invention stores a computer program, and when the program is executed by a processor, the steps of any one of the above-mentioned methods are implemented.

[0038] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: By mainly focusing on modeling the joint probability distribution of irradiance and temperature in the evaluation of the credibility of photovoltaic power generation capacity, considering the influence of meteorological variables such as irradiance and temperature on the volatility of photovoltaic output and the reliability of the system, a seasonal Copula function and a stochastic differential equation model are reasonably constructed. The capacity credibility evaluation takes into account the requirements of both system reliability analysis and output time series fluctuations, and gives full play to the advantages of stochastic processes and Monte Carlo simulation in high-precision evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0040] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0041] As Figure 1 shown, an embodiment of the present invention provides a method for evaluating the credibility of photovoltaic power generation capacity based on joint probability modeling and stochastic processes. First, historical irradiance and temperature data of the target area are collected, the hourly mean and standard deviation are extracted, and the seasonal data sets are divided; then, a Copula function is used to construct a joint probability distribution model of irradiance and temperature, where the Gumbel Copula function is selected in summer and the Clayton Copula function is selected in winter; subsequently, based on the stochastic differential equation, random fluctuation sequences of irradiance and temperature are generated, and the real-time photovoltaic output is calculated in combination with the photovoltaic cell characteristic equation; then, a two-state Markov model is used to simulate the faults of traditional units and load fluctuations, and the loss-of-load expectation (LOLE) of the system is quantified through Monte Carlo simulation; finally, the equivalent conventional capacity method (ECP) is used for dynamic iteration to calculate the capacity credibility of photovoltaic power generation. The specific steps are as follows:

[0042] S1. Collect historical irradiance data of the target area G t and ambient temperature data , and extract their hourly means G trend,t , and standard deviations σ G,t , σ T,t ;

[0043] S2. Divide the data according to seasons, and use the Gumbel Copula function to establish irradiance in summer Gt Joint probability distribution model with temperature In winter, the Clayton Copula function is used to establish the joint probability distribution model of irradiance G t and temperature The joint probability distribution model is as follows:

[0044] ;

[0045] where H( ) represents the joint cumulative distribution function; G t is the historical irradiance data of the target area; C θ is the Copula function; Z G is a standard normal distribution random number related to Z T Z T is a standard normal distribution random number related to Z G ; Z T and Z G consider their correlation through the joint probability distribution model; G trend,t is the hourly average irradiance; The hourly average of the ambient temperature data; is the ambient temperature data of the target area; σ G,t is the variance of the historical hourly solar irradiance; σ T,t is the variance of the historical hourly ambient temperature; Φ( Z G ) is Z G 's standard normal distribution; Φ( Z T ) is Z T 's standard normal distribution.

[0046] In summer, the Gumbel Copula function is as follows:

[0047] ;

[0048] In the formula, θ reflects the correlation strength, θ the closer it is to 1, the more independent it is, θ when it approaches infinity, it means complete correlation.

[0049] The specific method of using the Clayton Copula function in winter is as follows:

[0050] ;

[0051] In the formula, θ The closer it is to 0, the more independent it is, θ When it approaches infinity, it means complete correlation.

[0052] S3. Generate the random fluctuation sequences of irradiance and temperature using the stochastic differential equation (SDE). The specific process is as follows:

[0053] ;

[0054] In the formula: G n,t is the stochastic irradiance variable modeled by the SDE; is the stochastic ambient temperature variable modeled by the SDE; dW t represents the differential form of the Wiener process.

[0055] S4. Calculate the real-time photovoltaic output according to the photovoltaic cell characteristic equation P pv,t , and use the two-state Markov model to simulate the faults of traditional units and load fluctuations; The specific process of calculating the real-time photovoltaic output according to the photovoltaic cell characteristic equation P pv,t is as follows:

[0056] ;

[0057] In the formula: is t the output power of solar photovoltaic power generation at time is the rated power of solar photovoltaic power generation (W); T cell,t is the temperature of the solar cell (°C); G STC = 1000 W / m 2 is the standard test irradiance; T STC is the standard test temperature, T STC = 25 °C; γ is the temperature coefficient, -0.05 < γ<- 0.003; T NOC is the nominal operating temperature, T NOC = 46 °C; is the actual electric power of solar photovoltaic power generation at time t; is the conversion efficiency of solar photovoltaic electric power, = 98%;

[0058] The traditional unit faults and load fluctuations are simulated using a two-state Markov model, and the formula is as follows:

[0059] ;

[0060] In the formula: TTF is the fault time or the duration of the availability of the power generation equipment; TTR is the repair time or the time when the power generation equipment is unavailable; λ is the failure rate of each power generation unit in the two-state Markov model; r is the average repair time of each power generation unit, equal to ; is the repair rate of each power generation unit in the two-state Markov model; U is a random value uniformly distributed in [0,1], Z is a random value of the standard normal distribution; is the variance of the repair time of each generator, represented by 0.1 r ; L t is t the load size at time is t the predicted value of the load size at time α is the load prediction error coefficient; Z is a random number conforming to the standard normal distribution, Z ~ N (0,1).

[0061] S5. Generate the photovoltaic output, traditional unit status, and load time series data based on Monte Carlo simulation, and calculate the system loss of load expectation; specifically as follows:

[0062] ;

[0063] In the formula: LOLE is the system loss of load expectation; d ( P t < L t ) is the duration when the total system output is less than the load; T is the total simulation duration.

[0064] S6. Use the equivalent conventional capacity method ECP to determine the photovoltaic capacity credibility CC pv. Specifically as follows: First, calculate the reference LOLE , and keep the photovoltaic installed capacity C pvand the original traditional unit capacity C conv,initial Remain unchanged, generate photovoltaic output time series data based on steps S1 - S5; based on step S4, simulate the traditional unit random failure states TTF and TTR, and generate the available capacity sequence of unit j P conv,t ; Superimpose the actual electric power of solar photovoltaic power generation at time t, and calculate the total system output P t , where: P t = P conv,t + P e,pv,t ; Finally, calculate the reference LOLE value LOLE base ;

[0065] Then, perform iterative calculations on the equivalent traditional capacity, remove the photovoltaic system, set the step size ΔC = 1 MW, and gradually increase the traditional unit capacity; in the k - th iteration, the traditional unit capacity is updated to C conv,k , ; Calculate the new LOLE value LOLE new,k when the condition ∣ LOLE new,k − LOLE base ∣≤ is met, where is the tolerance threshold, = 0.09 h / year; finally record the final equivalent traditional capacity C conv，end ;

[0066] Finally, calculate the credibility of the photovoltaic power generation capacity CC pv , and its formula is:

[0067] .

Claims

1. A method for evaluating the credibility of photovoltaic power generation capacity based on joint probability modeling and stochastic processes, characterized in that, Including the following steps: S1. Collect historical irradiance data of the target area G t and ambient temperature data , and extract their hourly means G trend,t , and standard deviations σ G,t , σ T,t ; S2. Divide the data according to seasons. In summer, use the Gumbel Copula function to establish the joint probability distribution model of irradiance G t and temperature . In winter, use the Clayton Copula function to establish the joint probability distribution model of irradiance G t and temperature . S3. Use the stochastic differential equation (SDE) to generate a stochastic fluctuation sequence of irradiance and temperature; S4. Calculate the real-time PV output according to the PV cell characteristic equation P pv,t , and use a two-state Markov model to simulate the faults of traditional units and load fluctuations; S5. Generate time series data of photovoltaic output, traditional unit status, and load based on Monte Carlo simulation, and calculate the expected load shedding of the system; S6. Determine the credibility of PV capacity using the equivalent conventional capacity method (ECP) for PV CC pv; specifically as follows: First, calculate the reference LOLE , keep the PV installed capacity C pv and the original capacity of traditional units C conv,initial unchanged, and generate PV output time series data based on steps S1 - S5; based on step S4, simulate the random failure states TTF and TTR of traditional units to generate the unit available capacity sequence P conv,t ; Then, superimpose the actual electric power of solar PV generation at time t, and calculate the total system output P t , where: P t =P conv,t + P e,pv,t ; Finally, calculate the reference LOLE value LOLE base ; Again, perform iterative calculations on the equivalent traditional capacity. Remove the photovoltaic system, set the step size ΔC = 1 MW, and gradually increase the capacity of the traditional unit; in the k-th iteration, the capacity of the traditional unit is updated to C conv,k , ; Calculate a new one based on step S5 LOLE value LOLE new,k , when the condition ∣ LOLE new,k − LOLE base ∣≤ is satisfied, terminate the iteration, where is the tolerance threshold, = 0.09 h / year; finally record the final equivalent traditional capacity C conv，end ; Finally, calculate the reliability of photovoltaic power generation capacity CC pv , and its formula is: 。 2. The method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic process according to claim 1, wherein In step S2, the joint probability distribution model is specifically as follows: ； where \(H()\) represents the joint cumulative distribution function; G t is the historical irradiance data of the target area; C θ is the Copula function; Z G is a standard normal distribution random number related to Z T and \(Z\) T is a standard normal distribution random number related to Z G ; Z T is related to Z G and their correlation is considered through the joint probability distribution model; G trend,t is the average irradiance per hour; is the average environmental temperature data per hour; is the environmental temperature data of the target area; σ G,t is the variance of the historical hourly solar irradiance; σ T,t is the variance of the historical hourly environmental temperature; \(\varPhi( Z G )\) is Z G 's standard normal distribution; \(\varPhi( Z T )\) is Z T 's standard normal distribution.

3. A method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic processes according to claim 1, wherein, In step S2, the Gumbel Copula function is used in summer, specifically as follows: ； Among them, θ reflects the strength of correlation, θ the closer to 1 indicates the more independent, θ when approaching infinity, it indicates complete correlation.

4. A method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic processes according to claim 1, characterized in that In step S2, the Clayton Copula function is used in winter, specifically as follows: ； Among them, θ The closer it is to 0, the more independent it is. θ When it approaches infinity, it means complete correlation.

5. A method for evaluating the reliability of photovoltaic power generation capacity based on joint probability modeling and stochastic processes according to claim 1, characterized in that In step S3, the specific process of using the stochastic differential equation (SDE) to generate a stochastic fluctuation sequence of irradiance and temperature is as follows: ； wherein, G n,t is a stochastic irradiance variable modeled by the SDE; is a stochastic ambient temperature variable modeled by the SDE; dW t represents the differential form of the Wiener process.

6. A method for evaluating the credibility of photovoltaic power generation capacity based on joint probability modeling and stochastic processes according to claim 1, characterized in that In step S4, the real-time PV output is calculated according to the PV cell characteristic equation P pv,t The specific process is as follows: ； Among them, is t the output power of solar photovoltaic power generation at time the rated power (W) of solar photovoltaic power generation; T cell,t is the temperature (°C) of the solar cell; G STC = 1000 W / m 2 is the standard test irradiance; T STC is the standard test temperature; γ is the temperature coefficient, -0.05 < γ<- < 0.003; T NOC is the nominal operating temperature; is the actual electric power of solar photovoltaic power generation at time t; is the conversion efficiency of solar photovoltaic electric power; The two-state Markov model is used to simulate the traditional unit failure and load fluctuation, and the formula is as follows: ； Among them, TTF is the failure time or the duration of the availability of the power generation equipment; TTR is the repair time or the time when the power generation equipment is unavailable; λ is the failure rate of each power generation unit in the two-state Markov model; r is the average repair time of each power generation unit, equal to ; is the repair rate of each power generation unit in the two-state Markov model; U is a random value uniformly distributed in [0,1], Z is a random value of the standard normal distribution; is the variance of the repair time of each generator, represented by 0.1 r ; L t is t the load size at time is t the predicted value of the load size at time α is the load prediction error coefficient; Z is a random number conforming to the standard normal distribution, Z ~ N (0,1).

7. A method for evaluating the credibility of photovoltaic power generation capacity based on joint probability modeling and stochastic processes according to claim 1, characterized in that Step S5 is specifically as follows: ； Among them, LOLE is the expected system load shedding; d ( P t < L t ) is the duration when the total system output is less than the load; T is the total simulation duration.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the program is executed by the processor, it implements the steps of the method according to any one of claims 1-7.

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