Successive approximation random dynamic planning method for watershed water-wind-light integrated system

Abstract

The invention relates to the field of multi-energy coupling complementary scheduling, and discloses a successive approximation random dynamic planning method for a watershed water-wind-light integrated system, and the method comprises the steps: 1, inputting the description of uncertainty; a plurality of characteristic discrete values are sampled from theoretical probability distribution functions of runoff, photovoltaic output and wind power output to represent known continuous probability distribution, and uncertainty of input of the watershed water-wind-light integrated system is described; 2, solving a transition probability matrix; describing the continuity of an input variable time sequence by adopting a simple discrete time Markov chain; 3, considering an objective function and constraint conditions of the watershed water-wind-light integrated system, and constructing a complementary optimization scheduling model; 4, solving by adopting a successive approximation-random dynamic programming method (SDP-SA), and deducing a scheduling rule, namely a scheduling decision table, of the watershed water-wind-light integrated system by taking the time period initial storage capacity, runoff, photovoltaic output and wind power output scenes of the adjustable reservoir in each stage of sub-complementary system as multi-dimensional state variables and the time period final storage capacity as a decision variable; and 5, when an actual inflow condition occurs, looking up the scheduling decision table to perform interpolation calculation according to the reservoir capacity and the inflow condition of the current sub-complementary system and the wind power output and the photovoltaic output which are obtained by forecasting in the period of time, obtaining the reservoir capacity at the end of the period of time, and completing an optimal scheduling decision.

Description

Technical Field

[0001] The present invention belongs to the field of multi-energy coupling and complementary scheduling, and specifically relates to a successive approximation random dynamic programming method for a watershed water-wind-solar integrated system. Background Art

[0003] In previous studies of complementary scheduling for integrated water, wind, and solar systems in river basins, most studies employed deterministic optimization methods to solve for optimal scheduling trajectories, subsequently deriving optimized scheduling rules to guide subsequent system scheduling. However, in the actual solution process, since the system inputs, such as runoff, photovoltaic power output, and wind power output, are often affected by various factors and exhibit randomness, volatility, and intermittency, the results of applying these rules derived from deterministic optimization methods to the actual system differ significantly from the actual situation. This makes them ineffective in guiding the complementary optimal scheduling of integrated water, wind, and solar systems in river basins, rendering the original scheduling rules inapplicable. Furthermore, to mitigate the "curse of dimensionality" in the solution process, traditional complementary scheduling models for integrated water, wind, and solar systems in river basins often simplify the hydraulic connections between cascade reservoirs and between complementary subsystems at each level. While this simplified assumption reduces computational complexity and improves efficiency to a certain extent, it also neglects the interactions between cascade reservoirs and between complementary subsystems at each level. The resulting scheduling rules for integrated water, wind, and solar systems in river basins fail to fully reflect the actual dynamics of hydrological and power scheduling, resulting in low resource utilization during actual scheduling.

[0004] The following problems exist in the existing technology:

[0005] (1) Traditional research on the complementary scheduling of integrated water, wind, and solar systems in river basins focuses on static optimization, ignoring the dynamic adjustment requirements of the system during actual scheduling. Due to changes in runoff, photovoltaic output, and wind power input, the state of the system is constantly changing, but traditional integrated water, wind, and solar systems in river basins are difficult to adapt to these changes, resulting in the inability to adjust the scheduling rules and failing to meet the needs of actual scheduling.

[0006] (2) In traditional basin-wide integrated water, wind, and solar power system optimization and scheduling models, the number of adjustable reservoirs involved is usually single, and the hydraulic connections between upstream and downstream reservoirs do not need to be considered. In other studies of multiple adjustable reservoirs, the hydraulic connections between adjustable reservoirs are often simplified to improve the computational efficiency of the model. These problems will reduce the accuracy of scheduling decisions, and cannot maximize the utilization of water resources and maximize scheduling benefits. Summary of the Invention

[0007] The present invention is made to solve the above problems, and aims to provide a successive approximation stochastic dynamic programming method for a basin water-wind-solar integrated system considering multiple resource uncertainties. This method fully considers the uncertainties of runoff, photovoltaic power output, wind power output, etc. of the bundled complementary systems at all levels in the basin water-wind-solar integrated system, as well as the hydraulic connection between cascade hydropower stations. By fully considering the multiple complexities of the actual dispatching process, it effectively ensures the stable operation of the basin water-wind-solar integrated system, significantly improves the accuracy of dispatching decisions, optimizes the system dispatching results, and realizes the maximization of resource utilization rate and dispatching benefits of the basin water-wind-solar integrated system.

[0008] To achieve the above object, the present invention provides the following technical solution: A successive approximation stochastic dynamic programming method for a basin water-wind-solar integrated system, the method comprising:

[0009] Step 1, description of input uncertainties; sample a number of characteristic discrete values from the theoretical probability distribution functions of runoff, photovoltaic power output, and wind power output to represent the known continuous probability distribution, and describe the input uncertainties of the basin water-wind-solar integrated system.

[0010] Step 2, solution of the transition probability matrix; use a simple discrete-time Markov chain to describe the continuity of the time series of input variables.

[0011] Step 3, considering the objective function and constraint conditions of the basin water-wind-solar integrated system, construct a complementary optimization dispatching model.

[0012] Step 4, use the successive approximation - stochastic dynamic programming (SDP - SA) method for solution. Take the initial storage capacity, runoff, photovoltaic power output, and wind power output scenarios of the adjustable reservoirs within each sub-complementary system as multi-dimensional state variables, and the end-of-period storage capacity as the decision variable to derive the dispatching rules and dispatching decision tables of the basin water-wind-solar integrated system.

[0013] Step 5, when the actual inflow situation occurs, according to the reservoir storage capacity and inflow situation of the current sub-complementary system, as well as the wind power output and photovoltaic power output obtained through forecasting for this period, look up the dispatching decision table for interpolation calculation to obtain the reservoir storage capacity at the end of this stage and complete the optimized dispatching decision.

[0014] Further, in Step 1, description of input uncertainties; the input variables of the basin water-wind-solar integrated system include the reservoir inflow, photovoltaic power output, and wind power output of the bundled complementary systems at all levels; it is considered that the runoff follows the Pearson type III distribution, and its probability distribution function is as follows:

[0015]

[0016] where f(I r(t)) is the probability of the inflow runoff of the sub-complementary system r in the t-th scheduling period; α, β, a0 are the shape, scale, and location parameters respectively, with α > 0 and β > 0; Γ(α) is the gamma function of parameter α;

[0017] The photovoltaic output power follows a Log-Normal distribution, and its probability distribution function is as follows:

[0018]

[0019] In the formula, is the probability of the photovoltaic output power of the sub-complementary system r in the t-th scheduling period; μ, σ are the mean and standard deviation of the logarithm of the photovoltaic output power value of the sub-complementary system r in the t-th scheduling period;

[0020] The wind power output follows a Weibull distribution, and its probability distribution function is as follows:

[0021]

[0022] In the formula, is the probability of the wind power output of the sub-complementary system r in the t-th scheduling period; λ, k are the scale parameter and shape parameter respectively;

[0023] After calibrating the parameters of the probability distribution function, assuming that the runoff has m characteristic discrete values, and its theoretical cumulative probabilities are 1 / (m + 1), 2 / (m + 1), …, m / (m + 1), the characteristic discrete values corresponding to each theoretical cumulative probability are deduced by the probability distribution function; similarly, the deduction of the characteristic discrete values of the photovoltaic output power and the wind power output will not be elaborated here.

[0024] Furthermore, in step 2, the solution of the transition probability matrix; taking the runoff as an example, based on the m characteristic discrete values obtained in step 1, within the allowable numerical range of the t-th and (t + 1)-th scheduling periods, the runoff is divided into m discrete value intervals respectively;

[0025] (1) For the long-term sequence data with a total time period of T, all the annual data corresponding to the t-th and (t + 1)-th scheduling periods are taken out from the runoff sequence, a total of B years;

[0026] (2) For the m×m discrete interval combinations of the t-th and (t + 1)-th scheduling periods, count the number of years b when the runoff in the t-th period and the runoff in the (t + 1)-th period both fall into a certain discrete interval combination, then p ij = P(I r,j (t + 1)|I r,i (t)) = b / B;

[0027] (3) Similarly, the conditional transition probabilities of other discrete interval combinations can be obtained; then the one-step transition probability matrix is:

[0028]

[0029] wherein, p ij = P(I r,j (t + 1)|I r,i (t)) is the probability that when the runoff value of the sub - complementary system r is I r,i (t), (i = 1, 2,..., m) during the t - th scheduling period and the runoff value is I r,j (t + 1), (j = 1, 2,..., m) during the (t + 1) - th scheduling period, and ∑p = 1.

[0030] Furthermore, in step 3, a complementary optimization scheduling model for the integrated water - wind - solar system of the basin is constructed;

[0031] The objective function is:

[0032]

[0033] wherein, E is the total power generation (MWh) of the integrated water - wind - solar system of the basin; T and t are the total length and serial number of the scheduling period; R and r are the total number and serial number of the sub - complementary systems; are the hydropower output, wind power output and photovoltaic output (MW) of the sub - complementary system r during the t - th scheduling period respectively; ΔT t is the number of hours (h) within the scheduling period; F is the total power generation guarantee rate of the integrated water - wind - solar system of the basin; N firm is the total guaranteed output (MW) of the integrated water - wind - solar system of the basin, is the number of scheduling periods during the entire scheduling period of the integrated water - wind - solar system of the basin when the total output is greater than or equal to the total guaranteed output;

[0034] The constraint conditions include 3 aspects:

[0035] 1) Physical constraints for the hydropower station:

[0036] ① Water balance constraint

[0037] S r (t) = S r (t - 1)+I r (t)-Q r (t) (7)

[0038] wherein, S r (t - 1), S r (t) are the reservoir storage capacities at the beginning and end of the adjustable reservoir within the sub - complementary system r during the t - th scheduling period (m 3 ) respectively; I r (t), Q r (t) are the inflow and outflow discharges of the adjustable reservoir within the sub - complementary system r during the t - th scheduling period (m3 / s);

[0039] ② Water level constraint

[0040]

[0041] Wherein, Z r (t) , are respectively the minimum allowable water level and the maximum allowable water level (m) of the adjustable reservoir in the sub-complementary system r during the t-th scheduling period; generally, the minimum allowable water level is the dead water level, and the maximum allowable water level is the flood limit water level during the flood season and the normal storage water level during the non-flood season;

[0042] ③ Discharge constraint

[0043]

[0044] Wherein, Q r (t), are respectively the minimum allowable discharge and the maximum allowable discharge (m 3 / s) of the adjustable reservoir in the sub-complementary system r during the t-th scheduling period;

[0045] ④ Hydraulic connection

[0046] I r+1 (t) = I r (t) + I qj (t) (10)

[0047] Wherein, I r+1 (t) is the inflow of the adjustable reservoir in the sub-complementary system r + 1 during the t-th scheduling period (m 3 / s), and I qj (t) is the lateral inflow between the sub-complementary system r and the sub-complementary system r + 1 during the t-th scheduling period (m 3 / s);

[0048] 2) For the power transmission constraints of each level of sub-complementary systems:

[0049]

[0050] Wherein, is the guaranteed output (MW) of the sub-complementary system r; is the power transmission capacity limit (MW) of the sub-complementary system r;

[0051] 3) For the power transmission constraints of the basin water-wind-solar integrated system:

[0052]

[0053] Wherein, N firmis the total guaranteed output of the integrated water, wind and solar power system in the basin (MW); N trans is the transmission capacity limit of the power grid (MW).

[0054] Furthermore, in step 4, the proposed successive approximation stochastic dynamic programming (SDP-SA) method belongs to an explicit stochastic optimization method. The method adopts the idea of successive iterative approximation when solving, and only uses SDP to solve one sub-complementary system in the watershed water-wind-solar integrated system each time. Due to the setting of boundary conditions, recursive iterative calculations are required in the internal solution process of SDP, and it is assumed that the scheduling process of other sub-complementary systems is a multi-year average scheduling process. After a sub-complementary system is solved by SDP to obtain a provisional optimized scheduling decision table, the simulated scheduling of multi-year inputs, i.e., runoff, photovoltaic output, and wind power output processes, is used as the multi-year average scheduling update process of the sub-complementary system in the next successive iterative approximation process. Then, the scheduling process of each level of sub-complementary system is continuously updated through the successive iterative approximation solution process. Finally, after the total power generation and total power generation guarantee rate of the watershed water-wind-solar integrated system are iteratively solved to convergence, the optimal scheduling strategy set of each level of sub-complementary system in the watershed water-wind-solar integrated system can be obtained.

[0055] The specific steps are as follows:

[0056] First, we need to clarify the time representation method. In the calculation of the SDP-SA solution for the complementary optimization scheduling model of the integrated water, wind and solar system in the basin, the scheduling period is 12 months, that is, t = 1, 2, ..., A, A = 12. In the simulation scheduling calculation, the scheduling period is the total number of periods in the long sequence, that is, t = 1, 2, ..., T, T = A × B, where A is the number of months in a year and B is the number of years of the scheduling period.

[0057] (1) Based on the feasible interval of dead water level-normal water level, i.e., flood limit water level, the dispatching process of each sub-complementary system in the watershed water-wind-solar integrated system, i.e., the water level change process, is assigned initial values, and simulated dispatching is performed to solve the total power generation E of the watershed water-wind-solar integrated system under the initial values. 0 , power generation guarantee rate F 0 Indicators; The initial scheduling process of each level of sub-complementary system is as follows:

[0058]

[0059] In the formula, each row represents the initial storage capacity (m 3 );

[0060] (2) Determine the main tone complementary systems as 1, 2,..., R in sequence from upstream to downstream; first optimize the sub-complementary system 1 and solve it using SDP; specifically:

[0061] ① Stage variable: Taking a month as the scheduling period, t = 1, 2,..., A, A = 12;

[0062] ② State variable: Discretize the reservoir storage capacity within the main tone complementary system into K cases, and use the combination scenario of the reservoir storage capacity, inflow, PV output, and wind power output at the beginning of each period as the multi-dimensional state variable, that is

[0063] where S r,k (t - 1) represents that the initial reservoir storage capacity of the adjustable reservoir in the t-th scheduling period is the k-th case, and I r,i (t) represents that the inflow of the adjustable reservoir in the t-th scheduling period is the i-th scenario, represents that the PV output of the adjustable reservoir in the t-th scheduling period is the u-th scenario, represents that the wind power output of the adjustable reservoir in the t-th scheduling period is the n-th scenario;

[0064] ③ Decision variable: Under various discrete reservoir storage capacity cases, for various inflow, PV output, and wind power output scenarios, the optimal end-of-period reservoir storage capacity S r,l (t) of the adjustable reservoir;

[0065] ④ State transition equation: S r (t) = S r (t - 1) + I r (t) - Q r (t);

[0066] ⑤ Recursive equation: During the scheduling period, under the satisfaction of various constraint conditions, seek the scheduling decision that maximizes the long-term average expected power generation of the basin's water-wind-solar integrated system;

[0067]

[0068] f A (·) = 0 (15)

[0069] In the formula, is the optimal total benefit value (MWh) when the initial reservoir storage capacity of the main tone complementary system in the t-th scheduling period is the k-th discrete reservoir storage capacity, and the i-th inflow scenario, u-th PV output scenario, and n-th wind power output scenario occur within the t-th scheduling period; is when the initial reservoir storage capacity of the main tone complementary system in the t-th scheduling period is the k-th discrete reservoir storage capacity, and the i-th inflow scenario, u-th PV output scenario, and n-th wind power output scenario occur within the t-th scheduling period, make the scheduling decision S r,l(t) represents the benefit during a time period, i.e., the power generation (MWh) of the main tone complementary system during that time period; is the average annual power generation (MWh) of other sub-complementary systems other than the non-main tone complementary system during this scheduling period, i.e., the current month; is the remaining benefit (MWh) of the basin water-wind-solar integrated system with this sub-complementary system as the main tone system (when the adjustable reservoir storage capacity of this sub-complementary system at the end of the t-th scheduling period is the l-th discrete reservoir storage capacity, and the j-th inflow scenario, the v-th PV output scenario, and the h-th wind power output scenario occur during the (t + 1)-th scheduling period); f A (·) = 0 is the boundary condition, that is, when each level of sub-complementary system performs the first reverse time-step recursive iteration calculation as the main tone complementary system, the remaining benefit at the A-th scheduling period is 0;

[0070] Calculation of the facing benefit: The facing stage total benefit of the basin water-wind-solar integrated system under this main tone complementary system calculated here is equal to the power generation benefit of this main tone complementary system plus the average annual scheduling benefit of other sub-complementary systems When it is the first successive approximation iteration calculation, it is the average annual scheduling benefit in the initial solution; when it is the 2nd, 3rd,... successive approximation iteration calculations, it is the updated average annual scheduling benefit of the simulated scheduling after the previous successive approximation iteration calculation;

[0071] Calculation of the remaining benefit: The remaining stage total benefit of the basin water-wind-solar integrated system under this main tone complementary system calculated here is equal to the maximum benefit under the optimal scheduling trajectory of the main tone complementary system, plus the average annual scheduling benefit of other sub-complementary systems;

[0072] Completing the calculation from the last time period A of the year to the first time period of the year by reverse time-step recursion is called one recursive iteration calculation, denoted as: Here, multiple recursive iteration calculations are required. For the subsequent recursive iteration calculations, the optimal benefit of the first scheduling period of the previous time is used as the remaining benefit of the A-th scheduling period of this recursive iteration calculation, that is Perform several recursive iteration calculations in sequence until ε is a minimum value, the recursive loop ends, and a stable scheduling decision table for this main tone complementary system is obtained;

[0073] Through the above process of solution, the optimal reservoir storage capacity at the end of each time period corresponding to each scheduling period of this main tone complementary system under each reservoir storage capacity, inflow, PV output, and wind power output scenario can be obtained, and it is recorded in the form of a scheduling decision table, as shown in Table 1. The data in the table are arranged in ascending order:

[0074] Table 1 Scheduling Decision Table

[0075]

[0076]

[0077] After determining all the scheduling periods of the sub complementary system, that is, the scheduling decision table for 12 months, long sequence simulation scheduling is carried out; given the initial water level, long sequence runoff, photovoltaic output and wind power output are used for multi-year simulation scheduling to obtain the scheduling process and update the scheduling process of the main sub complementary system;

[0078]

[0079] In the formula, is the updated storage capacity (m 3 ) at the end of each period during the scheduling period of the main sub complementary system in the first successive approximation iterative calculation;

[0080] (3) Then, optimize the next-level sub complementary system and perform SDP solution. The specific steps are the same as those in (2); it should be noted that the inflow runoff of the downstream sub complementary system is the sum of the outflow from the upstream sub complementary system simulation scheduling and the inflow from the interval;

[0081] Similarly, after determining all the scheduling periods of the sub complementary system, that is, the scheduling decision table for 12 months, multi-year simulation scheduling is carried out using long sequence runoff, photovoltaic output and wind power output to obtain the scheduling process; finally, through the first successive approximation iterative calculation, the updated scheduling processes of each-level sub complementary systems of the basin water-wind-solar integrated system are as follows:

[0082]

[0083] In the formula, each row represents the updated storage capacity (m 3 ) at the end of each period during the scheduling period of each-level sub complementary system (r = 1, 2,..., R) in the first successive approximation iterative calculation;

[0084] (4) The complete calculation of one successive approximation means that SDP is used to complete the solution of all sub complementary systems level by level from upstream to downstream, and the total generated electricity E iter and the total guarantee rate F iter of the basin water-wind-solar integrated system are solved, where iter is the iteration number of successive approximation; then, compare E iter and F iter with the results of the previous successive approximation iterative calculation; if |E iter+1 - E iter | < λ1 and |F iter+1 - F iterIf < λ2, where λ1 and λ2 are minimum values, the calculation stops. At this time, the scheduling decision tables of each level of sub-complementary systems obtained are the final optimized scheduling decision tables, which are used to guide future scheduling. If the iteration accuracy is not met, update the multi-year average water storage processes of each reservoir and return to step (2) for calculation.

[0085] When the actual inflow situation has occurred, according to the reservoir storage capacity and inflow situation of the current sub-complementary system, as well as the wind power output and photovoltaic power output obtained through forecasting during this period, look up the scheduling decision table for interpolation calculation to obtain the reservoir storage capacity at the end of this stage and complete the optimized scheduling decision.

[0086] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0087] 1. The successive approximation stochastic dynamic programming method for the integrated basin water-wind-solar system considering multiple resource uncertainties proposed by the present invention fully considers various uncertainty factors (runoff, photovoltaic power output, wind power output) in the system, and can provide optimal scheduling strategies for different input scenarios to better cope with the changes in the input of the integrated basin water-wind-solar system.

[0088] 2. The successive approximation stochastic dynamic programming method for the integrated basin water-wind-solar system considering multiple resource uncertainties proposed by the present invention can more realistically simulate the operation state of the integrated basin water-wind-solar system by considering the hydraulic connections between cascade reservoirs and between each level of sub-complementary systems, making the scheduling results closer to the actual requirements.

[0089] 3. The successive approximation stochastic dynamic programming method for the integrated basin water-wind-solar system considering multiple resource uncertainties proposed by the present invention innovatively combines the probability distribution models of multiple resources and the successive approximation algorithm. The uncertainties of multiple resources such as runoff, photovoltaic power output, and wind power output are described through fine probability distributions and state transition probability matrices, so as to accurately capture the system uncertainties. Then, the optimal solution is gradually approximated through step-by-step iteration, effectively solving the curse of dimensionality problem caused by multi-dimensional state variables in traditional methods and significantly improving the calculation efficiency. At the same time, the SDP-SA method dynamically adjusts decision variables in each step of the iteration process, enhancing the adaptability of the optimized scheduling strategy. The combination of this multiple resource probability distribution model and the successive approximation algorithm enables the method to more accurately and efficiently generate scheduling decisions that meet the actual requirements when facing complex and changeable actual working conditions, improving the overall scheduling efficiency of the integrated basin water-wind-solar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flow chart of the successive approximation stochastic dynamic programming method for the integrated basin water-wind-solar system considering multiple resource uncertainties in the embodiment of the present invention.

[0091] Figure 2 It is the optimized scheduling trajectory diagram of the sub-complementary system 1 in the embodiment of the present invention;

[0092] Figure 3 It is the optimized scheduling trajectory diagram of the sub-complementary system 2 in the embodiment of the present invention. Specific implementation manners

[0093] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0094] As Figure 1 shown, the successive approximation stochastic dynamic programming method for the integrated basin water-wind-solar system considering multiple resource uncertainties provided in this embodiment includes the following steps:

[0095] In step 1, the description of uncertainty is input. The input variables of the integrated basin water-wind-solar system include the inflow runoff, photovoltaic power output, and wind power output of each level of bundled sub-complementary systems. Here, it is considered that the runoff follows the Pearson type III distribution, and its probability distribution function is as follows:

[0096]

[0097] In the formula, f(I r (t)) is the probability of the inflow runoff of the sub-complementary system r in the t-th scheduling period; α, β, a0 are the shape, scale, and position parameters (α>0, β>0) respectively; Γ(α) is the gamma function of the parameter α.

[0098] The photovoltaic power output follows the Log-Normal distribution, and its probability distribution function is as follows:

[0099]

[0100] In the formula, is the probability of the photovoltaic power output of the sub-complementary system r in the t-th scheduling period; μ, σ are the mean and standard deviation of the logarithm of the photovoltaic power output value of the sub-complementary system r in the t-th scheduling period respectively.

[0101] The wind power output follows the Weibull distribution, and its probability distribution function is as follows:

[0102]

[0103] In the formula, is the probability of the wind power output of the sub-complementary system r in the t-th scheduling period; λ, k are the scale parameter and shape parameter respectively.

[0104] According to the above equations (1), (2), and (3), combined with the complexity of solving the integrated water, wind, and photovoltaic system in the basin and the representativeness of the input of water, wind, and photovoltaic resources, the number of characteristic discrete values of runoff, photovoltaic output, and wind power output is finally determined to be 3, 3, and 3. The specific characteristic discrete values and theoretical cumulative probability data of each sub-complementary system are shown in Tables 1 and 2 below (this method embodiment includes 2 sub-complementary systems, where sub-complementary system 1 is a water-wind-photovoltaic complementary system and sub-complementary system 2 is a water-photovoltaic complementary system):

[0105] Table 1 Characteristic discrete values of the input of sub-complementary system 1

[0106]

[0107] Table 2 Characteristic discrete values of the input of sub-complementary system 2

[0108]

[0109] In step 2, the solution of the transition probability matrix. Taking the data of January and February of the runoff of sub-complementary system 1 as an example, based on the 3 characteristic discrete values obtained in step 1, within the allowable numerical range of January and February, the runoff is divided into 9 discrete value intervals respectively.

[0110] (1) For the long sequence data with a total time period length of 61, all the annual data corresponding to January and February in the runoff sequence are taken out, a total of 61 years.

[0111] (2) For the 3×3 discrete interval combinations of January and February, count the number of years b in which the runoff in January and the runoff in February both fall into a certain discrete interval combination, then p ij =P(I r,j (t + 1)|I r,i (t)) = b / B.

[0112] (3) Similarly, the conditional transition probabilities of other discrete interval combinations can be obtained. Then the one-step transition probability matrix is:[[]]

[0113]

[0114] In the formula, p ij =P(I r,j (t + 1)|I r,i (t)) is the probability that when the runoff value of sub-complementary system r is I r,i (t),(i = 1, 2,..., m) in the t-th scheduling period and the runoff value is I r,j (t + 1),(j = 1, 2,..., m) in the t + 1-th scheduling period, and ∑p = 1.

[0115] Finally, the transfer probability matrix of runoff from January to February is obtained according to equation (4) as follows:

[0116]

[0117] In step 3, a complementary optimal scheduling model for the integrated water, wind, and solar power system in the basin is constructed.

[0118] The objective function is:

[0119]

[0120] In the formula, E is the total power generation (MWh) of the integrated water, wind, and solar power system in the basin; T and t are the total length and serial number of the scheduling period; R and r are the total number and serial number of the sub-complementary systems; are the hydropower output, wind power output, and photovoltaic output (MW) of the sub-complementary system r in the t-th scheduling period respectively; ΔT t is the number of hours (h) in the scheduling period; F is the total power generation guarantee rate of the integrated water, wind, and solar power system in the basin; N firm is the total guaranteed output (MW) of the integrated water, wind, and solar power system in the basin, is the number of scheduling periods in which the total output of the integrated water, wind, and solar power system in the entire scheduling period is greater than or equal to the total guaranteed output.

[0121] The constraint conditions include three aspects:

[0122] (1) Physical constraints for hydropower stations:

[0123] ① Water balance constraint

[0124] S r (t) = S r (t - 1) + I r (t) - Q r (t) (7)

[0125] In the formula, S r (t - 1), S r (t) are the reservoir storage capacities at the beginning and end of the adjustable reservoir in the sub-complementary system r in the t-th scheduling period (m 3 ); I r (t), Q r (t) are the inflow and outflow discharges of the adjustable reservoir in the sub-complementary system r in the t-th scheduling period (m 3 / s).

[0126] ② Water level constraint

[0127]

[0128] In the formula, Z r (t) , They are the minimum and maximum allowable water levels (m) of the adjustable reservoir in the sub-complementary system r during the t-th scheduling period, respectively. Generally, the minimum allowable water level is the dead water level, and the maximum allowable water level is the flood limit water level during the flood season and the normal storage water level during the non-flood season.

[0129] ③ Discharge constraint

[0130]

[0131] [[ID=^{9}]]In the formula, Q r (t), They are the minimum and maximum allowable discharge rates (m 3 / s) of the adjustable reservoir in the sub-complementary system r during the t-th scheduling period, respectively.

[0132] ④ Hydraulic connection

[0133] I r+1 (t) = I r (t) + I qj (t) (10)

[0134] In the formula, I r+1 (t) is the inflow rate (m 3 / s) of the adjustable reservoir in the sub-complementary system r + 1 during the t-th scheduling period, and I qj (t) is the lateral inflow (m 3 / s) between the sub-complementary systems r and r + 1 during the t-th scheduling period.

[0135] (2) For the power transmission constraints of each level of sub-complementary system:

[0136]

[0137] In the formula, is the guaranteed output (MW) of the sub-complementary system r; is the power transmission capacity limit (MW) of the sub-complementary system r.

[0138] (3) For the output constraints of the basin water-wind-solar integrated system:

[0139]

[0140] In the formula, N firm is the total guaranteed output (MW) of the basin water-wind-solar integrated system; N trans is the power grid transmission capacity limit (MW).

[0141] In step 4, first, clarify the representation method of time. In the calculation of solving the complementary optimal scheduling model of the basin water-wind-solar integrated system using SDP-SA, the scheduling period is 12 months (t = 1, 2,..., A, A = 12); in the simulation scheduling calculation, the scheduling period is the total number of periods in the long sequence (t = 1, 2,..., T, T = A × B, A is the number of months in a year, and B is the number of historical years of the scheduling period).

[0142] (1) Based on the feasible interval of the dead water level - normal storage level (flood limit level), assign initial values to the scheduling processes (water level change processes) of each level of sub-complementary systems in the basin water-wind-solar integrated system, and conduct simulation scheduling to solve the total power generation E of the basin water-wind-solar integrated system under the initial values 0 , power generation guarantee rate F 0 indexes. The initial scheduling processes of each level of sub-complementary systems are as follows:

[0143]

[0144] In the formula, each row represents the initial reservoir storage volume (m 3 ) of each level of sub-complementary systems (r = 1, 2,..., R) at each period during the scheduling period.

[0145] (2) Determine the main sub-complementary systems as 1, 2,..., R in sequence from upstream to downstream. In this patent, taking the optimized sub-complementary system 1 as an example, SDP is used for solution. Specifically:

[0146] ① Stage variable: Taking a month as the scheduling period, t = 1, 2,..., A, A = 12;

[0147] ② State variable: Discretize the reservoir storage volume in sub-complementary system 1 into 100 cases, and use the combination scenarios of the initial reservoir storage volume, inflow, photovoltaic power output, and wind power output at each period as multi-dimensional state variables, that is

[0148]

[0149] ③ Decision variable: Under various discrete storage volume cases, various inflow scenarios, various photovoltaic power output scenarios, and various wind power output scenarios, the optimal storage volume S r,l (t) at the end of the period of the adjustable reservoir;

[0150] ④ State transition equation: S r (t) = S r (t - 1) + I r (t) - Q r (t);

[0151] ⑤ Recursive equation: During the scheduling period, under the satisfaction of various constraint conditions, seek the scheduling decision that maximizes the multi-year average expected power generation of the basin water-wind-solar integrated system.

[0152]

[0153] f A (·) = 0 (15)

[0154] In the formula, is the optimal total benefit value (MWh) of the sub-complementary system 1 when the reservoir storage at the beginning of the t-th scheduling period is the k-th discrete storage, and the i-th inflow scenario, the u-th PV output scenario, and the n-th wind power output scenario occur within the t-th scheduling period; is the period benefit faced when making the scheduling decision S r,l (t) when the reservoir storage at the beginning of the t-th scheduling period of the sub-complementary system 1 is the k-th discrete storage, and the i-th inflow scenario, the u-th PV output scenario, and the n-th wind power output scenario occur within the t-th scheduling period, that is, the period power generation (MWh) of the main sub-complementary system; is the multi-year average power generation (MWh) of other sub-complementary systems other than the sub-complementary system 1 during this scheduling period (current month); is the period remaining benefit (MWh) of the basin water-wind-solar integrated system with the sub-complementary system 1 as the main regulating system (when the adjustable reservoir storage at the end of the t-th scheduling period of the sub-complementary system 1 is the l-th reservoir discrete storage, and the j-th inflow scenario, the v-th PV output scenario, and the h-th wind power output scenario occur within the t + 1-th scheduling period); f A (·) = 0 is the boundary condition, that is, when the sub-complementary system 1 conducts the first recursive iteration calculation as the main sub-complementary system, the remaining benefit in the A-th scheduling period is 0.

[0155] Completing the calculation from the last period A of the year to the first period of the year in reverse time steps is called a recursive iteration calculation, denoted as: For the subsequent recursive iteration calculations, the optimal benefit of the first scheduling period of the previous time is used as the remaining benefit of the A-th scheduling period of this recursive iteration calculation, that is Perform several recursive iteration calculations in sequence until (ε is a minimum value), the recursive loop ends, and a stable scheduling decision table of the sub-complementary system 1 is obtained.

[0156] Through the above process of solution, the optimal reservoir storage at the end of each period corresponding to each scheduling period of the main sub-complementary system 1 under each reservoir storage, each inflow scenario, each PV output scenario, and each wind power output scenario can be obtained, and it is recorded in the form of a scheduling decision table. The data in the table are arranged in ascending order:

[0157] Table 3 Scheduling decision table of the sub-complementary system 1

[0158]

[0159]

[0160] After determining the scheduling decision tables for all scheduling periods (12 months) of the sub-complementary system 1, long-term sequence simulation scheduling is carried out. Given the initial water level, long-term sequence runoff, photovoltaic output sequence, and wind power output sequence are used for multi-year simulation scheduling to obtain the scheduling process and update the scheduling process of this main sub-complementary system.

[0161]

[0162] In the formula, is the updated storage capacity (m 3 ) at the end of each period during the scheduling period of the sub-complementary system 1 in the first successive approximation iterative calculation.

[0163] (3) Then optimize the next-level sub-complementary system and perform SDP solution. The specific steps are the same as those in (2). It should be noted that the incoming runoff of the downstream sub-complementary system is the sum of the outflow from the upstream sub-complementary system's simulation scheduling and the inflow from the interval.

[0164] Similarly, after determining the scheduling decision tables for all scheduling periods (12 months) of this sub-complementary system, long-term sequence runoff, photovoltaic output sequence, and wind power output sequence are used for multi-year simulation scheduling to obtain the scheduling process. Finally, through the first successive approximation iterative calculation, the updated scheduling processes of each-level sub-complementary systems of the basin water-wind-solar integrated system are as follows:

[0165]

[0166] In the formula, each row represents the updated storage capacity (m 3 ) at the end of each period during the scheduling period of each-level sub-complementary systems (r = 1, 2,..., R) in the first successive approximation iterative calculation.

[0167] (4) The complete calculation for one successive approximation means that SDP is used to complete the solution of all sub-complementary systems level by level from upstream to downstream, and the total generated electricity E iter and the total guarantee rate F iter of the basin water-wind-solar integrated system are solved (iter is the iteration number of successive approximation). Then, compare E iter and F iter with the results of the previous successive approximation iterative calculation. If |E iter+1 - E iter | < λ1 and |F iter+1 - F iterIf < λ2 (where λ1 and λ2 are minimum values), the calculation stops. At this time, the scheduling decision tables of each level of the sub-complementary system obtained are the final optimized scheduling decision tables, which are used to guide future scheduling. If the iterative accuracy is not met, update the annual average water storage process of each reservoir and return to step (2) for calculation.

[0168] Finally, the optimal power generation of the integrated water, wind, and solar system in this basin obtained from step 4 is 32.68 billion kWh, and the power generation guarantee rate is 77%. Among them, the optimal hydropower, photovoltaic power generation, and wind power generation of sub-complementary system 1 are 15.42, 6.75, and 3.33 billion kWh respectively; the optimal hydropower and photovoltaic power generation of sub-complementary system 2 are 5.77 and 1.41 billion kWh respectively. The specific scheduling processes of sub-complementary systems 1 and 2 are shown by Figure 2 and Figure 3 respectively. Correspondingly, the optimal power generation of the integrated water, wind, and solar system in this basin obtained by the traditional successive approximation dynamic programming method (DPSA) is 33.32 billion kWh. Among them, the optimal hydropower, photovoltaic power generation, and wind power generation of sub-complementary system 1 are 15.62, 6.75, and 3.33 billion kWh respectively; the optimal hydropower and photovoltaic power generation of sub-complementary system 2 are 6.20 and 1.41 billion kWh respectively.

[0169] Meanwhile, in step 4, the final optimized scheduling decision tables of sub-complementary system 1 and sub-complementary system 2 are obtained, which are specifically shown in Tables 4 and 5 below. Since a relatively large number of discrete values of the initial reservoir storage at each time period are set in the process of solving the system, only partial scheduling decision tables of the 2 sub-complementary systems are shown in this method.

[0170] Table 4 Partial optimized scheduling decision table of sub-complementary system 1

[0171]

[0172]

[0173]

[0174] Table 5 Partial optimized scheduling decision table of sub-complementary system 2

[0175]

[0176]

[0177] In step 5, when the actual inflow situation has occurred, according to the current reservoir storage, inflow, photovoltaic output, and wind power output conditions, or the predicted runoff, photovoltaic output, and wind power output values, consult the scheduling decision table and perform multi-dimensional linear interpolation calculation to obtain the reservoir storage at the end of this stage and make a scheduling decision.

[0178] In summary, by introducing the explicit random optimization scheduling method and comprehensively considering the uncertainties of multiple resources and the complex interactions within the system, the present invention has significant advantages in improving the adaptability of complementary scheduling of the system, optimizing resource allocation, and enhancing scheduling benefits, providing a more accurate and efficient solution for the complementary optimal scheduling of the basin water-wind-solar integrated system.

[0179] It should be noted that, in this document, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device.

[0180] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A successive approximation stochastic dynamic programming method for a basin water, wind, and solar integrated system, characterized in that: The method includes the following steps: Step 1: Description of input uncertainty; sample a number of characteristic discrete values from the theoretical probability distribution functions of runoff, photovoltaic power output, and wind power output to represent the known continuous probability distribution, and describe the uncertainty of the input to the integrated water, wind, and solar power system in the basin. Step 2: Solution of the transition probability matrix; use a simple discrete-time Markov chain to describe the continuity of the time series of input variables. Step 3: Considering the objective function and constraint conditions of the integrated water, wind, and solar power system in the basin, construct a complementary optimization scheduling model. Step 4: Use the successive approximation-stochastic dynamic programming (SDP-SA) method for solution. Take the initial storage capacity, runoff, photovoltaic power output, and wind power output scenarios of the adjustable reservoirs in each sub-complementary system as multi-dimensional state variables, and the end-of-period storage capacity as the decision variable to derive the scheduling rules of the integrated water, wind, and solar power system in the basin, that is, the scheduling decision table. Step 5: When the actual inflow situation occurs, according to the reservoir storage capacity and inflow situation of the current sub-complementary system, as well as the wind power output and photovoltaic power output obtained through forecasting in this period, look up the scheduling decision table for interpolation calculation to obtain the reservoir storage capacity at the end of this stage and complete the optimized scheduling decision.

2. A successive approximation stochastic dynamic programming method for an integrated water, wind, and solar power system in a basin according to claim 1, characterized in that: Among them, In step 1, description of input uncertainty; the input variables of the integrated water, wind, and solar power system in the basin include the incoming runoff, photovoltaic power output, and wind power output of each bundled sub-complementary system; it is considered here that the runoff follows the Pearson type III distribution, and its probability distribution function is as follows: where f(I r (t)) is the probability of the inflow runoff of the sub-complementary system r in the t-th scheduling period; α, β, and a0 are the shape, scale, and location parameters respectively, with α > 0 and β > 0; Γ(α) is the gamma function of the parameter α; The photovoltaic power output follows a Log-Normal distribution, and its probability distribution function is as follows: In the formula, is the probability of the photovoltaic output of the sub-complementary system r in the t-th scheduling period; μ and σ are the mean and standard deviation of the logarithm of the photovoltaic output value of the sub-complementary system r in the t-th scheduling period; The wind power output follows a Weibull distribution, and its probability distribution function is as follows: In the formula, is the probability of the wind power output of the sub-complementary system r in the t-th scheduling period; λ and k are the proportionality parameter and the shape parameter respectively; After calibrating the parameters of the probability distribution function, assume that the runoff has m characteristic discrete values, and its theoretical cumulative probabilities are 1 / (m + 1), 2 / (m + 1),..., m / (m + 1). Inverse-derive the characteristic discrete values corresponding to each theoretical cumulative probability from the probability distribution function; similarly, the derivation of the characteristic discrete values of photovoltaic power output and wind power output will not be elaborated.

3. A successive approximation stochastic dynamic programming method for a basin water, wind and light integration system according to claim 1, 1]]Its characteristics are as follows: Among them, In step 2, solution of the transition probability matrix; taking runoff as an example, based on the m characteristic discrete values obtained in step 1, within the allowable numerical range of the t and t + 1 scheduling periods, divide the runoff into m discrete value intervals respectively. (1) For the long sequence data with a total time period of T, take out all the annual data corresponding to the t and t + 1 scheduling periods in the runoff sequence, a total of B years. (2) For the m×m discrete interval combinations in the t and t+1 scheduling periods, count the number of years b in which the runoff in the t period and the runoff in the t+1 period both fall into a certain discrete interval combination. Then p ij = P(I r,j (t + 1)|I r,i (t)) = b / B; (3) Similarly, the conditional transition probabilities of other discrete interval combinations can be obtained; then the one-step transition probability matrix is: where p ij = P(I r,j (t + 1)|I r,i (t)) is the probability that when the runoff value of the sub-complementary system r is I r,i (t), (i = 1, 2,..., m), and the runoff value in the (t + 1)-th scheduling period is I r,j (t + 1), (j = 1, 2,..., m), and ∑p = 1.

4. A successive approximation stochastic dynamic programming method for an integrated water, wind, and solar power system in a basin according to claim 1, characterized in that: Among them, In step 3, construct a complementary optimization scheduling model for the integrated water, wind, and solar power system in the basin. The objective function is: Wherein, E is the total power generation (MWh) of the integrated water, wind and solar system in the basin; T and t are the total length and serial number of the scheduling period; R and r are the total number and serial number of the sub-complementary systems; are the hydropower output, wind power output and photovoltaic output (MW) of the sub-complementary system r in the t-th scheduling period respectively; ΔT t is the number of hours (h) in the scheduling period; F is the total power generation guarantee rate of the integrated water, wind and solar system in the basin; N firm is the total guaranteed output (MW) of the integrated water, wind and solar system in the basin, is the number of scheduling periods during the entire scheduling period when the total output of the integrated water, wind and solar system in the basin is greater than or equal to the total guaranteed output; [[ID=]]19]]The constraint conditions include 3 aspects: 1) Physical constraints for hydropower stations: ① Water balance constraint S r S(t) = r S(t - 1)+I r S(t)-Q r S(t) (7) Where, S r (t - 1) and S r (t) are the reservoir storage volumes of the adjustable reservoir in the sub - complementary system r at the beginning and end of the t - th scheduling period respectively (m 3 ); I r (t) and Q r (t) are the inflow and outflow discharges of the adjustable reservoir in the sub - complementary system r during the t - th scheduling period respectively (m 3 / s); ② Water level constraint wherein, Z r (t) , are respectively the minimum allowable water level and the maximum allowable water level (m) of the adjustable reservoir in the sub-complementary system r during the t-th scheduling period; generally, the minimum allowable water level is the dead water level, and the maximum allowable water level is the flood limit water level during the flood season and the normal storage water level during the non-flood season; ③ Flow constraint where Q r (t), are respectively the minimum allowable discharge and the maximum allowable discharge of the adjustable reservoir in the sub-complementary system r during the t-th scheduling period (m 3 / s); ④ Hydraulic connection I r+1 I(t) = I r + I(t) qj × 10 Where, I r+1 (t) is the inflow (m 3 / s) of the adjustable reservoir in the sub-complementary system r + 1 during the t-th scheduling period, and I qj (t) is the lateral inflow (m 3 / s) between the sub-complementary system r and the sub-complementary system r + 1 during the t-th scheduling period; 2) Power transmission constraints for each sub-complementary system: Wherein, is the guaranteed output (MW) of the sub-complementary system r; is the power transmission capacity limit (MW) of the sub-complementary system r; 3) Power transmission constraints for the integrated water, wind, and solar power systems in the basin: Where, N firm is the total guaranteed output (MW) of the integrated water, wind and solar power system in the basin; N trans is the grid transmission capacity limit (MW).

5. The successive approximation stochastic dynamic programming method for a basin water-wind-light integration system according to claim 1, Its characteristics are: Among them, in step 4, the proposed successive approximation stochastic dynamic programming (SDP-SA) method belongs to an explicit stochastic optimization method. This method adopts the idea of successive iterative approximation when solving, and only uses SDP to solve one sub-complementary system in the watershed water-wind-solar integrated system each time; due to the setting of boundary conditions, recursive iterative calculations are required in the internal solution process of SDP, and it is assumed that the scheduling process of other sub-complementary systems is a multi-year average scheduling process; after the SDP is used to solve a sub-complementary system and obtain a provisional optimized scheduling decision table, the simulated scheduling of multi-year inputs, i.e., runoff, photovoltaic output, and wind power output, is used as the multi-year average scheduling update process of the sub-complementary system in the next successive iterative approximation process, and the scheduling process of other sub-complementary systems when solving SDP is then continuously updated through the successive iterative approximation solution process; finally, after the total power generation and total power generation guarantee rate of the watershed water-wind-solar integrated system are iteratively solved to convergence, the optimal scheduling strategy set of each sub-complementary system in the watershed water-wind-solar integrated system can be obtained; The specific steps are as follows: First, we need to clarify the time representation method. In the calculation of the SDP-SA solution for the complementary optimization scheduling model of the integrated water, wind and solar system in the basin, the scheduling period is 12 months, that is, t = 1, 2, ..., A, A = 12. In the simulation scheduling calculation, the scheduling period is the total number of periods in the long sequence, that is, t = 1, 2, ..., T, T = A × B, where A is the number of months in a year and B is the number of years of the scheduling period. (1) Based on the feasible interval of the dead water level - normal storage level, that is, the flood control limited water level, assign initial values to the scheduling process of each level of sub - complementary systems in the basin water - wind - solar integrated system, that is, the water level change process, and conduct simulated scheduling to solve the total power generation E of the basin water - wind - solar integrated system under the initial values. 0 and the power generation guarantee rate F 0 index; The initial scheduling processes of each level of sub - complementary systems are as follows: In the formula, each row represents the initial storage capacity (m 3 ) of each level of the sub-complementary system, i.e., r = 1, 2,..., R, at each time period within the scheduling period; (2) From upstream to downstream, the main complementary subsystems are determined as 1, 2, ..., R. First, the complementary subsystem 1 is optimized and solved using SDP. Specifically: ① Phase variables: Monthly scheduling period, t = 1, 2, ..., A, A = 12; ② State variables: The reservoir storage capacity in the main sub-complementary system is discretized into K cases, and the combined scenarios of the reservoir storage capacity, inflow, PV output, and wind power output at the beginning of each time period are used as multi-dimensional state variables, that is Among them, S r,k (t - 1) represents that the initial storage of the adjustable reservoir in the t-th scheduling period is the k-th case, I r,i (t) represents that the inflow of the adjustable reservoir in the t-th scheduling period is the i-th scenario, represents that the photovoltaic output of the adjustable reservoir in the t-th scheduling period is the u-th scenario, represents that the wind power output of the adjustable reservoir in the t-th scheduling period is the n-th scenario; ③ Decision variables: the optimal storage capacity S(t) of the adjustable reservoir at the end of each period under various discrete storage capacities, various scenarios of inflow, PV output, and wind power output r,l (t); ④ State transition equation: S r (t) = S r (t - 1) + I r (t) - Q r (t); ⑤ Recursive equation: Under various constraints, seek the scheduling decision that maximizes the average expected power generation of the integrated water, wind and solar system in the basin over many years; f A (·)＝0 (15) In the formula, is the optimal total benefit value (MWh) of the main tone complementary system when the initial reservoir storage at the t-th scheduling period is the k-th discrete reservoir storage, and the i-th inflow scenario, the u-th photovoltaic power output scenario, and the n-th wind power output scenario occur during the t-th scheduling period; is the period facing benefit when the initial reservoir storage of the main tone complementary system at the t-th scheduling period is the k-th discrete reservoir storage, and the i-th inflow scenario, the u-th photovoltaic power output scenario, and the n-th wind power output scenario occur during the t-th scheduling period, that is, the period power generation (MWh) of the main tone complementary system; r,l (t); is the multi-year average power generation (MWh) of other sub-complementary systems outside the non-main tone complementary system during this scheduling period, that is, the current month; is the period remaining benefit (MWh) of the integrated water, wind and solar system in the basin with this sub-complementary system as the main tone system (when the adjustable reservoir storage of this sub-complementary system at the end of the t-th scheduling period is the l-th reservoir discrete storage, and the j-th inflow scenario, the v-th photovoltaic power output scenario, and the h-th wind power output scenario occur during the t + 1-th scheduling period); f A (·) = 0 is the boundary condition, that is, the remaining benefit of each level of sub-complementary system during the first reverse time-step recursive iteration calculation as the main tone complementary system is 0 at the A-th scheduling period; Calculation of the facing benefits: The total facing benefits of the basin water-wind-solar integrated system under this dominant complementary system are calculated here, which is equal to the power generation benefits of this dominant complementary system plus the average annual scheduling benefits of other sub-complementary systems When it is the first successive approximation iteration calculation, it is the average annual scheduling benefits in the initial solution; when it is the second, third,... successive approximation iteration calculation, it is the updated average annual scheduling benefits of the simulated scheduling after the previous successive approximation iteration calculation; Calculation of residual benefits: The total residual benefits of the integrated water, wind, and solar power system in the basin under the main regulation sub-complementary system are calculated here. This is equal to the maximum benefit under the optimal scheduling trajectory of the main regulation complementary system plus the multi-year average scheduling benefits of other sub-complementary systems. Completing the calculation by recursively pushing backward from the last period A within the year until the first period of the year is called a single recursive iteration calculation, which is expressed as: Multiple recursive iteration calculations are required here. For each subsequent recursive iteration calculation, the optimal benefit of the first scheduling period in the previous calculation is used as the remaining benefit of the A scheduling period in the current recursive iteration calculation, that is Perform a number of recursive iteration calculations in sequence until ε is a minimum value, the recursive loop ends, and a stable scheduling decision table for the main tone-complementary system is obtained; Through the above process, we can obtain the optimal reservoir capacity at the end of each scheduling period for each scenario of reservoir capacity, inflow, photovoltaic output, and wind power output for the main-mode complementary system. This is recorded in the form of a scheduling decision table, see Table 1. The data in the table are arranged in ascending order: Table 1 Scheduling decision table After determining all scheduling periods for the sub-complementary system, i.e., a 12-month scheduling decision table, a long-sequence scheduling simulation is performed. Given an initial water level, a multi-year scheduling simulation is performed using a long-sequence runoff, photovoltaic output, and wind power output to obtain the scheduling process and update the scheduling process of the main-modulation sub-complementary system. In the formula, is the updated storage capacity (m 3 ) at the end of each period within the scheduling period in the first successive approximation iteration for the main tone complementary system; (3) Then, optimize the next-level sub-complementary system and perform SDP solution. The specific steps are the same as those in 2). It should be noted that the incoming runoff into the downstream sub-complementary system is the sum of the outflow from the upstream sub-complementary system's simulated scheduling and the inflow from the interval. Similarly, after determining all the scheduling periods of this sub-complementary system, that is, the scheduling decision table for 12 months, use the long-term runoff, PV output, and wind power output for multi-year simulated scheduling to obtain the scheduling process. Finally, through the first successive approximation iterative calculation, the updated scheduling processes of the sub-complementary systems at all levels of the basin's integrated water, wind, and solar system are as follows: In the formula, each row represents the updated storage capacity (m 3 ) at the end of each time period within the scheduling period for each level of the sub-complementary system (r = 1, 2,..., R) in the first successive approximation iterative calculation; (4) A complete successive approximation calculation means that the SDP is used level by level from upstream to downstream to complete the solution of all sub-complementary systems, and the total generated electricity E of the basin's integrated water, wind, and solar power system is solved. iter And the total guarantee rate F iter , where iter is the number of iterations of successive approximation; then, compare E iter and F iter with the results of the previous successive approximation iterative calculation; if |E iter +1 - E iter | < λ1 and |F iter+1 - F iter | < λ2, where λ1 and λ2 are minimum values, then the calculation stops, and the scheduling decision table of each level of sub-complementary system obtained at this time is the final optimized scheduling decision table for guiding future scheduling; if the iterative accuracy is not met, update the multi-year average water storage process of each reservoir and return to step (2) for calculation; When the actual inflow situation occurs, according to the reservoir storage capacity and inflow situation of the current sub-complementary system, as well as the wind power output and PV output obtained through forecasting for this period, look up the scheduling decision table for interpolation calculation to obtain the reservoir storage capacity at the end of this stage and complete the optimal scheduling decision.

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