Cascade reservoir dispatching method and system
By constructing a medium- and long-term random optimization scheduling model and introducing orthogonal experimental design, the problem of poor scheduling effect of cascade reservoirs is solved, efficient scheduling decisions are achieved, the problems of computational complexity and dimensional disasters are alleviated, and the computing efficiency is improved.
Patent Information
- Application Number
- CN202510561399.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-30
- Publication Date
- 2025-08-12
AI Technical Summary
The existing medium- and long-term scheduling methods for cascade reservoirs have the problem of poor scheduling effect, which is mainly due to the difficulty in accurately predicting medium- and long-term runoff and the complexity of reservoir operation, which leads to difficulties in solving and presents random, high-dimensional, and non-convex nonlinear characteristics.
A medium- and long-term random optimization scheduling model for cascade reservoirs is constructed, and the random dynamic programming method is used to express the randomness of runoff, and the optimization solution is carried out in combination with the random dynamic programming method. Orthogonal experimental design is introduced during the solution process. The combination of reservoir capacity and runoff state is determined through discrete treatment and Cartesian product operation, which reduces the combined traversal calculation amount.
On the premise of ensuring the calculation accuracy, the calculation efficiency is greatly improved, and the optimal scheduling decisions for the cascade reservoir are quickly obtained, which alleviates the dimensional disaster problem and improves the calculation efficiency and scheduling effect.
Smart Images
Figure CN120471730A_ABST
Abstract
Description
Technical Field
[0001] The invention discloses a cascade reservoir scheduling method and system, in particular a medium- and long-term scheduling method and system for cascade reservoirs based on improved random dynamic programming, belonging to the technical field of reservoir scheduling. Background Art
[0002] The medium- and long-term operation of cascade reservoirs is a classic problem in reservoir operation. It typically uses objective functions such as maximizing power generation and overall benefits, taking into account constraints such as runoff inflow, water balance, cascade hydropower connections, reservoir operating limitations, and hydropower generation functions, to determine the optimal reservoir operation decision through optimization calculations. Decision variables include reservoir water level, outflow, and power generation output at various times during the operation period. Due to the difficulty in accurately predicting medium- and long-term runoff and the inherent complexity of reservoir operation, the medium- and long-term operation of cascade reservoirs exhibits stochasticity, high dimensionality, and non-convex nonlinearity. This makes solving the problem challenging and leads to poor operation results. Summary of the Invention
[0003] The purpose of the present invention is to provide a cascade reservoir scheduling method and system to solve the technical problem of poor scheduling effect in existing cascade reservoir scheduling methods.
[0004] A first aspect of the present invention provides a cascade reservoir scheduling method, comprising:
[0005] Step 1: Construct a medium- and long-term stochastic optimization scheduling model for cascade reservoirs. The state variables of the medium- and long-term stochastic optimization scheduling model include runoff and storage capacity.
[0006] Step 2: Based on the storage capacity data and runoff data of each reservoir in the cascade reservoirs, the storage capacity state combination and runoff state combination of the cascade reservoirs are determined through discretization processing, Cartesian product operation, and orthogonal experimental design.
[0007] Step 3: Determine the storage capacity state transfer equation and runoff state transfer probability of each reservoir in adjacent time periods according to the storage capacity state combination and the runoff state combination.
[0008] Step 4: Combining the reservoir capacity state transition equation and the runoff state transition probability, the medium- and long-term stochastic optimization scheduling model is optimized and solved using a stochastic dynamic programming method to obtain a scheduling plan for the cascade reservoirs in each time period.
[0009] Preferably, step 2 specifically includes:
[0010] According to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoirs, the storage capacity state combination of the cascade reservoirs is determined through discretization processing, Cartesian product operation and orthogonal experimental design.
[0011] According to the runoff observation value of each reservoir and the extreme values of the historical runoff data, the runoff state combination of the cascade reservoirs is determined through discretization processing and Cartesian product operation.
[0012] Preferably, according to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoirs, the storage capacity state combination of the cascade reservoirs is determined through discretization processing, Cartesian product operation, and orthogonal experimental design, specifically including:
[0013] According to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoirs, the initial storage capacity state combination of the cascade reservoirs is determined through discretization processing and Cartesian product operation.
[0014] An orthogonal table is constructed based on the discrete quantity of the number of reservoirs and storage capacity status in the cascade reservoirs.
[0015] The orthogonal table is used to sample the initial storage capacity state combination to obtain the final storage capacity state combination of the cascade reservoirs.
[0016] Preferably, according to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoirs, the initial storage capacity state combination of the cascade reservoirs is determined by discretization processing and Cartesian product operation, specifically including:
[0017] Get the discrete quantity of preset storage capacity status for each reservoir.
[0018] According to the preset discrete number of storage capacity states, dead storage capacity and maximum storage capacity, the discrete value of the storage capacity state corresponding to each reservoir is determined through discretization processing to obtain the storage capacity state set.
[0019] According to the storage capacity state set of each reservoir, the initial storage capacity state combination of the cascade reservoirs is determined through Cartesian product operation.
[0020] Preferably, in step 3, the storage capacity state transfer equation of each reservoir in adjacent time periods is determined according to the storage capacity state combination, specifically including:
[0021] The storage capacity status of each reservoir in time period t and time period t+1 is obtained from the storage capacity status combination.
[0022] According to the storage capacity status of time period t and time period t+1, the storage capacity state transfer equation of each reservoir in adjacent time periods is determined.
[0023] Preferably, in step 3, determining the runoff state transition probability of each reservoir in adjacent time periods according to the runoff state combination specifically includes:
[0024] The runoff state of each reservoir in time period t-1 and time period t is obtained from the runoff state combination.
[0025] According to the runoff status of period t-1 and period t, the runoff state transition probability of each reservoir in adjacent periods is determined.
[0026] Preferably, the runoff state transition probability of each reservoir in adjacent time periods is determined based on the runoff state in time period t-1 and time period t, specifically including:
[0027] Determine the total number of times runoff state ni appears in each reservoir during period t-1 and the number of transitions from runoff state ni in period t-1 to runoff state nj in period t.
[0028] The runoff state transfer probability of each reservoir in adjacent time periods is determined according to the total number of times and the number of transfers.
[0029] Preferably, the mid- to long-term stochastic optimization scheduling model is optimized and solved using a stochastic dynamic programming method, specifically including:
[0030] The mid- to long-term stochastic optimization scheduling model is optimized and solved using the reverse recursion in the stochastic dynamic programming method.
[0031] A second aspect of the present invention provides a cascade reservoir scheduling system based on the above-mentioned cascade reservoir scheduling method, comprising a model building module, a first determination module, a second determination module and a scheduling module;
[0032] The model building module is used to build a medium- and long-term stochastic optimization scheduling model for cascade reservoirs, and the state variables of the medium- and long-term stochastic optimization scheduling model include storage capacity and runoff.
[0033] The first determination module is used to determine the storage capacity state combination and runoff state combination of the cascade reservoirs according to the storage capacity data and runoff data of each reservoir in the cascade reservoirs through discretization processing, Cartesian product operation, and orthogonal experimental design.
[0034] The second determination module is used to determine the storage capacity state transfer equation and runoff state transfer probability of each reservoir in adjacent time periods in combination with the storage capacity state combination and the runoff state combination.
[0035] The scheduling module is used to combine the storage capacity state transfer equation and the runoff state transfer probability, and use the stochastic dynamic programming method to optimize and solve the medium- and long-term stochastic optimization scheduling model to obtain a scheduling plan for the cascade reservoirs in each time period.
[0036] Compared with the prior art, the cascade reservoir scheduling method and system of the present invention have the following beneficial effects:
[0037] The present invention utilizes a Markov process to represent the randomness of runoff and constructs a medium- and long-term stochastic optimization scheduling model for cascade reservoirs. The model is solved using a stochastic dynamic programming method. An orthogonal experimental design is introduced into the traversal of the combined storage capacity and runoff states for each time period to reduce the computational complexity of the combined traversal and alleviate the curse of dimensionality. The optimal scheduling decision for the cascade reservoirs is obtained through reverse recursive calculation. The present invention introduces an orthogonal experimental design into the process of solving the cascade reservoir scheduling model using the stochastic dynamic programming method. This significantly reduces the number of combined traversals and the computational complexity of the algorithm, significantly improving computational efficiency while ensuring computational accuracy, and enabling the rapid acquisition of a cascade reservoir scheduling decision plan. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Figure 1 The figure is a flow chart of a method for scheduling cascade reservoirs according to an embodiment of the present invention.
[0039] Figure 2 Schematic diagram of the spatial combination of runoff states of cascade reservoirs in an embodiment of the present invention.
[0040] Figure 3 (a) is the state combination space distribution before the introduction of orthogonal experimental design, and (b) is the state combination space distribution after the introduction of orthogonal experimental design. DETAILED DESCRIPTION
[0041] In the following description, specific details such as particular system structures and techniques are provided for purposes of illustration, not limitation, to facilitate a thorough understanding of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
[0042] A first aspect of an embodiment of the present invention provides a cascade reservoir scheduling method, such as Figure 1 Shown, including:
[0043] Step 1: Construct a medium- and long-term stochastic optimization scheduling model for cascade reservoirs. The state variables of the medium- and long-term stochastic optimization scheduling model include runoff and storage capacity.
[0044] The embodiment of the present invention takes the maximum expected value of power generation of cascade reservoirs as the objective function, regards reservoir runoff as a random variable, considers constraints such as cascade hydraulic connections, water balance equations, hydropower generation functions, and hydropower operation boundaries, and constructs a medium- and long-term random optimization scheduling model for cascade reservoirs.
[0045] 1.1 Scheduling Objective Function
[0046] Taking the maximum expected value of power generation of cascade reservoirs as the objective function, it is expressed as follows:
[0047]
[0048] Where: t, i are the time period number and reservoir number respectively; T, I are the number of scheduling time periods and reservoirs respectively; PH i,t is the output of reservoir i in time period t; Δt is the time conversion coefficient; represents the expected value function, that is, the expected value of power generation after considering the probability distribution of the runoff random variable.
[0049] 1.2 Operational constraints
[0050] During the operation of cascade reservoirs, constraints such as cascade hydraulic connections, water balance equations, water level-storage capacity function relationship, tailwater level-discharge flow function relationship, head constraints, hydropower generation functions, and hydropower operation boundaries need to be met.
[0051] 1.2.1 Cascade hydraulic connection
[0052]
[0053] Where: is the inflow of reservoir i in period t; kh is the number of the upstream reservoir of reservoir i; τ i is the set of upstream reservoirs of reservoir i; Q kh,t is the discharge flow of reservoir kh in time period t; i,t is the interval runoff of reservoir i in period t, which is a random variable.
[0054] 1.2.2 Water balance equation
[0055]
[0056] Where: S i,t is the initial storage capacity of reservoir i in period t, S i,t+1 is the initial storage capacity of reservoir i in time period t+1, Q i,t is the outflow of reservoir i in period t.
[0057] 1.2.3 Water level-reservoir capacity function relationship
[0058]
[0059] Where: ZB i,t is the initial water level of reservoir i in time period t; is the water level-capacity function relationship of reservoir i.
[0060] 1.2.4 Tailwater level-discharge function relationship
[0061]
[0062] In the formula: ZE i,t is the tailwater level of reservoir i in time period t; is the tailwater level-discharge function relationship of reservoir i.
[0063] 1.2.5 Head constraint
[0064]
[0065] Where: ZH i,t is the net water head of power generation of reservoir i in period t; ZB i,t+1 is the initial water level of reservoir i in time period t+1; is the head loss of reservoir i, which is a constant.
[0066] 1.2.6 Hydropower Generation Function
[0067] PH i,t =η i Q i, ZH i,t (7)
[0068] Where: η i is the comprehensive output coefficient of reservoir i, which is a constant.
[0069] Combining equations (4)-(7), we get
[0070]
[0071] In formula (8), S i,t+1 Can be obtained by i,t 、S i,t , Q i,t Calculated, η i 、 is a constant, so PH i,t Only with ξ i,t 、S i,t , Q i,t The formula (8) can be further expressed as:
[0072] PH i,t =g i (ξ i,t ,S i,t ,Q i,t ) (9)
[0073] Where: g i is the power generation function of reservoir i, which is calculated by the simultaneous equations (4)-(7).
[0074] 1.2.7 Hydropower Operation Boundary
[0075]
[0076] Where: are the lower and upper limits of the storage capacity of reservoir i in time period t, respectively; are the lower and upper limits of the discharge flow of reservoir i in time period t, respectively; are the lower and upper limits of the output of reservoir i in time period t, respectively; are the storage capacities of reservoir i at the beginning and end of the scheduling period, respectively.
[0077] Step 2: Based on the storage capacity data and runoff data of each reservoir in the cascade reservoirs, the storage capacity state combination and runoff state combination of the cascade reservoirs are determined through discretization processing, Cartesian product operation, and orthogonal experimental design.
[0078] Step 2.1: Based on the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoirs, determine the storage capacity state combination of the cascade reservoirs through discretization processing, Cartesian product operation, and orthogonal experimental design, specifically including:
[0079] Step 2.1.1: Based on the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoirs, determine the storage capacity state set of each reservoir and the initial storage capacity state combination of the cascade reservoirs through discretization processing and Cartesian product operation. Specifically:
[0080] A. Obtain the discrete number of preset storage capacity states for each reservoir.
[0081] In the embodiment of the present invention, the storage capacity state space of reservoir i is defined as Where: m and M are the state number and state quantity respectively, and the discrete number of preset storage capacity states of each reservoir is M.
[0082] B. According to the preset discrete number of storage capacity states, dead storage capacity and maximum storage capacity, the discrete value of the storage capacity state corresponding to each reservoir is determined to obtain the storage capacity state set.
[0083] The embodiment of the present invention discretizes the storage capacity state and determines the discrete value of the storage capacity state according to the following formula:
[0084]
[0085] Where, s i 、 are the dead storage capacity and maximum storage capacity of reservoir i, respectively; m and M are the state number and discrete number of storage capacity states in the storage capacity state space, respectively.
[0086] C. Based on the storage capacity state set of each reservoir, the initial storage capacity state combination of the cascade reservoirs is obtained through Cartesian product operation.
[0087]
[0088] Where: represents the Cartesian product operator; is the storage capacity state space of the cascade reservoirs.
[0089] There are M I Different combinations of cascade storage capacity states, for any cascade storage capacity state combination a(1≤a≤M I ), expressed as:
[0090] sv a =[sv 1,a ,…,sv i,a …,sv I,a ] (13)
[0091] Where: sv a is the ath state vector in the step storage capacity state space; sv i,a is the state of reservoir i in the cascade storage capacity state a, satisfying
[0092] Step 2.1.2: Construct an orthogonal table based on the number of reservoirs and the discrete quantity of storage capacity status in the cascade reservoirs.
[0093] Orthogonal experimental design is a multi-factor and multi-level experimental design method. It uses an orthogonal table to extract a small number of representative experiments from a comprehensive experiment for testing. The sample experimental combination extracted has the characteristics of balanced dispersion, neatness and comparability, which can significantly reduce the number of experiments without losing accuracy. In the subsequent application of the random dynamic programming method to solve the scheduling model, the embodiment of the present invention uses the initial storage capacity S of the time period. t , storage capacity at the end of the period S t+1 The factors are regarded as experimental factors, and the number of discrete states of each factor is the experimental level of each factor, which forms a multi-factor and multi-level experiment.
[0094] The orthogonal table constructed in the embodiment of the present invention is specifically as follows: in time period t, according to the total number of reservoirs I and the discrete number of storage capacity states M in the cascade reservoirs, an orthogonal table L is constructed. B (M I ), where L represents the orthogonal table; B is the number of rows in the orthogonal table, that is, the number of experiments required. Orthogonal table L B (M I ) is obtained by querying the existing standard orthogonal table according to the parameters M and I.
[0095] Step 2.1.3: Use orthogonal table to combine the initial storage capacity of cascade reservoirs Sampling is carried out to obtain the final storage capacity status combination of the cascade reservoirs.
[0096] The embodiment of the present invention determines the combined traversal scheme of the cascade reservoir states according to the orthogonal table. Specifically, according to the constructed orthogonal table L B (M I ), and obtain B storage capacity states of the cascade reservoirs at the beginning and end of the period respectively. Then the number of combinations of storage capacity states at the beginning and end is given by M 2I Lowered to B 2 The experimental combinations obtained by sampling in orthogonal experimental design are evenly distributed in the state space, have strong representativeness and typicality, and can better guarantee the calculation accuracy.
[0097] Step 2.2: Based on the runoff observations of each reservoir and the extreme values of the historical runoff data, the runoff state combination of the cascade reservoirs is determined through discretization processing and Cartesian product operation.
[0098] The present invention uses a Markov process to represent runoff randomness. A Markov process is a type of random process with the following properties: given the current state, the probability distribution of the future state of a random variable depends only on the current state and is independent of the historical state. This property is also called the Markov property. On medium- to long-term timescales (such as monthly or quarterly), the runoff in the next reservoir period is only strongly correlated with the runoff level in the current period and is less affected by runoff in earlier periods. This satisfies the Markov property, and therefore, the Markov process can be used to model medium- and long-term runoff randomness.
[0099] Define the runoff state space of reservoir i Where: n and N are the state number and the number of states respectively. Each state q in i,n Represents a runoff interval range, expressed as Determine the state q according to the principle of equal distance division i,n The range is as follows:
[0100]
[0101] Where: are the minimum and maximum historical runoff of reservoir i, respectively.
[0102] If the runoff random variable ξ i,t The observed value is in the interval q i,n , then the runoff of reservoir i in period t is considered to be in state n.
[0103] The runoff state space of the cascade reservoirs is obtained by performing Cartesian product operations on the runoff state spaces of each reservoir, as shown in the following formula:
[0104]
[0105] Where: represents the Cartesian product operator; is the runoff state space of cascade reservoirs.
[0106] Figure 2 Schematic diagram of the spatial combination of runoff states of cascade reservoirs. There are N I There are different cascade runoff states. For any cascade runoff state k (1≤k≤K), it can be expressed as:
[0107] qs k =[qs 1,k ,…,qs i,k …,qs I,k ] (16)
[0108] Where: qs k is the kth state vector in the runoff state space of the cascade reservoirs; K is the number of states, satisfying K=N I ;qs i,k is the state of reservoir i in the cascade runoff state k, satisfying
[0109] When the embodiment of the present invention uses the random dynamic programming method to optimize the scheduling model, it is necessary to traverse and optimize the state combination of storage capacity and runoff. t , storage capacity at the end of the period S t+1 、Period runoffζ t The number of states is M I 、M I 、N I , so after the combination, a total of (M 2 N) I The whole scheduling cycle needs T(M 2 N) I The time complexity of the algorithm is O(TM 2 IN I ), which grows exponentially with the number of cascade reservoirs I, and faces the challenge of the curse of dimensionality.
[0110] To solve the above problem, the embodiment of the present invention uses an orthogonal table to sample the initial storage capacity state combination to obtain the storage capacity state combination of each reservoir. After further considering the runoff state, the number of storage capacity and runoff state combinations is given by (M 2 N) I Lowered to B 2 N I , the calculation scale is greatly reduced and the calculation efficiency is greatly improved.
[0111] Taking T = 12, M = 3, N = 3, and I = 3 as an example, in any time period t, the number of states of the initial storage capacity, the final storage capacity, and the runoff are all 27. After the combination of storage capacity and runoff states, 19683 traversal calculations are required. The entire scheduling cycle requires 2.4×10 5 After the orthogonal experimental design is introduced, the parameters M = 3, I = 3 are used to query the standard orthogonal table to obtain the orthogonal table L9 (3 3 ), as shown in Table 1. In Table 1, each row represents an experimental scheme, and there are 9 experimental schemes in total. Taking experiment (5) as an example, factors I, II, and III select the 2nd, 2nd, and 3rd factor levels respectively to form the experimental scheme. Then, according to the obtained orthogonal table L9(3 3 ), the states of initial storage capacity, final storage capacity, and runoff in each period t are 9, 9, and 27 respectively. After the combination, 2187 traversal calculations are required in each period, and 2.6×10 4 When the sampling combination is used for subsequent random dynamic programming, the improved random dynamic programming after the orthogonal experimental design is introduced in the present invention, and the amount of state combination traversal calculation is reduced by 89% compared with the conventional random dynamic programming. In addition, the spatial distribution of state combinations before and after the introduction of the orthogonal experimental design is shown in the figure below. Figure 3 As shown in Figure 2, it can be seen that the state combinations obtained through orthogonal experimental design are evenly distributed in the state space, have strong representativeness and typicality, and can better guarantee the calculation accuracy.
[0112] Table 1L9(3 3 )Orthogonal array
[0113]
[0114] Step 3: Determine the storage capacity state transfer equation and runoff state transfer probability of each reservoir in adjacent time periods based on the storage capacity state combination and the runoff state combination, specifically including:
[0115] Step 3.1: Obtain the storage capacity state of each reservoir in time period t and time period t+1 from the storage capacity state combination, and determine the storage capacity state transfer equation of each reservoir in adjacent time periods based on the storage capacity state in time period t and time period t+1.
[0116] In the embodiment of the present invention, at time period t, the storage capacity state variable of the cascade reservoir is expressed as S t =[S 1,t ,S 2,t ,…,S I,t ] T .
[0117] The storage capacity state transfer equation of each reservoir in adjacent time periods in the embodiment of the present invention is obtained by combining formula (2) and formula (3):
[0118]
[0119] Use ψ i Represents the functional relationship between variables, and formula (17) is expressed as: S i,t+1 =ψ i (S i,t ,ξ i,t ,Q i,t ).
[0120] The vectorized expression of the storage capacity state transfer equation of the cascade reservoir is:
[0121] S t+1 =ψ(S t ,ξ t ,Q t ) (18)
[0122] Step 3.2: Determine the runoff state of each reservoir in time period t-1 and time period t from the runoff state combination, and determine the runoff state transition probability of each reservoir in adjacent time periods based on the runoff state in time period t-1 and time period t, specifically including:
[0123] Step 3.2.1. Determine the total number of times fn the runoff state ni appears in each reservoir during time period t-1. ni,t-1 and the number of transitions fr from the runoff state ni at time period t-1 to the runoff state nj at time period t ni,nj,t ;
[0124] Step 3.2.2, based on the total number of fr ni,t-1 and the number of transfers fr ni,nj,t Determining the runoff state transition probability of each reservoir in adjacent time periods, specifically including: determining the runoff state transition probability of each reservoir in adjacent time periods according to the quotient of the number of transitions and the total number of times.
[0125] The embodiment of the present invention collects the runoff history data of each reservoir and determines the total number of times fn the runoff state ni appears in each reservoir within the time period t-1. ni,t-1 and the number of transitions fr from the runoff state ni at time period t-1 to the runoff state nj at time period t ni,nj,t ; Then determine the runoff state transfer probability of each reservoir based on the total number and transfer number As shown below:
[0126]
[0127] Where: fr ni,nj,t is the number of transitions from the runoff state ni in period t-1 to the runoff state nj in period t; fn ni,t-1is the total number of occurrences of flow state ni in time period t-1. Formula (19) represents the random variable ξ i,t The probability distribution of .
[0128] In order to use the subsequent stochastic dynamic programming method, for the runoff state nj of time period t, the midpoint of the interval is taken to represent the runoff value under this state, and it is calculated as follows:
[0129]
[0130] Where: represents the runoff state q i,nj Represents discrete values of runoff.
[0131] Furthermore, the present invention can determine the runoff state transition probability of the cascade reservoirs in adjacent time periods based on the runoff state transition probability of each reservoir, specifically:
[0132] Let ξ t =[ξ 1,t ,ξ 2,t ,…,ξ I,t ] T represents the random vector of runoff of the cascade reservoir in period t. Then, the cascade reservoir changes from the runoff state qs in period t-1 to ki Transfer to the runoff state qs at time period t kj The probability of
[0133]
[0134] Where: θ i (·) is the conversion function, θ i (ξ i,t ) represents ξ i,t The sample observation value qs i,kj exist The corresponding status number in .
[0135] Step 4: Combine the reservoir capacity state transition equation and runoff state transition probability, use the stochastic dynamic programming method to optimize and solve the scheduling model, and obtain the scheduling plan of the cascade reservoirs in each time period.
[0136] The above-mentioned optimization and solution of the scheduling model by using the stochastic dynamic programming method is specifically to optimize and solve the scheduling model by using the reverse recursion in the stochastic dynamic programming method.
[0137] The embodiment of the present invention, based on the principle of stochastic dynamic programming, first determines the stage variables, state variables, and decision variables, and then uses the state transition equation to perform reverse recursion on a time-period basis to obtain the optimal scheduling decision. The details are as follows:
[0138] (1) Stage variables.
[0139] Divide by time stage and let t be the stage variable.
[0140] (2)State variables.
[0141] Let runoff and storage capacity be state variables. At time period t, the storage capacity state variable of the cascade reservoir is expressed as S t =[S 1,t ,S 2,t ,…,S I,t ] T , the runoff state variable is expressed as ξ t =[ξ 1,t ,ξ 2,t ,…,ξ I,t ] T .
[0142] (3) Decision variables.
[0143] The decision variable of reservoir i at stage t is the outflow Q i,t Therefore, the decision variables of the system at stage t are expressed as: Q t =[Q 1,t ,Q 2,t ,…,Q I,t ] T .
[0144] 4) State transfer equation.
[0145] The above formula (18) and formula (21) together constitute the state transfer equation of the cascade reservoir.
[0146] (5)Indicator function.
[0147] The benefit value of the system at stage t is the indicator function. Taking the maximum cascade hydropower generation as the goal, the indicator function is expressed as follows:
[0148]
[0149] Substitute equation (18) into equation (22) and use variable S t+1 Substitution variable Q t , then formula (22) is further transformed into
[0150] w t (S t ,ξ t ,S t+1 )=u t (S t ,ξ t ,Q t ) (twenty three)
[0151] (6) Recursive equation
[0152] Starting from t=T, reverse the formula and continue until t=1.
[0153]
[0154] Where: Indicates the state from period t (S t ,ξ t ) to the optimal indicator value at the end of the scheduling period.
[0155] When t=1, the optimal indicator function value is obtained and its corresponding storage capacity at the end of the period S2, and then substituted into formula (2) to obtain the optimal decision vector Q1, which is the scheduling decision taken by the cascade reservoir in period t = 1. Subsequently, as the period progresses, the scheduling problem is optimized in a rolling manner, and the scheduling decision is updated period by period.
[0156] The present invention first takes maximizing the expected value of power generation of cascade reservoirs as the goal, considers constraints such as cascade hydraulic connections, water balance equations, hydropower generation functions, and hydropower operation boundaries, and constructs a medium- and long-term random optimization scheduling model for cascade reservoirs; then, a Markov process is used to represent the randomness of runoff between reservoirs, and a reverse recursive solution is performed using stochastic dynamic programming with runoff and storage capacity as state variables; during the solution process, considering the dimensionality curse problem faced by the stochastic dynamic programming method, an improved stochastic dynamic programming method coupled with orthogonal experimental design is proposed, and an orthogonal table is introduced to sample and reduce the state combinations, which can significantly reduce the number of traversal calculations of state combinations during the calculation process, quickly obtain high-quality scheduling decisions, and alleviate the dimensionality curse problem.
[0157] In the embodiment of the present invention, the runoff and reservoir capacity are regarded as state variables in the stochastic dynamic programming (SDP) method, and a number of state combinations are obtained by discretization, and then traversal is performed to solve them. SDP can effectively overcome the difficulties of randomness, non-convex nonlinearity and the like in the scheduling problem. At the same time, in order to solve the problem that a large number of state combinations will be generated when the state variables are discretized in SDP, the number of state combinations is exponentially increasing with the number of reservoirs, and the dimensionality curse problem is significant, the present invention adopts orthogonal experimental design (OED). OED is a statistical method used to deal with multi-factor and multi-level experimental design problems. OED selects some representative sample combinations from the comprehensive test based on orthogonality for testing. The sample combinations have the characteristics of balanced dispersion, neatness and comparability, can better reflect the overall characteristics, can greatly reduce the number of experiments, and effectively achieve dimensionality reduction. OED is currently widely used in aerospace, medicine and health, agricultural production and other fields, but there is little research in the field of reservoir scheduling.
[0158] The present invention uses orthogonal experimental design to sample and reduce the massive state combinations generated during the random dynamic programming calculation process, which can greatly reduce the number of state combination traversals, improve calculation efficiency, and enhance the timeliness of scheduling decisions.
[0159] A second aspect of an embodiment of the present invention provides a cascade reservoir scheduling system based on the above-mentioned cascade reservoir scheduling method, comprising a model building module, a first determination module, a second determination module and a scheduling module; wherein the model building module is used to construct a medium- and long-term random optimization scheduling model for the cascade reservoirs, and the state variables of the medium- and long-term random optimization scheduling model include storage capacity and runoff; the first determination module is used to determine the storage capacity state combination and runoff state combination of the cascade reservoirs according to the storage capacity data and runoff data of each reservoir in the cascade reservoirs through discretization processing, Cartesian product operation, and orthogonal experimental design; the second determination module is used to determine the storage capacity state transfer equation and runoff state transfer probability of each reservoir in adjacent time periods in combination with the storage capacity state combination and the runoff state combination; the scheduling module is used to combine the storage capacity state transfer equation and the runoff state transfer probability, and use the random dynamic programming method to optimize and solve the medium- and long-term random optimization scheduling model to obtain a scheduling plan for the cascade reservoirs in each time period.
[0160] The present invention utilizes a Markov process to represent the randomness of runoff and constructs a medium- and long-term stochastic optimization scheduling model for cascade reservoirs. Stochastic dynamic programming is used to solve the medium- and long-term stochastic optimization scheduling model. Orthogonal experimental design is introduced into the combined traversal of cascade reservoir capacity and runoff status at each time period to reduce the amount of combined traversal computation and alleviate the curse of dimensionality. The optimal scheduling decision for the cascade reservoirs is obtained through reverse recursive calculation. In the process of solving the cascade reservoir scheduling model using stochastic dynamic programming, the present invention introduces orthogonal experimental design, significantly reducing the number of combined traversals and the computational complexity of the algorithm. This significantly improves computational efficiency while ensuring computational accuracy, enabling rapid determination of cascade reservoir scheduling decisions.
[0161] The above descriptions are merely several embodiments of the present invention and do not constitute any form of limitation to the present invention. Although the present invention is disclosed as above in terms of preferred embodiments, they are not intended to limit the present invention. Any technician familiar with the present profession who, without departing from the scope of the technical solution of the present invention, makes slight changes or modifications using the technical contents disclosed above are equivalent to equivalent implementation cases and fall within the scope of the technical solution.
Claims
1. A cascade reservoir scheduling method, characterized in that: include: Step 1: constructing a medium- and long-term stochastic optimization scheduling model for cascade reservoirs, wherein the state variables of the medium- and long-term stochastic optimization scheduling model include storage capacity and runoff; Step 2: Based on the storage capacity data and runoff data of each reservoir in the cascade reservoirs, the storage capacity state combination and runoff state combination of the cascade reservoirs are determined through discretization processing, Cartesian product operation, and orthogonal experimental design; Step 3: determining the storage capacity state transfer equation and runoff state transfer probability of each reservoir in adjacent time periods according to the storage capacity state combination and the runoff state combination; Step 4: Combining the reservoir capacity state transition equation and the runoff state transition probability, the medium- and long-term stochastic optimization scheduling model is optimized and solved using a stochastic dynamic programming method to obtain a scheduling plan for the cascade reservoirs in each time period.
2. The cascade reservoir scheduling method according to claim 1, characterized in that: Step 2 specifically includes: According to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoir, the storage capacity state combination of the cascade reservoir is determined through discretization processing, Cartesian product operation and orthogonal experimental design; According to the runoff observation value of each reservoir and the extreme values of the historical runoff data, the runoff state combination of the cascade reservoirs is determined through discretization processing and Cartesian product operation.
3. The cascade reservoir scheduling method according to claim 2, characterized in that: According to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoir, the storage capacity state combination of the cascade reservoir is determined through discretization processing, Cartesian product operation, and orthogonal experimental design, including: According to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoir, the initial storage capacity state combination of the cascade reservoir is determined through discretization processing and Cartesian product operation; Construct an orthogonal table based on the discrete quantities of the number of reservoirs and storage capacity status in the cascade reservoirs; The orthogonal table is used to sample the initial storage capacity state combination to obtain the final storage capacity state combination of the cascade reservoirs.
4. The cascade reservoir scheduling method according to claim 3, characterized in that: According to the dead storage capacity and maximum storage capacity of each reservoir in the cascade reservoir, the initial storage capacity state combination of the cascade reservoir is determined through discretization processing and Cartesian product operation, specifically including: Get the discrete quantity of preset storage capacity status of each reservoir; According to the preset discrete number of storage capacity states, dead storage capacity and maximum storage capacity, the discrete value of the storage capacity state corresponding to each reservoir is determined through discretization processing to obtain a storage capacity state set; According to the storage capacity state set of each reservoir, the initial storage capacity state combination of the cascade reservoirs is determined through Cartesian product operation.
5. The cascade reservoir scheduling method according to claim 1, characterized in that: In step 3, the storage capacity state transfer equation of each reservoir in adjacent time periods is determined according to the storage capacity state combination, which specifically includes: Obtaining the storage capacity status of each reservoir in time period t and time period t+1 from the storage capacity status combination; According to the storage capacity status of time period t and time period t+1, the storage capacity state transfer equation of each reservoir in adjacent time periods is determined.
6. The cascade reservoir scheduling method according to claim 1, characterized in that: In step 3, the runoff state transition probability of each reservoir in adjacent time periods is determined according to the runoff state combination, which specifically includes: Obtaining the runoff state of each reservoir in time period t-1 and time period t from the runoff state combination; According to the runoff status of period t-1 and period t, the runoff state transition probability of each reservoir in adjacent periods is determined.
7. The cascade reservoir scheduling method according to claim 6, characterized in that: According to the runoff status of time period t-1 and time period t, the runoff status transition probability of each reservoir in adjacent time periods is determined, including: Determine the total number of occurrences of runoff state ni in time period t-1 and the number of transitions from runoff state ni in time period t-1 to runoff state nj in time period t for each reservoir; The runoff state transfer probability of each reservoir in adjacent time periods is determined according to the total number of times and the number of transfers.
8. The cascade reservoir scheduling method according to claim 1, characterized in that: The mid- to long-term stochastic optimization scheduling model is optimized and solved using a stochastic dynamic programming method, specifically including: The mid- to long-term stochastic optimization scheduling model is optimized and solved using the reverse recursion in the stochastic dynamic programming method.
9. A cascade reservoir scheduling system based on the cascade reservoir scheduling method according to any one of claims 1 to 8, characterized in that: It includes a model building module, a first determination module, a second determination module and a scheduling module; The model building module is used to build a medium- and long-term stochastic optimization scheduling model for cascade reservoirs, wherein the state variables of the medium- and long-term stochastic optimization scheduling model include storage capacity and runoff; The first determination module is used to determine the storage capacity state combination and runoff state combination of the cascade reservoirs respectively according to the storage capacity data and runoff data of each reservoir in the cascade reservoirs through discretization processing, Cartesian product operation, and orthogonal experimental design; The second determination module is used to determine the storage capacity state transfer equation and runoff state transfer probability of each reservoir in adjacent time periods in combination with the storage capacity state combination and the runoff state combination; The scheduling module is used to combine the storage capacity state transfer equation and the runoff state transfer probability, and use the stochastic dynamic programming method to optimize and solve the medium- and long-term stochastic optimization scheduling model to obtain a scheduling plan for the cascade reservoirs in each time period.