A Stochastic Dynamic Programming Algorithm Coupling Feasible Region and Parallel Computing

Abstract

The present invention provides a stochastic dynamic programming algorithm that couples the feasible region and parallel computing, comprising the following steps: S1. Construct a long-term reservoir operation model and select the maximum power generation as the objective function; S2. Select the initial water level of the time period as the state variable and the final water level of the time period as the decision variable, and calculate the feasible region of the final water level corresponding to each initial water level according to the incoming water and constraint conditions; S3. Introduce the feasible region into the stochastic dynamic programming algorithm, only calculate the final water levels within the feasible region, and adopt parallel computing during the calculation to finally obtain the long-term reservoir operation rule. Based on the stochastic dynamic programming algorithm, this algorithm introduces the feasible region and parallel computing in the calculation, reduces the calculation scale, and improves the calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the field of reservoir operation, and particularly to a stochastic dynamic programming algorithm that couples the feasible region and parallel computing. Background Art

[0002] Stochastic dynamic programming is a common method for solving the optimal operation of hydropower stations under stochastic inflow. Stochastic runoff can be regarded as a Markov process (without aftereffect), that is, the runoff in future periods is only related to the runoff in the current period. The specific mathematical relationship can be described by a transition matrix. Compared with the deterministic inflow with only one inflow condition, the stochastic inflow situation is more complex, and the computational workload of reservoir operation increases significantly. Due to the randomness of runoff and the complexity of the hydropower station operation problem, the curse of dimensionality often appears in the calculation process of using stochastic dynamic programming to obtain the operation rule, and the computational workload will increase exponentially with the increase of the reservoir scale. Therefore, it is necessary to optimize the stochastic dynamic programming algorithm to reduce the computational scale. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a stochastic dynamic programming algorithm that couples the feasible region and parallel computing. Based on the stochastic dynamic programming algorithm, the feasible region and parallel computing are introduced in the calculation to reduce the computational scale and improve the computational efficiency.

[0004] To solve the above technical problem, the technical solution adopted by the present invention is: a stochastic dynamic programming algorithm that couples the feasible region and parallel computing, including the following steps:

[0005] S1. Construct a long-term reservoir operation model, and select the maximum power generation as the objective function;

[0006] S2. Select the initial water level of the period as the state variable and the final water level of the period as the decision variable, and calculate the feasible region of the final water level corresponding to each initial water level according to the inflow and constraint conditions;

[0007] S3. Introduce the feasible region into the stochastic dynamic programming algorithm, only calculate the final water levels within the feasible region, and use parallel computing during the calculation to finally obtain the long-term reservoir operation rule.

[0008] In a preferred solution, in the above S1, the objective function is:

[0009]

[0010]

[0011] In the formula, E represents power generation, q represents the hydropower generation flow rate, N represents the hydropower station output, μ represents the water consumption rate of power generation of the power station, and Δt represents the period length.

[0012] In a preferred solution, the above S2 includes the following steps:

[0013] S21. Analyze the upper and lower limits of the random inflow to the reservoir;

[0014] S22. Collect the boundary constraints and water balance constraints in the long-term operation model of the reservoir operation;

[0015] S23. Calculate the range of the water level at the end of each period that satisfies each constraint condition for the water level at the beginning of each period respectively:

[0016] Obtain the first water level range by using the out - flow constraint and water balance, as shown below:

[0017] Z_1 = f -1 (f(Z1)+(Q - R)Δt) (3)

[0018] In the formula, Z_1 represents the range of the feasible region of the first decision-making reservoir water level, Z1 represents the water level of the state reservoir, f represents the relationship between the reservoir water level and the reservoir capacity, Q represents the inflow, R represents the out - flow, and Δt represents the period length;

[0019] Z_2 = f -1 (f(Z1)+(Q - N×μ)Δt) (4)

[0020] In the formula, Z_2 represents the range of the feasible region of the second decision-making reservoir water level, N represents the power generation of the hydropower station, and μ represents the water consumption rate of power generation of the power station;

[0021] S24. Take the intersection of the ranges of the feasible regions of the water levels at the end of each period for each constraint in S23 as the feasible region of the water level at the end of the period:

[0022]

[0023] Z = Z_1∩Z_2∩Z_3 (6)

[0024] In the formula, Z represents the feasible region of the reservoir water level, Z_3 represents the range of the feasible region of the third decision-making reservoir water level, and Z represent the upper and lower limits of the reservoir water level respectively.

[0025] In the preferred solution, in S22, the boundary constraints include the out - flow constraint, the power generation constraint, and the water level constraint:

[0026]

[0027]

[0028]

[0029] R = q + q_s (10) In the formula, R represents the out - flow; and Rrespectively represent the upper and lower limits of the outgoing flow; N represents the power output of the hydropower station; and N respectively represent the upper and lower limits of the power output of the hydropower station; q represents the power generation flow of the hydropower station; q_s represents the water discharge flow.

[0030] In the preferred solution, in S22, the water balance constraint satisfies the following conditions:

[0031] V t+1 = V t + 3600(Q - R)Δt (11)

[0032] In the formula, V t is the reservoir storage at time t.

[0033] In the preferred solution, S3 includes the following steps:

[0034] S31. Obtain the relevant parameters of the hydropower station, including multi-year historical runoff data, reservoir parameters, and scheduling constraints, and artificially simulate the runoff of the hydropower station using the first-order Thomas-Fiering model based on the historical runoff data to extend the runoff length;

[0035] S32. Calculate the power generation of the initial water level and the combined final water levels within the feasible region in reverse time steps, and perform parallel calculations at the final water level layer;

[0036] S33. Obtain the optimal final water level and the maximum expected power generation E for each initial water level;

[0037] S34. Determine whether the current time step is the initial time step. If not, adjust the calculation time step to the previous time step and return to step S32. If so, perform convergence analysis on the results. If the convergence condition is met, output the scheduling rule. If the convergence condition is not met, adjust the time step to the final time step and then return to step S32.

[0038] A stochastic dynamic programming algorithm that couples the feasible region and parallel computing provided by the present invention is based on the stochastic dynamic programming algorithm. The feasible region and parallel computing are introduced in the calculation to reduce unnecessary computational workload, reduce the computational scale, and improve the computational efficiency, providing a new and efficient method for alleviating the long-term scheduling calculation under the condition of random runoff inflow to the reservoir. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The present invention will be further described below with reference to the drawings and embodiments:

[0040] Figure 1 is a schematic diagram of the feasible region of the present invention;

[0041] Figure 2 is the scheduling rule result of Xiaowan Hydropower Station in January;

[0042] Figure 3 The scheduling rule results for Xiaowan Hydropower Station in February;

[0043] Figure 4 The scheduling rule results for Xiaowan Hydropower Station in March;

[0044] Figure 5 The scheduling rule results for Xiaowan Hydropower Station in April;

[0045] Figure 6 The scheduling rule results for Xiaowan Hydropower Station in May;

[0046] Figure 7 The scheduling rule results for Xiaowan Hydropower Station in June;

[0047] Figure 8 The scheduling rule results for Xiaowan Hydropower Station in July;

[0048] Figure 9 The scheduling rule results for Xiaowan Hydropower Station in August;

[0049] Figure 10 The scheduling rule results for Xiaowan Hydropower Station in September;

[0050] Figure 11 The scheduling rule results for Xiaowan Hydropower Station in October;

[0051] Figure 12 The scheduling rule results for Xiaowan Hydropower Station in November; Specific implementation method

[0052] Taking Xiaowan Hydropower Station as a research example, a stochastic dynamic programming that couples the feasible region with parallel computing is used to calculate the reservoir scheduling rule under stochastic inflow, and the computing time required by the stochastic dynamic programming and this method is compared to show the effect achieved by the present invention.

[0053] A stochastic dynamic programming algorithm that couples the feasible region with parallel computing includes the following steps:

[0054] S1. Construct a long-term scheduling model for Xiaowan Reservoir, and select the maximum power generation as the objective function.

[0055]

[0056] In the formula, E represents power generation, q represents the power generation flow of the hydropower station, N represents the output of the hydropower station, μ represents the water consumption rate of power generation of the station, and Δt represents the time period length.

[0057] S2. Select the water level at the beginning of the time period as the state variable and the water level at the end of the time period as the decision variable, and calculate the feasible region of the water level at the end corresponding to each initial water level according to the inflow and constraint conditions as follows:

[0058] S21. Analyze the upper and lower limits of the random inflow of the reservoir.

[0059] S22. Collect the boundary constraints and water balance constraints in the long-term operation model of the reservoir.

[0060] The boundary constraints include the outflow discharge constraint, power output constraint, and water level constraint:

[0061]

[0062]

[0063]

[0064] R = q + q_s (10)

[0065] In the formula, R represents the outflow discharge; and R represent the upper and lower limits of the outflow discharge respectively; N represents the power output of the hydropower station; and N represent the upper and lower limits of the power output of the hydropower station respectively; q represents the power generation flow of the hydropower station; q_s represents the waste water flow.

[0066] The water balance constraint satisfies the following conditions:

[0067] V t+1 = V t + 3600(Q - R)Δt (11)

[0068] In the formula, V t is the reservoir storage at time t.

[0069] S23. Calculate the range of the water level at the end of each time period that satisfies each constraint condition for the water level at the beginning of each time period respectively.

[0070] Use the outflow discharge constraint and water balance to obtain the first water level range as follows:

[0071] Z_1 = f -1 (f(Z1)+(Q - R)Δt) (3)

[0072] In the formula, Z_1 represents the range of the feasible region of the first decision-making reservoir water level, Z1 represents the state reservoir water level, f represents the relationship between the reservoir water level and the storage, Q represents the inflow discharge, R represents the outflow discharge, and Δt represents the time period length;

[0073] Z_2 = f -1 (f(Z1)+(Q - N×μ)Δt) (4)

[0074] Wherein, Z_2 represents the range of the second decision-making reservoir water level feasible region, N represents the output of the hydropower station, and μ represents the water consumption rate of power generation of the power station.

[0075] S24. Take the intersection of the range of the feasible water level at the end of each period for each constraint in S23 as the feasible water level at the end of the period:

[0076]

[0077] Z = Z_1 ∩ Z_2 ∩ Z_3 (6)

[0078] Wherein, Z represents the feasible region of the reservoir water level, and Z_3 represents the range of the third decision-making reservoir water level feasible region. And Z respectively represent the upper and lower limits of the reservoir water level.

[0079] S3. Introduce the feasible region into the stochastic dynamic programming algorithm, only calculate the water levels at the end of the period within the feasible region, and use parallel computing during the calculation to finally obtain the long-term reservoir operation rule:

[0080] S31. Obtain the relevant parameters of the hydropower station, including historical runoff data over the years, reservoir parameters, and operation constraints; use the first-order Thomas-Fiering model to artificially simulate the runoff of the hydropower station based on the historical runoff data to extend the runoff length; initialize the calculation parameters, set the initial iteration period ge = 1, and the initial number of periods t = 12.

[0081] S32. Calculate the power generation of each combination of initial and end water levels within the period t of the reservoir in the reverse time period, where only the end water levels within the feasible region are used, and parallel computing is adopted during the calculation.

[0082] S33. Obtain the optimal end water level and the maximum expected power generation E for each initial water level.

[0083] S34. Determine whether the current period is the initial period, that is, whether t = 1 is satisfied. If not, then t = t - 1, and return to step S32; if satisfied, then conduct a convergence analysis on the results, compare whether the optimal end water levels of the same initial water level at any period in the current iteration period and the previous iteration period are the same. If not, ge = ge + 1, t = 12, return to step S32. If the same, then output the results to obtain the operation rule.

[0084] Figure 1 shows a schematic diagram of the feasible region. During the calculation process of the stochastic dynamic programming, the feasible region and parallel computing are introduced. The upper and lower limits of the random runoff of the Xiaowan Hydropower Station and the constraint conditions in the mathematical model are used to calculate the feasible region of the end water levels corresponding to all initial water levels in each period, and the end water levels within the feasible region are calculated in parallel to obtain the operation rule of the Xiaowan Power Station, see Figures 2 to 12In the calculation, the water levels at the beginning of the January period and at the end of the December period are both set to the normal high water level. Therefore, the dispatching rule for January is only a scatter plot of ten points, and the dispatching diagram is no longer drawn for December.

[0085] To prove Figures 2 to 12 the feasibility of the dispatching rule in [reference], the above dispatching rule and dynamic programming are used to calculate the power generation of Xiaowan Hydropower Station under a certain deterministic runoff process respectively. The comparison results are shown in Table 1.

[0086] Table 1 Comparison of power generation (unit: 100 million kW·h)

[0087]

[0088]

[0089] It can be seen from the comparison and analysis of the results that the total power generations obtained by the two methods are similar. Among them, the global optimal solution is obtained by dynamic programming, and the result obtained by the dispatching rule is 96% of the dynamic programming result, which is very close. This proves that the stochastic dynamic programming method coupling the feasible region and parallel computing is feasible and can obtain the dispatching rule of the hydropower station.

[0090] To compare the improvement of the computational efficiency of the stochastic dynamic programming algorithm coupling the feasible region and parallel computing, this method and stochastic dynamic programming are used to solve the dispatching rules with different discrete step lengths of Xiaowan Hydropower Station respectively. The time spent is shown in Table 2.

[0091] Table 2 Comparison of time consumption of methods

[0092]

[0093] According to the result analysis, as the number of calculated water level points increases by 2 times, the time of stochastic dynamic programming increases exponentially by 4 times, and under the condition of the same step length, the computational duration of stochastic dynamic programming is dozens of times that of the stochastic dynamic programming coupling the feasible region and parallel computing.

[0094] Based on the above analysis, the present invention reduces the unnecessary computational amount and effectively improves the computational efficiency by introducing the feasible region and parallel computing into the stochastic dynamic programming algorithm, providing a new efficient method for alleviating the long-term dispatching calculation under the condition of random runoff inflow of the reservoir.

Claims

1. A stochastic dynamic programming algorithm coupling a feasible region and parallel computing, characterized in that, It includes the following steps: S1. Construct a long-term reservoir operation model and select the maximum power generation as the objective function; S2. Select the initial water level of the time period as the state variable and the final water level of the time period as the decision variable, and calculate the feasible region of the final water level corresponding to each initial water level according to the incoming water and constraint conditions, including the following steps: S21. Analyze the upper and lower limits of the random incoming water of the reservoir; S22. Collect the boundary constraints and water balance constraints in the long-term reservoir operation model; S23. Calculate the range of the final water level of each time period when the initial water level of each time period meets each constraint condition respectively: Obtain the first water level range by using the outflow discharge constraint and water balance, as follows: （3）； In the formula, Z _1 represents the feasible range of the water level in the first decision-making reservoir, Z1 represents the water level in the state reservoir, f represents the relationship between the reservoir water level and the storage capacity, Q represents the inflow, R represents the outflow, represents the time interval length; （4）； In the formula, Z _2 represents the second feasible region range of the decision-making reservoir water level, N represents the hydropower station output, μ represents the water consumption rate for power generation of the power station; S24. Take the intersection of the feasible region ranges of the final water level for each constraint in S23 as the feasible region of the final water level; （5）； （6）； Where Z represents the feasible region of reservoir water level, Z _3 represents the range of the third decision-making feasible region of reservoir water level, and represent the upper and lower limits of the reservoir water level respectively; S3. Introduce the feasible region into the stochastic dynamic programming algorithm, only calculate the final water levels within the feasible region, and use parallel computing during the calculation to finally obtain the long-term reservoir operation rule, including the following steps: S31. Obtain the relevant parameters of the hydropower station, including multi-year historical runoff data, reservoir parameters, and operation constraints, and artificially simulate the runoff of the hydropower station using the first-order Thomas-Fiering model based on the historical runoff data to extend the runoff length; S32. Calculate the power generation of the combination of the initial water level and the final water level within the feasible region in the reverse time period, and perform parallel computing at the final water level layer; S33. Obtain the optimal final water level and the maximum expected power generation for each initial water level E ; S34. Determine whether the current time period is the initial time period. If not, adjust the calculation time period to the previous time period and return to step S32. If so, conduct a convergence analysis on the results. If the convergence condition is met, output the operation rule. If the convergence condition is not met, adjust the time period to the final time period and then return to step S32.

2. A stochastic dynamic programming algorithm coupling a feasible region and parallel computing according to claim 1, characterized in that In S1, the objective function is: （1）； （2）； In the formula, E represents the power generation amount, q represents the power generation flow rate of the hydropower station, N represents the output of the hydropower station, represents the water consumption rate for power generation of the power station, ∆ t represents the time period length.

3. A stochastic dynamic programming algorithm coupling a feasible region and parallel computing according to claim 1, characterized in that, In S22, the boundary constraints include the outflow discharge constraint, the power output constraint, and the water level constraint: （7）； （8）； （9）； （10）； In the formula, represents the outflow rate; and represent the upper and lower limits of the outflow rate respectively; represents the hydropower station output; and represent the upper and lower limits of the hydropower station output respectively; q represents the power generation flow rate of the hydropower station; represents the water discharge flow rate.

4. A stochastic dynamic programming algorithm coupling a feasible region and parallel computing according to claim 1, characterized in that In S22, the water balance constraint satisfies the following conditions: （11）； In the formula, V t is the reservoir storage volume during the time period t .

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