CN107341567B - Storage capacity replacement calculation method for cascade reservoir group - Google Patents

Abstract

The invention provides a storage capacity replacement calculation method for a cascade reservoir group, which can quantify a storage capacity replacement relational expression between an upper cascade reservoir and a lower cascade reservoir and is characterized by comprising the following steps of: step 1, dividing a large cascade reservoir group system into secondary systems; step 2, establishing a multi-objective optimization model of the upper and lower reservoir groups; step 3, normalizing the multiple targets, carrying out optimization solution on the multiple-target model, and calculating to obtain Pareto front edges of the storage capacity distribution between the upper and lower water reservoir groups; step 4, the storage capacity replacement relation between the upper subsystem and the lower subsystem is calculated

And 5, calculating a reservoir capacity replacement matrix among subsystems in the large cascade reservoir group system.

Description

Calculation Method of Storage Capacity Replacement for Cascade Reservoir Group

technical field

The invention relates to the technical field of reservoir scheduling, in particular to a storage capacity replacement calculation method for cascaded reservoir groups.

Background technique

Flood disaster is one of the most serious natural disasters in my country. Reservoir is the main engineering measure. It can adjust the flow process by retaining flood water and reducing the peak flow of flood into the downstream river, so as to achieve the purpose of reducing flood disaster. Under the premise of advocating the utilization of flood resources in my country, the establishment of the multi-objective optimization model for reservoir flood control and benefit development has begun to develop gradually, while the reservoir flood limit water level is the key water level characteristic parameter to coordinate the contradiction between flood control and benefit benefit of the reservoir. It reflects the flood resource allocation of storage capacity among multiple targets. At present, technologies such as the design of limited water level during flood season and the dynamic control of water level during flood season are relatively mature, and a relatively complete theoretical system has been formed. However, compared with the theoretical research progress of a single reservoir, the joint application of cascade reservoir groups and the dynamic control of the flood-limited water level are more complicated, and most of them focus on the analysis of engineering cases, lacking a systematic theoretical system. For a large system of cascade reservoirs, there is a certain hydraulic connection between the cascade reservoirs, and there is storage capacity compensation between the upper and lower reservoirs. Simply raising the flood limit water level of a reservoir or optimizing the scheduling rules of a reservoir will not It will definitely improve the overall flood resource utilization rate of the cascade reservoir system. Moreover, with the increase of the number (dimension) of the reservoirs in the cascade reservoir system, more and more information needs to be considered, and the control of the flood-limited water level of the reservoirs will also become more and more complicated. At present, the research on the joint dispatching problem of cascade reservoir groups mostly focuses on the establishment of an optimization model for the overall reservoir group system and how to use the optimization algorithm to solve the dimensionality reduction. The mechanism of its storage capacity replacement has not been studied in depth.

There are the following problems in the existing technology: At present, for the joint operation of reservoir groups and storage capacity allocation, most of them focus on the establishment of the overall optimization model and the study of the optimization algorithm solution of the multi-dimensional model.

SUMMARY OF THE INVENTION

The present invention is carried out to solve the above problems, and the purpose is to provide a storage capacity replacement calculation method for cascade reservoir groups, which can quantify the storage capacity replacement relationship between the upper and lower reservoirs of the cascade, and calculate the storage capacity between subsystems in the cascade reservoir system. permutation matrix.

The invention provides a storage capacity replacement calculation method for cascade reservoir groups, which is characterized in that it includes the following steps:

Step 1, regard the cascade reservoir group as a large system, regard each reservoir in the cascade reservoir group as a subsystem, and number the reservoirs in the cascade reservoir group in the order from upstream to downstream, and mark them as 1, 2. ,…,N, take any two reservoirs connected in series up and down in the large system as a secondary system, numbered 1,2,…,N-1 in sequence from upstream to downstream, subsystem i and subsystem i +1 constitutes the secondary system i, i=1,2,...,N-1; regard the two reservoirs connected in series in each secondary system as the upper and lower subsystems;

In step 2, a multi-objective optimization model is established for the secondary system i, and the objective functions of the optimization model are the maximum power generation and the maximum flood control storage capacity. The specific objective functions include:

Objective function 1

Objective function 2

为次级系统i的汛期发电量，

为次级系统i中子系统k的汛期发电量，

为次级系统i的防洪库容，

为次级系统i中子系统k的防洪库容；i＝1,2,…,N-1，k＝1,2；where:

is the flood season power generation of secondary system i,

is the flood season power generation of subsystem k in secondary system i,

is the flood protection storage capacity of secondary system i,

is the flood control storage capacity of subsystem k in secondary system i; i=1,2,...,N-1, k=1,2;

The solution of the multi-objective optimization model of the secondary system should be constrained by the conventional flood control standards and the total power generation:

为次级系统i的常规调度下的防洪库容值，

为次级系统i的常规调度下的汛期发电量值；where:

is the flood control storage capacity value under the conventional dispatch of the secondary system i,

is the power generation value during the flood season under the conventional dispatch of the secondary system i;

Step 3, the multi-objective optimization model established for the secondary system i in step 2 is normalized by the weight method, and the objective function is:

In the formula: α is the weight coefficient, the value range is 0～1;

Transform the weight coefficient α, and obtain the multi-objective non-inferior solution set of the secondary system by successive optimization, that is, obtain a series of storage capacity allocation Pareto fronts between the upper and lower subsystems in the secondary system i;

Step 4, infer the storage capacity replacement relationship between the upper and lower subsystems of the secondary system i, the specific implementation is as follows:

Step 4-1, the non-inferior solution calculated in step 3 is the solution set of the upper and lower subsystem storage capacity in the non-inferior solution set, and the solution set G of the storage capacity of the upper and lower subsystems is obtained. The solution set expression is:

和

分别为次级系统i的解集G中上、下子系统的第j组解，m为解集G中解的个数，U＝i表示子系统i，D＝i+1表示子系统i+1；where:

and

are the jth solutions of the upper and lower subsystems in the solution set G of the secondary system i respectively, m is the number of solutions in the solution set G, U=i represents subsystem i, and D=i+1 represents subsystem i+ 1;

及

式中g(V_D)＝f^-1(V_D)；Step 4-2, according to the solution set G of the storage capacity of the upper and lower subsystems, fit the functional relationship V _U =f(V _D ) of the storage capacity of the upper and lower subsystems, and deduce the replacement relationship of the storage capacity of the upper and lower subsystems

and

where g(V _D )=f ^-1 (V _D );

Step 5, infer the storage capacity replacement matrix between each subsystem in the cascade reservoir group large system, the specific implementation is as follows:

Repeat steps 2, 3, and 4, carry out multi-objective optimization solution for N-1 secondary systems in turn, and calculate the storage capacity replacement matrix between subsystems in the large system of cascade reservoir groups. The expression of the replacement matrix is:

According to the storage capacity replacement matrix among the subsystems in the large system of cascade reservoir groups, the equivalent relationship of the storage capacity of each subsystem in the large system of cascade reservoir groups can be derived:

可以置换子系统l+1的

库容值，以及可以置换子系统l+2的

库容值,l＝1,2,…,N-2。Expression meaning for subsystem l

Subsystem l+1 can be replaced

storage capacity value, and can replace subsystem l+2

Storage capacity value, l=1,2,...,N-2.

Compared with the prior art, the beneficial effects of the present invention are:

(1) The present invention proposes a storage capacity replacement calculation method for cascade reservoir groups, which can quantify the storage capacity replacement function relationship between the upper and lower reservoirs of the cascade

可以置换子系统i+1的

库容值，以及可以置换子系统i+2的

库容值，从而在不借助优化算法求解的情况下，简化推导子系统间库容组合方案。(2) The storage capacity replacement matrix of the cascade reservoir group in the storage capacity replacement calculation method of the cascade reservoir group proposed by the present invention can be used to recursively calculate the storage capacity replacement relationship between the subsystems, such as the storage capacity replacement relationship of the subsystem i.

Subsystem i+1 can be replaced

storage capacity value, and can replace subsystem i+2

storage capacity value, so that the storage capacity combination scheme between subsystems can be simplified and deduced without resorting to the optimization algorithm.

Description of drawings

Fig. 1 is the flow chart of the storage capacity replacement calculation method of a kind of cascade reservoir group according to the first embodiment of the present invention;

2 is a schematic diagram of a non-inferior solution of a multi-objective optimization model of a secondary system according to Embodiment 1 of the present invention;

FIG. 3 is a schematic diagram of the storage capacity relationship between the upper and lower subsystems in the secondary system according to Embodiment 1 of the present invention.

Detailed ways

The specific embodiments of the storage capacity replacement calculation method for cascade reservoir groups involved in the present invention will be described in detail below with reference to the accompanying drawings.

<Example 1>

As shown in FIG. 1 , a storage capacity replacement calculation method for a cascade reservoir group provided in the first embodiment includes the following steps:

Step 1. Consider the cascade reservoir group as a large system, regard each reservoir in the cascade reservoir group as a subsystem, and number the reservoirs in the cascade reservoir group in the order from upstream to downstream, and mark them as 1, 2. ,…,N, take any two reservoirs connected in series up and down in the large system as a secondary system, numbered 1,2,…,N-1 in sequence from upstream to downstream, subsystem i and subsystem i +1 constitutes the secondary system i, i=1,2,...,N-1; regard the two reservoirs connected in series in each secondary system as the upper and lower subsystems;

Step 2. Establish a multi-objective optimization model for the secondary system i, then the objective functions of the optimization model are the maximum power generation and the maximum flood control storage capacity. The specific objective functions include:

Objective function 1

Objective function 2

为次级系统i的汛期发电量，

为次级系统i中子系统k的汛期发电量，

为次级系统i的防洪库容，

为次级系统i中子系统k的防洪库容；i＝1,2,…,N-1，k＝1,2；where:

is the flood season power generation of secondary system i,

is the flood season power generation of subsystem k in secondary system i,

is the flood protection storage capacity of secondary system i,

is the flood control storage capacity of subsystem k in secondary system i; i=1,2,...,N-1, k=1,2;

The solution of the multi-objective optimization model of the secondary system should be constrained by the conventional flood control standards and the total power generation:

为次级系统i的常规调度下的防洪库容值，

为次级系统i的常规调度下的汛期发电量值；where:

is the flood control storage capacity value under the conventional dispatch of the secondary system i,

is the power generation value during the flood season under the conventional dispatch of the secondary system i;

Other general constraints will not be repeated;

Step 3. The multi-objective optimization model established for the secondary system i in step 2 is normalized by the weight method, and the objective function is:

In the formula: α is the weight coefficient, the value range is 0～1;

Transform the weight coefficient α, and obtain the multi-objective non-inferior solution set of the secondary system by successive optimization, that is, to obtain a series of storage capacity allocation Pareto frontiers between the upper and lower subsystems in the secondary system i (as shown in Figure 2);

Step 4. Infer the storage capacity replacement relationship between the upper and lower subsystems of the secondary system i, the specific implementation is as follows:

Step 4-1. Statistical Step 3 Calculate the non-inferior solutions of the upper and lower subsystem storage capacity in the solution set, and get the solution set G of the upper and lower subsystem storage capacity, the solution set expression is:

和

分别为次级系统i的解集G中上、下子系统的第j组解，m为解集G中解的个数，U＝i表示子系统i，D＝i+1表示子系统i+1；where:

and

are the jth solutions of the upper and lower subsystems in the solution set G of the secondary system i respectively, m is the number of solutions in the solution set G, U=i represents subsystem i, and D=i+1 represents subsystem i+ 1;

及

式中g(V_D)＝f^-1(V_D)；Step 4-2. According to the solution set G of the storage capacity of the upper and lower subsystems, fit the functional relationship V _U =f(V _D ) of the storage capacity of the upper and lower subsystems (as shown in Figure 3), and calculate the storage capacity of the upper and lower subsystems. permutation relation

and

where g(V _D )=f ^-1 (V _D );

Step 5, infer the storage capacity replacement matrix between each subsystem in the cascade reservoir group large system, the specific implementation is as follows:

Repeat steps 2, 3, and 4, carry out multi-objective optimization solution for N-1 secondary systems in turn, and calculate the storage capacity replacement matrix between subsystems in the large system of cascade reservoir groups. The expression of the replacement matrix is:

According to the storage capacity replacement matrix among the subsystems in the large system of cascade reservoir groups, the equivalent relationship of the storage capacity of each subsystem in the large system of cascade reservoir groups can be derived:

可以置换子系统l+1的

库容值，以及可以置换子系统l+2的

库容值,l＝1,2,…,N-2。Expression meaning for subsystem l

Subsystem l+1 can be replaced

storage capacity value, and can replace subsystem l+2

Storage capacity value, l=1,2,...,N-2.

It should be understood that the parts not described in detail in this specification belong to the prior art. The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention pertains can make various modifications or additions to the described specific embodiments or substitute in similar manners, but will not deviate from the spirit of the present invention or go beyond the definition of the appended claims range.

Claims (1)

1. a storage capacity replacement calculation method of cascade reservoir group, is characterized in that, comprises the following steps: Step 1, regard the cascade reservoir group as a large system, regard each reservoir in the cascade reservoir group as a subsystem, and number the reservoirs in the cascade reservoir group in the order from upstream to downstream, and mark them as 1, 2. ,…,N, take any two reservoirs connected in series up and down in the large system as a secondary system, numbered 1,2,…,N-1 in sequence from upstream to downstream, subsystem i and subsystem i +1 constitutes the secondary system i, i=1,2,...,N-1; regard the two reservoirs connected in series in each secondary system as the upper and lower subsystems; In step 2, a multi-objective optimization model is established for the secondary system i, and the objective functions of the optimization model are the maximum power generation and the maximum flood control storage capacity. The specific objective functions include: Objective function 1

Objective function 2

where:

is the flood season power generation of secondary system i,

is the flood season power generation of subsystem k in secondary system i,

is the flood protection storage capacity of secondary system i,

is the flood control storage capacity of subsystem k in secondary system i; i=1,2,...,N-1, k=1,2; The solution of the multi-objective optimization model of the secondary system should be constrained by the conventional flood control standards and the total power generation:

where:

is the flood control storage capacity value under the conventional dispatch of the secondary system i,

is the power generation value during the flood season under the conventional dispatch of the secondary system i; Step 3, the multi-objective optimization model established for the secondary system i in step 2 is normalized by the weight method, and the objective function is:

In the formula: α is the weight coefficient, the value range is 0～1; Transform the weight coefficient α, and obtain the multi-objective non-inferior solution set of the secondary system by successive optimization, that is, obtain a series of storage capacity allocation Pareto fronts between the upper and lower subsystems in the secondary system i; Step 4, infer the storage capacity replacement relationship between the upper and lower subsystems of the secondary system i, the specific implementation is as follows: Step 4-1, the non-inferior solution calculated in step 3 is the solution set of the upper and lower subsystem storage capacity in the non-inferior solution set, and the solution set G of the storage capacity of the upper and lower subsystems is obtained. The solution set expression is:

where:

and

are the jth solutions of the upper and lower subsystems in the solution set G of the secondary system i respectively, m is the number of solutions in the solution set G, U=i represents subsystem i, and D=i+1 represents subsystem i+ 1; Step 4-2, according to the solution set G of the storage capacity of the upper and lower subsystems, fit the functional relationship V _U =f(V _D ) of the storage capacity of the upper and lower subsystems, and deduce the replacement relationship of the storage capacity of the upper and lower subsystems

and

where g(V _D )=f ^-1 (V _D ); Step 5, infer the storage capacity replacement matrix between each subsystem in the cascade reservoir group large system, the specific implementation is as follows: Repeat steps 2, 3, and 4, carry out multi-objective optimization solution for N-1 secondary systems in turn, and calculate the storage capacity replacement matrix between subsystems in the large system of cascade reservoir groups. The expression of the replacement matrix is:

According to the storage capacity replacement matrix among the subsystems in the large system of cascade reservoir groups, the equivalent relationship of the storage capacity of each subsystem in the large system of cascade reservoir groups can be derived:

Expression meaning for subsystem l

Subsystem l+1 can be replaced

storage capacity value, and can replace subsystem l+2

Storage capacity value, l=1,2,...,N-2.

Images