A one-dimensional linear approximation method for hydropower output

Abstract

The present invention discloses a one-dimensional linear approximation processing method for hydropower output. First, the hydropower output relationship is expressed as a binary function of water head and power generation diversion flow rate, a P-q-H three-dimensional coordinate system is constructed, and N H + 1 coordinate points are taken on the H axis. For the m-th interval [H m , H m+1 , its center point #imgabs0# is taken as the representative of the interval, and N H unary functions #imgabs1# are obtained. For each given #imgabs2# unary function, linear piecewise processing is performed according to the segmentation points #imgabs3#, the constraint conditions corresponding to the hydropower output relationship are constructed, and finally a mixed-integer programming solver is called for solution to obtain the optimal hydropower output process. The present invention approximately processes the binary inseparable non-linear hydropower output relationship into a linear relationship, taking into account both accuracy and efficiency, and can be used for developing and deploying reservoir power generation scheduling models or power system optimal scheduling models involving hydropower.

Description

Technical Field

[0001] The invention relates to the field of optimized operation of hydropower energy systems, and in particular to a one-dimensional linear approximation processing method for hydropower output. Background Art

[0002] Hydropower energy is a cheap, efficient, clean and renewable energy. The management and operation of the hydropower energy system uses optimization theory and methods to study the optimal utilization and control of water energy and water resources, that is, to seek the optimal operation and scheduling method, optimal strategy and optimal decision for the system and hydropower stations and their reservoirs.

[0003] In essence, reservoir power generation optimization scheduling is a complex non-convex nonlinear mathematical optimization problem. There are many nonlinear relationships involved in reservoir power generation scheduling. Hydropower output is a binary function relationship between water head and power generation reference flow, which involves other nonlinear relationships, including water storage-water level, outflow-tail water level, water head-water consumption rate, water head-maximum power generation reference flow limit, etc. These nonlinear factors are interrelated and affect each other, and lead to the non-convex characteristics of the model, making the model difficult to solve or locally optimal.

[0004] Mathematical programming methods are rigorous in theory and are also called exact algorithms. They ensure convergence to a certain target value in a limited time and are reliable methods for engineering scheduling practice. Due to nonlinear factors such as hydropower output, mathematical programming methods often encounter difficulties in application, or the accuracy of the model is greatly reduced due to over-approximation, or the solution time is too long due to the introduction of too many integer variables. Summary of the invention

[0005] The purpose of the present invention is to improve and innovate the shortcomings and problems existing in the background technology. The present invention provides a one-dimensional linear approximation processing method for hydropower output.

[0006] To achieve the above object, the present invention provides the following technical solution: a one-dimensional linear approximation processing method for hydropower output, specifically comprising the following steps:

[0007] Step S1: Collect and organize hydropower output data, analyze the hydropower output relationship, and express the hydropower output relationship as a binary function of water head and power generation reference flow:

[0008] P=f(q,H)(1)

[0009] Where P represents hydropower output, q represents the power generation reference flow, and H represents the water head;

[0010] Step S2: Build Three-dimensional coordinate system, take N on the H axis H +1 coordinate point, For the mth interval [H m,H m+1 ], take its center point As a representative of the interval, we get N H Unary Function ;

[0011] Step S3: For each given The univariate function of Perform linear segmentation processing;

[0012] Step S4: constructing constraints corresponding to the hydropower output relationship, wherein the constraints include interval head limit, power generation reference flow limit and power generation output limit;

[0013] Step S5: calling a mixed integer programming solver to solve and obtain the optimal hydropower output process.

[0014] A further solution is that the constraints include interval head limit, power generation reference flow limit and power generation output limit. The specific expressions are:

[0015] ①The head limit of the interval is expressed as:

[0016] (2)

[0017] (3)

[0018] In formula (2-3), α m (m=1 ,…,N H ) is a set of 0-1 binary variables introduced, and formula (3) limits the existence of only one α m The value of is 1, which means that the water head H in a certain period of time is in the interval;

[0019] ② The power generation reference flow limit is expressed as:

[0020] (4)

[0021] (5)

[0022] (6)

[0023] (7)

[0024] In formula (4-5) is the introduced “weight” variable, whose value is between 0 and 1, and the sum is 1, as The weight of the segmentation point; the 0-1 binary variable introduced in formula (6-7) , it is limited that there are only two adjacent weights that take non-zero values, and the other weights are zero;

[0025] ③The hydropower output limit is expressed as:

[0026] (8)

[0027] Where M is the upper limit of hydropower output. is a set of 0-1 binary variables introduced, with only one α m The value of is 1, and the rest of α m The value of α is 0. m =1, formula (8) is transformed into:

[0028] (9)

[0029] show The unary output relation representing the interval is used to approximate the output of the corresponding area; conversely, for any , formula (8) is transformed into

[0030] (10).

[0031] A further solution is that the solver is a Gurobi solver.

[0032] Compared with the prior art, the present invention has the following beneficial effects: (1) it can directly use the hydropower output relationship in tabular form to avoid errors caused by curve fitting;

[0033] (2) The linear model has excellent mathematical properties and stable calculation results;

[0034] (3) This approximate method takes into account both accuracy and efficiency and can be used to develop and deploy reservoir power generation scheduling models or power system optimization scheduling models involving hydropower. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of a one-dimensional linear approximation processing method for hydropower output of the present invention;

[0036] Figure 2 It is a schematic diagram of the one-dimensional approximation method of hydropower output of the present invention. DETAILED DESCRIPTION

[0037] The following is a further detailed description of the claims of the present invention in conjunction with specific implementation methods, but does not constitute any limitation to the present invention. Any limited modifications made within the scope of protection of the claims of the present invention are still within the scope of protection of the claims of the present invention.

[0038] In this embodiment, see the attached Figures 1-2A hydrothermal power system includes 4 hydropower stations and 3 thermal power stations. Its short-term dispatch model involves nonlinear thermal power cost function and binary inseparable hydropower output function. The dispatch target is to minimize thermal power cost. The hydrothermal power dispatch model and data can be found in the literature Mandal, KK, M. Basu, and N. Chakraborty, Particle swarm optimization technique based short-term hydrothermal scheduling. Applied Soft Computing, 2008.8(4): p.1392-1399.

[0039] Processing and solving the scheduling model according to the method provided by the present invention specifically includes the following steps:

[0040] Step S1: Collect and organize hydropower output data, analyze the hydropower output relationship, and express the hydropower output relationship as a binary function of water head and power generation reference flow:

[0041] P=f(q,H)(1)

[0042] Where P represents hydropower output, q represents the power generation reference flow, and H represents the water head;

[0043] Step S2: As shown in the attached Figure 2 As shown, construct Three-dimensional coordinate system, take N on the H axis H +1 coordinate point, (where H 1 and are the lower and upper bounds of the working water head of the hydropower station respectively), for the mth interval [H m ,H m +1 ], take its center point As a representative of the interval, we get N H Unary Function ;

[0044] Step S3: For each given A univariate function of Perform linear segmentation processing;

[0045] Step S4: constructing constraints corresponding to the hydropower output relationship, wherein the constraints include interval head limit, power generation reference flow limit and power generation output limit;

[0046] ①The head limit of the interval is expressed as:

[0047] (2)

[0048] (3)

[0049] In formula (2-3), α m (m=1 ,…,N H ) is a set of 0-1 binary variables introduced, and formula (3) limits the existence of only one α m The value of is 1, which means that the water head H in a certain period of time is in the interval;

[0050] ② The power generation reference flow limit is expressed as:

[0051] (4)

[0052] (5)

[0053] (6)

[0054] (7)

[0055] In formula (4-5) is the introduced “weight” variable, whose value is between 0 and 1, and the sum is 1, as The weight of the segmentation point; To ensure that valid segments are used for approximation, the 0-1 binary variable introduced in equations (6-7) , it is limited that there are only two adjacent weights that take non-zero values, and the other weights are zero; note that η n β n The number of variables is one less, that is, the number of segments is one less than the segment points.

[0056] ③ To ensure that the selected unitary output relationship has a water head and an α value of 1 m Correspondingly, the hydropower output limit is expressed as:

[0057] (8)

[0058] Where M is the upper limit of hydropower output. is a set of 0-1 binary variables introduced, with only one α m The value of is 1, and the rest of α m The value of α is 0. m =1, formula (8) is transformed into:

[0059] (9)

[0060] show The unary output relation representing the interval is used to approximate the output of the corresponding area; conversely, for any , formula (8) is transformed into

[0061] (10);

[0062] This is a free constraint because the large M makes the left side less than the lower limit of the output and the right side greater than the upper limit of the output. In this case, the formula is always valid.

[0063] At this point, the binary inseparable hydropower output relationship is approximated as a linear relationship, while avoiding the complex coupling relationship of integer variables and reducing the complexity of the model.

[0064] Step S5: calling a mixed integer programming solver to solve the model and obtain the optimal hydropower output process, wherein the solver is a Gurobi solver, and the minimum thermal power cost is $39894.0, and the calculation time is 14 seconds, which is better than the results reported in existing literature.

[0065] The above description is only a preferred embodiment of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A one-dimensional linear approximation method for hydropower output, It is characterized in that The specific steps include: Step S1: Collect and organize hydropower output data, analyze the hydropower output relationship, and express the hydropower output relationship as a binary function of water head and power generation reference flow: P=f(q,H)(1) Where P represents hydropower output, q represents the power generation reference flow, and H represents the water head; Step S2: Build Three-dimensional coordinate system, take N on the H axis H +1 coordinate point, For the mth interval [H m ,H m+1 ], take its center point As a representative of the interval, we get N H Unary Function ; Step S3: For each given The univariate function of Perform linear segmentation processing; Step S4: constructing constraints corresponding to the hydropower output relationship, wherein the constraints include interval head limit, power generation reference flow limit and power generation output limit; ①The head limit of the interval is expressed as: （2） （3） In formula (2-3), α m (m=1 ,…,N H ) is a set of 0-1 binary variables introduced, and formula (3) limits the existence of only one α m The value of is 1, which means that the water head H in a certain period of time is in the interval; ② The power generation reference flow limit is expressed as: （4） （5） （6） (7) In formulas (4 - 5) is the introduced "weight" variable, whose value ranges from 0 to 1 and the sum is 1, and serves as the weight of the segmentation point; the 0 - 1 binary variable introduced in formulas (6 - 7) limits that only two adjacent weights take non - zero values and the other weights are zero; ③The hydropower output limit is expressed as: （8） Where M is the upper limit of hydropower output. is a set of 0-1 binary variables introduced, with only one α m The value of is 1, and the rest of α m The value of α is 0. m =1, formula (8) is transformed into: （9） show The unary output relation representing the interval is used to approximate the output of the corresponding area; conversely, for any , formula (8) is transformed into （10）； Step S5: calling a mixed integer programming solver to solve and obtain the optimal hydropower output process.

2. A one-dimensional linear approximation processing method for hydropower output according to claim 1, It is characterized in that The solver is a Gurobi solver.

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