Method for simulating annual hourly fast operation of step reversible hydropower station

Abstract

The present application relates to a kind of step reversible hydroelectric station annual hour level fast operation simulation method, comprising the following steps: S1, according to the operation of reversible hydroelectric station, considering output, head, flow and reservoir capacity constraint condition, with the maximum total output of power station as objective function, establish reversible hydroelectric station operation simulation model;Based on the first-order Taylor expansion and linearization method of nonlinear function, the nonlinear part in operation simulation model is linearized, and the model is simplified into mixed integer linear programming model;According to the runoff data and operating parameters of the upstream of reversible hydroelectric station, the operation simulation model is solved, and the operation simulation result is obtained.The present application is solved in the form of simple linear programming or mixed integer linear programming, improves solving speed and stability, better optimizes the power system operation strategy of reversible hydroelectric station, improves energy utilization efficiency, reduces system operation cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electrical engineering, more particularly to a kind of annual hour level fast operation simulation method of cascade reversible hydropower station. BACKGROUND

[0002] Reversible hydropower station can carry out power generation and energy storage operation, with the ability to regulate grid load, store energy and balance power supply and demand. In the operation optimization of power system, accurate and efficient operation simulation of hydropower station is crucial for the economic operation of the system. In the traditional long-term operation simulation method of power system, due to the need to consider various complex constraints in the process of hydropower station operation simulation, such as power output, water head change, flow limit and reservoir capacity limit, etc. Nonlinear, non-convex optimization problem, it is difficult to ensure that the global optimal solution is found, and the complexity and computational burden of simulation are increased, often ignoring the water head change, operation constraints, etc. Lead to inaccurate simulation of operation, difficult to practical application. SUMMARY

[0003] The technical problem to be solved by the present application is to provide an annual hour level fast operation simulation method of cascade reversible hydropower station, which can simulate the operation of cascade reversible hydropower station more quickly and accurately.

[0004] The technical scheme adopted by the present application to solve its technical problem is: a kind of annual hour level fast operation simulation method of cascade reversible hydropower station is constructed, including the following steps:

[0005] S1, operation simulation model establishment: according to the operation of reversible hydropower station, considering the output, water head, flow and reservoir capacity constraint condition, taking the maximum total power output of power station as objective function, establish reversible hydropower station operation simulation model;

[0006] S2, model linearization: based on the first-order Taylor expansion and linearization method of nonlinear function, the bilinear part in the operation simulation model is linearized, and the model is simplified into a mixed integer linear programming model;

[0007] S3, model solution: according to the runoff data and operation parameters of upstream reversible hydropower station, the operation simulation model is solved, and the operation simulation result is obtained.

[0008] According to the above scheme, in step S1, the conventional cascade power station model formula is as follows:

[0009]

[0010] Among them, total power output, unit output, total power flow, unit power flow, Indicates total increase in reserve. Indicates that the unit is on standby. Indicates total downgrade reserve. Indicates that the unit is downgraded to standby, ρ indicates the density of water, g indicates the acceleration of gravity, η hydro Indicates the conversion efficiency of conventional cascade power stations. represents the generating head, Indicates the maximum output of the operating range in the vibration zone, H i,t Indicates the water level of the upper reservoir, Indicates the tailwater height, represents the head loss, Indicates the discharge flow, f HQ represents the tailwater height-total discharge curve, where the subscripts i, x, and t represent the power station, unit, and time number, respectively;

[0011] The operating constraint formula for conventional power station units is as follows:

[0012]

[0013] in, Indicates the minimum output in the operating range under the vibration zone. Indicates the minimum output of the operating range in the vibration zone. Indicates the maximum output in the operating range under the vibration zone. Indicates the maximum output of the operating range in the vibration zone, A state variable indicating whether the unit is operating in the lower operating range of the vibration zone. The state variable indicating whether the unit is operating in the vibration zone. Indicates the maximum downstream flow rate, Indicates the maximum power generation flow, f QH Represents the maximum discharge flow-upper reservoir water level curve, H min,i,x Indicates the minimum head, H max,i,x Indicates the maximum water head;

[0014] The operating model formula of the reversible power station is as follows:

[0015]

[0016]

[0017] in, Indicates the total output of the reversible power station, Represents the generating power of the reversible unit, Indicates the pumping power of the reversible unit, represents the total flow of the reversible power station, represents the power generation flow of the reversible unit, Indicates the pumping flow of the reversible unit, Indicates that the reversible power station is always on standby. Indicates that the generator set is put on standby. Indicates that the pumping unit is on standby. Indicates that the reversible power station is always in reserve. Indicates that the generator set is lowered to standby mode. Indicates that the pumping unit is lowered to standby, η gen Indicates the power generation energy conversion efficiency, represents the generating head, η pump represents the pumping energy conversion efficiency, Indicates the pumping head, Indicates the maximum power output. Indicates the maximum pumping power, H i,t Upstream reservoir water level, H i+1,t represents the water level of the downstream reservoir, Indicates head loss;

[0018] The operating constraints of a reversible power plant are as follows:

[0019]

[0020]

[0021] in, Indicates the minimum power output, Indicates the maximum power output. represents the minimum pumping power, Indicates the maximum pumping power, Indicates the state variable of the unit working in power generation condition, Indicates the state variable of the unit working in pumping condition, represents the minimum generating head, represents the maximum generating head, Indicates the minimum pumping head, Indicates the maximum pumping head;

[0022] The reservoir operation model and constraint formula are as follows:

[0023]

[0024]

[0025] Among them, f HV represents the water level-reservoir capacity curve, Represents the average storage capacity of the reservoir during the period, V i,t represents the reservoir capacity at the beginning of the period, V i,t+1 Represents the reservoir capacity at the end of the period, Vmin Indicates the minimum storage capacity, V max Indicates the maximum storage capacity, It represents the total discharge of the reservoir to the lower level reservoir, Δt represents the length of the time period, represents natural runoff;

[0026] The formula for maximizing the total output optimization objective function is as follows:

[0027]

[0028] Where T represents the total time period and N represents the total number of power stations.

[0029] According to the above scheme, in step S2, the first-order Taylor expansion linearization formula of the cascade hydropower output function is as follows:

[0030]

[0031] in, Indicates the flow rate of the operating interval in the vibration zone, Indicates the flow rate in the operating interval under the vibration zone;

[0032] The first-order Taylor expansion linearization formula for the reversible unit output function is as follows:

[0033]

[0034] The linearization formulas for the tailwater height-total discharge curve, the maximum discharge flow-upper reservoir water level curve, and the water level-storage capacity curve are as follows (taking the water level-storage capacity curve as an example):

[0035]

[0036] Among them, a and b are unknown coefficients.

[0037] According to the above scheme, in step S3, the model solving process is as follows: the cascade reversible hydropower station operation model obtained by first-order Taylor expansion and linearization of nonlinear functions is a mixed integer linear programming model, which can be solved by calling gurobipy solving software in Python.

[0038] According to the above scheme, the specific process of converting the cascade reversible hydropower station operation model into a mixed integer linear programming model through the first-order Taylor expansion and linearization of nonlinear functions includes the following steps:

[0039] S301. Define non-decision variables in the model based on actual data, including natural runoff, water flow time lag, output, head, head, upper and lower flow limits, and energy conversion efficiency;

[0040] S302, input the objective function and constraints of the model into the solver, and define the solution parameters, including the number of iterations and tolerance error;

[0041] S303. Output the model solution results to obtain the operation simulation results of the cascade reversible hydropower station.

[0042] The method for simulating the rapid operation of a cascade reversible hydropower station at the hourly level throughout the year according to the present invention has the following advantages:

[0043] Beneficial effects:

[0044] 1. This invention meticulously considers all aspects of the operation of cascade reversible hydropower stations. It uses a first-order Taylor expansion and linearization technique based on nonlinear functions to transform nonlinear problems into linear problems. By introducing additional variables and constraints to approximate the original nonlinear function, the problem can be solved in the form of linear programming or mixed-integer linear programming, thereby improving the speed and stability of the solution. Advanced mathematical methods are used to improve simulation technology, thereby better optimizing the operation strategy of the hydropower station, improving energy efficiency, and reducing operating costs.

[0045] 2. In order to improve the accuracy of simulation and the efficiency of solution, the present invention adopts the first-order Taylor expansion and linearization technology based on nonlinear functions to transform nonlinear problems into linear problems; there is no need to introduce additional variables and constraints to approximate the original nonlinear function, so that the problem can be solved in the form of simple linear programming or mixed integer linear programming, thereby improving the speed and stability of solution; by balancing the operation of hydropower stations and the difficulty of system solution, and using mathematical methods to improve simulation technology, the operation strategy of the power system including reversible hydropower stations can be better optimized, the energy utilization efficiency can be improved, and the system operation cost can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0047] Figure 1 This is a flow chart of the method for simulating the rapid operation of a cascade reversible hydropower station at the hourly level throughout the year according to the present invention. DETAILED DESCRIPTION

[0048] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0049] like Figure 1 As shown, the method for simulating the rapid operation of a cascade reversible hydropower station at the hourly level throughout the year of the present invention comprises the following steps:

[0050] S1. Run simulation model establishment

[0051] According to the operation status of the reversible hydropower station, considering the constraints such as output, head, flow and reservoir capacity, and taking the maximization of the total output of the power station as the objective function, a reversible hydropower station operation simulation model is established;

[0052] The formula for the conventional cascade power station model is as follows:

[0053]

[0054] in, Indicates the total output, Indicates the unit output. represents the total power generation flow, Indicates the power generation flow of the unit, Indicates total increase in reserve. Indicates that the unit is on standby. Indicates total downgrade reserve. Indicates that the unit is downgraded to standby, ρ indicates the density of water, g indicates the acceleration of gravity, η hydro Indicates the conversion efficiency of conventional cascade power stations. represents the generating head, Indicates the maximum output of the operating range in the vibration zone, H i,t Indicates the water level of the upper reservoir, Indicates the tailwater height, represents the head loss, Indicates the discharge flow, f HQ represents the tailwater height-total discharge curve, where the subscripts i, x, and t represent the power station, unit, and time number, respectively;

[0055] The operating constraint formula for conventional power station units is as follows:

[0056]

[0057]

[0058] in, Indicates the minimum output in the operating range under the vibration zone. Indicates the minimum output of the operating range in the vibration zone. Indicates the maximum output in the operating range under the vibration zone. Indicates the maximum output of the operating range in the vibration zone, A state variable indicating whether the unit is operating in the lower operating range of the vibration zone. The state variable indicating whether the unit is operating in the vibration zone. Indicates the maximum downstream flow rate, Indicates the maximum power generation flow, f QH Represents the maximum discharge flow-upper reservoir water level curve, H min,i,x Indicates the minimum head, Hmax,i,x Indicates the maximum water head;

[0059] The operating model formula of the reversible power station is as follows:

[0060]

[0061] in, Indicates the total output of the reversible power station, Represents the generating power of the reversible unit, Indicates the pumping power of the reversible unit, represents the total flow of the reversible power station, represents the power generation flow of the reversible unit, Indicates the pumping flow of the reversible unit, Indicates that the reversible power station is always on standby. Indicates that the generator set is put on standby. Indicates that the pumping unit is on standby. Indicates that the reversible power station is always in reserve. Indicates that the generator set is lowered to standby mode. Indicates that the pumping unit is lowered to standby, η gen Indicates the power generation energy conversion efficiency, represents the generating head, η pump represents the pumping energy conversion efficiency, Indicates the pumping head, Indicates the maximum power output. Indicates the maximum pumping power, H i,t Upstream reservoir water level, H i+1,t represents the water level of the downstream reservoir, Indicates head loss;

[0062] The operating constraints of the reversible power plant are as follows:

[0063]

[0064] in, Indicates the minimum power output, Indicates the maximum power output. represents the minimum pumping power, Indicates the maximum pumping power, Indicates the state variable of the unit working in power generation condition, Indicates the state variable of the unit working in pumping condition, represents the minimum generating head, represents the maximum generating head, Indicates the minimum pumping head, Indicates the maximum pumping head;

[0065] The reservoir operation model and constraint formula are as follows:

[0066]

[0067] V min ≤V i,t ≤V max

[0068]

[0069]

[0070] Among them, f HV represents the water level-reservoir capacity curve, Represents the average storage capacity of the reservoir during the period, V i,t represents the reservoir capacity at the beginning of the period, V i,t+1 Represents the reservoir capacity at the end of the period, V min Indicates the minimum storage capacity, V max Indicates the maximum storage capacity, It represents the total discharge of the reservoir to the lower level reservoir, Δt represents the length of the time period, represents natural runoff;

[0071] The formula for optimizing the objective function to maximize total output is as follows:

[0072]

[0073] Where T represents the total time period and N represents the total number of power stations.

[0074] S2. Model linearization

[0075] Based on the first-order Taylor expansion and linearization method of nonlinear functions, the nonlinear part of the running simulation model is linearized and the model is simplified into a mixed integer linear programming model;

[0076] The first-order Taylor expansion linearization formula of the cascade hydropower output function is as follows:

[0077]

[0078] in, Indicates the flow rate of the operating interval in the vibration zone, Indicates the flow rate in the operating interval under the vibration zone;

[0079] The first-order Taylor expansion linearization formula for the reversible unit output function is as follows:

[0080]

[0081]

[0082] The linearization formulas for the tailwater height-total discharge curve, the maximum discharge flow-upper reservoir water level curve, and the water level-storage capacity curve are as follows (taking the water level-storage capacity curve as an example):

[0083]

[0084] Among them, a and b are unknown coefficients.

[0085] S3. Model solution

[0086] According to the runoff data and operation parameters upstream of the reversible hydropower station, the operation simulation model is solved and the operation simulation results are obtained.

[0087] The model solving process is as follows:

[0088] The cascade reversible hydropower station operation model, developed through the first-order Taylor expansion and linearization of nonlinear functions, is a mixed-integer linear programming model, which can be solved using the gurobipy solver in Python. First, the non-decision variables in the model are defined based on actual data, including step size, natural runoff, flow lag, output, head, head, upper and lower flow limits, and energy conversion efficiency. The model's objective function and constraints are then input into the solver, and solution parameters, including the number of iterations and tolerance, are defined. Finally, the model solution is output to obtain the operational simulation results of the cascade reversible hydropower station.

[0089] Example

[0090] The example analysis is performed using simplified simulated data. The data is shown in Table 1 below:

[0091] Table 1 Data of upstream and downstream conventional hydropower stations

[0092]

[0093]

[0094] According to the model establishment in step S1, the model linearization in step S2, and the model solution in step S3, the results are shown in Table 2 below:

[0095] Table 2 Simulation results

[0096]

[0097]

[0098]

[0099] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A method for simulating the rapid operation of a cascade reversible hydropower station at the hourly level throughout the year, characterized in that: The following steps are involved: S1. Based on the operation of cascade reversible hydropower stations, considering the output, head, flow and reservoir capacity constraints, and taking the maximization of the total output of the power station as the objective function, a cascade reversible hydropower station operation simulation model is established; The established cascade reversible hydropower station operation simulation model includes: conventional cascade power station model and reversible power station operation model. The operating model formula of the reversible power station is as follows: in, Indicates the total output of the reversible power station, Represents the generating power of the reversible unit, Indicates the pumping power of the reversible unit, represents the total flow of the reversible power station, represents the power generation flow of the reversible unit, Indicates the pumping flow of the reversible unit, Indicates that the reversible power station is always on standby. Indicates that the generator set is put on standby. Indicates that the pumping unit is on standby. Indicates that the reversible power station is always in reserve. Indicates that the generator set is lowered to standby mode. Indicates that the pumping unit is lowered to standby, η gen Indicates the power generation energy conversion efficiency, represents the generating head, η pump represents the pumping energy conversion efficiency, Indicates the pumping head, Indicates the maximum power output. Indicates the maximum pumping power, H i,t Upstream reservoir water level, H i+1,t represents the water level of the downstream reservoir, represents the head loss, ρ represents the density of water, and g represents the acceleration due to gravity; S2. Based on the first-order Taylor expansion and linearization method of nonlinear functions, the bilinear part of the running simulation model is linearized and the model is simplified into a mixed integer linear programming model; S3. Solve the operation simulation model based on the runoff data and operation parameters upstream of the cascade reversible hydropower station to obtain the operation simulation results.

2. The method for simulating the rapid operation of a cascade reversible hydropower station at an hourly level throughout the year according to claim 1, characterized in that: In step S1, the conventional cascade power station model formula is as follows: in, Indicates the total output, Indicates the unit output. represents the total power generation flow, Indicates the power generation flow of the unit, Indicates total increase in reserve. Indicates that the unit is on standby. Indicates total downgrade reserve. Indicates that the unit is lowered to standby, η hydro Indicates the conversion efficiency of conventional cascade power stations. represents the generating head, Indicates the maximum output of the operating range in the vibration zone, H i,t Indicates the water level of the upper reservoir, Indicates the tailwater height, represents the head loss, Indicates the discharge flow, f HQ represents the tailwater height-total discharge curve, where the subscripts i, x, and t represent the power station, unit, and time number, respectively; The operating constraint formula for conventional power station units is as follows: in, Indicates the minimum output in the operating range under the vibration zone. Indicates the minimum output of the operating range in the vibration zone. Indicates the maximum output in the operating range under the vibration zone. Indicates the maximum output of the operating range in the vibration zone, A state variable indicating whether the unit is operating in the lower operating range of the vibration zone. The state variable indicating whether the unit is operating in the vibration zone. Indicates the maximum downstream flow rate, Indicates the maximum power generation flow, f QH Represents the maximum discharge flow-upper reservoir water level curve, H min,i,x Indicates the minimum head, H max,i,x Indicates the maximum water head; The operating constraints of the reversible power plant are as follows: in, Indicates the minimum power output, Indicates the maximum power output. represents the minimum pumping power, Indicates the maximum pumping power, Indicates the state variable of the unit working in power generation condition, Indicates the state variable of the unit working in pumping condition, represents the minimum generating head, represents the maximum generating head, Indicates the minimum pumping head, Indicates the maximum pumping head; The reservoir operation model and constraint formula are as follows: Among them, f HV represents the water level-reservoir capacity curve, Represents the average storage capacity of the reservoir during the period, V i,t represents the reservoir capacity at the beginning of the period, V i,t+1 Represents the reservoir capacity at the end of the period, V min Indicates the minimum storage capacity, V max Indicates the maximum storage capacity, It represents the total discharge of the current reservoir to the lower reservoir, Δt represents the length of the time period, represents natural runoff; The formula for maximizing the total output optimization objective function is as follows: Where T represents the total time period and N represents the total number of power stations.

3. The method for simulating the rapid operation of a cascade reversible hydropower station at an hourly level throughout the year according to claim 2, characterized in that: In step S2, the first-order Taylor expansion linearization formula of the cascade hydropower output function is as follows: in, Indicates the flow rate of the operating interval in the vibration zone, Indicates the flow rate in the operating interval under the vibration zone; The first-order Taylor expansion linearization formula for the reversible unit output function is as follows: The linearization formula for the water level-reservoir capacity curve is as follows: Among them, a and b are unknown coefficients.

4. The method for simulating the rapid operation of a cascade reversible hydropower station at an hourly level throughout the year according to claim 1, characterized in that: The operation model of the cascade reversible hydropower station is a mixed integer linear programming model through the first-order Taylor expansion and linearization of nonlinear functions, which can be solved by calling the gurobipy solving software in Python.

5. The method for simulating the rapid operation of a cascade reversible hydropower station at the hourly level throughout the year according to claim 4, characterized in that: In step S3, the model solving process is as follows: S301. Define non-decision variables in the model based on actual data, including natural runoff, water flow time lag, output, head, head, upper and lower flow limits, and energy conversion efficiency; S302, input the objective function and constraints of the model into the solver, and define the solution parameters, including the number of iterations and tolerance error; S303. Output the model solution results to obtain the operation simulation results of the cascade reversible hydropower station.

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