A method for calculating the theoretical minimum height of a pressure stabilizing tower in a water conveyance system
The optimization model using a particle swarm algorithm addresses the challenge of determining the maximum operating water level in pressure stabilizing towers, providing an efficient method to calculate the minimum tower height, enhancing safety and reducing costs in complex water supply systems.
Patent Information
- Application Number
- CN202210246598.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-14
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2042-03-14
AI Technical Summary
Conventional methods fail to accurately determine the maximum operating water level in pressure stabilizing towers of multi-branch water supply systems, leading to inefficiencies and increased costs due to the need for trial-and-error calculations, which are not suitable for complex systems with varying operating conditions.
A method involving an optimization model using a particle swarm algorithm to calculate the theoretical minimum height of a pressure stabilizing tower, based on constraints and a fitness function, to optimize the maximum operating water level, thereby determining the minimum required tower height.
Efficiently calculates the theoretical minimum height of pressure stabilizing towers, reducing blindness and workload in selecting tower height, and ensuring system safety and cost-effectiveness in long-distance multi-branch water supply projects.
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Figure CN114611057B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a method for calculating the theoretical minimum height of a pressure stabilizing tower, in particular to a method for calculating the theoretical minimum height of a pressure stabilizing tower of a water delivery system. Background Art
[0002] Long-distance water transfer projects are the most direct and effective way to solve the problems of uneven temporal and spatial distribution of water resources and insufficient urban water supply in my country. With the development of cities and the acceleration of urbanization, long-distance water transfer projects are becoming increasingly large-scale and multi-branched, and engineering safety issues are becoming increasingly prominent. Power failure of the water pump or sudden closure of the valve will cause water hammer, threatening the safety of the water transfer system. Since the engineering investment of the pressure stabilizing tower is relatively low and it has a good water hammer protection effect on both water hammer boost and pressure drop waves, it is highly favored in long-distance water supply projects.
[0003] However, the height of the pressure stabilizing tower is often too large due to the limitation of the terrain conditions of the water transmission line. In order to reduce the height of the pressure stabilizing tower, a flow regulating valve is often added upstream of the pressure stabilizing tower. When the flow of the water transmission system is large, the flow regulating valve at the bottom of the pressure stabilizing tower needs to be kept fully open; when the flow of the water transmission system is small, the actual water level in the pressure stabilizing tower can be controlled at a certain critical value by the flow regulating valve, so as to achieve the purpose of reducing the height of the pressure stabilizing tower. In the joint setting scheme of the pressure stabilizing tower and the flow regulating valve, the maximum critical water level in the pressure stabilizing tower is the key factor affecting the height of the pressure stabilizing tower. If the critical water level is selected to be large, the pressure stabilizing tower will be too high and the purpose of reducing the height of the pressure stabilizing tower will not be achieved; if the critical water level is selected to be small, the pressure stabilizing tower will be too low, and the flow regulating valve in front of the tower will excessively reduce the pressure to prevent the pressure stabilizing tower from overflowing, and the pump behind the tower needs to be started to pressurize to meet the downstream water supply requirements, resulting in increased operating costs. For a simpler water transmission system, the maximum critical water level in the pressure stabilizing tower can be obtained by trial calculation. However, in a multi-branch water supply project, the flow of the branch water plants along the line may take any value between zero and the design value, so there are infinite combinations of operating conditions in actual operation. The water level of the surge tower corresponding to each operating condition may be different, and the conventional trial calculation method is obviously unable to meet the needs of actual projects. How to find the maximum operating water level of the surge tower from a large number of combined operating conditions is crucial to the selection of the surge tower height. Summary of the invention
[0004] Purpose of the invention: The purpose of the present invention is to provide a method for calculating the theoretical minimum height of a pressure-stabilizing tower in a water supply system, thereby reducing the blindness and workload in the process of selecting the height of the pressure-stabilizing tower.
[0005] Technical solution: The calculation formula of the theoretical minimum height of the stabilizing tower of the present invention is:
[0006] h tmin =H tmax -Z d +Hsm (1)
[0007] In the formula, h tmin The theoretical minimum height of the pressure stabilizing tower required for the water delivery system to meet normal operation; H tmax It is the maximum water level that may exist in the pressure stabilizing tower when the water delivery system is operating normally; Z d H is the installation height of the bottom of the pressure stabilizing tower; sm The safety height reserved for the voltage stabilizing tower;
[0008] The maximum water level H in the pressure stabilizing tower tmax The optimization model is as follows:
[0009]
[0010] Among them, formula (2) satisfies the following constraints
[0011] Self-flow condition constraints:
[0012]
[0013] Upper and lower limits of upstream reservoir water level:
[0014] H umin ≤H u ≤H umax (4)
[0015] Upper and lower limits of branch water plant flow:
[0016] 0≤q si ≤q di i=1,2…n (5)
[0017] In the formula, H t is the actual operating water level in the pressure stabilizing tower; H v H is the water head of the pressure measuring pipe before the flow regulating valve during normal operation; u Actual operating water level of upstream reservoir; H umax ,H umin are the maximum and minimum operating water levels allowed by the upstream reservoir respectively; h si is the operating water level of the i-th branch water plant; q si is the actual flow of the i-th branch water plant; q ck is the actual flow rate of the kth section of the water main pipeline; q di is the design flow of the i-th branch water plant; α si is the head loss coefficient of the i-th branch water plant; α ck is the head loss coefficient of the kth section of the main pipeline.
[0018] The optimization model is solved based on the particle swarm algorithm.
[0019] The optimization model solving process is as follows:
[0020] 1) The optimization model variables are the water level of the upstream reservoir and the flow of n water plants, so the optimization model space search dimension D = n + 1;
[0021] 2) Assuming that the group consists of M particles, the position of the jth particle (j = 1, 2, ..., M) in the D-dimensional search space is expressed as
[0022] 3) The best position that a particle passes through is recorded as The best position passed by all particles in the entire group is recorded as The velocity of particle j is in The constraint conditions (4) and (5) together constitute the maximum and minimum position range of each particle, which are respectively expressed as
[0023] 4) According to the objective function of formula (2), the fitness function formula (6) is constructed to transform the above constrained optimization problem into an unconstrained optimization problem. The speed and position update formulas of the population particles in the b+1th iteration are written as equations (7) and (8) respectively:
[0024]
[0025]
[0026]
[0027] Where ω is the inertia factor; c1 and c2 are non-negative acceleration constants; r1 and r2 are random numbers ranging from 0 to 1;
[0028] 5) Obtain the maximum operating water level H in the pressure stabilizing tower through the optimization model tmax Then, substituting it into formula (1) can obtain the theoretical minimum height of the stabilizing tower.
[0029] The water delivery system comprises an upstream reservoir, a booster pump station and several branch water plants, wherein a flow regulating valve and a pressure stabilizing tower are arranged in sequence between the upstream reservoir and the booster pump station.
[0030] The flow regulating valve is closely attached to the pressure stabilizing tower.
[0031] When the water delivery system is running at a high flow rate, the flow regulating valve is fully opened; when the water delivery system is running at a low flow rate, the flow regulating valve is used to reduce the excess pressure head of the system, and the water level in the pressure stabilizing tower is controlled at the maximum water level H tmax .
[0032] Beneficial effects: The present invention provides a method for efficiently and accurately calculating the theoretical minimum height of a pressure stabilizing tower by establishing an optimization model for the maximum operating water level in a pressure stabilizing tower in a long-distance multi-branch water supply system, thereby avoiding blindness in the process of selecting the height of the pressure stabilizing tower and effectively reducing the workload. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 It is a schematic diagram of the plan layout of the long-distance multi-branch water delivery system of the present invention;
[0034] Figure 2 This is a schematic diagram of the plan layout of the water delivery project of this embodiment;
[0035] Figure 3 This is a cross-sectional view of the water delivery project of this embodiment;
[0036] Figure 4 This is a graph showing the convergence process of the optimal fitness value of the optimization model. DETAILED DESCRIPTION
[0037] The present invention will be further described below in conjunction with the accompanying drawings.
[0038] like Figure 1 As shown, the long-distance multi-branch water delivery system of the present invention includes an upstream reservoir, a booster pump station and several branch water plants, wherein a flow regulating valve and a pressure stabilizing tower are arranged in sequence between the upstream reservoir and the booster pump station, and the flow regulating valve is close to the pressure stabilizing tower. When the water delivery system is running at a large flow rate, the flow regulating valve remains fully open, and the water supply demand is met by pressurizing the pump station; when the water delivery system is running at a small flow rate, the pressure head of the water delivery system is abundant, and the excess pressure head of the system is reduced by the flow regulating valve, and the water level in the pressure stabilizing tower is controlled at the maximum water level H tmax .
[0039] The calculation formula for the theoretical minimum height of the stabilizing tower is:
[0040] h tmin =H tmax -Z d +H sm (1)
[0041] In the formula, h tmin The theoretical minimum height of the pressure stabilizing tower required for the water delivery system to meet normal operation; H tmax It is the maximum water level that may exist in the pressure stabilizing tower when the water delivery system is operating normally; Z d H is the installation height of the bottom of the pressure stabilizing tower; sm A safe height is reserved for the voltage stabilizing tower.
[0042] Maximum water level H in the pressure stabilizing tower tmax The optimization model is as follows:
[0043]
[0044] Among them, formula (2) satisfies the following constraints
[0045] Self-flow condition constraints:
[0046]
[0047] Upper and lower limits of upstream reservoir water level:
[0048] H umin ≤H u ≤H umax (4)
[0049] Upper and lower limits of branch water plant flow:
[0050] 0≤q si ≤q di i=1,2…n (5)
[0051] In the formula, H t is the actual operating water level in the pressure stabilizing tower; H v H is the water head of the pressure measuring pipe before the flow regulating valve during normal operation; u Actual operating water level of upstream reservoir; H umax ,H umin are the maximum and minimum operating water levels allowed by the upstream reservoir respectively; h si is the operating water level of the i-th branch water plant; q si is the actual flow of the i-th branch water plant; q ck is the actual flow rate of the kth section of the water main pipeline; q di is the design flow of the i-th branch water plant; α si is the head loss coefficient of the i-th branch water plant; α ck is the head loss coefficient of the kth section of the main pipeline.
[0052] The above optimization model is solved based on the particle swarm algorithm, and the solution process is as follows:
[0053] The optimization model variables are the water level of the upstream reservoir and the flow of n water plants, so the optimization model space search dimension is D = n + 1. Assuming that the group consists of M particles, the position of the jth particle (j = 1, 2, ..., M) in the D-dimensional search space is expressed as The position of each particle is a potential solution, that is, a possible operating condition in the water delivery system. The best position that the particle passes through is recorded as The best position passed by all particles in the entire group is recorded as The velocity of particle j is in The constraint conditions (4) and (5) together constitute the maximum and minimum position range of each particle, which are respectively expressed as According to the objective function of formula (2), the fitness function formula (6) is constructed to transform the above constrained optimization problem into an unconstrained optimization problem. The speed and position update formulas of the population particles in the b+1th iteration are written as equations (7) and (8) respectively.
[0054]
[0055]
[0056]
[0057] Where ω is the inertia factor; c1 and c2 are non-negative acceleration constants; r1 and r2 are random numbers ranging from 0 to 1.
[0058] The maximum operating water level H in the pressure stabilizing tower is obtained by optimizing the model tmax Then, substituting it into formula (1) can obtain the theoretical minimum height of the stabilizing tower.
[0059] The present invention establishes an optimization model for the maximum operating water level in a stabilizing tower in a long-distance multi-branch water transmission system, provides a method for directly calculating the theoretical minimum height of the stabilizing tower, reduces the blindness and workload in the process of selecting the height of the stabilizing tower, and is of great significance to long-distance multi-branch water transmission projects.
[0060] Example
[0061] like Figure 2 As shown, the total length of the water transmission line is about 234.1km, of which the main water transmission pipeline is 131.8km long. The total designed flow of the water transmission system is 43.3m 3 / s, the highest operating water level of the upstream reservoir is 70m, the normal operating water level is 65m, and the lowest operating water level is 52m. Other basic parameters of the water delivery system are shown in Tables 1 and 2. A pressure pump station is set up along the water delivery project. In order to protect the safety of the output pipeline and the pump station, a pressure stabilizing tower is planned to be set up between the upstream reservoir and the pump station. The pressure stabilizing tower is located at pile number 95+000, and the tower bottom elevation is 0.7m. The longitudinal section of the main pipeline of the water delivery system and the water head line of the pressure measuring pipe of the water delivery system under small flow conditions are shown in Figure 1. Figure 3 When the water delivery system operates at the normal water storage level design flow, the pumping stations need to be put into operation at the same time, while when it operates at a small flow, the pumping stations do not need to be put into operation to meet the water supply demand.
[0062] Table 1 Basic parameters of branch lines of water delivery system
[0063]
[0064] Table 2 Basic parameters of the main line of the water delivery system
[0065]
[0066] In order to reduce the height of the pressure stabilizing tower, a flow regulating valve is often added upstream of the pressure stabilizing tower. When the flow of the water delivery system is large, the flow regulating valve at the bottom of the pressure stabilizing tower needs to be kept fully open; when the flow of the water delivery system is small, the actual water level in the pressure stabilizing tower can be controlled at a certain critical value by relying on the flow regulating valve. After adding the flow regulating valve, the selection of the maximum critical water level in the pressure stabilizing tower is crucial. If the critical water level is selected to be large, the pressure stabilizing tower will be too high, and the purpose of reducing the height of the pressure stabilizing tower will not be achieved; if the critical water level is selected to be small, the pressure stabilizing tower will be too low, and the flow regulating valve in front of the tower will excessively reduce the pressure to prevent the pressure stabilizing tower from overflowing, and the pump behind the tower will need to be started to pressurize to meet the downstream water supply requirements, resulting in increased operating costs. For this implementation case, during normal operation, the upstream reservoir may take any value between the lowest and highest operating water levels, and the flow of the branch water plant along the line may also be any value between zero and the design value. Therefore, there are an infinite number of combined operating conditions in actual operation. The water level of the pressure stabilizing tower corresponding to each operating condition may be different, and the conventional trial calculation method is obviously unable to meet the needs of actual engineering. Since the maximum operating water level in the pressure stabilizing tower is to be obtained when the pump station behind the pressure stabilizing tower is not in operation as far as possible, the method of the present invention is used to solve the minimum height of the pressure stabilizing tower that meets the safety requirements of the water delivery system.
[0067] Depend on Figure 2 It is known that for this implementation case, a=6, m=11, n=11. According to the empirical values of the particle swarm optimization algorithm parameters, the number of particles M=30, the inertia factor ω=0.8, and the acceleration constants c1=2.0 and c2=2.0 are taken in this calculation. The optimization model is used to perform three independent calculations, and the convergence process of the best fitness value is as follows: Figure 4 The corresponding feasible solutions are shown in Table 3. Figure 4 From the results in Table 3, we can see that the optimal solutions of the three calculations appear in the 5th, 7th and 6th generations respectively, and the number of iterations of the optimal solution does not exceed 10 generations. The optimal solutions obtained by the three independent calculations are all different, that is, there are multiple feasible solutions, but the optimal fitness value of the optimization model is the same, which is 33.506. The optimization model established in this paper is not only efficient, but also has good stability. Take H in formula (1) sm =5.0, so the minimum tower height that meets the safety requirements of the water delivery system is 37.8m. The calculation method of the present invention is used to obtain the minimum tower height of the stabilizing tower, which takes only 0.001s, while the ordinary trial calculation method takes several hours.
[0068] Table 3 Feasible solutions of optimization model
[0069]
Claims
1. A method for calculating the theoretical minimum height of a water delivery system stabilizing tower, characterized in that: The calculation formula for the theoretical minimum height of the stabilizing tower is: h tmin =H tmax -Z d +H sm (1) In the formula, h tmin The theoretical minimum height of the pressure stabilizing tower required for the water delivery system to meet normal operation; H tmax It is the maximum water level in the pressure stabilizing tower when the water delivery system is operating normally; Z d H is the installation height of the bottom of the pressure stabilizing tower; sm The safety height reserved for the voltage stabilizing tower; The maximum water level H in the pressure stabilizing tower tmax The optimization model is as follows: Among them, formula (2) satisfies the following constraints Self-flow condition constraints: Upper and lower limits of upstream reservoir water level: H umin ≤H u ≤H umax (4) Upper and lower limits of branch water plant flow: 0≤q si ≤q di i=1,2…n (5) In the formula, H t is the actual operating water level in the pressure stabilizing tower; H v H is the water head of the pressure measuring pipe before the flow regulating valve during normal operation; u Actual operating water level of upstream reservoir; H umax ,H umin are the maximum and minimum operating water levels allowed by the upstream reservoir respectively; h si is the operating water level of the i-th branch water plant; q si is the actual flow of the i-th branch water plant; q ck is the actual flow rate of the kth section of the water main pipeline; q di is the design flow of the i-th branch water plant; α si is the head loss coefficient of the i-th branch water plant; α ck is the head loss coefficient of the kth section of the main pipeline.
2. The method for calculating the theoretical minimum height of a water delivery system stabilizing tower according to claim 1, characterized in that: The optimization model is solved based on the particle swarm algorithm.
3. The method for calculating the theoretical minimum height of a water delivery system stabilizing tower according to claim 1 or 2, characterized in that: The solution process of the optimization model is: 1) The optimization model variables are the water level of the upstream reservoir and the flow of n water plants, so the optimization model space search dimension D = n + 1; 2) Assuming that the group consists of M particles, the position of the jth particle in the D-dimensional search space is expressed as 3) The best position that a particle passes through is recorded as The best position passed by all particles in the entire group is recorded as The velocity of particle j is in The constraint conditions (4) and (5) together constitute the maximum and minimum position range of each particle, which are respectively expressed as 4) According to the objective function of formula (2), the fitness function formula (6) is constructed to transform the above constrained optimization problem into an unconstrained optimization problem. The speed and position update formulas of the population particles in the b+1th iteration are written as equations (7) and (8) respectively: Where ω is the inertia factor; c1 and c2 are non-negative acceleration constants; r1 and r2 are random numbers ranging from 0 to 1; 5) Obtain the maximum operating water level H in the pressure stabilizing tower through the optimization model tmax Then, substituting it into formula (1) can obtain the theoretical minimum height of the stabilizing tower.
4. The method for calculating the theoretical minimum height of a water delivery system stabilizing tower according to claim 1, characterized in that: The water delivery system comprises an upstream reservoir, a booster pump station and several branch water plants, wherein a flow regulating valve and a pressure stabilizing tower are arranged in sequence between the upstream reservoir and the booster pump station.
5. The method for calculating the theoretical minimum height of a water delivery system stabilizing tower according to claim 4, characterized in that: The flow regulating valve is closely attached to the pressure stabilizing tower.
6. The method for calculating the theoretical minimum height of a water delivery system stabilizing tower according to claim 4, characterized in that: When the water delivery system is running at a high flow rate, the flow regulating valve is fully opened; when the water delivery system is running at a low flow rate, the flow regulating valve is used to reduce the excess pressure head of the system, and the water level in the pressure stabilizing tower is controlled at the maximum water level H tmax .