Optimization method for water hammer protection of long-distance heating pipelines based on PSO algorithm

Abstract

The present invention discloses a method for optimizing water hammer protection of a long-distance heating pipeline during pump stop based on a PSO algorithm. The method uses the PSO algorithm to optimize the protection of a long-distance heating pipeline during pump stop based on the fast closing time t1, fast closing angle β1, slow closing time t2, slow closing angle β2 of a two-stage slow closing butterfly valve, the initial gas volume V of a gas pressure tank, and the initial gas volume V of a gas pressure tank. a0 , initial liquid level H s0 , cross-sectional area A s Using the pipeline's maximum pressure head #imgabs0#, minimum pressure head #imgabs1#, and maximum centrifugal pump reverse speed #imgabs2# as the objective function, the optimal equipment parameters for the two-stage slow-closing butterfly valve and gas pressure tank are determined, ensuring the pipeline's pressure-bearing capacity and without compromising the performance of the pump unit. This reduces the maximum pressure of pump-off water hammer and eliminates negative pressure in the pipeline. Based on the calculation results of steady-state and pump-off water hammer conditions, this paper establishes an optimization mathematical model for the two-stage slow-closing butterfly valve and gas pressure tank, and simultaneously optimizes them using a PSO algorithm. This results in an effective, reliable, and economical optimization solution for pump-off water hammer protection in long-distance heating pipelines.

Description

Technical Field

[0001] The present invention relates to the technical field of long-distance heating pipelines, and in particular to a PSO algorithm-based optimization method for preventing water hammer during pump shutdown in long-distance heating pipelines. Background Art

[0002] With the maturity and promotion of large temperature difference heating technology, long-distance heat transmission has more obvious economic advantages and has become an effective solution to solve the problem of increasing urban heating area and insufficient pipeline transmission capacity. For example, a long-distance heating project uses a power plant in the suburbs of a city as a heat source, and through the use of exhaust steam waste heat and large temperature difference heating technology, it can achieve heating to the urban area of ​​a city (such as Figure 1 However, because long-distance heating systems often require a large number of relay pumping stations with high pump heads, large height differences, and multiple pumping stations connected in series, a pump failure at a relay pumping station can produce significant water hammer. The resulting water hammer pressure and vaporization can cause severe damage to pipelines. Therefore, water hammer has become a major issue in the heating industry that needs to be addressed urgently.

[0003] Pump-stop water hammer occurs when a pump unit stops due to a momentary power outage or other incident, resulting in the valve not actuating. This sudden change in flow velocity at the pump outlet causes a series of rapid, alternating pressure and flow shocks within the pipeline. The positive pressure wave generated by water hammer can cause pipe ruptures, heat interruptions, and equipment damage. The negative pressure wave generated by water hammer causes a pressure drop within the pipeline. When the pressure falls below the vaporization pressure of the hot water, a steam cavity is created within the pipeline, leading to the separation of the water columns. When the pressure rises, the steam cavity disappears, and the two separated water columns reunite, creating a higher pressure rise and greater damage. High pressure can significantly shorten the life of pipelines.

[0004] In order to avoid or reduce the damage of water hammer, water hammer protection devices should be installed in the system. Common ones include two-stage slow-closing butterfly valves, gas pressure tanks, etc. (such as Figure 2Two-stage slow-closing butterfly valves are typically installed at the outlet of water pumps in long-distance heating systems. By programming the valve's closing action and closing time, the valve automatically closes to a specific angle after a pump shutdown, preventing excessive backflow and excessive reverse speed. It then closes more slowly to prevent water hammer. A gas pressure tank contains a metal water tank filled with a constant amount of compressed air. When pipeline pressure rises, the air in the tank is compressed again, reducing the pressure buildup from water hammer. When pipeline pressure decreases, the air in the tank expands, allowing water to flow into the pipeline, avoiding the flow-interruption and bridging water hammer caused by the separation of the water column and mitigating the risk of overpressure and pipe bursts. Long-distance transmission systems typically incorporate a variety of water hammer protection measures. The closing procedure of the two-stage slow-closing butterfly valve and the size of the gas pressure tank are crucial to the economic and safety aspects of the project, so both require optimization.

[0005] Due to the large scale of the long-distance heating system, using traditional algorithms to solve the above optimization problem will result in excessive computational complexity and long calculation time, and the initial value of the iteration needs to be limited. Otherwise, it is easy to fail to converge or the optimal solution sought may not be the global optimal solution. Summary of the Invention

[0006] The purpose of the present invention is to address the technical defects existing in the prior art and provide a long-distance heating pipeline pump stop water hammer protection optimization method based on the PSO algorithm with higher global convergence. Based on the PSO algorithm, under the conditions of meeting the pipeline pressure bearing capacity and not damaging the performance of the water pump unit, the two-stage slow-closing butterfly valve closing procedure and the main characteristic parameters of the gas pressure tank that affect the water hammer protection effect are simultaneously optimized to reduce the maximum pressure of the pump stop water hammer, eliminate the negative pressure state of the pipeline, realize the reliable operation of the long-distance heating system, and reduce the project investment.

[0007] The technical solution adopted to achieve the purpose of the present invention is:

[0008] A PSO-based optimization method for water hammer protection of long-distance heating pipelines during pump shutdown is proposed. The PSO algorithm is used to calculate the fast closing time t1, fast closing angle β1, slow closing time t2, slow closing angle β2 of the two-stage slow closing butterfly valve, the initial gas volume V of the gas pressure tank, and the initial gas volume V of the gas pressure tank. a0 , initial liquid level H s0 , cross-sectional area A s As the decision variable, the maximum pressure head of the pipeline Minimum pressure head Maximum centrifugal pump reverse speed As the objective function, under the conditions of meeting the pipeline pressure bearing capacity and not damaging the performance of the water pump unit, the optimal equipment parameters of the two-stage slow-closing butterfly valve and the gas pressure tank are solved to reduce the maximum pressure of the water hammer when the pump is stopped and eliminate the negative pressure state in the pipeline.

[0009] Based on the calculation results of steady-state working conditions and pump-stop water hammer working conditions, the present invention establishes a two-stage slow-closing butterfly valve and a gas pressure tank optimization mathematical model, and uses the PSO algorithm to optimize both simultaneously, which can obtain an effective, reliable and economical optimization scheme for long-distance heating pipeline pump-stop water hammer protection measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of a long-distance heat supply system according to an embodiment of the present invention.

[0011] Figure 2 This is a schematic diagram of the arrangement of a long-distance heating system according to an embodiment of the present invention, in which a two-stage slow-closing butterfly valve and a gas pressure tank are simultaneously provided.

[0012] Figure 3 This is a flow chart of a method for optimizing water hammer protection during pump shutdown in long-distance heating pipelines based on a PSO algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0014] For long-distance heating systems, a single water hammer protection measure often fails to meet protection requirements. A comprehensive protection solution, encompassing multiple different water hammer protection devices, is often necessary. Therefore, the design of comprehensive water hammer protection measures often involves optimizing numerous equipment parameters.

[0015] Based on simulation results of water hammer conditions during long-distance heating system shutdown, this embodiment of the present invention establishes a mathematical model for optimizing the parameters of a two-stage slow-closing butterfly valve and a gas pressure tank. This model is solved using a PSO algorithm, and based on the calculation results, an effective, reliable, and economical optimization scheme for protective measures is derived. This approach simplifies design work and improves efficiency; it also provides the optimal solution for a given project, conserving resources. This approach is of great significance for the design of water hammer protection for long-distance heating system shutdowns and their safe and stable operation.

[0016] like Figure 1 As shown, the optimization method for water hammer protection of long-distance heating pipelines based on the PSO algorithm in the embodiment of the present invention converts the optimization problem of water hammer protection measures for long-distance heating pipelines to the following optimization problem:

[0017] Taking the fast closing time, fast closing angle, slow closing time, slow closing angle of the two-stage slow-closing butterfly valve, the initial gas volume, initial liquid level and cross-sectional area of ​​the gas pressure tank as decision variables, and the maximum pressure head, minimum pressure head and maximum reverse speed of the centrifugal pump as objective functions, the optimal equipment parameters of the two-stage slow-closing butterfly valve and the gas pressure tank are solved under the conditions of meeting the pipeline pressure capacity and not damaging the performance of the water pump unit, so as to reduce the maximum pressure of the water hammer when the pump is stopped and eliminate the negative pressure state in the pipeline, thereby achieving reliable operation of the long-distance heating system and reducing project investment.

[0018] The optimization problem can be described mathematically as follows:

[0019] Objective function:

[0020] 1. To prevent overpressure damage to the pipeline, the maximum pressure head of the pipeline must be as small as possible, less than the pressure bearing capacity of the pipeline. The smaller the better.

[0021]

[0022] Where i is the pipeline node; NS is the number of nodes; j is the calculation time; T max To calculate the final time; is the maximum pressure head of the pipeline, and min represents its minimum value.

[0023] 2. To prevent pipeline damage caused by negative pressure, the minimum pressure head of the pipeline must be as large as possible, the larger the better;

[0024]

[0025] Where, is the minimum pressure head in the pipeline, and max is its maximum value.

[0026] 3. Centrifugal pump ( Figure 2 Reverse speed of the water pump

[0027]

[0028] Where, is the reverse speed of the centrifugal pump.

[0029] The weighted combination method is used to unify the above multi-objective optimization problem into a single-objective optimization problem for solution.

[0030] In order to avoid large differences in the order of magnitude of each sub-objective function, each sub-objective function is first divided by its own benchmark value to achieve dimensionlessness, and then multiplied by the corresponding weight coefficient and summed to obtain a new objective function, which is expressed as follows:

[0031]

[0032] Where, Respectively represent the benchmark values ​​of each sub-objective function; They represent the weight coefficients of each sub-objective function, and their values ​​can be set according to the actual project conditions.

[0033] Decision variables:

[0034] Select the fast closing time t1, fast closing angle β1, slow closing time t2, slow closing angle β2 of the two-stage slow closing butterfly valve, and the initial gas volume V of the gas pressure tank a0 , initial liquid level H s0 , cross-sectional area A s As a decision variable, the objective function can be rewritten as follows:

[0035] min(F)=f(t1, β1, t2, β2, V a0 , H s0 ,As) (2)

[0036] Constraints:

[0037] (1) System constraints

[0038] ΔH V =C V Q 2 (3)

[0039]

[0040]

[0041] Equations (3)-(5) are the boundary conditions of the two-stage slow-closing butterfly valve; where ΔH V C is the head loss of the fluid passing through the valve; V is the characteristic parameter of the valve; Q is the flow rate through the valve; ξ is the valve plate at a certain closing angle α g The local resistance coefficient when T g A is the total valve closing time; V The valve plate is at a certain closing angle α g The effective flow area when g is the acceleration due to gravity.

[0042] PV z =C (6)

[0043] Q in =Q out +Q s (7)

[0044]

[0045]

[0046]

[0047] Equations (6)-(10) are the boundary conditions at the gas pressure tank; where P is the absolute pressure of the gas in the tank; V is the volume of the gas in the tank; z is the polytropic index when the gas changes; C is the polytropic constant of the gas change in the tank; Q in , Q out , Q s They represent the flow rates flowing into and out of the bottom pipe node of the air tank and the flow rate flowing into the air tank respectively; H s is the height of the liquid in the pressure tank; Δt is the calculation time step; Q s0 is the initial flow rate into the air tank; σ is the resistance coefficient of the throttling orifice; v is the flow velocity through the throttling orifice; H p is the pressure value of the node at the bottom of the pressure tank; γ is the bulk density of water; H b is a standard atmospheric pressure value; H a H is the resistance loss of water flowing through the throttle port of the air pressure tank; t is the geometric height of the pipe where the air tank is installed.

[0048] (2) Pressure head constraints

[0049]

[0050]

[0051]

[0052] According to the requirements of the "Pump Station Design Specifications", after taking water hammer protection measures, the maximum water hammer pressure of the pipeline should be less than 1.3 to 1.5 times the rated working pressure of the pump.

[0053] Where H P P is the rated working pressure of the water pump. To ensure the safety of the system, take the minimum value of 1.3 times. No water column separation should occur in any part of the system. Due to the different temperatures of hot water transported in actual heating projects, the pressure value when water vaporization produces steam cavity and then water column separation occurs is different. s The saturated steam pressure of water at a certain heating temperature should be determined based on actual project parameters. Negative pressure is not permitted in the system, and the minimum pressure head in the pipeline is usually higher than -2 meters of water column.

[0054] (3) Reverse rotation constraints of centrifugal pumps

[0055]

[0056] t re ≤120 (15)

[0057] According to the requirements of the "Pump Station Design Code", after taking water hammer protection measures, the maximum reverse speed of the centrifugal pump should not exceed 1.2 times the rated speed, and the duration of exceeding the rated speed should not exceed 2 minutes. n is the rated speed of the centrifugal pump; t re The time during which the centrifugal pump reverses and exceeds the rated speed.

[0058] (4) Two-stage slow closing valve constraints

[0059] T g ≤T g ′ (16)

[0060]

[0061] The total closing time of the two-stage slow-closing valve should not exceed the maximum allowable time, and the fast closing speed should be greater than the slow closing speed. g ' is the maximum allowed time.

[0062] Since the above optimization problem is a nonlinear optimization problem, conventional pure mathematical calculation methods are difficult to solve and have poor global convergence, so the particle swarm optimization (PSO) algorithm is used for optimization solution.

[0063] Particle swarm optimization (PSO) algorithm is a bionic algorithm based on swarm intelligence, which solves optimization problems by imitating the foraging of bird flocks.

[0064] The basic idea of ​​the particle swarm optimization (PSO) algorithm is:

[0065] In a D-dimensional search space, a population of N random particles is designed. The optimal solution (food location) of the optimization problem is searched by imitating the foraging behavior of birds in a flock. Particles are individuals in the group. Each individual has its own position X and velocity V. The position represents the direction of movement, and the velocity represents the speed of movement. The position of the nth particle is X n =[X n，1 , X n，2 ,…,X n，D ] T , the speed is V n =[V n，1 , V n，2 ,…,V n，D ] T .

[0066] First, each individual searches for the optimal solution in the search space independently. Then, by imitating the flock of birds, it adjusts its search path (position and speed) based on its own experience (the optimal location of its own historical search) and communication between the flock (the optimal location of the flock's historical search). In other words, the particle continuously iterates and optimizes itself through its "learning ability". The position of each individual closest to the optimal solution during the iterative process is called the "individual extreme value" of the particle, denoted as pbest. is the “individual extreme value” of the nth particle at the kth iteration. The position of all particles in the entire population that is closest to the optimal solution during the iteration process is called the “global extreme value” of the population, denoted as gbest, gbest (k) is the “global extreme value” of the population at the kth iteration.

[0067] The quality of the position searched by each particle is judged by the particle's "fitness value", which is determined by the objective function F, denoted as f. is the fitness of the nth particle at the kth iteration, and the calculation formula is as follows:

[0068]

[0069] When calculating the fitness f, hydraulic calculations can be performed according to the algorithm program in patent number CN202111272286.5 "Numerical simulation algorithm for water hammer caused by pump stoppage in long-distance heating system considering steam cavity interruption and bridging" to obtain the maximum pressure head of the pipeline. Minimum pipeline pressure head Centrifugal pump reverse speed

[0070] For the particle swarm optimization (PSO) algorithm, the introduction of inertia weight can speed up the convergence of the algorithm. The k-th iteration update formula of the velocity V and position X of the n-th particle is as follows:

[0071]

[0072]

[0073] Where, is the d-th component of the velocity of the n-th particle at the k-th iteration; is the d-th dimension component of the position of the n-th particle at the k-th iteration; ω (k) is the inertia weight at the kth iteration, c1 and c2 are learning factors, corresponding to the particle's ability to summarize itself and learn from other excellent particles, respectively. Usually c1=c2=2 is used; rand represents a random number between (0, 1), which is automatically updated at each iteration, reflecting the randomness of the algorithm. is the d-th dimension component of the “individual extreme value” of the n-th particle at the k-1-th iteration; It is the d-th dimension component of the “global extreme value” of the group at the k-1th iteration; where n = 1, 2, ..., N; d = 1, 2, ..., D (the dimension D of the search space is the degree of freedom of the optimization problem).

[0074] It is worth noting that if the particle speed V is too fast, it is likely to skip the optimal solution directly, but if the speed is too slow, the convergence speed will be slow and the optimal solution will not be reached for a long time. Therefore, a reasonable speed limit must be set, that is, V min ≤V≤V max If the particle speed exceeds the set limit during the iteration, it is necessary to do out-of-bounds processing, that is, when V<V min When V = V min , when V>V max When V = V max .

[0075] Similarly, the particle position X must also be restricted. The search space of the particle should be constrained by the degree of freedom of the optimization problem, that is, the range of the independent variable should satisfy X min ≤X≤X max If the position of the particle exceeds the set limit during the iteration, it is also necessary to do out-of-bounds processing; that is, when X<X min When X=X min , when X>X max When X=X max .

[0076] The speed and position limits of the particles should be set according to the specific optimization problem. For this optimization problem, they should be set according to the constraints of equations (3)-(17).

[0077] For the inertia weight ω, a non-steady-state inertia weight that decreases linearly with the iteration process is generally used, which can make the algorithm more capable of exploration in the early stage and more capable of convergence in the later stage. The inertia weight ω at the kth iteration is (k) The calculation formula is:

[0078]

[0079] Where: ω1 is the initial inertia weight, usually ω1 = 0.9; ω2 is the final inertia weight, usually ω2 = 0.4; G is the maximum number of iterations.

[0080] When applying PSO for optimization calculations, if the population particle number N and the maximum number of iterations G are too large, the accuracy of the pipeline water hammer protection optimization is guaranteed, but the calculation time is too long. On the other hand, if the population particle number N and the maximum number of iterations G are too small, the calculation time is shortened but the accuracy of the optimization cannot be guaranteed. Therefore, the population particle number N and the maximum number of iterations G need to be set according to the specific optimization problem.

[0081] The following combination Figure 3 The present invention is further described. Figure 3 As shown in the figure, the optimization method for water hammer protection of long-distance heating pipelines based on PSO algorithm is now explained. The parameter settings involved are as follows: population size, that is, the number of particles is N = 30, the maximum number of iterations is G = 500, the search space dimension D = 7, the fast closing time t1, fast closing angle β1, slow closing time t2, slow closing angle β2 of the two-stage slow closing butterfly valve, the initial gas volume V of the gas pressure tank a0 , initial liquid level H s0 , cross-sectional area A s .

[0082] The specific optimization process includes the following steps:

[0083] Step 1: Input the number of swarm particles N, the search space dimension D, and the particle velocity limit V min 、V max , the limit boundary of the particle position X min 、X max , maximum number of iterations G, inertia weights ω1 and ω2, learning factors c1 and c2;

[0084] Step 2: Let k = 0 and randomly initialize the position of each particle in the population within the search space and velocity range. speed

[0085] Step 3: Calculate the initial fitness of all particles according to formula (18)

[0086] Step 4: Update the individual historical optimal position, that is, take the position of each particle As the "individual extreme value", Update the global optimal position of the population and take The position of the particle corresponding to the minimum value in is taken as the "global extreme value" of the population, denoted as gbest (0) ;

[0087] Step 5: Enter the iteration loop, i.e. k = k + 1, update the inertia weight, and calculate the inertia weight ω according to formula (21) (k) ; Update the velocity and position of the particles, and calculate the velocity of each particle according to equations (19) and (20) Location If the particle's speed and position exceed the set range, out-of-bounds processing is required;

[0088] Step 6: Calculate the fitness of all particles

[0089] Step 7: Update the individual historical optimal position. Each search requires comparing the current fitness of all particles with the historical "individual extreme value" of the previous iteration. If the current fitness of the particle is better than the historical value, the "individual extreme value" of the particle is updated, otherwise the historical value is retained. Then order Otherwise, Update the global optimal position of the population and take The position of the particle corresponding to the minimum value in is taken as the "global extreme value" of the group, denoted as gbest (k) ;

[0090] Step 8: Record the current individual optimal position The global optimal position of the population gbest (k) ;

[0091] Step 9: Determine whether the number of iterations k reaches the maximum number of iterations G. If so, output the global optimal position gbest of the population (k) (i.e. the optimal solution to the optimization problem); otherwise, return to step 5.

[0092] The output result of the above-mentioned optimization algorithm is the optimal solution of the optimization problem, that is, the optimized equipment parameters of the two-stage slow-closing valve and the gas pressure tank.

[0093] The basic principles, main features and advantages of the present invention are shown and described above. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments and that the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention.

[0094] Therefore, from any point of view, the embodiments should be regarded as illustrative and non-restrictive, and the scope of the invention is limited by the appended claims rather than the above description. Therefore, it is intended that all changes that fall within the meaning and range of equivalent elements of the claims are included in the present invention, and any figure signs in the claims should not be regarded as limiting the claims involved.

[0095] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on PSO algorithm is characterized by: The PSO algorithm is used to calculate the fast closing time of the two-stage slow closing butterfly valve. , quick closing angle , slow closing time , Slow closing angle , the initial gas volume of the gas pressure tank , initial liquid level , cross-sectional area As the decision variable, the maximum pressure head of the pipeline , minimum pressure head , Maximum centrifugal pump reverse speed As the objective function, under the conditions of meeting the pipeline pressure bearing capacity and not damaging the performance of the water pump unit, the optimal equipment parameters of the two-stage slow-closing butterfly valve and the gas pressure tank are solved to reduce the maximum pressure of the water hammer when the pump is stopped and eliminate the negative pressure state in the pipeline; The steps of optimizing water hammer protection for long-distance heating pipelines using the PSO algorithm are as follows: Step 1: Input the number of particles in the group N, the search space dimension D, and the limit of the particle speed 、 , the limiting boundary of the particle position 、 , maximum number of iterations G, initial inertia weight ω1 and final inertia weight ω2, learning factors c1 and c2; search space dimension D = 7, respectively, the fast closing time of the two-stage slow closing butterfly valve , quick closing angle , slow closing time , Slow closing angle , the initial gas volume of the gas pressure tank , initial liquid level , cross-sectional area ; Step 2: Randomly initialize the position of each particle in the population within the search space and velocity range ,speed ; Step 3: Calculate the fitness of all initial particles ; Step 4: Update the individual historical optimal position and take the position of each particle As an individual extreme value, ; Update the global optimal position of the population and take The position of the particle corresponding to the minimum value in is taken as the global extreme value of the population, which is recorded as ; Step 5: Enter the iteration loop, update the inertia weight, and calculate the inertia weight ; Update the speed and position of the particles and calculate the speed of each particle ,Location The particle's speed and position meet the set speed range and position range. If they exceed the set limit range, they will be processed as out-of-bounds. ； ； In the formula, rand represents a random number between (0, 1), which is automatically updated at each iteration; ; ; Step 6: Calculate the fitness of all particles ; Step 7: Update the individual historical optimal position. Each time the search is performed, the current fitness of all particles is compared with the individual extreme value of the previous iteration. If the current fitness of the particle is better than the historical value, the individual extreme value of the particle is updated. Otherwise, the historical value is retained. , then let = , otherwise let , = ; Update the global optimal position of the population and take The position of the particle corresponding to the minimum value in is taken as the global extreme value of the group, which is recorded as ; Step 8: Record the current individual optimal position , the global optimal position of the population ; Step 9: Determine the number of iterations Whether the maximum number of iterations G is reached, if so, the global optimal position of the population is output ; Otherwise, return to step 5; the output result is the optimal solution to the optimization problem, that is, the optimized two-stage slow-closing valve and gas pressure tank parameters.

2. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on the PSO algorithm according to claim 1 is characterized in that: The maximum pressure head of the pipeline , minimum pressure head , Maximum centrifugal pump reverse speed After the multi-objective optimization problem is transformed into a single-objective optimization problem, the objective function is as follows: ； ； Where, , , Respectively represent the maximum pressure head of the pipeline , minimum pressure head , Maximum centrifugal pump reverse speed The corresponding sub-objective function benchmark value, , , Respectively represent the weight coefficients of the corresponding sub-objective functions.

3. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on the PSO algorithm according to claim 2 is characterized in that: Maximum pressure head , minimum pressure head , Maximum reverse speed of centrifugal pump The corresponding sub-objective functions are as follows: ； Where, is a pipeline node; is the number of nodes, To calculate the time; To calculate the final time; ； 。 4. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on the PSO algorithm according to claim 3 is characterized in that: The constraints of the objective function include: (1) System constraints, including boundary conditions at the two-stage slow-closing butterfly valve and the gas pressure tank: The boundary conditions at the two-stage slow-closing butterfly valve are as follows: ； ； ； Where, The head loss of the fluid passing through the valve; is the characteristic parameter of the valve; is the flow rate through the valve; The valve plate is at a certain closing angle The local resistance coefficient when is the total valve closing time; The valve plate is at a certain closing angle The effective flow area when is the acceleration due to gravity; Among them, the boundary conditions at the gas pressure tank are as follows: ； ； ； ； ； in, is the absolute pressure of the gas in the tank; is the volume of gas in the tank; It is the polynomial index when the gas changes; is the variable constant of the gas change in the tank; 、 、 They represent the flow rates flowing into and out of the pipe node at the bottom of the air tank and the flow rate flowing into the air tank respectively; is the height of the liquid in the pressure tank; is the calculation time step; is the initial flow rate into the air tank; is the throttling orifice resistance coefficient; is the flow rate through the throttling orifice; is the node pressure value at the bottom of the pressure tank; is the bulk density of water; is a standard atmospheric pressure value; It is the resistance loss of water flowing through the throttle of the air pressure tank; The geometric height of the pipe where the air tank is installed; (2) Pressure head constraint ； ； ； Where, is the rated working pressure of the pump, It is the saturated steam pressure of water at a certain heating temperature. Negative pressure is not allowed. The minimum pressure head of the pipeline is higher than -2m water column. (3) Centrifugal pump reversal constraints ； ； Where, is the rated speed of the centrifugal pump; The time during which the centrifugal pump reverses and exceeds the rated speed; (4) Two-stage slow-closing valve constraints ； ； The total closing time of the two-stage slow-closing valve does not exceed the maximum allowed time , the fast closing speed is greater than the slow closing speed.

5. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on the PSO algorithm according to claim 1 is characterized in that: The calculation formula for each particle's fitness is as follows: 。 6. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on the PSO algorithm according to claim 1 is characterized in that: The inertia weight The calculation formula is as follows: 。 7. The optimization method for water hammer protection during pump shutdown of long-distance heating pipelines based on the PSO algorithm according to claim 1 is characterized in that: The speed and position of the particle meet the set speed range and position range. If they exceed the set limit range, the particle will be processed as out of bounds: satisfy ,when When, take ,when When, take ; Make the particle position satisfy , when X When, take ,when When, take .

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