Centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm

Abstract

The invention belongs to the technical field of compressor group control, and particularly discloses a centrifugal air compressor group combination optimization solution algorithm based on a discrete PSO (particle swarm optimization) algorithm, which comprises the following steps: S1, acquiring operating parameters and 24-hour air flow in a centrifugal air compressor group; s2, calculating power consumption; s3, performing initialization operation on the parameters; s4, calculating the fitness of each individual in the population; s5, finding individual optimal and global optimal particles in the population; s6, updating the speed and the position of the particle; s7, judging whether the updating of the particles is subjected to a certain number of iterations or not; s8, judging whether the population is hopeful or not according to the population diameter; s9, judging whether an error value of calculation results of two previous and later iterations of each group is less than 1% or not; and S10, judging whether the number of iterations reaches 1000 or not. According to the algorithm, on the basis of a basic discrete PSO algorithm, the constraint of the fixed particle flight direction is added, the singular perturbation phenomenon of a particle swarm between a feasible region and an infeasible region of a problem is effectively avoided, and the search efficiency of the discrete PSO algorithm is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of compressor group control, and in particular to a centrifugal air compressor group combination optimization solution algorithm based on a discrete PSO algorithm. Background Art

[0002] The air compressor station is an important facility for providing compressed air in the factory. It adopts a multi-unit fixed load and single-unit adjustment operation mode to set the supply pressure. The process flow of the air compressor station mainly includes air intake, air compression, cooling, water removal, oil removal, storage and transportation. In the whole process flow, it is also necessary to monitor and control each equipment of the air compressor station to ensure the safe and stable operation of the equipment. For example, the pressure and temperature of the compressed air are monitored through pressure sensors and temperature sensors, and the operating parameters of the centrifugal air compressor are adjusted through the control system to meet different gas demand.

[0003] In the existing technology, air compressor stations are basically equipped with remote monitoring systems, which can realize remote data monitoring and start and stop functions. However, they do not have the functions of intelligently controlling the operating status of centrifugal air compressors and automatically adjusting the operating parameters of centrifugal air compressors according to terminal demand, nor can they achieve an efficient operation mode with a balance between supply and demand. Instead, they adjust the gas consumption and pressure by manually starting and stopping the machine according to scheduling requirements to meet the needs of the user end.

[0004] The above-mentioned centrifugal air compressor control method has the following problems: the compressed air system air supply and air consumption cannot be adaptively matched, and the centrifugal air compressors are controlled independently, which aggravates the system pressure fluctuation. Therefore, the output pressure has to be increased, thereby increasing energy consumption. Summary of the invention

[0005] The purpose of the present invention is to provide a centrifugal air compressor group combined optimization solution algorithm based on the discrete PSO algorithm to solve the problem that the air supply and air consumption of the compressed air system cannot be adaptively matched, and the centrifugal air compressors are independently controlled, which aggravates the system pressure fluctuations. For this reason, the output pressure has to be increased, thereby increasing energy consumption.

[0006] To achieve the above object, the basic solution provided by the present invention is: a centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm, comprising the following steps:

[0007] S1: Collect the power, rated flow and other operating parameters of each centrifugal air compressor in the centrifugal air compressor group, the 24-hour air flow in the pneumatic system, and the power consumption of each centrifugal air compressor;

[0008] S2: Based on the 24-hour gas flow rate in S1 and the rated flow rate of each centrifugal air compressor, determine the number of centrifugal air compressors that need to be started, and calculate the total power consumption of the started centrifugal air compressors according to the corresponding power consumption of each centrifugal air compressor to obtain the total power consumption;

[0009] S3: Initialize the total power consumption and check whether the initial population is a feasible solution. If it is a feasible solution, proceed to the next step. If it is an infeasible solution, re-initialize.

[0010] S4: Calculate the fitness of each individual in the initialized population according to the total gas consumption and the total rated gas consumption of the centrifugal air compressor;

[0011] S5: Find the best individual particle in the population and the global best particle, compare the current fitness of the individual with its historical best fitness, take the minimum value as the individual extreme value pbest, and take the minimum value of pbest in the entire population as gbest;

[0012] S6: Update the velocity and position of the particle;

[0013] S7: Determine whether the particle update is iterated 50 times. If it reaches 50 iterations, perform a heuristic quasi-mutation operation. If it does not reach 50 iterations, continue iterating until the particle iterates 50 times, then perform a heuristic quasi-mutation operation.

[0014] S8: judging whether the population that has been subjected to the heuristic quasi-mutation operation in S7 has hope according to the population diameter, and if so, proceeding to the next step; if not, reinitializing the population, generating a new population, and re-judging whether the new population has hope;

[0015] S9: Compare the current power consumption of the promising population in S8 with the power consumption corresponding to the previous iteration. If the power consumption error value is less than 1%, it means that the population is promising, and then proceed to the next step. If the power consumption error value is greater than or equal to 1%, it means that the population is hopeless, then reinitialize 10% of the particles in the population to generate a new population, and return to step S4;

[0016] S10: Check whether the number of iterations reaches 1000. If so, the optimization process ends and the last generation of gbest is the optimal solution. If not, return to step S4.

[0017] The working principle of the present invention is to check whether the current population has the hope of reaching the optimal solution of the objective function by calculating the diameter of the population. In the optimization process, if the diameter of the population is not zero, it means that the population has hope and the optimization continues; if the diameter is equal to or close to zero and the optimal solution or quasi-optimal solution has not been obtained, it means that the population has no hope and the optimization is continued according to the re-optimization ratio r. re-init or number n re-init , reinitialize in the neighborhood of the optimal solution, obtain a new population, and continue the optimization process.

[0018] The beneficial effect of the present invention is that the improved discrete PSO algorithm adds a constraint of a fixed particle flight direction on the basis of the particle position change rule of the basic discrete PSO algorithm. If the position vector of a particle in the population has reached the optimum in a certain dimension, its change probability is reduced or even set to zero, and the corresponding component of the particle position vector remains unchanged in its original state, effectively avoiding the singular perturbation phenomenon of the particle group between the feasible domain and the infeasible domain of the problem, and improving the search efficiency of the discrete PSO algorithm.

[0019] Solution 2 is the preferred basic solution. The specific steps of the initialization operation in step S3 are as follows:

[0020] a. Determine the solution space of the problem and clarify the number and value range of the problem's variables;

[0021] b. Use a random number generator to randomly generate the initial position of the particle;

[0022] c. Randomly generate the initial velocity of particles;

[0023] d. Determine whether the initialization is reasonable. If it is reasonable, proceed to the next step. If it is unreasonable, reinitialize;

[0024] The criterion for judging whether the initialization is reasonable is to ensure that the generated initial population is within the solution space and has diversity. If so, it means that the initialization is reasonable. If not, it means that the initialization is unreasonable.

[0025] Solution 3, which is the preferred basic solution, updates the particle speed and position in step S6 as follows:

[0026]

[0027] where S(·) is the constraint transformation function, rand(·) is a random number uniformly distributed in the interval [0,1], ε is a sufficiently small positive real number, and “x id (K+1)=x id (k)ifv id (k+1)|≤ε” is a constraint on the flight direction of a fixed particle.

[0028] Scheme 4 is the preferred basic scheme. The operation process of the heuristic quasi-mutation in step S7 is as follows:

[0029] Using binary coding, 1 bit in the individual matrix represents the on / off status at a moment, the status 1 represents on, and the status 0 represents off;

[0030] a. For a certain particle, find the start and stop change time of the unit in the control cycle;

[0031] b. Use the counter to calculate the continuous start-up time and continuous shutdown time of the centrifugal air compressor before the change time;

[0032] c. Determine whether the continuous start-stop time is greater than the minimum start-stop time:

[0033] If it is greater than the minimum on / off time, subtract the minimum on / off time from the continuous on / off time to get the number of redundant digits.

[0034] If it is less than the minimum start-up and shutdown time, the missing digits are recorded and the missing digits are supplemented with redundant digits.

[0035] Scheme 5 is the preferred basic scheme. The specific steps of judging whether the population is promising according to the population diameter in step S8 are as follows:

[0036] The no-hope / high-hope criterion introduced in the PSO algorithm,

[0037] First, define the concept of population diameter:

[0038] θ(k)=max (i,j)∈(1,N) D |X i -X j

[0039] For a D-dimensional search space, the search diameter of each dimension is:

[0040] θ d (k) = max (i,j)∈(1,N) D |x i,d -x j,d |d=1,2,....,D

[0041] Among them, θ(k) is the diameter of the population at the kth iteration, X i is the i-th individual in the population, X j is the position of the jth individual in the population, N is the population size, D is the dimension of the search space,

[0042] If the population diameter is greater than zero, it means that this population is promising and proceed to the next step;

[0043] If the population diameter is equal to zero and the optimal solution or quasi-optimal solution has been obtained, it means that this population has hope and proceed to the next step;

[0044] If the population diameter is equal to zero and the optimal solution or quasi-optimal solution has not been found, it means that the population is hopeless. The population is reinitialized to obtain a new population, and then the hope of the population is judged again based on the diameter of the new population.

[0045] Solution 6, which is the preferred basic solution, the modeling formula in step S9 is specifically:

[0046]

[0047] Where Q i,t represents the real-time gas production of centrifugal air compressor i in time period t, U i,t = 0, Q i,t =0;Q imax , Q imin is the upper and lower limits of the gas output of centrifugal air compressor i; ΔT is the time period; E is the total energy consumption of each centrifugal air compressor in the system's 24-hour control cycle; S up,i , S dn,i is the startup and shutdown consumption of centrifugal air compressor i; C m,i is the life loss of each start and stop of centrifugal air compressor i; T1 and T2 are the minimum continuous downtime and minimum continuous operation time of each centrifugal air compressor within 24 hours respectively; T3 is the start-up gas production delay time of each centrifugal air compressor. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of a centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm of the present invention;

[0049] Figure 2 It is the calculation result of the start and stop state of an 8-machine system of a centrifugal air compressor group combined optimization solution algorithm based on a discrete PSO algorithm of the present invention;

[0050] Figure 3 It is a power consumption comparison diagram of two control algorithms before and after improvement of a centrifugal air compressor group combined optimization solution algorithm based on discrete PSO algorithm of the present invention;

[0051] Figure 4 It is a waveform diagram of power saving of the current control algorithm of a centrifugal air compressor group combined optimization solution algorithm based on discrete PSO algorithm of the present invention;

[0052] Figure 5 It is an optimization convergence characteristic diagram of a centrifugal air compressor group combined optimization solution algorithm based on a discrete PSO algorithm before and after improvement of the present invention. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below through specific embodiments:

[0054] As attached Figure 1 As shown:

[0055] A centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm includes the following steps:

[0056] S1: Collect the power, rated flow and other operating parameters of each centrifugal air compressor in the centrifugal air compressor group, the 24-hour air flow in the pneumatic system and the power consumption of each centrifugal air compressor. The parameters of the centrifugal air compressor are shown in Table 1:

[0057] Table 1 Nameplate parameters of each unit in the 8-unit system of the centrifugal air compressor group

[0058]

[0059] S2: Based on the 24-hour gas flow rate in S1 and the rated flow rate of each centrifugal air compressor, determine the number of centrifugal air compressors that need to be started, and calculate the total power consumption of the started centrifugal air compressors according to the corresponding power consumption of each centrifugal air compressor to obtain the total power consumption;

[0060] S3: Initialize the total power consumption and check whether the initial population is a feasible solution. If it is a feasible solution, proceed to the next step. If it is an infeasible solution, re-initialize. The specific steps of the initialization operation are as follows:

[0061] a. Determine the solution space of the problem and clarify the number and value range of the problem's variables;

[0062] b. Use a random number generator to randomly generate the initial position of the particle;

[0063] c. Randomly generate the initial velocity of particles;

[0064] d. Determine whether the initialization is reasonable. If it is reasonable, proceed to the next step. If it is unreasonable, reinitialize;

[0065] The criterion for judging whether the initialization is reasonable is: to ensure that the generated initial population is within the solution space and has diversity. If so, it means that the initialization is reasonable. If not, it means that the initialization is unreasonable.

[0066] S4: Calculate the fitness of each individual in the initialized population according to the total gas consumption and the total rated gas consumption of the centrifugal air compressor;

[0067] S5: Find the best individual particle in the population and the global best particle, compare the current fitness of the individual with its historical best fitness, take the minimum value as the individual extreme value pbest, and take the minimum value of pbest in the entire population as gbest;

[0068] S6: Update the speed and position of the particle. The method of updating the speed and position of the particle is:

[0069]

[0070] where S(·) is the constraint transformation function, rand(·) is a random number uniformly distributed in the interval [0,1], ε is 0.01, and “x id (K+1)=x id (k)ifv id (k+1)|≤ε” is a constraint on the flight direction of a fixed particle. The algorithm control parameters are as follows:

[0071] Inertia weight ω=0.9~0.4, in the iteration process, ω=ω max -β(ω max -ω min ) / β max Uniformly decreases, β is the number of iterations, β max is the maximum number of iterations; the acceleration factor c1=c2=2.0; the re-optimization ratio r re_init =0.1; pseudo mutation rate p m =0.05; the size of the population varies according to the size of the system, the centrifugal air compressor population size = 30;

[0072] S7: Determine whether the particle update has been iterated 50 times. If it has been iterated 50 times, perform the heuristic quasi-mutation operation. If it has not been iterated 50 times, continue iterating until the particle has been iterated 50 times, then perform the heuristic quasi-mutation operation. The operation process of the heuristic quasi-mutation is as follows:

[0073] Using binary coding, 1 bit in the individual matrix represents the on / off status at a moment. The status of 1 represents on, and the status of 0 represents off.

[0074] a. For a certain particle, find the start and stop change time of the unit in the control cycle;

[0075] b. Use the counter to calculate the continuous start-up time and continuous shutdown time of the centrifugal air compressor before the change time;

[0076] c. Determine whether the continuous start-stop time is greater than the minimum start-stop time:

[0077] If it is greater than the minimum on / off time, subtract the minimum on / off time from the continuous on / off time to get the number of redundant digits.

[0078] If it is less than the minimum start-up and shutdown time, the missing digits are recorded and the redundant digits are used to make up for the missing digits;

[0079] S8: Calculate the power consumption of the promising population in S8 according to the modeling formula, and compare the current power consumption with the power consumption corresponding to the previous iteration. If the power consumption error value is less than 1%, it means that the population is promising, and then proceed to the next step. If the power consumption error value is greater than or equal to 1%, it means that the population is hopeless, then reinitialize 10% of the particles in the population to generate a new population, and return to step S4. The specific steps for determining whether the population is promising are as follows:

[0080] The no-hope / high-hope criterion introduced in the PSO algorithm,

[0081] First, define the concept of population diameter:

[0082] θ(k)=max (i,j)∈(1,N) D |X i -X j

[0083] For a D-dimensional search space, the search diameter of each dimension is:

[0084] θ d (k) = max (i,j)∈(1,N) D |x i,d -x j,d |d=1,2,....,D

[0085] Among them, θ(k) is the diameter of the population at the kth iteration, X i is the i-th individual in the population, X j is the position of the jth individual in the population, N is the population size, D is the dimension of the search space,

[0086] If the population diameter is greater than zero, it means that this population is promising and proceed to the next step;

[0087] If the population diameter is equal to zero and the optimal solution or quasi-optimal solution has been obtained, it means that this population has hope and proceed to the next step;

[0088] If the population diameter is equal to zero and the optimal solution or quasi-optimal solution has not been found, it means that the population has no hope. The population is reinitialized to obtain a new population, and the population is judged again based on the diameter of the new population.

[0089] S9: Calculate the power consumption of the promising population in S8 according to the modeling formula, and compare the current power consumption with the power consumption corresponding to the previous iteration. If the power consumption error value is less than 1%, it means that the population is promising, and then proceed to the next step. If the power consumption error value is greater than or equal to 1%, it means that the population is hopeless, then reinitialize 10% of the particles in the population to generate a new population, and return to step S4. The modeling formula is:

[0090]

[0091] Where Q i,t represents the real-time gas production of centrifugal air compressor i in time period t, U i,t = 0, Q i,t =0;Q imax , Q imin is the upper and lower limits of the gas output of centrifugal air compressor i; ΔT is the time period; E is the total energy consumption of each centrifugal air compressor in the system's 24-hour control cycle; S up,i , S dn,i is the startup and shutdown consumption of centrifugal air compressor i; C m,i is the life loss of each start and stop of centrifugal air compressor i; T1 and T2 are the minimum continuous downtime and minimum continuous operation time of each centrifugal air compressor within 24 hours respectively; T3 is the start-up gas production delay time of each centrifugal air compressor. The constraint parameters of each machine in the centrifugal air compressor group are shown in Table 2:

[0092] Table 2 Constraint parameters of each unit in the 8-unit system of centrifugal air compressor group

[0093]

[0094] S10: Check whether the number of iterations reaches 1000. If so, the optimization process ends and the last generation of gbest is the optimal solution. If not, return to step S4.

[0095] As attached Figure 2 As shown: a heuristic quasi-mutation operation mechanism is introduced into the discrete PSO algorithm, and binary coding is adopted. One bit in the individual matrix represents the on / off state at one moment. The state of 1 represents on-state, and the state of 0 represents off-state. If it is greater than the minimum on / off time, the minimum on / off time is subtracted from the continuous on / off time to obtain the redundant number of bits. If it is less than the minimum on / off time, the missing number of bits is recorded, and the redundant number of bits is used to make up for the missing number of bits, so as to ensure that the on / off state of the centrifugal air compressor group is 4 on and 4 off.

[0096] As attached Figure 3 , 4 As shown: the new control algorithm controls the operation of the centrifugal air compressor group units and achieves an energy saving effect of 6.73% compared with the current control strategy, which is equivalent to a daily power saving of 3165kW·h. Assuming that the centrifugal air compressor group runs 350 days a year and the electricity fee is 0.7 yuan / kWh, 3165*350*0.7=775425 (yuan), which can save the company 775425 yuan in electricity fees a year.

[0097] As attached Figure 5As shown in the figure: the general discrete PSO algorithm converges faster in the initial stage of optimization, but falls into a local minimum around the 36th generation, while the convergence speed of the new discrete PSO algorithm in the initial stage of iteration is similar to that of the general discrete PSO algorithm, but it can jump out of the local optimal solution during the search process and continuously approach the global optimal solution, thus converging to a quasi-optimal solution that meets the requirements and improving the convergence accuracy.

[0098] The above is only an embodiment of the present invention, and the common knowledge such as the known specific structure and characteristics in the scheme is not described in detail here. It should be pointed out that for those skilled in the art, several deformations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm, characterized in that: The following steps are involved: S1: Collect the power, rated flow and other operating parameters of each centrifugal air compressor in the centrifugal air compressor group, the 24-hour air flow in the pneumatic system, and the power consumption of each centrifugal air compressor; S2: Based on the 24-hour gas flow rate in S1 and the rated flow rate of each centrifugal air compressor, determine the number of centrifugal air compressors that need to be started, and calculate the total power consumption of the started centrifugal air compressors according to the corresponding power consumption of each centrifugal air compressor to obtain the total power consumption; S3: Initialize the total power consumption and check whether the initial population is a feasible solution. If it is a feasible solution, proceed to the next step. If it is an infeasible solution, re-initialize. S4: Calculate the fitness of each individual in the initialized population according to the total gas consumption and the total rated gas consumption of the centrifugal air compressor; S5: Find the best individual particle in the population and the global best particle, compare the current fitness of the individual with its historical best fitness, take the minimum value as the individual extreme value pbest, and take the minimum value of pbest in the entire population as gbest; S6: Update the particle's velocity and position; S7: Determine whether the particle update is iterated 50 times. If it reaches 50 iterations, perform a heuristic quasi-mutation operation. If it does not reach 50 iterations, continue iterating until the particle iterates 50 times, then perform a heuristic quasi-mutation operation. S8: judging whether the population that has been subjected to the heuristic quasi-mutation operation in S7 has hope according to the population diameter, and if so, proceeding to the next step; if not, reinitializing the population, generating a new population, and re-judging whether the new population has hope; S9: Calculate the power consumption of the promising population in S8 according to the modeling formula, and compare the current power consumption with the power consumption corresponding to the previous iteration. If the power consumption error value is less than 1%, it means that the population is promising, and then proceed to the next step. If the power consumption error value is greater than or equal to 1%, it means that the population is hopeless, then reinitialize 10% of the particles in the population to generate a new population, and return to step S4; S10: Check whether the number of iterations reaches 1000. If so, the optimization process ends and the last generation of gbest is the optimal solution. If not, return to step S4.

2. According to claim 1, a centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm is characterized in that: The specific steps of the initialization operation in step S3 are as follows: a. Determine the solution space of the problem and clarify the number and value range of the problem's variables; b. Use a random number generator to randomly generate the initial position of the particle; c. Randomly generate the initial velocity of particles; d. Determine whether the initialization is reasonable. If it is reasonable, proceed to the next step. If it is unreasonable, reinitialize; The criterion for judging whether the initialization is reasonable is to ensure that the generated initial population is within the solution space and has diversity. If so, it means that the initialization is reasonable. If not, it means that the initialization is unreasonable.

3. The centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm according to claim 1 is characterized in that: The method of updating the particle speed and position in step S6 is: where S(·) is the constraint transformation function, rand(·) is a random number uniformly distributed in the interval [0,1], ε is 0.01, and "x id (K+1)=x id (k)if|v id (k+1)|≤ε” is a constraint on the flight direction of a fixed particle.

4. The centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm according to claim 1 is characterized in that: The operation process of the heuristic quasi-mutation in step S7 is as follows: Using binary coding, 1 bit in the individual matrix represents the on / off status at a moment, the status 1 represents on, and the status 0 represents off; a. For a certain particle, find the start and stop change time of the unit in the control cycle; b. Use the counter to calculate the continuous start-up time and continuous shutdown time of the centrifugal air compressor before the change time; c. Determine whether the continuous start-stop time is greater than the minimum start-stop time: If it is greater than the minimum on-off time, the minimum on-off time is subtracted from the continuous on-off time to obtain the redundant digits. If it is less than the minimum on-off time, the missing digits are recorded and the redundant digits are used to make up for the missing digits.

5. The centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm according to claim 1 is characterized in that: The specific steps of judging whether a population is promising according to the population diameter in step S8 are as follows: The no-hope / high-hope criterion introduced in the PSO algorithm, First, define the concept of population diameter: θ(k)=max (i,j)∈(1,N) D |X i -X j | For a D-dimensional search space, the search diameter of each dimension is: i d (k)=max (i,j)∈(1,N) D |x i,d -x j,d |d=1,2,....,D Among them, θ(k) is the diameter of the population at the kth iteration, X i is the i-th individual in the population, X j is the position of the jth individual in the population, N is the population size, D is the dimension of the search space, If the population diameter is greater than zero, it means that this population has hope and proceed to the next step; If the population diameter is equal to zero and the optimal solution or quasi-optimal solution has been obtained, it means that this population has hope and proceed to the next step; If the population diameter is equal to zero and the optimal solution or quasi-optimal solution has not been found, it means that the population is hopeless. The population is reinitialized to obtain a new population, and then the hope of the population is judged again based on the diameter of the new population.

6. The centrifugal air compressor group combination optimization solution algorithm based on discrete PSO algorithm according to claim 1 is characterized in that: The modeling formula in step S9 is specifically: Where Q i,t represents the real-time gas production of centrifugal air compressor i in time period t, U i,t = 0, Q i,t =0;Q imax , Q imin are the upper and lower limits of the gas output of centrifugal air compressor i; ΔT is the time period; E is the total energy consumption of each centrifugal air compressor in the system's 24-hour control cycle; S up,i , S dn,i is the startup and shutdown consumption of centrifugal air compressor i; C m,i is the life loss of centrifugal air compressor i each time it is started and stopped; T1 and T2 are the minimum continuous downtime and minimum continuous operation time of each centrifugal air compressor within 24 hours respectively; T3 is the start-up gas production delay time of each centrifugal air compressor.

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