A Circuitized Analog Modeling Method for Transmission Delay of a Water Distribution System

Abstract

The present invention discloses a circuitized analog modeling method for the transmission delay of a water distribution system. The water distribution system includes four components: pipelines, water pumps, pressure reducing valves, and water storage tanks. By using the circuitized analog modeling method, circuitized analog models of pipelines, water pumps, and pressure reducing valves are established, so that the partial differential equations of the time-delay effect of the water distribution system are transformed into algebraic equations by the Laplace transform method, reducing the computational complexity and facilitating the maximum exploitation of the dispatchable potential of the electricity consumption power of the water distribution system.

Description

Technical Field

[0001] The present invention belongs to the field of coordinated dispatching of electric - water systems, and particularly relates to a circuit - based analog modeling method for transmission delay in a water distribution system. Background Art

[0002] With the advancement of the carbon neutrality goal, the situation of renewable energy consumption in China will become more severe, and it is urgent to explore more system regulation resources. The electricity consumption of the water distribution system can reach 5% - 10% of the total annual electricity consumption in China. Through the start - stop of pumping stations and the regulation of water storage tanks, the coordinated dispatching of the electric - water system can be realized, which can greatly improve the consumption of renewable energy without additional investment. However, in the water distribution system, it takes a certain transmission time for water to be transported from the water source to users. In a large - scale water distribution system network, the time required to transport water can reach several hours, and its impacts mainly include two aspects: on the one hand, ignoring the transmission delay of the water distribution system may have an adverse impact on the optimal coordinated operation strategy of the power system and the water distribution system; on the other hand, the transmission delay of the water distribution system may provide a new solution idea for the power system to adapt to the large - scale access of future renewable energy. Existing research rarely considers the modeling of the "time - delay effect" characteristic of the water distribution system. Therefore, it is necessary to first model the time - delay effect of the water distribution system, and a dynamic partial differential model of the time - delay effect of the water distribution system can be constructed by analyzing its physical mechanism. Although modeling components from the perspective of physical characteristics is the most accurate, the large number of partial differential equations introduced in the modeling makes the model solution too complex to be practically applied. And traditional methods for dealing with differential models, whether it is the finite - difference method, the finite - element method, or the spectral method, inevitably introduce processes such as function operations, numerical calculations, and differential conversions, resulting in a much more complex solution process than that of algebraic equations. Summary of the Invention

[0003] Aiming at the above - mentioned deficiencies of the existing technology, the purpose of the present invention is to provide a circuit - based analog modeling method for transmission delay in a water distribution system. This modeling method can transform the partial differential equations of the time - delay effect of the water distribution system into algebraic equations by using the Laplace transform method, thereby effectively reducing the computational complexity and maximizing the exploitation of the dispatchable potential of the electricity consumption of the water distribution system.

[0004] The technical solution of the present invention is realized as follows:

[0005] A circuit - based analog modeling method for transmission delay in a water distribution system, which models the pipelines, water pumps, pressure - reducing valves, and water storage tanks involved in the water distribution system, specifically including the following steps:

[0006] S1: Establish a circuit - based analog model of the pipeline

[0007] Use the motion equation (1) and the continuity equation (2) to describe the movement of water flow in the pipeline:

[0008]

[0009]

[0010] Where: v is the water flow velocity in the pipeline; H is the head pressure in the pipeline; α is the water hammer wave velocity; g is the acceleration of gravity; D is the pipeline diameter; t is the time; x is the position along the pipeline length;

[0011] Simplifying (1) and (2) respectively gives (3) and (4):

[0012]

[0013]

[0014] Where: Q is the actual flow rate of water in the pipeline; A is the cross-sectional area of the pipeline;

[0015] Further transforming (3) and (4) into (5) and (6) respectively:

[0016]

[0017]

[0018] Where: sign(Q) is the sign function, when Q > 0, sign(Q) = 1; when Q < 0, sign(Q) = -1; and when Q = 0, sign(Q) = 0;

[0019] Q = Q b + ΔQ, and ΔQ ≈ 0, then:

[0020] Q 2 = (Q b + ΔQ) 2 ≈ (Q b ) 2 + 2Q b ΔQ ≈ 2Q b Q - (Q b ) 2 (7)

[0021] Where: Q b is the reference flow rate of water in the pipeline; ΔQ is the difference between the actual flow rate and the reference flow rate of water in the pipeline;

[0022] Then substituting (7) into (5) gives:

[0023]

[0024] Making an electrical circuit analogy for the pipeline, the analogy results are as follows:

[0025]

[0026] Then, applying the Laplace transform to (6) and (8) to convert them into frequency-domain models respectively gives (9) and (10).

[0027]

[0028]

[0029] where: s is the Laplace operator

[0030] Taking the derivatives of (9) and (10) with respect to x respectively gives (11) and (12).

[0031]

[0032]

[0033] where: γ 2 =(R b +sL b )sC b ; ζ = C b U sb ;

[0034] Solving (11) and (12) respectively gives (13) and (14).

[0035]

[0036]

[0037] where: There are n pipes numbered 1, 2, …, i, …, n in the water distribution system, and i represents the i-th pipe;

[0038] Substituting (13) into (9) gives:

[0039]

[0040] Comparing (14) and (15) gives:

[0041]

[0042]

[0043] Therefore, the flow rate and head pressure of water flowing along the pipe are:

[0044]

[0045] By detecting any two of the four variables of the flow rate and head pressure at the beginning and end of the pipe, it is possible to determine and The value, and then the water flow rate and the change in head pressure input along the pipeline are obtained through (18);

[0046] S2: Establish a circuit-based analog model of the water pump

[0047] When the water pump speed is fixed, the hydraulic model of the water pump can be quantitatively expressed as (19) and (20)

[0048] When the water pump is turned on:

[0049]

[0050] When the water pump is turned off:

[0051]

[0052] In the formula: a Pm , b Pm , c Pm are all conventional coefficients of the water pump; is the head pressure gain of the water pump; is the actual flow rate of the water flow in the water pump; is the minimum flow rate of the water flow in the water pump; is the maximum flow rate of the water flow in the water pump;

[0053] q t p m = q t p m,b +Δq t p m , and Δq t p m ≈0, then:

[0054] (q t p m ) 2 =(q t p m,b +Δq t p m ) 2 ≈(q t p m,b ) 2 +2q t p m,b Δq t p m ≈2q t p m,b q t p m -(q t p m,b ) 2 (21)

[0055] In the formula: qt p m,b is the reference flow rate of the water flow in the water pump; Δq t p m is the difference between the actual flow rate and the reference flow rate of the water flow in the water pump;

[0056] Substituting (21) into (19) gives:

[0057]

[0058] By making a circuit analogy for the water pump, it can be obtained that: is equal to the head pressure H' at the rear end of the water pump Pm minus the head pressure H at the front end of the water pump Pm , that is the resistance of the water pump the voltage source of the water pump Calculated in this way RPm and UPm, and then substituting into (22) can obtain the actual flow rate of the water flow in the water pump

[0059] As the only power-consuming device in the water distribution system, the total power consumption of the water distribution system can be calculated by calculating the power consumption of all water pumps in the system. The power consumption of the water pump and the power consumption of the water distribution system are calculated respectively as:

[0060]

[0061]

[0062] In the formula: k 1 、k 2 、k 3 are all conventional coefficients of the water pump; there are 1, 2,..., j,..., in total water pumps in the water distribution system, and j represents the jth water pump;

[0063] S3: Establish a circuit analogy model for the pressure reducing valve

[0064] The hydraulic model of the pressure reducing valve is:

[0065]

[0066] In the formula: is the head pressure gain of the pressure reducing valve; is the actual flow rate of the water flow passing through the pressure reducing valve m at time t; k V is the opening coefficient of the pressure reducing valve;

[0067] q t Vm = qt V m,b +Δq t Vm and Δq t Vm ≈0 then:

[0068] (q t Vm ) 2 =(q t Vm,b +Δq t Vm ) 2 ≈(q t Vm,b ) 2 +2q t Vm,b Δq t Vm ≈2q t Vm,b q t Vm -(q t Vm,b ) 2 (26)

[0069] Where: q t Vm,b is the reference flow rate of the water flow through the pressure reducing valve; Δq t Vm is the difference between the actual flow rate and the reference flow rate of the water flow through the pressure reducing valve;

[0070] Substituting (26) into (25) gives:

[0071]

[0072] By making an electrical analogy to the water pump, it can be obtained that: is equal to the head pressure H′ at the rear end of the pressure reducing valve Vm minus the head pressure H at the front end of the pressure reducing valve Vm , that is the resistance of the pressure reducing valve the voltage source of the pressure reducing valve Calculated in this way RVm, UVm, and then substituting into (27) can obtain the actual flow rate of the water flow through the pressure reducing valve

[0073] S4: Establish a reservoir model

[0074] Modeling is carried out through a linear water pressure constraint relationship, and the specific constraint relationship is as follows:

[0075]

[0076]

[0077]

[0078] In the formula: is the inlet flow rate of the reservoir at time t; is the outlet flow rate of the reservoir at time t; is the head pressure of the reservoir at time t; is the head pressure of the reservoir at time t + Δt; is the cross-sectional area of the reservoir; is the inlet flow rate of the reservoir at time t - Δt; is the outlet flow rate of the reservoir at time t - Δt; W Jm,t is the total water storage of the reservoir at time t; is the minimum total water storage of the reservoir; is the maximum total water storage of the reservoir; μw is the water storage loss rate of the reservoir.

[0079] Furthermore, the head pressures at both ends of the pipeline and the water flow rate along the pipeline should satisfy the following constraint conditions:

[0080] H i (0, t) ≥ H min (31)

[0081] H i (L i , t) ≥ H' min (32)

[0082] Q min ≤ Q i (x, t) ≤ Q max (33)

[0083] In the formula: H min is the minimum head pressure required at the beginning of the pipeline; H′ min is the minimum head pressure required at the end of the pipeline; Q min is the minimum water flow rate in the pipeline; Q max is the maximum water flow rate in the pipeline; H i (x, t) is the head pressure at position x of the i-th pipeline at time t; Q i (x, t) is the actual water flow rate at position x of the i-th pipeline at time t; L i is the length of the i-th pipeline; H i (0, t) is the head pressure at the beginning of the i-th pipeline.

[0084] Furthermore, the actual flow rate through the pressure reducing valve should satisfy the following constraint conditions:

[0085]

[0086] Wherein: is the minimum allowable flow rate of the pressure reducing valve; is the maximum allowable flow rate of the pressure reducing valve.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] The present invention adopts a circuitized analog modeling method, and transforms the partial differential equation of the water flow time-delay effect of the water distribution system into an algebraic equation set by using the Laplace transform method, that is, transforms the existing non-convex, non-linear and difficult-to-solve model into a linear model, greatly reducing the calculation amount, significantly reducing the calculation complexity and calculation time, and at the same time being beneficial to maximizing the exploitation and utilization of the schedulable potential of the electric power consumption of the water distribution system. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 - Equivalent circuit diagram of the pipeline.

[0090] Figure 2 - Equivalent circuit diagram of the water pump.

[0091] Figure 3 - Equivalent circuit diagram of the pressure reducing valve.

[0092] Figure 4 - Schematic diagram of the node test system. DETAILED DESCRIPTION OF THE INVENTION

[0093] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0094] A circuitized analog modeling method for the transmission delay of a water distribution system, which models the pipelines, water pumps, pressure reducing valves and water storage tanks involved in the water distribution system, specifically including the following steps:

[0095] S1: Establish a circuitized analog model of the pipeline

[0096] Use the motion equation (1) and the continuity equation (2) to describe the movement of water flow in the pipeline:

[0097]

[0098]

[0099] Wherein: v is the water flow velocity in the pipeline; H is the head pressure in the pipeline; α is the water hammer wave velocity; g is the acceleration of gravity; D is the pipeline diameter; t is the time; x is the position along the pipeline length direction.

[0100] Simplify the two partial differential equations (1) and (2) to obtain (3) and (4) respectively:

[0101]

[0102]

[0103] Where: Q is the actual flow rate of water in the pipeline; A is the cross-sectional area of the pipeline.

[0104] Further transform the two partial differential equations (3) and (4) into (5) and (6) respectively:

[0105]

[0106]

[0107] Where: sign(Q) is the sign function. When Q > 0, sign(Q) = 1; when Q < 0, sign(Q) = -1; and when Q = 0, sign(Q) = 0.

[0108] Assume Q = Q b +ΔQ, and ΔQ≈0, then:

[0109] Q 2 =(Q b +ΔQ) 2 ≈(Q b ) 2 +2Q b ΔQ≈2Q b Q-(Q b ) 2 (7)

[0110] Where: Q b is the reference flow rate of water in the pipeline; ΔQ is the difference between the actual flow rate and the reference flow rate of water in the pipeline.

[0111] Then substitute (7) into (5) to get:

[0112]

[0113] Perform an electrical circuit analogy on the pipeline model. Its equivalent circuit is as Figure 1 shown. The analogy results obtained from the pipeline electrical circuit analogy are shown in Table 1.

[0114] Table 1. Analogy results of pipeline electrical circuit analogy

[0115]

[0116] Then, apply the Laplace transform to convert (6) and (8) into frequency-domain models to obtain (9) and (10) respectively

[0117]

[0118]

[0119] where: s is the Laplace operator

[0120] Taking the derivatives of (9) and (10) with respect to x respectively gives (11) and (12)

[0121]

[0122]

[0123] where: γ 2 =(R b +sL b )sC b ; ζ = C b U sb ;

[0124] Solving (11) and (12) respectively gives (13) and (14)

[0125]

[0126]

[0127] where: there are n pipes numbered 1, 2, …, i, …, n in the water distribution system, and i represents the i-th pipe;

[0128] Substituting (13) into (9) gives:

[0129]

[0130] Comparing (14) and (15) gives:

[0131]

[0132]

[0133] Therefore, the flow rate and head pressure of water flowing in the pipe are:

[0134]

[0135] In this way, both the water flow rate and head pressure in the pipe are expressed as algebraic equations in the Laplace domain. As long as the four variables Q Figure 1 shown in b (the flow rate at the beginning of the pipe), H b (the head pressure at the beginning of the pipe), Q′ b (the flow rate at the end of the pipe) and H′ bAny two of (the head pressure at the end of the pipeline) can determine and values. Then, by performing the inverse Laplace transform on (18), the water flow rate and the change in head pressure along the pipeline can be obtained.

[0136] Meanwhile, the head pressures at both ends of the pipeline and the water flow rate along the pipeline should satisfy the following constraint conditions:

[0137] H i (0, t) ≥ H min (19)

[0138] H i (L i , t) ≥ H' min (20)

[0139] Q min ≤ Q i (x, t) ≤ Q max (21)

[0140] In the formula: H min is the minimum head pressure required at the beginning of the pipeline; H′ min is the minimum head pressure required at the end of the pipeline; Q min is the minimum water flow rate in the pipeline; Q max is the maximum water flow rate in the pipeline; H i (x, t) is the head pressure at position x of the i-th pipeline at time t; Q i (x, t) is the actual water flow rate at position x of the i-th pipeline at time t; L i is the length of the i-th pipeline; H i (0, t) is the head pressure at the beginning of the i-th pipeline.

[0141] S2: Establish a circuit analogy model of the water pump

[0142] Assume that the rotational speed of the water pump is fixed. Then, the hydraulic model of the water pump can be quantitatively expressed as (22) and (23)

[0143] When the water pump is turned on:

[0144]

[0145] When the water pump is turned off:

[0146]

[0147] In the formula: a Pm , b Pm , c Pm are all conventional coefficients of the water pump. For water pumps of different models, their values are different; is the head pressure gain of the water pump; is the actual flow rate of the water flow in the water pump; is the minimum flow rate of the water flow in the water pump; is the maximum flow rate of the water flow in the water pump.

[0148] q t p m = q t p m,b + Δq t p m , and Δq t p m ≈ 0 then:

[0149] (q t p m ) 2 = (q t p m,b + Δq t p m ) 2 ≈ (q t p m,b ) 2 + 2q t p m,b Δq t p m ≈ 2q t p m,b q t p m - (q t p m,b ) 2 (24)

[0150] In the formula: q t p m,b is the reference flow rate of the water flow in the water pump; Δq t p m is the difference between the actual flow rate and the reference flow rate of the water flow in the water pump.

[0151] Substituting (24) into (22) gives:

[0152]

[0153] That is:

[0154] The equivalent circuit diagram of the water pump is as shown in Figure 2 shown, Figure 2 The correlation between the physical quantities in Pm and the variables in (25) is: The head pressure H' at the rear end of the water pump Pm minus the head pressure H at the front end of the water pump That is The resistance of the water pump Voltage source of the water pump In this way, the head pressures at the front and rear ends of the water pump can be obtained through measurement, and then At the same time, the parameters involved in the resistance and voltage source are constants, so that R can be calculated Pm 、U Pm Then R Pm 、U Pm are substituted into (25) to obtain the actual flow rate of the water flow in the water pump

[0155] As the only power-consuming device in the water distribution system, the total power consumption of the water distribution system can be calculated by calculating the power consumption of all water pumps in the system. The power consumption of the water pump and the power consumption of the water distribution system are calculated respectively as follows:

[0156]

[0157]

[0158] In the formula: k 1 、k 2 、k 3 are all conventional coefficients of the water pump, and their values are different for different models of water pumps; there are 1, 2,..., j,..., in total water pumps in the water distribution system, and j represents the jth water pump.

[0159] S3: Establish an analog model of the pressure reducing valve circuit

[0160] The hydraulic model of the pressure reducing valve is:

[0161]

[0162] In the formula: is the head pressure gain of the pressure reducing valve; is the actual flow rate of the water flow passing through the pressure reducing valve m at time t; k V is the opening coefficient of the pressure reducing valve.

[0163] Assume q t Vm = q t V m,b +Δq t Vm And Δq t Vm ≈0 then:

[0164] (q t Vm ) 2 =(qt Vm,b +Δq t Vm ) 2 ≈(q t Vm,b ) 2 +2q t Vm,b Δq t Vm ≈2q t Vm,b q t Vm -(q t Vm,b ) 2 (29)

[0165] Where: q t Vm,b is the reference flow rate of the water flow through the pressure reducing valve; Δq t Vm is the difference between the actual flow rate and the reference flow rate of the water flow through the pressure reducing valve.

[0166] Substituting (29) into (28) gives:

[0167]

[0168] That is:

[0169] The equivalent circuit of the pressure reducing valve is as Figure 3 shown, Figure 3 The correlation between the physical quantities in and the variables in (30) is: Vm is equal to the head pressure H′ at the back end of the pressure reducing valve Vm minus the head pressure H at the front end of the pressure reducing valve That is, the resistance of the pressure reducing valve The voltage source of the pressure reducing valve In this way, by measurement, the head pressures at the front and back ends of the pressure reducing valve can be obtained, and thus Since the parameters involved in the resistance and power supply voltage of the pressure reducing valve are constants, R Vm and U Vm can be calculated. Then, substituting R Vm and U Vm into (30) can obtain the actual flow rate of the water flow through the pressure reducing valve

[0170] At the same time, the actual flow rate through the pressure reducing valve should satisfy the following constraint conditions:

[0171]

[0172] S4: Establish a reservoir model

[0173] Modeling is carried out through a linear water pressure constraint relationship, and the specific constraint relationship is as follows:

[0174]

[0175]

[0176]

[0177] In the formula: is the inflow rate of the reservoir at time t; is the outflow rate of the reservoir at time t; is the head pressure of the reservoir at time t; is the head pressure of the reservoir at time t + Δt; is the cross-sectional area of the reservoir; is the inflow rate of the reservoir at time t - Δt; is the outflow rate of the reservoir at time t - Δt; W Jm,t is the total water storage of the reservoir at time t; is the minimum total water storage of the reservoir; is the maximum total water storage of the reservoir; μw is the water storage loss rate of the reservoir. Specific embodiments

[0179] Use a relatively small test system to illustrate the performance of the proposed electro - water simulation model in detail, as Figure 4 shown. There are 3 load nodes in the 6 - node power system, and each load node is connected to 1 water distribution system. The time interval is 15 minutes, so there are 96 time periods in a day.

[0180] Compare the above - mentioned circuit analogy method (electro - water analogy method) with the traditional finite - difference method, and the comparison of the calculation results is shown in Table 2. Scenarios a, b, c, and d respectively represent the typical scenarios of spring, summer, autumn, and winter.

[0181] Table 2. Comparison of calculation results between the circuit analogy method and the finite - difference method

[0182]

[0183] The results show that compared with the finite - difference method, the circuit - based analogy method of the present invention significantly reduces the calculation time while maintaining the same operating cost.

[0184] To further demonstrate the advantages of the circuit analogy method over the finite difference method, the circuit analogy method and the finite difference method were used to perform calculations in the IEEE-RTS 24-node test system, and the results are shown in Table 3.

[0185] Table 3. Comparison of calculation results between the circuit analogy method and the finite difference method

[0186]

[0187] As can be seen from Table 3, the circuit analogy method not only has almost exactly the same operating cost as that calculated by the finite difference method, but also significantly reduces the calculation time; the circuit analogy method takes about 44 seconds on average to obtain the result, while the finite difference method takes 1272 seconds.

[0188] Finally, it should be noted that the above embodiments of the present invention are only examples for explaining the present invention, and are not limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes and modifications can be made based on the above description. It is impossible to list all the implementation manners here. Any obvious changes or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A circuitized analog modeling method for the transmission delay of a water distribution system, characterized in that, models for pipelines, water pumps, pressure reducing valves, and water storage tanks involved in the water distribution system are established, and the specific steps are as follows: S1: Establish a circuitized analog model of the pipeline The motion of water flow in the pipeline is described by the motion equation (1) and the continuity equation (2): In the formula: v is the water flow velocity in the pipeline; H is the head pressure in the pipeline; α is the water hammer wave velocity; g is the acceleration due to gravity; D is the pipeline diameter; t is the time; x is the position along the pipeline length direction; Simplify (1) and (2) to obtain (3) and (4) respectively: In the formula: Q is the actual flow rate of water flow in the pipeline; A is the cross-sectional area of the pipeline; Further transform (3) and (4) into (5) and (6) respectively: In the formula: sign(Q) is the sign function. When Q > 0, sign(Q) = 1; when Q < 0, sign(Q) = -1; and when Q = 0, sign(Q) = 0; Q = Q b + ΔQ, and if ΔQ ≈ 0, then: Q 2 = (Q b + ΔQ) 2 ≈ (Q b ) 2 + 2Q b ΔQ ≈ 2Q b Q - (Q b ) 2 (7) Where: Q b is the reference flow rate of the water flow in the pipeline; ΔQ is the difference between the actual flow rate and the reference flow rate of the water flow in the pipeline; Then substitute (7) into (5) to get: Perform circuitized analogy on the pipeline, and the obtained analogy results are as follows: Circuit Pipeline Current Q Voltage H Resistor R b = sign(Q)fQ b / (gDA 2 ) Inductor L b = 1 / gA Capacitor C b = gA / α 2 Voltage source Then, applying the Laplace transform to (6) and (8) to convert them into frequency-domain models respectively yields (9) and (10). In the formula: s is the Laplace operator Take the derivative of (9) and (10) with respect to x to obtain (11) and (12) respectively Where: γ 2 =(R b +sL b )sC b ; ζ = C b U sb ; Solve (11) and (12) to obtain (13) and (14) respectively In the formula: There are a total of n pipelines 1, 2,..., i,..., n in the water distribution system, and i represents the i-th pipeline; Substitute (13) into (9) to get: Compare (14) and (15) to get: Therefore, the flow rate and head pressure of water flowing along the pipeline are: By detecting any two of the four variables of the flow rate and head pressure at the beginning and end of the pipeline, it is possible to determine and values, and then obtain the changes in water flow rate and head pressure input along the pipeline through (18); S2: Establish a circuitized analog model of the water pump When the water pump speed is fixed, the hydraulic model of the water pump can be quantitatively expressed as (19) and (20) When the water pump is turned on: When the water pump is turned off: Where: a Pm , b Pm , c Pm are all conventional coefficients of the water pump; is the head pressure gain of the water pump; is the actual flow rate of the water flow in the water pump; is the minimum flow rate of the water flow in the water pump; is the maximum flow rate of the water flow in the water pump; while then: Wherein: is the reference flow rate of the water flow in the water pump; is the difference between the actual flow rate and the reference flow rate of the water flow in the water pump; Substitute (21) into (19) to get: The following electrical analogy can be made for the water pump: is equal to the head pressure H' at the rear end of the water pump Pm minus the head pressure H at the front end of the water pump Pm , that is the resistance of the water pump the voltage source of the water pump Calculated in this way RPm and UPm are obtained, and then substituting them into (22) can obtain the actual flow rate of the water flow in the water pump As the only power-consuming device in the water distribution system, the total power consumption of the water distribution system can be calculated by calculating the power consumption of all pumps in the system. The power consumption of the pump and the power consumption of the water distribution system are calculated respectively as follows: Where: k 1 , k 2 , k 3 are all conventional coefficients of the water pump; in the water distribution system, there are 1, 2,..., j,..., in total water pumps, and j represents the jth water pump; S3: Establish a circuitized analog model of the pressure reducing valve The hydraulic model of the pressure reducing valve is: Wherein: is the head pressure gain of the pressure reducing valve; is the actual flow rate of the water flowing through the pressure reducing valve m at time t; k V is the opening coefficient of the pressure reducing valve; while then: In the formula: is the reference flow rate of the water flowing through the pressure reducing valve; is the difference between the actual flow rate and the reference flow rate of the water flowing through the pressure reducing valve; Substitute (26) into (25) to get: The following electrical analogy can be made for the water pump: equals the head pressure H' at the rear end of the pressure reducing valve Vm minus the head pressure H at the front end of the pressure reducing valve Vm , that is the resistance of the pressure reducing valve the voltage source of the pressure reducing valve Calculated in this way RVm and UVm, and then substituting into (27), the actual flow rate of the water flowing through the pressure reducing valve can be obtained S4: Establish a water storage tank model Modeling is carried out through a linear water pressure constraint relationship, and the specific constraint relationship is as follows: Where: is the inflow rate of the reservoir at time t; is the outflow rate of the reservoir at time t; is the head pressure of the reservoir at time t; is the head pressure of the reservoir at time t + Δt; is the cross-sectional area of the reservoir; is the inflow rate of the reservoir at time t - Δt; is the outflow rate of the reservoir at time t - Δt; W Jm,t is the total water storage of the reservoir at time t; is the minimum total water storage of the reservoir; is the maximum total water storage of the reservoir; μw is the water storage loss rate of the reservoir.

2. According to the circuitized analog modeling method for the transmission delay of a water distribution system described in claim 1, characterized in that, The head pressures at both ends of the pipeline and the water flow rate along the pipeline should satisfy the following constraint conditions: H i (0,t)≥H min (31) H i (L i ,t) ≥ H' min (32) Q min ≤Q i (x,t)≤Q max (33) Where: H min is the minimum head pressure required at the beginning of the pipeline; H′ min is the minimum head pressure required at the end of the pipeline; Q min is the minimum flow rate of the water flow in the pipeline; Q max is the maximum flow rate of the water flow in the pipeline; H i (x, t) is the head pressure at position x of the i-th pipeline at time t; Q i (x, t) is the actual flow rate of the water flow at position x of the i-th pipeline at time t; L i is the length of the i-th pipeline; H i (0, t) is the head pressure at the beginning of the i-th pipeline.

3. According to the circuitized analog modeling method for the transmission delay of a water distribution system described in claim 1, characterized in that, The actual flow rate passing through the pressure reducing valve should satisfy the following constraint conditions: In the formula: is the minimum allowable flow rate of the pressure reducing valve; is the maximum allowable flow rate of the pressure reducing valve.

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