Conventional hydraulic models can be used to analyze operational scenarios for a variable-speed pump (VSP) delivering target hydraulic characteristics of either the fixed hydraulic head or the desired pump flow. However, modelers must repeatedly adjust relative speed factors for achieving the target hydraulic performance, which can be a time-consuming task. A new solution method has been developed for directly calculating the required VSP speed to provide a fixed hydraulic head. However, this method needs to be extended as a generic modeling approach for practical applications. This article presents an enhanced VSP solution method that extends the previously developed VSP hydraulic network solver to automatically calculate the relative pump-speed coefficient for attaining the prescribed hydraulic head or pumping the preferred amount of flow. Using this improved method, engineers can model not only a single VSP but also multiple VSPs with rule-based logic controls. This allows the target control head to be specified at any location or for the target flow to be specified for VSPs of different capacities. The extended method provides a flexible, robust modeling approach for engineers to analyze a variety of VSP configurations in water and wastewater collection systems.

Modeling variable-speed pump operations for target hydraulic characteristics BY ZHENG YI WU, MICHAEL TRYBY, EZIO TODINI, AND THOMAS M. WALSKI

54

variety of pumps are designed and installed to move water through a water distribution or wastewater collection system and provide adequate services to communities. Pumps are classified either as constantspeed pumps (CSPs), which continuously supply flow and pressure defined by a pump characteristics curve at a single speed, or variable-speed pumps (VSPs), which operate at different speeds using a number of variablespeed drives (most commonly a variable-frequency drive, or VFD) to adjust the pump motor speed. CSPs and VSPs are controlled and operated in such a way that the target hydraulic characteristics of desired pump flows or target hydraulic heads are achieved. Generally, CSPs are less flexible than VSPs when serving target hydraulic characteristics in a system. Pump operation is characterized by the performance curve, or pump curve, that is established by the pump manufacturer. A pump curve is defined by the pairs of points representing pump flow versus pumping head (to overcome the resistance for moving the flow through a system), as shown in Figure 1. CSPs without a VFD controller operate on one performance curve. In other words, the operation point can only move left or right along the pump curve with the relative speed factor of 1.0, noted as , which is the ratio of actual speed to the speed at which a pump curve is developed. When greater system resistance occurs, a CSP delivers a smaller flow. A larger flow can only be supplied with a smaller pumping head (corresponding to overcoming a smaller system resistance). This could prevent the CSP from achieving a target hydraulic characteristic, for

A

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Pump Head

instance, moving adequate flow with FIGURE 1 Pump performance curves with and without VFD target hydraulic head or moving a tarMaximum pump speed get flow into a system. Changing pump speed By contrast, a VFD controller alConstant speed pump H lows a pump to vary its speed according to the preset target requirement of the pumping system and thus to achieve target hydraulic characteristics. The prescribed target can be a ω htarget nodal pressure or VSP discharge for With VFD, ω  1.0 water distribution and wastewater collection systems. To provide a target h Without VFD, ω = 1.0 pressure head, a pressure transducer is used to send an analog signal to the VFD. An internal proportional-inteWith VFD, ω 1.0 gral-derivative controller loop processes the signal and adjusts the speed of the pump to match the preset pressure. If the pressure is lower than the set qi Q q point, the VFD will speed up the pump Pump Flow to increase the system hydraulic head. Then the pump operation point will H—pump head, Q—pump flow, VFD—variable-frequency drive, ω—relative pump-speed factor move up and toward the operation zone of  > , as shown in Figure 1. length and width of the wet-well construction under the Conversely, if the pressure is higher than the set point, the same site conditions; a smaller motor and shorter pump VFD will slow down the pump, and the pump operation columns for vertical-type pumps, thus a smaller-horsepoint will move down and toward the operation zone of power pump and consequently less energy consumption;  < . The VFD speed calibration is then matched against and more flexibility to operate at different speeds but as a pressure indicator, which is used for comparative adjustclosely as possible to the best efficiency curve to further ments so that the operator knows the system pressure at minimize energy costs (Rishel, 2003). all times. The same principle is applied to the flow-rate VSPs can be modeled in many ways. Using a convencontrol with the corresponding signal from a flowmeter. tional hydraulic model, engineers can simulate VSPs by Therefore, VSPs offer more flexibility in realizing preset manually adjusting the pump-speed factor at each time target hydraulic characteristics. step to ensure that the target hydraulic head is mainFor water systems with little or no storage, it is tained at a certain location. However, this ad hoc apdesirable to attain a fixed hydraulic head at a pump proach can be time-consuming when a number of VSPs discharge side in order to provide adequate water supare expected to meet the target over an extended period. ply. These water systems are directly supplied by VSPs. Todini et al (2007) developed an approach to directly The primary objective of installing a VSP in such a calculate the pump-speed factor for a single VSP at one system is to deliver a target hydraulic head at a desired pump station. This is accomplished based on the user’s location over a 24-h period in order to provide the specified target control head at a nonstorage node downrequired pressures. To achieve this goal, VSPs are constream of a pump. However, there are many different trolled to automatically change pumping speed accordVSP configurations and operational scenarios that include ing to the variation in system demand and in some multiple VSPs at one pump station, discharge-side storage cases to minimize excess pressure and energy use (Linhead control, suction-side target head control, and fixed gireddy & Wood, 1998). However, a low-efficiency pump flow control. All control cases need to be analyzed VFD is likely to result in a greater life-cycle cost than accurately. In this article, the original approach by Todini constant-speed pumping (Walski et al, 2003). et al (2007) is extended as a robust and flexible VSP soluFor wastewater collection systems, a fixed hydraulic tion methodology to directly calculate relative operahead at the suction side of a pump is required to hold tional speed coefficients of multiple VSPs to reach a tarthe wet-well-level constant and prevent overflow. Mainget hydraulic head or desirable pump flow. A number of taining constant wet-well-level control is more cost-effecchallenging cases are presented to illustrate applications tive than using the traditional variable-level float switch of the enhanced method. This type of modeling approach to empty a tank (wet well)—an approach that is typiis implemented as the advanced feature for efficiently cally called pump-down control of CSPs. The cost savings modeling water and wastewater systems. are achieved in many ways, including having smaller WU ET AL | 101:1 • JOURNAL AWWA | PEER-REVIEWED | JANUARY 2009

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SOLUTION METHOD Efficient and robust modeling systems consist of many integral components, including the computation module, or the hydraulic solver, which is the core driving engine for modeling packages. The hydraulic solver performs the actual computational analysis for a given scenario. As such, improving the hydraulic solver to handle a wide range of operating scenarios, including different pump configurations and operational controls, is vitally important. Modeling of a VSP with the prescribed target head has been developed and implemented by reformulating the matrix system of a global gradient algorithm (GGA; Todini & Pilati, 1988). The gradient solution method begins with an initial estimate of flow in each pipe and proceeds with iterations until there is negligible change in new pipe flow distributions. For each GGA iteration, new nodal heads are calculated by solving the matrix equation AH = F

(1)

in which A is an (N × N) Jacobian matrix; H is an (N × 1) vector of unknown nodal heads; and F is an (N × 1) vector of right-hand-side terms, in which N is the number of nodes. Within the GGA, the hydraulic characteristic of a pump connecting from node i to node j is represented by a power law, given as Hi – Hj  2 [h0 – r (Qij/)n]

(3)

in which Hi and Hj are hydraulic heads at nodes i and j, respectively; h0 is the shutoff head for the pump; r, n, a0, b0, and c0 are the pump curve coefficients;  is the relative pump-speed factor; and Qij is the flow moved from node i to node j through a pump. The conventional modeling approach assumes that the relative pump-speed factor is given as a known value. In order to achieve a desired hydraulic characteristic, a trial-and-error modeling approach must be applied to work out the correct relative speed factor. To directly calculate pump speed for a given target hydraulic characteristic, e.g., hydraulic head, the pump power law equations (Eqs 2 and 3) are rearranged to add an extra head to account for a pump speed that is different from the constant pump-speed factor of 1.0. Thus, both Eqs 2 and 3 are equivalently transformed as Hi – Hj  (h0 – rQijn) + ij

(4)

or Hi – Hj  – (a0 + b0 Qij + c0 Qij2) + ij

(5)

in which ij is the head difference required for meeting the specified target head. It is the extra term ij that results in 56

冤 冥冤 冥冤冥 H k+1

=

Ass ⯗ Asn

–1

F1

…

………

…

k+1

Ans ⯗ 0

F2

(6)

in which Ass is the symmetrical part of the original matrix from which rows and columns have been eliminated for the newly fixed head nodes that are specified as VSP control targets; Asn is a matrix formed by the columns; Ans is a matrix formed from the rows eliminated from the matrix A; and F1 and F2 are the corresponding vectors of right-hand side terms. The detailed matrix derivation is given by Todini et al (2007). The partitioned matrix system is solved for the fixed-head VSP analysis within the same iteration loop of the original GGA as implemented in EPANET2 (Rossman, 2002). After the reformulated matrix system is solved for link flows and node hydraulic heads, the VSP relative speed factor can be solved by rearranging Eqs 2 and 4 for a pump using a power law pump curve, given as 2 h0 (1 – 2) – rQij 1 –  ij n

冢

(2)

or Hi – Hj  – (a02 + b0 Qij + c0 Qij2)

a nonsymmetrical solution matrix for GGA formulation. However, the nonsymmetrical GGA matrix system is solved by partitioning the governing matrix system into two portions—the symmetrical matrix and the nonsymmetrical matrix, which are given as follows (Todini et al, 2007):

冣

(7)

or by rearranging Eqs 3 and 5 for a pump using a quadratic pump curve, given as a02 b0Qij (ij – a0 – b0Qij)  0

(8)

Eq 8 can be directly solved for VSP relative speed factor whereas the nonlinear Eq 7 is solved for VSP speed factor using the Newton–Raphson method.

EXTENDED SOLUTION METHOD The solution method described previously enhances the conventional hydraulic model by directly computing the relative speed factor of a VSP to sufficiently keep up with a fixed hydraulic head at a control node. However, in order to develop a generic modeling tool, a wide range of VSP configurations in real systems must be effectively solved within the same context of the VSP solution method (Wu et al, 2007; Wu & Todini 2007). Typical and challenging VSP configurations include VSPs • delivering the target pump flow, i.e., fixed-flow VSPs; • in parallel delivering the target hydraulic characteristics; • for maintaining the fixed head of a storage tank located at either the discharge side or the suction side of a pump; and • imposed with rule-based controls in addition to target hydraulic characteristics of either fixed-head or fixed-pump flow.

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The original VSP solution method given by Eqs 1 through 8 is extended to solve for each of these VSP control configurations, as elaborated in the following sections. Fixed pump flow. When modeling the desired flow to be moved through a VSP in a water system with storage tanks, it is necessary to ensure that the calculated pump flow is the exact amount expected over the GGA iterations. Unlike the fixed-head VSP analysis, solving for fixed-flow VSP control requires that the VSP flow be kept constant over the iterations, given as qik 1  qik  qitarget

(9)

FIGURE 2 Solution flowchart of extended global gradient algorithm for direct calculation of VSP speed factor

Start

Initialize H and Q for fixed-flow VSP: q = qtarget

Compute system matrixes

Solve symmetric matrix

in which qik+1 is the calculated flow for pump i at the (k + 1)th iteration; Solve nonsymmetric matrix qik is the calculated flow for pump i at the kth iteration; and qitarget is the target flow for pump i. The governing equation system given by Eq 6 Update H and Q for fixed-flow VSP: q = qtarget along with Eq 9 is computationally adequate to guarantee the flow balance and also the target flow moved through a VSP. No  < tol The extended GGA solution procedure is shown in Figure 2. It starts with Yes initializing hydraulic heads and link flows, as is done with the EPANET2 Calculate pump speed factor hydraulic solver, and setting the target flow if a fixed-flow VSP is included in the model. After the matrix system No T > dur coefficients are calculated, they are partitioned into symmetric and nonsymYes metric matrixes, which are solved subsequently for new hydraulic heads. The Stop link flows are updated using the newly calculated hydraulic head while the target flow is kept constant for the fixeddur—duration, H—hydraulic head, Q—pump flow, tol—tolerance, T—time, VSP—variableflow VSPs. The iteration continues until speed pump, —flow change the flow change, noted as , is less than the preset accuracy tolerance, tol. Once a flow-balance calculation is achieved speed. These parallel VSPs are operated in one group and with known link flows and nodal hydraulic heads, the often led by one VSP, known as the lead VSP; the other actual VSP speed factor is calculated by solving Eq 7 or 8. VSPs at the same station are referred to as lag VSPs. A lag The model calculation may continue for each time step VSP is turned on and ramped up to the same speed as until the calculated time, T, is greater than the preset simthe lead VSP when the lead VSP cannot meet the target ulation duration, dur. head. If all standby VSPs run at allowed maximum speed Parallel VSPs. When multiple pumps are placed in parbut the target head is still not achieved, VSPs remain at allel and operated as VSPs at one pump station, it is the maximum speed. A lag VSP is turned off when the lead expected that they will deliver the same hydraulic head. VSP is able to deliver the target head. The VSP solution Typically, the parallel VSPs are operated at the same WU ET AL | 101:1 • JOURNAL AWWA | PEER-REVIEWED | JANUARY 2009

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method is enhanced to correctly analyze the typical operational scenario of parallel VSPs and further unified by introducing a new modeling element, the variable-speed pump battery (VSPB), to represent a group of identical pumps that meet the following criteria: • VSPs are parallel with each other; • VSPs share common upstream (inflow) and downstream (outflow) nodes; • VSPs are identical (have the same pump curve); • VSPs are controlled by the same target node and the same target head; or • VSPs are expected to move the same target flow. From the modeling perspective, a VSPB is treated the same as a single pump element, which can be defined as a VSP except that the number of lag pumps must be defined for each VSPB. Modelers do not have to specify the duplicated data for multiple pumps. For a fixed-head VSPB, the pumps within a VSPB are treated as an equivalent pump in the governing equations. Because the same characteristics of parallel VSPs are controlled by the same target head at the same node, the multiple VSPs can be represented by just one pumping equation, given as Eq 4 or 5. Consequently, the core solution method is the same.

TABLE 1

VSP Lead

Lag

However, the calculated flow for the equivalent VSP is expected to be shared by all parallel VSPs. The actual number of parallel VSPs on duty is determined by calculating the required relative speed factor within the specified minimum and maximum limits after the extended GGA is used to solve for the matrix system. For a fixedflow VSPB, all VSPs are expected to be on duty and evenly share the target flow. Tank head control. A VSP can be controlled by any node including a junction and storage tank. When a tank is selected as a VSP control node, the initial tank level can be used as the target hydraulic head. In order to meet the target head, the VSP must be ramped up and down in response to variation in system demand. There are two cases in which a tank is used as a VSP control node—when the control tank is located at the discharge side of the pump station and when the control tank is located at the suction side of the pump station. The first configuration is occasionally found in drinking water systems, and the second configuration is commonly found in sewer forced mains subsystems, where a wet well is located at the suction side of a VSP. Both cases require some specific improvement to the original VSP

Initial and calculated status for lead and lag VSPs

Initial Status

Calculated Setting

Comments

ON

ON

Target head is not met without lead VSP supply flow.

ON

OFF

Target head is met or exceeded without lead VSP supply flow.

OFF

OFF

A VSP with initial status of OFF cannot be a lead VSP; otherwise, all lag VSPs will remain OFF.

ON

ON

A lag VSP is standby and required for delivering target head and flow.

ON

OFF

A lag VSP is standby but not required for delivering target head and flow.

OFF

OFF

Not standby for operation. For instance, if there are two VSPs in parallel, one is selected as lead VSP with initial status of ON; if the other VSP’s initial status is OFF, then only one VSP is taken into account for calculation. It will not be standby until it is turned ON by a control rule.

VSP—variable-speed pump

TABLE 2

VSP Lead

Lag

Control setting and consequence for lead and lag VSPs

Control Setting

Calculated Setting

Comments

ON

ON

Lead VSP is set ON and required for delivering flow.

ON

OFF

Lead VSP is set ON but it is not required for delivering flow; all associated lag VSPs should be OFF.

OFF

OFF

Lead VSP is set OFF and remains OFF; associated lag VSPs are also OFF, unless another lag VSP is assigned as lead VSP.

ON

ON

Lag VSP is standby and required for delivering flow.

ON

OFF

Lag VSP is standby but not required for delivering flow.

OFF

OFF

Lag VSP is not standby, ignores its lead VSP’s call, and remains in OFF status.

VSP—variable-speed pump

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methodology in order to accuFIGURE 3 Water distribution system modeled with VSPB rately model tank head control for target head (example 1) strategies. Discharge-side tank. When a discharge-side tank controls a VSP, Node it is expected that the tank initial head will be sustained by increasing speed to fill the tank as soon as the tank begins to drain and by reducing speed to maintain the tank level as soon as the water level increases when the system demand decreases. VSP modeling is used to calculate the correct pump relative speed factor to retain the target tank head. However, it is not possible to solve for the target tank head by just employing the equation system of Eq 6 alone. The VSP algorithm given by Eqs 1 through 8 explicitly calculates pump speed needed to reach a preT-1 set target head. To handle the tank target head control correctly, the VSP solution method must be modified in order to automatically R-1 determine the tank demand (i.e., 113 how much tank inflow is needed to raise the tank level to the origiVSPB-2 nal head after it drops and while R—reservoir, T—tank, VSPB—variable-speed pump battery the pump is in the maximum allowed speed) and to determine when the pump is returned to VSP With the condition and action logic implemented as mode. This is achieved by extending the solution method described here, the method can be used to analyze a fixedto incorporate the following conditions: head VSP controlled by a discharge-side tank. • when the actual tank level is lower than the target Suction-side tank. Traditionally, to prevent rising water level, a VSP is ramped up to the maximum allowed levels in wet wells, pump operations are controlled within speed in case the target head cannot be met for a given a reasonable range of water levels. For CSPs, control rules time step; can be imposed to turn on a pump if the wetwell water level exceeds a certain threshold. Control rules can also be applied to shut off the pump when the water level is below a lower set point. Alternatively, each pump can be operated as a VSP, and its operating status and speed can be explicitly calculated to meet the wet well’s target water level. Where a suction-side tank is selected as the VSP control node, as in a wastewater system, the VSP is expected to keep the tank level constant. The logic is the exact opposite of that for a discharge-side control tank. In order to simulate the target • when the tank level is greater than the target level, head VSP operation for suction-side tank control, the algoa VSP is turned off to allow the tank to drain; and rithm is enhanced to incorporate the control logic as follows: • when the tank level is restored to the target level, a • when a VSP is turned on and the tank level is greater VSP is kept at the mode of variable-speed operation in than the target head, the VSP changes to constant speed order to maintain the target level.

F

or water systems with little or no storage, it is desirable to attain a fixed hydraulic head at a pump discharge side in order to provide adequate water supply.

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FIGURE 4 Water distribution system with VSPB for delivering the target hydraulic head of 137.16 m (450 ft) at discharge side (example 1)

VSPB-2 lead pump flow VSPB-2 lag pump flow VSPB-2 relative pump speed factor

1.0

180

0.9

160

0.8

140

0.7

120

0.6

100

0.5

80

0.4

60

0.3

40

0.2

20

0.1

0 0

2

4

6

8

10

12

14

16

18

20

22

Calculated Relative Pump Speed Factors

Calculated Flow—L/s

200

0.0 24

Time—h VSPB—variable-speed pump battery

FIGURE 5 Water distribution system modeled with VSP for target flow (example 2)

T-1

Node

R-1 PMP-1

PMP-2

PMP—pump, R—reservoir, T—tank, VSP—variable-speed pump

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(i.e., the maximum allowed speed) in order to bring the tank level down to the target level; and • when the tank level is lower than the target head, the VSP is slowed down or kept in the mode of variable-speed operation to allow the suction-side tank to return to the target level. With these suggested improvements, the suction-side tank level can be modeled as a control target for a VSP. It ramps up speed when the tank flow increases and ramps down speed as the tank flow is reduced. Rule-based controls. Both fixedhead and fixed-flow VSPs can also be controlled using rule-based controls specified in the semantics of IF-THEN and/or IFTHEN-ELSE statements. Because of the complexity of automated calculation of pump speed and the lead/lag pump combination, a pump’s initial status and expected control status must be carefully analyzed and implemented. Different combinations of userpreset VSP status, along with system hydraulics, could result in different calculated operating status. All possible control outcomes of VSP initial status, control settings, and calculated operation status are summarized in Tables 1 and 2. When VSPs are modeled as individual pumps or a pump battery, each VSP and VSPB can be modeled with the prescribed initial status and logic controls. The operating status of ON and OFF can also be calculated using VSP algorithms. For instance, a lag VSP is turned ON or OFF according to the capacity of the lead VSP. However, it can also be turned ON or OFF by a control setting preset using a stated value such as clock time, tank level, node pressure, or pipe flow. When a control rule triggers a lag VSP ON, that VSP is in standby for its lead VSP to be called upon for duty. Its lead VSP determines actual operation status (ON/OFF). The VSP will be turned ON if the lead VSP requires it; otherwise, it will remain in OFF mode.

When a control rule turns a lag VSP OFF, the lag VSP will not respond to a lead VSP’s call for duty. This means that a lag VSP in a preset OFF state (by initial status or control rule) is not contributing to the target head or flow.

FIGURE 6 Simulated results of example 2 modeled with VSP for target flow of 60 L/s

1.4

PMP-1 calculated relative speed factors PMP-1 calculated flows

80

APPLICATION EXAMPLES

Relative Pump Speed Factors

70 1.2 60

Pump Flow—L/s

Relative Pump Speed Factors

Pump Flow—L/s

The following four example VSP 1.0 50 configurations are based on real0.8 world water and wastewater systems. 40 Each system is modeled using the 0.6 30 improved VSP solution method for achieving target hydraulic character0.4 20 istics of either constant hydraulic 0.2 10 grades or fixed pump flows. Example 1: VSPB. This example, 0 0 which is based on the benchmark sys0 2 4 6 8 10 12 14 16 18 20 22 24 tem studied by Wu (2006), is expected Times—h to supply an average system demand PMP—pump, VSP—variable-speed pump of approximately 200 L/s (Figure 3). The original model is slightly modified by replacing three pumps with a VSPB (VSPB-2) that contains one lead FIGURE 7 Simulated results of example 2 modeled with two VSPs for target VSP and two lag VSPs. It is assumed flows of 60 L/s and 25 L/s, respectively that the pump battery is defined as a fixed-head VSP for delivering a PMP-2 calculated relative speed factors hydraulic grade of 137.16 m (450 ft) 40 PMP-1 calculated relative speed factors PMP-2 calculated flows at a target node of 113 located at the 1.4 PMP-1 calculated flows 35 pump station’s discharge side. 1.2 The improved VSP solution 30 method is applied to analyze the 1.0 25 use of a VSPB that is assumed to be on duty over a 24-h period. Sim0.8 20 ulation results for the pump rela0.6 tive speed factors and pump flows 15 are illustrated in Figure 4. The fig0.4 10 ure shows that only the lead pump is turned on at 12:00 a.m., because 0.2 5 system demand is low. However, 0 0.0 when demand increases beginning 0 2 4 6 8 10 12 14 16 18 20 22 24 at 1:00 a.m., the lead pump ramps Times—h up the speed and the lag pump PMP—pump, VSP—variable-speed pump remains on standby until the lead pump cannot meet the full-speed demand, which begins at 2:00 a.m. improved VSP solution method for reaching target pump From 2:00 a.m. to 6:00 a.m. the lag pump is loaded at flows. Two scenarios are analyzed: the same speed and flow as the lead pump. Demand on • Pump 1 (PMP-1) is set to deliver a fixed flow of 60 the system increases again at 9:00 a.m. At this time the lag L/s (950 gpm) over a 24-h period. The required pump pump is activated at the same speed and flow as the lead relative speed factor is to be directly calculated for each pump until 9:00 p.m. This example shows that the simulation time step. improved modeling approach is able to model the multi• PMP-1 and pump 2 (PMP-2) are set to deliver the ple VSPs as a VSPB element and achieve a fixed-head tarfixed flows of 34.69 L/s (550 gpm) and 25.23 L/s (400 get over a 24-h period. gpm), respectively. Their relative speed factors are directly Example 2: Fixed-flow VSP. The simple example shown calculated for each time step. in Figure 5 is used to demonstrate the application of the WU ET AL | 101:1 • JOURNAL AWWA | PEER-REVIEWED | JANUARY 2009

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Figure 6 shows the calculated pump-speed factors and flows over a 24-h period under the first operating scenario. PMP-1 is controlled to pump the fixed flow of 60 L/s (950 gpm), as specified, while the speed changes according to the system head variation. The results for two parallel fixed-flow VSPs are shown in Figure 7. PMP-1 and PMP-2 share a total flow of 60 L/s, and each pump is specified to move the target flow of 35 L/s and 25 L/s, respectively. As shown in Figure 7, the calculated pump speeds vary according to the hydraulic head across the system. This applicaFIGURE 8 Water distribution system modeled with VSP tion demonstrates that the with discharge-side target tank as control node (example 3) extended solution method can be Node used to model multiple VSPs with different pump characteristics (pump curves) for different tarPMP-1 W-1 get flows. Therefore, the fixedflow VSP solution method is more J-D4 flexible than the approach used PMP-2 W-2 HP-1 to model fixed-head VSPs. PMP-3 Example 3: VSP controlled by discharge-side tank. Example 3 applies to a small portion of a large water system (Figure 8). The system is supplied by plant clearwells W-1 and W-2 via three pumps— PMP-1, PMP-2, and PMP-3. PMP-1 is the primary pump and HP—hydropneumatic tank, J-D—node, PMP—pump, VSP—variable-speed pump, W—clearwell supplies the system with little storage capacity. All three pumps are installed with VFDs in order to FIGURE 9 Simulated results of the water distribution system with the VSP operate at different speeds to meet controlled by discharge-side tank as target node system demand and the nodal pressure requirement. A downstream hydropneumatic tank (HPHP-1 pressure head J-D4 pressure head with both VSPs 1.2 70 1) controls PMP-1 with a target J-D4 pressure head without VSP PMP-3 PMP-1 relative speed factors pressure head of 56 m. PMP-2 is PMP-3 relative speed factors 60 a standby pump used for emer1.0 gencies such as fire fighting. PMP3, also a VSP, moves water from 50 0.8 well W-2 at peak demand hours to keep the pressure head above 40 a target level. Two operating sce0.6 narios are simulated: 30 • PMP-1 is on duty and con0.4 trolled by target tank HP-1 to pro20 vide a fixed pressure head of 56 m over a 24-h period while PMP0.2 10 2 and PMP-3 are turned off. • PMP-1 is on duty as in sce0 0.0 nario 1 and VSP PMP-3 is to pro0 2 4 6 8 10 12 14 16 18 20 22 24 vide a target pressure head of 20 Times—h m at node J-D4. In addition, a HP—hydropneumatic tank, J-D—node, PMP—pump, VSP—variable-speed pump rule-based control is specified for PMP-3 so that it is turned on if Pressure Head—m

Pump Relative Speed Factors

Simulation runs for each case are performed using the enhanced hydraulic solver. For this example, the calculation for each time step is converged at the same number of iterations as for the simulation runs with a CSP. This indicates that the extended solution method is efficient and effective at simulating the control scenario of fixed-flow VSP operation. The results for the calculated pump flow and speed factor for each time step are shown in Figures 6 and 7.

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IF (T-5 hydraulic grade < 7.0 ft) THEN (PMP-5 pump status = OFF) IF (T-5 hydraulic grade > 13.0 ft) THEN (PMP-5 pump status = ON)

FIGURE 10 Sewer forced mains system modeled with VSP with suction-side target tank as control node (example 4) Node J-5

J-6

T-1

PMP-1

J-7

T-3

T-6

PMP-3

PMP-6 R-1

PMP-2

PMP-5

PMP-7

T-5

J-2

PMP-4

T-2

J-1

T-7 T-4

J-3

J-4 J—node, PMP—pump, R—reservoir, T—tank, VSP—variable-speed pump

FIGURE 11 Comparison of simulated results of sewer forced mains system modeled with CSPs and VSPs controlled by suction-side tank 1.4

45

PMP-5 VSP relative speed factor PMP-5 CSP relative speed factor PMP-5 VSP energy used (cumulative; k W · h) PMP-5 CSP energy used (cumulative; k W · h)

40 35

1.0 30 0.8

25

0.6

20 15

0.4 10

Accumulative Energy Consumption—kW·h

1.2

Relative Pump Speed Factors

the nodal pressure head at J-D4 drops below 20 m. The simulations are conducted with a time step of 15 min and a maximum speed factor of 1.5. The modeling results are illustrated in Figure 9, which shows that the tank head of HP-1 is kept constant with only PMP-1 turned on. The pressure heads at some nodes, such as node J-D4, may drop below 15 m during peak demand hours (e.g., 8:00 p.m.). Simulation results for the second scenario demonstrate that the nodal pressure is maintained as required for the 24-h service period, i.e., PMP3 is turned on to maintain the pressure head at node J-D4 above the target pressure head of 20 m. This example illustrates that the improved method is effective at modeling VSPs controlled by multiple control nodes of different target hydraulic heads together with rule-based controls. Example 4: VSP controlled by suction-side tank. The example illustrated in Figure 10 is typical of a sewer forced mains system where pumps move wastewater out of wet wells. A VSP is connected to each wet well to maintain a consistent water level in the wet well. When the water rises, pump operation must be controlled within a reasonable range of water levels. In order to prevent overflow from wet wells and to prevent the pump from operating with too little flow, two options can be adopted as follows: • Use CSPs with rule-based controls. For example, for wet well T-5, the control rules can be specified as:

0.2 5 0.0

0 0

2

4

6

8

10

12

14

16

18

20

22

24

Time—h CSP—constant-speed pump, PMP—pump, VSP—variable-speed pump

• Use VSP controlled by suction-side wet well; the pump speed is directly calculated for maintaining the fixed water level of a wet well. The first scenario is simulated by using the conventional modeling method for CSPs that are controlled by

rule-based controls. The second scenario is simulated by using the improved VSP solution method. The results presented in Figure 11 show both modeling approaches for PMP-5 controlled by wet well T-5. The results illustrate that

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the CSP frequently changes the pumping status with the rule-based controls in order to preserve the water level within the prescribed range. In contrast, the VSP adjusts its speed to attain the fixed wet-well water level over a 24h period. Figure 11 also shows that the pump with a VFD consumes less energy than the CSP. In addition, because of frequent start-up and shut-down of the CSP, a VSP seems more cost-effective for preventing the pump from quickly wearing out because of frequent cycling.

CONCLUSIONS This article describes an extended solution method for directly calculating pump speed under a wide range of VSP configurations in order to achieve the desired hydraulic characteristics of fixed hydraulic heads or fixed pump flows. The method is used to effectively model different challenging control scenarios including single and multiple VSPs at one pump station, VSPs controlled by discharge- or suction-side storage tanks, VSPs installed in parallel in order to achieve the common target of hydraulic characteristics, and VSPs controlled to move a fixed flow into a system. A new modeling element, the VSPB, is also introduced to leverage the extended method for rapid modeling of identical VSPs and associated controls. In addition, the improved method is used to directly calculate the pump speed of VSPs with the imposed rule-based control logic. This sophisticated VSP solution method provides an effective approach for modeling water distribution and wastewater collection systems. The integrated solution method is applied to several example systems. The results, which are typical of VSP uses, demonstrate that the extended solution method is flexible and robust for simulating a variety of VSP configurations and operating scenarios. The advanced pump modeling feature automatically cal-

culates the required relative pump-speed factors to reach the desired target hydraulic characteristics according to system demand load. It also enables engineers to efficiently analyze various pump operations in order to cost-effectively manage, plan, and operate water and wastewater systems. ABOUT THE AUTHORS

Zheng Yi Wu (to whom correspondence should be addressed) is the director of applied research for Bentley Systems Inc., 27 Siemon Company Dr., Ste. 200W, Watertown, CT, 06795; [email protected]. He received a BS degree in civil engineering from the Guizhou Institute of Technology, Guizhou, China; an MS degree in hydroinformatics from UNESCO-IHE, Delft, the Netherlands; and a PhD in civil and environmental engineering from the University of Adelaide, Australia. Michael Tryby is an environmental engineer with the US Environmental Protection Agency, Athens, Ga.; Ezio Todini is a professor at the University of Bologna, Italy; and Thomas Walski is senior product manager for Bentley Systems Inc., Nanticoke, Pa. Date of submission: 10/19/07 Date of acceptance: 05/23/08

If you have a comment about this article, please contact us at [email protected].

System Analysis and Simulation, (B. Coulbeck and Orr. ChunHou, editors.). John Wiley & Sons, London.

REFERENCES Lingireddy, S. & Wood, D.J., 1998. Improved Operation of Water Distribution Systems Using Variable Speed Pumps. Jour. Energy Engrg., ASCE, 124:3:90. Rishel, J.B., 2003. Constant Wet Well Level Control Saves Cost and Energy. Water World, September 2003, PennWell Corp., Tulsa, Okla. Rossman, L., 2002. EPANET2 User Manual. US Environmental Protection Agency, National Risk Management Research Laboratory, Cincinnati. Todini, E.; Tryby, M.; Wu, Z.Y.; & Walski, T., 2007. Direct Computation of Variable Speed Pumps for Water Distribution System Analysis. Proc. Community Clean Water Institute, De Montfort University, Leicester, United Kingdom. Todini, E. & Pilati, S., 1988. A Gradient Algorithm for the Analysis of Pipe Network. Computer Applications in Water Supply, Vol. 1,

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Walski, T.; Zimmerman, K.; Dudinyak, M.; & Dileepkumar, P., 2003. Some Surprises in Estimating the Efficiency of Variable-Speed Pumps With the Pump Affinity Laws. ASCE World Water Congress, Philadelphia. Wu, Z.Y. & Todini, E., 2007. Extended Approach for Modeling Fixed Flow Variable Speed Pumps. Proc. Community Clean Water Institute, De Montfort University, Leicester, United Kingdom. Wu, Z.Y., Todini, E. & Walski, T., 2007. Enhancements for Modeling Target Hydraulic Head by Automatic Calculation of Variable Pump Speed. Proc. World Environmental & Water Resources Congress, Tampa, Fla. Wu, Z.Y., 2006. Automatic Model Calibration Method for Water Distribution Water Quality Model. Jour. Envir. Science & Health (A), 41:7:1363.

JANUARY 2009 | JOURNAL AWWA • 101:1 | PEER-REVIEWED | WU ET AL

2009 © American Water Works Association