Combined energy and pressure management: Yorkshire Water case study

Deliverable 2.8A

by

Piotr Skworcow, Hossam AbdelMeguid and Bogumil Ulanicki Process Control - Water Software Systems, De Montfort University

April 2009

Contents 1 Introduction

1

2 Methodology overview

1

3 Optimal network scheduling problem

3

3.1 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

3.2 Model of water distribution system . . . . . . . . . . . . . . . . . . . . . . . . . .

4

3.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

4 Discretisation of continuous schedules

5

5 Implementation

7

6 Case Study

10

6.1 Network description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 6.1.1

Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.1.2

Current operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.1.3

Electricity tariffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.2.1

Elements to be scheduled . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.2.2

From Aquis model to Finesse model . . . . . . . . . . . . . . . . . . . . . . 13

6.2.3

Simplification and tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.3 Network scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6.3.1

Different leakage levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.3.2

Comparison of energy cost: current and optimised operation . . . . . . . . 17

6.3.3

Different demand levels and initial conditions . . . . . . . . . . . . . . . . 19

7 Conclusions and recommendations

20

References

22

Appendix A: Simplification of water network models

23

1

Introduction

Water distribution systems, despite operational improvements introduced over the last 10-15 years, still lose a considerable amount of potable water from their networks due to leakage, whilst using a significant amount of energy for water treatment and pumping. Reduction of leakage, hence savings of clean water, can be achieved by introducing pressure control algorithms (Ulanicki et al. 2000). Amount of energy used for pumping can be decreased through optimisation of pumps operation (pump scheduling) (Ormsbee and Lansey 2007, Bounds et al. 2006). Optimisation of pump schedules and algorithms for control of pressure are traditionally considered separately. However, if the pressure reducing valve (PRV) inlet pressure is higher than required, in many networks it could be reduced by adjusting pumping schedules in the upstream part of the network. Modern pumps are often equipped with variable speed drives, therefore, the pressure could be controlled by manipulating pump speed, thus reduce leakage and energy use. Furthermore, taking into account the presence of pressure-dependent leakage whilst optimising pumps operation is likely to influence the obtained schedules. In this report development and application of a new method for combined energy and pressure management via coordination of pumps operation with pressure control aspects is presented. Developed methodology is demonstrated on a medium-scale water distribution system.

2

Methodology overview

The proposed method for combined energy and pressure management, based on formulating and solving an optimisation problem, is an extension of the pump scheduling algorithms described in (Ulanicki et al. 1999, Bounds et al. 2006). The method involves utilisation of an hydraulic model of the network with pressure dependent leakage and inclusion of a PRV model with the PRV set-points included in a set of decision variables. The cost function represents the total cost of water treatment and pumping. Figure 1 illustrates that with such approach an excessive pumping contributes to a high total cost in two ways. Firstly, it leads to high energy usage. Secondly, it induces high pressure, hence increased leakage, which means that more water needs to be pumped and taken from sources. Therefore the optimizer, by minimising the total cost, attempts to reduce both energy usage and leakage. In the optimisation problem considered some of the decision variables are continuous (e.g. water production, pump speed, and valve position) and some are integer (e.g. number of pumps switched on). Problems containing both continuous and integer variables are called mixedinteger problems and are hard to solve numerically. Continuous relaxation of integer variables (e.g. allowing 2.5 pumps on) enables network scheduling to be treated initially as a continuous optimisation problem solved by a non-linear programming algorithm. Subsequently, the con-

1

High total cost

High energy usage

More water from sources and to be pumped

Excessive pumping High pressure

Increased leakage

Figure 1: Illustrating how excessive pumping contributes to high total cost when network model with pressure dependent leakage is used. tinuous solution can be transformed into an integer solution by manual post-processing, or by further optimisation, see (Bounds et al. 2006). For example, the result “2.5 pumps on” can be realised by a combination of 2 and 3 pumps switched over the time step. Section 3 describes continuous optimisation problem solved by a non-linear programming algorithm. In Section 4 a schedule discretisation algorithm that allows the user to interact with the discretisation process is described. Implementation of the overall scheduler is discussed in Section 5. Remark 1. An experienced network operator is able to manually transform continuous pump schedules into equivalent discrete schedules (Ulanicki et al. 2007). Optimisation methods described in this report are model-based and, as such, require hydraulic model of the network to be optimised. Such hydraulic model is usually developed in a modelling environment such as Epanet, Aquis, Finesse etc. and consists of three main components: boundary conditions (sources and exports), a hydraulic nonlinear network made up of pipes, pumps, valves, and reservoir dynamics. In order to reduce the size of the optimisation problem the full hydraulic model is simplified using module reduction algorithm (Ulanicki et al. 1996). In the simplified model all reservoirs and all control elements, such as pumps and valves, remain unchanged, but the number of pipes and nodes is significantly reduced. It should be noted that the connections (pipes) generated by module reduction algorithm may not represent actual physical pipes. However, parameters of these connections are computed such that the simplified and full models are equivalent mathematically. Details about model reduction are given in (Ulanicki et al. 1996) and in Appendix A of this report. Both the non-linear programming algorithm employed to compute the continuous schedule, and also schedule discretisation method, require a simulator of the hydraulic network. Simulators are part of modelling software such as Epanet, Aquis or Finesse. In this work a Finesse simulator called Ginas has been employed, however, other simulators could also be used and in future versions of the network scheduler Epanet simulator may be utilised.

2

3

Optimal network scheduling problem

Network scheduling calculates least-cost operational schedules for pumps, valves and treatment works for a given period of time, typically 24 hours. The decision variables are the operational schedules for control components, such as pumps, valves (including PRVs) and water works outputs. The problem has the following three elements: 1. objective function 2. hydraulic model of the network 3. constraints The scheduling problem is succinctly expressed as: minimise (pumping cost + treatment cost), subject to the network equations and operational constraints. The three elements of the problem are discussed in the following subsections. The problem is expressed in discrete-time, as in (Ulanicki et al. 1999, Bounds et al. 2006)

3.1

Objective function

The objective function to be minimised is the total energy cost for water treatment and pumping. Pumping cost depends on the efficiency of the pumps used and the electricity power tariff over the pumping duration. The tariff is usually a function of time with cheaper and more expensive periods. For given time step τc , the objective function considered over a given time horizon [k0 , kf ] is given by the following equation: 

φ=

kf XX

γpj (k)fj q j (k), cj (k) +


j∈Jp k=k0

kf XX

j∈Js k=k0



γsj (k)qsj (k) τc

(1)

where Jp is the set of indices for pump stations and Js is the set of indices for treatment works. The vector cj (k) represents the number of pumps on, denoted uj (k), and pump speed (for variable speed pumps) denoted sj (k). The function γpj (k) represents the electrical tariff. The treatment cost for each treatment works is proportional to the flow output with the unit price of γsj (k). The term fj (q j (k), cj (k)) represents the electrical power consumed by pump station j. The mechanical power of water is obtained by multiplying the flow q j (k) and the head increase ∆hj (k) across the pump station. The head increase ∆hj (k) can be expressed in terms of flow in the pump hydraulic equation, so that the cost term depends only on the pump station flow q j (k) and the control variable cj (k). From mechanical power of water, the electrical power consumed by the pump can be calculated using either the pump efficiency or pump power characteristics (Ulanicki et al. 2008). In this work pump power characteristics were used and electrical power

3

consumed by the pump station was calculated by adapting the formula, taken from (Ulanicki et al. 2008), given as follows:    us3 e P (q, u, s) =  0


q 3 us


q 2 us

+f

 q + g us + h if u, s > 0, otherwise

(2)

where e, f, g, h are power coefficients constant for given pump. Note that, for simplicity of notation, in equation 2 the time-indices k and superscripts j for terms q, u, s were omitted.

3.2

Model of water distribution system

Each network component has a hydraulic equation. The fundamental requirement in an optimal scheduling problem is that all calculated variables satisfy the hydraulic model equations. The network equations are non-linear and play the role of equality constraints in the optimisation problem. The network equations used to describe reservoir dynamics, components hydraulics and mass balance at reservoirs are those described in (Ulanicki et al. 2007). Since leakage is assumed to be at connection nodes, the equation to describe mass balance at connection nodes was modified to include the leakage term: Λc q(k) + dc (k) + lc (k) = 0

(3)

where Λc is node branch incidence matrix, q is vector of branch flows, dc denotes vector of demands and lc denotes vector of leakages calculated as: lc (k) = pα (k)κ

(4)

with p denoting vector of node pressures, α ∈ h0.5, 1.5i denoting leakage exponent and κ denoting vector of leakage coefficients, see (Ulanicki et al. 2000). Note that pα denotes each element of vector p raised to the power of α.

3.3

Constraints

In addition to equality constraints described by the hydraulic model equations, operational constraints are applied to keep the system-state within its feasible range. Practical requirements are translated from the linguistic statements into mathematical inequalities. The typical requirements of network scheduling are concerned with reservoir levels in order to prevent emptying or overflowing, and to maintain adequate storage for emergency purposes: max hmin (k) for k ∈ [k0 , kf ] f (k) ≤ hf (k) ≤ hf

4

Similar constraints must be applied to the heads at critical connection nodes in order to maintain required pressures throughout the water network. Another important constraint is on the final water level of reservoirs, such that the final level is not smaller than the initial level; without such constraint least-cost optimisation would result in emptying of reservoirs. The control variables such as the number of pumps switched on, pump speeds or valve positions, are also constrained by lower and upper constraints determined by the features of the control components.

4

Discretisation of continuous schedules

In this section a method of transforming the continuous pump schedules obtained by non-linear programming into discrete schedules is described. Let us first introduce some nomenclature and state the assumptions. Let τc (introduced in Section 3) denote time step for continuous pump schedules and τd denote time step for discrete pump schedules. Define tpi,j as electrical tariff period number i for pump station j ∈ Jp , i.e. ith period over which tariff γpj (k) is constant. Let T P Fc (tpi,j ) and T P Fd (tpi,j ) denote total flow through pump station j during tariff period tpi,j , obtained for continuous and discrete schedule, respectively. In addition to time index k we introduce kd which denotes time index for discrete schedules; note that time(k + 1)−time(k) = τc and time(kd + 1) − time(kd ) = τd . Continuous schedules, i.e. solution of continuous optimisation problem, consist of a set of pump station control vectors cj (k), each consisting of number of pumps on uj (k) and pump speed sj (k), where uj (k), sj (k) ∈ R; uj (k), sj (k) ≥ 0. Continuous schedules cannot be directly implemented in such form (we cannot have e.g. “0.3 of pump on”), thus require further processing. The goal of schedules discretisation process is to produce a set of equivalent control vectors denoted cjd (kd ), each consisting of number of pumps on ujd (kd ) and pump speed sjd (kd ), where sjd (kd ) ∈ R; sjd (kd ) ≥ 0 and ujd (kd ) ∈ N. Such discrete schedules can directly be implemented in the network. Remark 2. Solution of continuous optimisation problem is often such, that the results hit constraints (typically that of maximum and minimum allowed reservoir level), i.e. are on the border of feasibility. Therefore, discretisation of continuous schedules may result in minor violation of these constraints. Proposed schedules discretisation approach is based on concept of matching pump flows resulting from discrete schedule to pump flows resulting from continuous schedule, for each pump and each tariff period. Formally, the approach attempts to generate such discrete schedules that satisfy: ∀j ∈ Jp ∀tpi,j T P Fc (tpi,j ) ≈ T P Fd (tpi,j ) 5

(5)

Assumptions for the considered approach are stated as follows: 1. Time steps for continuous and discrete pump schedules are such that τd · n = τc ,

n ≥

2, n ∈ N. 2. Pump speeds sjd (kd ) and sj (k) are the same during corresponding periods. Note that second assumption imposes that condition given by Equation 5 needs to be achieved by manipulating number of pumps on in a given pump station, rather than by manipulating their speed. The reason for such assumption is that power consumption increases significantly when the pump speed is increased, see Equation 2. The idea behind the proposed schedules discretisation is that for example continuous result of “2.5 pumps on” can be realised by a combination of 2 and 3 pumps switched every time step, while “2.25 pumps on” can be realised by a sequence with 2 pumps on for three time steps and 3 pumps on for one time step. Detailed description of the proposed schedules discretisation process follows. For given pump station and given time step k, maximum and minimum number of pumps on for all discrete schedule periods kd corresponding to k are calculated as ceil (uj (k)) and integer (uj (k)), respectively, where ceil (uj (k)) denotes uj (k) rounded up and integer (uj (k)) denotes integer part of uj (k). Such maximum and minimum are imposed so that the discrete schedules are ‘close’ to the continuous schedules. Note that the decision variable describing number of pumps on for given pump station, during each kd corresponding to k, is thus binary, i.e. knowing that at least integer (uj (k)) pumps are on, we need to decide whether an additional pump should be on, that is whether ujd (kd ) = integer (uj (k)) or ujd (kd ) = ceil (uj (k)). Define η(k) as the number of discrete schedule periods kd corresponding to k when an additional pump is on. Value of η(k) is calculated as follows: 


τc η(k) = round frac u (k) · τd j



(6)

where frac (uj (k)) denotes fractional part of uj (k). To illustrate the above description consider the following example. Let τc = 60 min, τd = 15 min, uj (k) = 2.2 for given pump station and given k. For such τc and τd we have four discrete schedule periods kd corresponding to a single k. Maximum and minimum number of pumps on for all kd corresponding to k are ceil(2.2) = 3 and integer(2.2) = 2. Using Equation 6 we obtain
60 η(k) = round frac (2.2) · 15 = 1, therefore one out of four ujd (kd ) is equal 3, while remaining three ujd (kd ) are equal 2.

Having η(k), it needs to be decided to which kd an additional pump on is assigned. Using the above example, discrete schedule corresponding to uj (k) = 2.2 could be implemented as {2, 2, 2, 3}, {2, 2, 3, 2}, {2, 3, 2, 2} or {3, 2, 2, 2}. Potential options for choosing when additional pump is on are as follows: 6

1. alternating order to minimise constraint violation, e.g. {2, 3, 2, 2} (see remark 2) 2. maintaining continuity of pump operation to minimise amount of switching on/off, e.g. {2, 2, 2, 3} 3. random Due to remark 1, it was decided to allow the user (operator) to interact with the discretisation process. After η(k) is calculated for each k, an initial discrete schedule is automatically generated using option 3 from the above list (random order). Subsequently, the user can alter the discrete schedule by manipulating when an additional pump is on/off for each pump station. By manipulating the discrete schedule the user is therefore able to e.g. reduce the amount of switching on/off, and also to minimise the discrepancy between T P Fc (tpi,j ) and T P Fd (tpi,j ), whilst ensuring that the constraints are not violated, or such violation is minimal (see remark 2). To be able to compare T P Fc (tpi,j ) and T P Fd(tpi,j ) network simulator needs to be utilised. Further details on implementation of the proposed pump schedules discretisation are given in Section 5. Note that operator involvement is not essential during schedules discretisation process, but is likely to improve the quality of the obtained discrete schedules. For future versions of schedules discretiser, employment of fast genetic algorithms is considered to help the operator to minimise the discrepancy between T P Fc (tpi,j ) and T P Fd (tpi,j ) and to minimise violation of constraints. Such approach would combine the use of operator’s experience with benefits of heuristic optimisation.

5

Implementation

Developed energy and pressure management continuous scheduler was integrated into a modelling environment, called Finesse. The scheduler, as with all tools in Finesse, is general purpose in that it takes any data model of a network, simulates the network to initialise its decision variables for the network scheduler, and if the model is feasible it calculates the optimal continuous schedules. Using model of a network Finesse automatically generates optimal network scheduling problem written in a mathematical modelling language called GAMS (Brooke et al. 1998), which calls up a non-linear programming solver called CONOPT (Drud 1985) to calculate a continuous optimisation solution. CONOPT is a non-linear programming solver, which uses a generalised reduced gradient algorithm (Drud 1985). An optimal solution is fed back from CONOPT into Finesse for analysis and/or further processing. For further details on using GAMS and CONOPT for optimal network scheduling see (Ulanicki et al. 1999). Developed user interface (illustrated in Figure 2) allows to choose: the time step τc , presence of pressure dependent leakage (i.e. term lc (k) in Equation 3), whether power consumption for 7

pumps is calculated from pump efficiency or by using the formula given in Equation 2, CONOPT options for tolerance and iteration limit. Optimisation results are presented in the form of graphs: control and flow for elements (e.g. pumps), head and demand for nodes, see example in Figure 3. Obtained schedules can then be fed back into the Finesse input model, or exported to a text file.

Figure 2: Finesse: user interface of network scheduler Proposed interactive schedules discretisation method was implemented in Matlab environment. Developed user interface (illustrated in Figure 4) allows the user to: manipulate the discrete schedule proposed by the algorithm for each pump, export the schedule back to Finesse, load simulation results from Finesse, evaluate T P Fc (tpi,j ) and T P Fd (tpi,j ) for each pump and each tariff period. At present the discretisation software utilises Finesse hydraulic simulator (Ginas) to calculate the flows resulting from a given discrete schedule and requires some manual copying from Finesse tables, i.e. connection between the schedules discretiser and Finesse is not fully automated.

8

Figure 3: Finesse: visualisation of optimisation results

2 Pump station choice

1.8

tp

Discrete schedule

1.6

T P Fc

Continuous schedule

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

5

10

Time [h]

15

20

25

Figure 4: User interface for schedules discretiser software

9

T P Fd

6.2 6.2.1

Modelling Elements to be scheduled

The elements for which the schedules are to be calculated are summarised as follows: 1. Main pump stations, i.e. HH Tower WPS and Eccup/Harlow Hill WPS. For HH Tower WPS only number of pumps on (uj (k) and subsequently ujd (kd )) is calculated, since this pump station consist of fixed speed pumps. For Eccup/Harlow Hill WPS both number of pumps on and the pump speed (sj (k)) are calculated. Note that for HH Tower WPS local control rule has been removed to allow scheduling. Booster pumps speed depends directly on demand and hence they are not scheduled, i.e. their operation remains the same as in the original model. 2. Pressure reducing valve (one PRV). However, since the PRV is fed directly from reservoir, scheduling of the PRV together with pumps will not bring additional benefits, compared to scheduling only the PRV using pressure control algorithms (see e.g. (Ulanicki et al. 2000)). Moreover, flow through the PRV is about 1.5 l/s on average, hence any additional flow resulting from the leakage downstream from the PRV is negligible compared to total network flow, which is approximately 400 l/s on average. 3. Control valves that are not permanently closed (2 valves). It should however be noted that the considered control valves are: first between reservoirs Harlow Hill CTR and North Righton SRE, second between North Righton SRE and PRV. Their operation has therefore small impact on the pump schedules. 6.2.2

From Aquis model to Finesse model

The files initially provided by YWS were: Aquis model of the network, file with short description of the network and characteristics of the main pumping stations, further referred to as the description file. Later information about the electrical tariffs for pumps was provided. The first step was to analyse the structure and operation of the system and draw a diagram of its topology (illustrated in Figure 5). Having established the network structure and operation, next step was to convert Aquis model into Finesse model, with Epanet model being an intermediate step, since Aquis model cannot be imported into Finesse. Structure of nodes and pipes, data about demands, and partial information describing valves were automatically converted into Epanet format by Exeter University group. Obtained Epanet model was subsequently imported into Finesse. Other network elements, i.e. reservoirs, pumps and remaining data for valves, were added manually to the Finesse model. Pumps, valves and reservoirs parameters were described in Finesse using data from Aquis model and from the description file. This involved fitting parameters to data points, resolving 13

several issues and making some assumptions; the most important points are summarised below: 1. Reservoirs: few data points describing water level and corresponding volume given in Aquis model were used to estimate parameters of function describing ‘shape’ of the reservoir required for Finesse. This was done for all reservoirs. 2. Identical pumps belonging to the same pump station, modelled as parallel individual pumps in Aquis, were modelled as a single pump station in Finesse. This was done for HH Tower WPS and Eccup/Harlow Hill WPS. 3. Pumps: few data points describing head increase and corresponding flow given in Aquis model were used to estimate parameters of function describing head/flow characteristics of the pump required for Finesse. This was done for all pump stations. 4. Pumps: parameters of function describing power consumption characteristics (parameters e, f, g, h in Equation 2) were established using power curves: (i) provided in the description file in the form of plots for pump stations HH Tower WPS and Eccup/Harlow Hill WPS and (ii) taken from pump catalogue for HH Tower Booster, Beckwithshaw WPS and North Righton WPS - pumps that had similar head/flow characteristics were selected. 5. Local control rules were removed for HH Tower WPS. Instead, time-series describing pumps operation, taken from results of Aquis simulation, were fed into the Finesse model. It was found that in Aquis model, which allows variable simulation step, the pump in HH Tower WPS was switching at intervals as small as 7 minutes, due to tight margin (20 cm). To represent such irregular switching and model similar operation of this pump in Finesse, where minimal time step is 15 minutes, it was assumed that e.g. 0.5 pump is on during a single time step. 6. All permanently closed valves were removed from the Finesse model. 7. Pumps in Eccup/Harlow Hill WPS were marked as fixed-speed pumps. It was found that in fact they are variable-speed pumps, since their speed is changing during the day in the original Aquis model. 8. Minimum allowed speed was not given for Eccup/Harlow Hill WPS, it was assumed to be 800 RPM, i.e. 54% of the maximum speed. 9. Since the reservoirs HH 1 Comp A and HH 1 Comp B are identical, very close to each other, on the same elevations and interconnected, it was decided to merge them into one reservoir, further denoted as HH 1, with appropriate parameters to account for the combined volume of HH 1 Comp A and HH 1 Comp B.

14

6.2.3

Simplification and tuning

Once the Finesse model was completed, it was simplified using Finesse model reduction module (Ulanicki et al. 1996) to reduce the size of the optimisation problem. In the simplified model all control elements remained unchanged, but the number of pipes and nodes was reduced to 45 and 43, respectively. It was found that due to some incompatibilities of the environment in which Finesse was developed (C++ Borland 5) with current operating systems (Windows XP SP3) there was an error in obtained simplified model: calculated equivalent resistance of connection between nodes was higher than that of the pipes in the full model. Detailed investigation of full and simplified models confirmed that this was the only issue, whilst the structure, demands and other parameters of the obtained simplified model were correct. Note that the model reduction module was previously successfully applied without any errors to several networks of similar or higher complexity (e.g. with over 4000 nodes and pipes, approximately 20 pump stations and 20 reservoirs) than the one considered in this study. For this reason, it is likely that Finesse will be redeveloped in some more up-to-date environment to avoid such issues, see Section 7 for details. To rectify the problem of wrong resistances a Matlab script to calculate an equivalent resistance was developed and such obtained parameters of connection between nodes were manually fed into the simplified model. Subsequently, both full and simplified Finesse models were simulated and compared, with respect to pump flow and reservoir trajectories, against the reference Aquis model. Since the reservoirs HH 1 and HH 2 are directly connected, it is considered sufficient to compare average levels for these two reservoirs. Both Finesse models showed satisfactory agreement, see reservoir trajectories illustrated in Figure 6.

6.3

Network scheduling

In the provided Aquis model 15 minutes simulation step was used, although the pump in HH Tower WPS is switching on/off at periods as short as 7 minutes. For the purpose of network scheduling 1 hour time step for the continuous optimisation problem was used (τc = 60 min) and 15 minutes time step for the schedules discretiser (τd = 15 min). Only limited information about leakage in the considered network was available at the time this work was carried out. According to the description file there is a considerable leakage on the connection between Eccup/Harlow Hill WPS and reservoirs HH 1 and HH 2, due to significant distance and elevation difference which require high pressure at Eccup/Harlow Hill WPS outlet. Therefore, in the study described in next subsections the leakage was assumed to be on this connection. Leakage coefficient α in Equation 4 was chosen to be 1.1.

15

North Righton SRE

Head [m]

189.4 189.2 189 188.8 0

Head [m]

Finesse full Aquis Finesse simplified

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [h] HH CTR

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [h] HH 1 and HH 2

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 Time [h]

199.1 199 198.9 198.8 198.7 0

Head [m]

165.2 165 164.8

Figure 6: Illustrating reservoir level trajectories for full Finesse model, simplified Finesse model and reference Aquis model 6.3.1

Different leakage levels

The network optimiser was run for several scenarios, assuming different leakages levels. Information about the electrical tariffs in the considered water network was not available at the time this particular part of study was carried out. For this reason, during the study of different leakage levels, the tariffs were assumed to represent a typical scheme of cheap at night and expensive during day. Assumed tariffs were: 10 p/kWh between 22:00 - 07:00 and 20 p/kWh between 07:00 - 22:00. Initial reservoir levels were assumed to be in the middle of their bounds to allow more flexibility for optimisation; recall from Section 3 that due to constraints for each reservoir the final water level needs to be at least at the initial level. Three scenarios were considered for different leakage levels. Parameter κ in Equation 4 was chosen such that the leakage at a node close to the outlet of Eccup/Harlow Hill WPS was approximately 10%, 20% or 30% of the flow for scenarios 1, 2 and 3, respectively. Leakage was assumed to be zero at other nodes. The continuous optimisation ran for 2 minutes on a Pentium 4 3GHz PC. Obtained pump schedules for Eccup/Harlow Hill WPS for different scenarios are illustrated in Figure 7; only continuous solutions are illustrated for simplicity. Daily cost of electrical energy was £534, £547 and £562 for scenarios 1, 2 and 3, respectively. It was found that increased leakage coefficient, not surprisingly, led to increased cost, since 16

Scenario 1 (~10% leakage) 3

Pumps on Normalised speed

2 1 0 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [h] Scenario 2 (~20% leakage)

1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

3 2 1 0 0

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [h] Scenario 3 (~30% leakage)

3 2 1 0 0

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time [h]

Figure 7: Comparison of Eccup/Harlow Hill WPS pump schedules for three different leakage levels using assumed tariffs. harder pumping is required due to increased pump flow, as can be seen in Figure 7. The patterns of pump schedules for all cases exhibit intensive pumping during the cheap tariff period to fill reservoirs HH 1 and HH 2, which subsequently supply water during the expensive tariff period. It was observed that, despite indirect penalisation of high pressure in the cost function (see Figure 1), increased leakage coefficient did not result in lower Eccup/Harlow Hill WPS outlet pressure. Analysis of CONOPT solver logs revealed that this was a result of hydraulic equation constraints: Eccup/Harlow Hill WPS outlet pressure cannot be decreased, due to significant distance and elevation difference between Eccup/Harlow Hill WPS and reservoirs HH 1 and HH 2. 6.3.2

Comparison of energy cost: current and optimised operation

In this subsection a comparison, in terms of energy cost, between current and optimised operation is considered. Actual electricity tariffs, summarised in Section 6.1, were utilised in this study. To be able to compare the cost a case with no pressure-dependent leakage was considered, i.e. κ in Equation 4 was zero for all nodes. Initial reservoir levels were assumed to be in the middle of their bounds to allow more flexibility for optimisation. The continuous optimisation ran for 2 minutes on a Pentium 4 3GHz PC. Continuous solution was transformed into an integer solution

17

using the discretiser. Obtained pump schedules for HH Tower WPS and Eccup/Harlow Hill WPS are illustrated in Figure 8 and Figure 9, respectively. HH Tower WPS: Current operation 1 Pumps on 0.8 0.6 0.4 0.2 0 0

1

2

3

4

5

6

7

8

9

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Figure 8: Comparison of current and optimised network operation for HH Tower WPS It can be observed in Figure 8 that due to operational constraints, particularly small size of Harlow Hill CTR, current and optimal schedules are similar, i.e. both exhibit frequent switching throughout the 24h period. In Figure 9 it can be observed that optimal schedules for Eccup/Harlow Hill WPS cause an intensive pumping during the cheap tariff period to fill HH 1 and HH 2, which subsequently supply water during the expensive tariff period. The operational speed of Eccup/Harlow Hill WPS pumps is lower, compared to current operation, particularly during the expensive tariff period, which also contributes to reduced cost. Calculated daily cost of electrical energy1 for HH Tower WPS and Eccup/Harlow Hill WPS was as follows: £402 for current network operation, £264 for optimised continuous solution and £266 for integer solution. As expected, significant savings (35%) result from optimising the operation of Eccup/Harlow Hill WPS, whilst optimising the operation of HH Tower WPS reduced its energy cost only by 15%. This is due to: (i) Eccup/Harlow Hill WPS consisting of variable-speed pumps and (ii) large size of reservoirs HH 1 and HH 2 giving more flexibility than Harlow Hill CTR. The results also indicate that the schedule discretisation process did not increase the cost significantly compared to continuous schedules. 1

Recall from Section 6.1 that only the costs associated with KWh usage are taken into account and that winter

tariff was assumed.

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Eccup/Harlow Hill WPS: Current operation 2

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Figure 9: Comparison of current and optimised network operation for Eccup/Harlow Hill WPS Optimised schedules of Eccup/Harlow Hill WPS were fed back into the original Aquis model. Aquis simulation confirmed that optimised operation of Eccup/Harlow Hill WPS results in more capacity of reservoirs HH 1 and HH 2 (Comp A and B) being used, compared to current operation, see Figure 10. It can be observed that current operation uses 10% of the allowed range of reservoir level, whilst optimised operation uses 16% of this range. Note that the final reservoir level for optimised operation is lower than the initial one. This is due to modelling discrepancies between Finesse and Aquis model, since only few points given in Aquis model were used to estimate the parameters of function describing head/flow characteristics of the pump, which resulted in pump flow being up to 2.7% lower in Aquis compared to Finesse. 6.3.3

Different demand levels and initial conditions

This subsection considers network scheduling for different demand levels and different initial conditions, i.e. initial water levels in reservoirs. Actual electricity tariffs, summarised in Section 6.1, were utilised in this study. Parameter κ in Equation 4 was chosen such that the leakage at a node close to the outlet of Eccup/Harlow Hill WPS was approximately 15% of the flow. All nominal (from Aquis model) demands and import/export flows were multiplied by 0.75 and 1.25 for ‘low demands’ and ‘high demands’ scenarios, respectively. Demands for ‘medium demands’ scenarios remain unchanged. Initial reservoir water levels, chosen independently for each reservoir, were at 25%, 50% and 75% of the maximum level. In total 27 scenarios were 19

Reservoir level 5.5 Current operation Optimised operation 5

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Figure 10: Comparison of average HH 1 and HH 2 (Comp A and B) reservoirs levels for current and optimised operation of Eccup/Harlow Hill WPS - results of Aquis simulation. scheduled; generated library of schedules will be utilised by Exeter University group as a basis to develop an expert system for rule-based pump control. Three example schedules of Eccup/Harlow Hill WPS, obtained for initial reservoir water levels at 50% and three different demand levels, are illustrated in Figure 11. It can be observed in Figure 11 that increased demands, not surprisingly, required more intensive pumping in terms of both speed and number of pumps on. The cost, taking into account only Eccup/Harlow Hill WPS, was £164, £255 and £388 for low, medium and high demands, respectively. Note that increase in demands by a factor of 1.25 (for high demands scenario) resulted in increase of cost by a factor of 1.5, compared to medium demands. Similarly, decrease in demands by a factor of 0.75 (for low demands scenario) resulted in decrease of cost by a factor of 0.65. This indicates that the pumping cost increases exponentially with demand levels.

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Conclusions and recommendations

In this report a method was described for combined energy and pressure management via integration and coordination of pump scheduling with pressure control aspects. The method is based on formulating and solving an optimisation problem and involves utilisation of an hydraulic model of the network with pressure dependent leakage and inclusion of a PRV model with the PRV set-points included in a set of decision variables. The cost function of the optimisation problem represents the total cost of water treatment and pumping. Developed network scheduling algorithm consists of two stages. First stage involves solving of a continuous problem, where 20

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Figure 11: Comparison of schedules of Eccup/Harlow Hill WPS for 3 demand levels operation of each pump is described by continuous variable, and utilises GAMS modelling language and CONOPT non-linear programming solver. Subsequently, in second stage continuous pump schedules are discretised, such that operation of each pump is described by binary variable (on/off). The case study selected was Harlow Hill water distribution network, being part of Yorkshire Water Services (YWS). Network topology and current operation has been described, followed by description of the process of obtaining the network model for scheduling. Developed models, both full and simplified, showed good agreement with the reference Aquis model provided by YWS. Network scheduling studies considered different leakage levels, initial reservoir levels and demand levels. A comparison has been made between the cost of the current network operation and the optimised operation. Taking into account only the costs associated with KWh usage of scheduled pumping stations and assuming winter tariff the optimised operation reduced the daily electricity cost from £402 to £266. A library of 27 schedules for different scenarios was generated for the purpose of developing an expert system for rule-based pump control by Exeter University group. Results obtained for different demand levels indicate that the pumping cost increases exponentially with demand levels. For the considered network it is recommended that more capacity of reservoirs should be used, with Eccup/Harlow Hill WPS pumping more intensively during the cheap tariff period and using the stored water during the expensive tariff period. For Eccup/Harlow Hill WPS it 21

is also suggested to use more pumps but with lower speed, since currently they operate at 95% of their maximum speed. Operation of HH Tower WPS may remain locally controlled, since no significant savings on this pump station can be achieved due to small capacity of Harlow Hill CTR. However, the margin of 20 cm controlling the pump in HH Tower WPS should be extended to avoid frequent switching on/off. For future study the following is recommended: 1. More than just a few data points should be available for pumps and reservoirs characteristics to improve the accuracy of modelling for scheduling. 2. There are issues with the current version of Finesse due to some incompatibilities of the environment in which Finesse was developed (C++ Borland 5) with current operating systems (Windows XP SP3 or Vista). It is recommended that the scheduler is redeveloped in some more up-to-date environment, such as MS Visual Studio C#. 3. Schedules discretisation algorithm could be extended by merging operator involvement with fast genetic algorithms or other heuristics.

References Bounds, P., J. Kahler, B. Ulanicki. 2006. Efficient energy management of a large-scale water supply system. Civil Engineering and Environmental Systems 23(3) 209 – 220. Brooke, A., D. Kendrick, A. Meeraus, R. Raman. 1998. GAMS: A user’s guide. GAMS Development Corporation, Washington, USA. Drud, A.S. 1985. Conopt: A grg code for large sparse dynamic non-linear optimisation problems. Mathematical Programming 31 153–191. Ormsbee, L., K. Lansey. 2007. Optimal control in water-supply pumping system. Journal of Water Resources Planning and Management, 120(2) 237–252. Ulanicki, B., P. Bounds, J. Rance, L. Reynolds. 2000. Open and closed loop pressure control for leakage reduction. Urban Water 2(2) 105–114. Ulanicki, B., P.L.M. Bounds, J.P. Rance. 1999. Using a gams modelling environment to solve network scheduling problems. Measurement + Control 32 110–115. Ulanicki, B., J. Kahler, B. Coulbeck. 2008. Modeling the efficiency and power characteristics of a pump group. Journal of Water Resources Planning and Management 134(1) 88–93. Ulanicki, B., J. Kahler, H. See. 2007. Dynamic optimization approach for solving an optimal scheduling problem in water distribution systems, , vol. 1, pp. Journal of Water Resources Planning and Management 133(1) 23–32.

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Ulanicki, B., A. Zehnpfund, F. Martinez. 1996. Simplification of water network models. A. Muller, ed., Hydroinformatics 1996: Proceedings of the 2nd International Conference on Hydroinformatics, Switzerland, vol. 2. 493–500.

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