EWRI2009 - Combined Energy and Pressure Management in Water Distribution Systems
EWRI2009 - Combined Energy and Pressure Management in Water Distribution Systems
EWRI2009 - Combined Energy and Pressure Management in Water Distribution Systems
SPONSORED BY
Environmental and Water Resources Institute (EWRI)
of the American Society of Civil Engineers
EDITED BY
Steve Starrett, Ph.D., P.E., D.WRE
ABSTRACT
In this paper a method is proposed for combined energy and pressure management
via integration and coordination of pump scheduling with pressure control aspects.
The proposed solution involves: formulation of an optimisation problem with the
cost function being the total cost of water treatment and pumps energy usage,
utilisation of an hydraulic model of the network with pressure dependent leakage,
and inclusion of a PRV model with the PRV set-points included as a set of decision
variables. Such problem formulation led to the optimizer attempting to reduce both
energy usage and leakage. The developed algorithm has been integrated into a
modelling, simulation and optimisation environment called FINESSE. The case
study selected is a major water supply network, being part of Yorkshire Water
Services, with a total average demand of 400 l/s.
1. INTRODUCTION
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
main differences between these methods and the one proposed in this paper are in the
network model and in the decision variables set.
The proposed 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 as a set of decision variables. The cost function remains as
in (Ulanicki et al 1999; Bounds et al 2006), i.e. 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.
Figure 1. Illustrating how excessive pumping contributes to high total cost when
network model with pressure dependent leakage is used.
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. Note that other
costs (such as pump switching cost) could be included in the objective function.
However, the switching cost is rarely considered due to insufficient data available to
formulate it within the objective function (Ormsbee and Lansey 1994). For given
time step ∆t, the objective function considered over a given time horizon [k 0 , k f ] is
given by the following equation:
kf kf
⎛ ⎞
φ =⎜ ∑ ∑γ
⎜ j∈J k = k0
j
p (k ) f j (q (k ), c (k )) +
j j
∑ ∑γ
j∈ J s k = k 0
s
j
(k ) × qsj (k ) ⎟Δt
⎟
(1)
⎝ p ⎠
where J p is the set of indices for pump stations and J s is the set of indices for
treatment works. The c j (k ) vector represents the number of pumps on, denoted
u j (k ) , and pump speed (for variable speed pumps) denoted s j (k ) . The function
γ pj (k ) represents the electrical tariff. The treatment cost for each treatment works is
proportional to the flow output with the unit price of γ sj (k ) . The term
f j (q j (k ), c j (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 Δ h j across the pump station. The head increase Δ h j 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 c j (k ) . From mechanical power
of water, the electrical power consumed by the pump can be calculated using the
pump efficiency or using pump power characteristics (Ulanicki et al 2008).
World Environmental and Water Resources Congress 2009: Great Rivers © 2009 ASCE 712
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 in this paper 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 is modified to include the
leakage term:
Λc q(k ) + d c (k ) + l c (k ) = 0 (2)
l c = pα κ (3)
with p denoting vector of node pressures, α ∈ 0.5, 1.5 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 .
h min
f ≤ h f (k ) ≤ h max
f for k ∈ [k0 , k f ]
Similar constraints must be applied to the heads at critical connection nodes in order
to maintain required pressures throughout the water network. Another constraint is
on the final level of reservoirs, such that the final level is not smaller than the initial
level. 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. IMPLEMENTATION
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).
5. CASE STUDY
5.1. Network description. The case study selected is a major water supply network,
being part of Yorkshire Water Services (YWS). The network is fed by two major
sources and has two major exports. The network consists of 2074 nodes, 2212 pipes,
4 reservoirs, 12 pumps and 56 valves (including one PRV) with a total average
demand of 400 l/s. However, only 8 out of 12 pumps were actually used for
scheduling, since other 4 pumps are in standby mode and should not be used unless
in an emergency situation such as failure of other pumps. It was also found that only
8 out of 56 valves could be scheduled, while others are to remain fully closed.
Schematic of the case study network is illustrated in Figure 2. Description of current
operation of the network follows.
demand
~0.5 l/s demand
~6 l/s
PS1 PS3
(1 VSP) (1 VSP)
RES2
demand demand
~10 l/s ~9 l/s PS4
(2 FSP)
PS2 RES1
(1 VSP) RES3
demand import/export
demand ~5 l/s import ~240l/s ~40/120 l/s
~0.1 l/s
RES4
export ~320l/s
PRV
import ~160l/s
PS5
(3 VSP)
PS1, PS2 and PS3 consist of small pumps that operate to maintain given
outlet pressure. Their speed, therefore, changes together with demand. PS4 is
World Environmental and Water Resources Congress 2009: Great Rivers © 2009 ASCE 714
controlled by water level in reservoir RES2 (on/off control with 20 cm water level
margin); typically only one pump is used. Due to tight margin (20 cm) the pump in
PS4 is switched on/off frequently, every 7 to 30 minutes. PS5 consists of three large
pumps with variable speed drives. They operate to number of preset flow bands;
typically only one or two pumps are on. Opening of the top-feed valve for RES1 is
controlled by water level in RES1. The top-feed valves for RES2-5 are fully open.
Information about the electrical tariffs in the considered water network was
not available at the time this work was carried out. For this reason the tariffs were
assumed to represent a typical scheme of cheap at night and expensive during day.
Assumed tariffs were: 0.1 £/kWh between 22.00 – 07.00 and 0.2 £/kWh between
07.00 – 22.00.
5.2. Modelling and simplification. A model of the network was provided in Aquis
format. Structure of nodes and pipes was automatically converted into EPANET
format and subsequently imported into FINESSE. Other network element, i.e.
reservoirs, pumps and valves, were added manually to the FINESSE model. Pumps,
valves and reservoirs parameters were described in FINESSE using data from Aquis
model and additional information provided by YWS.
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. Both full and
simplified FINESSE models were simulated and compared, with respect to pump
flow and reservoir trajectories, against the reference Aquis model. It was found that
in Aquis model, which allows variable simulation step, the pump in PS4 was
switching at intervals as small as 7 minutes. To represent such irregular switching
and model similar operation of the PS4 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. Both
FINESSE models showed satisfactory agreement, see reservoir trajectories illustrated
in Figure 3. Since RES3 and RES4 are directly connected, it is considered sufficient
to compare average levels for these two reservoirs. Note that for the purpose of
comparison of FINESSE models with Aquis model local control rules, such as
control of RES1 top-feed valve, were kept. Subsequently, these local rules were
removed to enable scheduling of all control elements.
Only limited information about leakage in the considered network was
available at the time this work was carried out. For this reason the network optimiser
was run for several scenarios, assuming different leakages levels. According to YWS
there is a considerable leakage on the connection between PS5 and reservoirs RES3
and RES4, due to significant distance and elevation difference which require high
pressure at PS5 outlet. Therefore, in the scenarios described in next subsections the
leakage was assumed to be on this connection.
World Environmental and Water Resources Congress 2009: Great Rivers © 2009 ASCE 715
RES1
189.4
Finesse full
Aquis
Head [m]
189.2
Finesse simplified
189
188.8
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]
RES2
199.1
Head [m]
199
198.9
198.8
198.7
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]
RES3 and RES4
165.2
Head [m]
165
164.8
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]
5.4. Network scheduling: with leakage term. Three scenarios were considered for
different leakage levels. Parameter κ in Equation (3) was chosen such that the
leakage at a node close to the outlet of PS5 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. Only continuous solution was considered for simplicity. Obtained pump
schedules for PS5 for different scenarios are illustrated in Figure 6. Daily cost of
electrical energy was £534, £547 and £562 for scenarios 1, 2 and 3, respectively.
World Environmental and Water Resources Congress 2009: Great Rivers © 2009 ASCE 716
0.6
0.4
0.2
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]
0.5
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]
0.5
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]
1.5
0.5
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]
Pumps on
Scenario 1 (~10% leakage) Normalised speed
3
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)
3
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 3 (~30% leakage)
3
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]
Figure 6. Comparison of PS5 pump schedules for three different leakage levels.
5.5. Discussion. It can be observed in Figure 4 that due to operational constraints not
much savings can be achieved for PS4, since current and optimal schedules are
similar, i.e. both exhibit switching 0-1 pumps on throughout the 24h period.
However, recall from Section 5.1 that PS4 switches frequently due to tight margin
(20 cm) for reservoir level controlling the pump operation. Optimal schedules
resulted in less frequent switching which is beneficial for pump durability.
In Figure 5 it can be observed that optimal schedules for PS5 cause an
intensive pumping during the cheap tariff period to fill RES3 and RES4, which
subsequently supply water during the expensive tariff period. The operational speed
of PS5 pumps is lower, compared to current operation, during the expensive tariff
period, which also contributes to reduced cost. The total cost was reduced by 38%. It
should, however, be noticed that these results were obtained for an assumed
electrical tariff, which could significantly differ from the actual tariff, and did not
take into account standing charge and other costs.
It was found that increased leakage coefficient, not surprisingly, led to
increased cost, since harder pumping is required due to increased pump flow.
Nevertheless, the pump schedules are similar to the ‘no leakage’ case, with intensive
pumping during the cheap tariff period; compare Figures 5 and 6. 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 PS5 outlet pressure. Analysis of
CONOPT logs revealed that this was a result of hydraulic equation constraints: PS5
outlet pressure cannot be decreased, due to significant distance and elevation
difference between PS5 and RES3.
World Environmental and Water Resources Congress 2009: Great Rivers © 2009 ASCE 718
6. CONCLUSIONS
In this paper a method was proposed for combined energy and pressure management
via integration and coordination of pump scheduling with pressure control aspects.
The proposed solution is an extension of the pump scheduling method based on
formulation and solving of an optimisation problem. Proposed method utilises an
hydraulic model of the network with pressure dependent leakage and takes into
account PRV model with the PRV set-points included as a set of decision variables.
Such formulation leads to the optimiser attempting to reduce both energy usage and
leakage. The developed algorithm has been integrated into a modelling, simulation
and optimisation environment called FINESSE, which utilises GAMS modelling
language and CONOPT non-linear programming solver.
The method was applied to optimise the operation of a major water supply
network, being part of Yorkshire Water Services. A network model provided in
Aquis format was converted to Epanet format, imported to Finesse, simplified and
validated against original Aquis model. Optimised network schedules resulted in the
total cost of electrical energy reduced by 38%, albeit for an assumed electrical tariff,
which could significantly differ from the actual tariff. The developed algorithm is
currently further investigated using other case studies.
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optimisation problems, Mathematical Programming, 31, pp.153-191
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