Content uploaded by Justus Hoffstaedt

Author content

All content in this area was uploaded by Justus Hoffstaedt on Nov 14, 2022

Content may be subject to copyright.

System model development and numerical simulation of low-head

pumped hydro storage

J.P. Hoffstaedt & A.J. Laguna

Department of Maritime and Transport Technology, Delft University of Technology, Delft, the Netherlands

J.Fahlbeck & H. Nilsson

Department of Mechanics and Maritime Sciences, Division of Fluid Dynamics, Chalmers University of

Technology, Gothenburg, Sweden

ABSTRACT: To tackle the growing demand for grid-scale energy storage, the ALPHEUS project proposes a

novel low-head pumped hydro storage system aimed for coastal application in countries where the topography

does not allow for traditional high-head storage. This system consists of a reversible pump-turbine technology

with two contra-rotating runners coupled to their respective axial-ﬂux motor-generators as well as a dedicated

control, optimising for energy balancing and the provision of ancillary services. To better understand the inte-

gration and dynamic interaction of the individual components of the plant and to allow for the simulation of a

wide variety of operating conditions and scenarios, this research aims at developing a system model coupling

the hydraulic, mechanical and electrical components. Numerical results are compared and veriﬁed based on

CFD simulations. While some inaccuracies have to be expected, the comparison shows an overall good match

with only minor deviations in dynamic behaviour and steady state results.

1 INTRODUCTION

With electricity generation being one of the major

contributors to the emission of greenhouse gases,

countries worldwide are rapidly increasing their share

of renewable electricity sources. Depending on the re-

gion, solar PV and wind turbines are considered the

preferred solution to achieve this aim. Such typically

inverter coupled renewable generators introduce inter-

mittency and a reduction in spinning reserves to the

electrical grids designed for centralised power plants.

To balance the increasing mismatch between demand

and supply as well as to provide crucial ancillary ser-

vices (AS) to stabilise the grid, large-scale energy

storage is required.

While pumped hydro storage (PHS) is responsible

for the overwhelming majority of energy storage to-

day (REN21 2021), it is traditionally applied in sce-

narios with high-head differences between the upper

and lower reservoir. To enable the technology for us-

age in regions without sufﬁcient elevation changes,

the ALPHEUS project proposes a novel system aimed

at low- and ultra low-head (2 - 20 m) scenarios. For

such a system it has been proposed that axial-ﬂow re-

versible pump-turbines (RPT) coupled to axial-ﬂux

permanent magnet synchronous machines utilising

variable speed drives is one of the most promising

solutions (Hoffstaedt et al. 2022). Additionally, util-

ising two counter-rotating opposed to a single runner

bears the potential to increase efﬁciency, operating

range and reduce the overall size of the pump-turbine

(Qudaih et al. 2020).

Aimed at coastal applications, the proposed sys-

tem can utilise the sea as the upper reservoir with the

lower reservoir being separated by a dam. The pro-

totype developed as part of the project uses two run-

ners with a diameter of 6 m each coupled to their in-

dividual motor-generator placed in a hub adjacent to

the RPT. With a design power rating of 10 MW for

each pump-turbines set, multiple sets can be utlised

to reach the desired capacity. The lower reservoir is

scaled to fulﬁll the required storage in the timescale

of hours to days.

To maximise the potential of a low-head PHS plant

contributing to grid stability through energy balanc-

ing and AS, reduced switching times between pump

and turbine mode and rapid power ramp rates are de-

sired. The transient behaviour of the proposed low-

head PHS plant is, however, not yet well understood.

To investigate its dynamic behaviour as well as the in-

teraction and inﬂuence of the individual components,

experiments and numerical simulations are conducted

within the ALPHEUS project. Experiments and CFD

simulations provide high accuracy results but are

also time and resource intensive and hence limit the

amount of scenarios that can be tested. The goal of

this research is to develop a comprehensive system

model covering the more relevant dynamics of the

proposed low-head PHS system while signiﬁcantly

reducing computational resources required.

Despite existing modelling approaches for hy-

dropower and PHS, there is a lack of research on

models tailored to low-head scenarios, utilising vari-

able speed operation and integrating two individual

runners. Coupling individual components such as the

conduit, drivetrain and control into a system model

further allows for the investigation of the dynamic in-

teraction of various components. The choice of mod-

elling approaches for these components is determined

by weighing up accuracy and performance require-

ments. Here, the characteristics of the proposed sys-

tem should be considered. An example for this would

be the shift towards lower heads resulting in higher

mass ﬂow rates for the same desired power. This shift

means inertial effects are more important during sud-

den changes to the ﬂow rate potentially leading to a

higher risk of high amplitude pressure waves com-

monly known water hammer effects.

This paper presents the system model developed

before applying it to a model-scale version of the sys-

tem proposed by ALPHEUS to be used for a later ex-

perimental validation of the project. The results are

compared to CFD simulations done by Fahlbeck et al.

(2022b). For this, two cases are evaluated. A start-up

sequence and rapid change of operating points.

2 SYSTEM MODEL OF LOW-HEAD PUMPED

HYDRO STORAGE

2.1 Flow model inside the conduit

Several approaches exist to model the conduit of

PHS plants depending on the required accuracy and

computational performance. Approaches that neglect

compressibility of the ﬂuid and elasticity of the con-

duit are computationally efﬁcient and can cover the

basic dynamics of the system. However, if transients

are to be investigated these effects have to be con-

sidered (Mohanpurkar et al. 2018). Hence, for this

model a one-dimensional compressible ﬂow approach

is chosen. These coupled partial differential equations

shown in Eq. 1 and Eq. 2 (Stecki and Davis 1986) are

based on the fundamental equations of conservation

of mass and momentum and are also known as water

hammer equations.

∂H

∂t =−U∂H

∂x −a2

g

∂U

∂x (1)

∂U

∂t =−U∂U

∂x −g∂H

∂x −S(2)

Here His the pressure head, Uthe ﬂuid velocity,

athe effective pressure wave velocity in the ﬂuid, g

the gravitational acceleration, Dthe conduit diameter

and Sthe friction losses. If the pressure wave veloc-

ity in the pipe is much greater than the ﬂuid veloc-

ity and the conduit is cylindrical the convective terms

given by −U∂H

∂x and −U∂ U

∂x can be neglected (Sharma

and Kumar 2014). The speed of pressure waves within

the conduit depends on the stiffness of the pipe and

the compressibility of the liquid (Ghidaoui 2004). In

a stiff conduit of a hydroelectric power plant with

potentially some gas bubbles forming due to cavita-

tion caused by pressure transients, the pressure wave

velocity can be assumed to be between 1000 and

1480 m/s. In the scenario considered, the ﬂuid ve-

locity will not exceed 6 m/s.

Conical pipe sections such as draft tubes can be

modelled using an approximation based on equiva-

lent pipe elements. Alternatively, changes to the ve-

locity head have to be considered in the momentum

equation and the continuity equation is extended as

shown in Eq. 3 (Adamkowski 2003) with Abeing the

cross-sectional area of the conduit. Additional expan-

sion and contraction losses should be considered.

∂H

∂t =−a2

g

∂U

∂x −a2

gU∂ln A

∂x (3)

While only considering steady friction is sufﬁcient

to estimate the initial magnitude of a pressure tran-

sient in the system, an additional unsteady friction

term will improve the simulated dissipation of such a

pressure wave over time (Chaudhry 2014). The equa-

tions resulting from these changes and adapted to rep-

resent ﬂow rates rather than ﬂuid velocities are shown

in Eq. 4 and Eq. 5.

∂H

∂t =−a2

gA

∂Q

∂x (4)

∂Q

∂t =−gA∂H

∂x −Ss−Su(5)

The additional Q,A,Ssand Suare volumetric ﬂow

rate, cross-sectional area of the conduit, steady and

unsteady friction losses. The steady friction losses

can be calculated using the Darcy-Weisbach for-

mulations using the friction factor fas shown in

Eq. 6 (Riasi et al. 2010). For the unsteady friction

losses, a one-coefﬁcient model, k, of an instanta-

neous acceleration-based method is used as shown

in Eq. 7 (Chaudhry 2014). The ﬂuid accelerations

that induce these losses, are calculated from the av-

eraged cross-sectional values. With values between

0.015 and 0.06 m/s2the coefﬁcient khas been shown

to closely match experimental results.

Ss=fQ|Q|

2DA (6)

Su=k

g∂Q

∂t + Sign(Q)a

∂Q

∂x

(7)

To solve the conduit equations, the partial differ-

ential equations are transformed to ordinary differ-

ential equations using a central schemed ﬁnite dif-

ference method. In order to accurately simulate hy-

draulic transients within the system, the states of pres-

sure and ﬂow rates should be known across the whole

space and time. Practically, the spatial dimension is

discretised and the temporal steps solved via a nu-

merical integration scheme. Results are obtained si-

multaneously along the spatial dimension and con-

secutively for the temporal steps. The resulting grid

of nodes is illustrated in ﬁgure 1. The temporal incre-

ments are indicated by the subscript iand the spatial

by j.

Figure 1: Node grid used for spatial and temporal discretization.

Using the central ﬁnite difference method the ∂Qi,j

∂x

and ∂Hi,j

∂x terms can now be replaced by Qi,j+1 −Qi,j−1

2∆x

and Hi,j+1 −Hi,j−1

2∆xwith ∆xreferring to the spatial dis-

tance between nodes. The ﬁnite difference method is

chosen due to its simplicity and ease of implemen-

tation when applied to sets of coupled equation with

one of the disadvantages being the requirement of a

regular node grid (Benito et al. 2001).

2.2 Boundary conditions

To solve for the transient-state pressure head and ﬂow

rate at the boundaries of the conduit and to the two

contra-rotating runners, Eq. 4 and Eq. 5 need to be

simultaneously solved with the boundary conditions

imposed. To develop these boundary conditions, the

method of characteristics is used resulting in alge-

braic equations describing the relationship between

pressure head and ﬂow rate. The basic characteristic

equations for upstream and downstream boundaries

as described by Chaudhry (2014) are shown in Eq. 8

and Eq. 9.

Qi,j =Qi,j+1 −gA

aHi,j+1 −f

2DA ∆tQi,j+1 |Qi,j +1|

+gA

aHi,j (8)

Qi,j =Qi,j−1+gA

aHi,j−1−f

2DA ∆tQi,j−1|Qi,j −1|

−gA

aHi,j (9)

If the upstream and downstream boundaries repre-

sent the connection to a reservoir, the entrance losses

can be accounted for using Eq. 10 and Eq. 11. Here he

are the entrance head losses to the conduit, keis the

entrance loss coefﬁcient and Hres the total head at the

reservoir.

he=keQ2

i,j

2gA2

j

(10)

Hi,j =Hres −he(11)

If the reservoir is assumed to be large enough that

travelling pressure waves would be entirely absorbed,

non-reﬂecting boundaries can be implemented. To do

so, the terms accounting for the pressure difference

between the boundary and the neighbouring node

are removed. In a friction-less system this leaves the

boundary ﬂow rate to be equal to the ﬂow rate at the

neighbouring node.

If characteristic equations are used, the spatial and

temporal steps have to be chosen correctly to ensure a

stable solution and hence accurately represent a pres-

sure wave propagating through the conduit. Neglect-

ing non-linear terms the Courant condition shown in

Eq. 12 can be used to determine the appropriate spa-

tial distance between nodes for a given time step or

vice versa (Ghidaoui et al. 2005). E.g. assuming a

maximum wave velocity of 1480 m/s combined with

a spatial distance between nodes of 0.148 m would re-

sult in 0.1 ms timesteps. To reach a sufﬁcient level of

accuracy a minimum node density is required. In an

iterative process the spatial distance can be reduced

until no further improvements are achieved.

∆x≥a∆t(12)

To fully develop the boundaries at the turbine as

well as to couple the conduit model to the other

sub-models, characterising the hydrodynamic perfor-

mance of the rotors is required.

2.3 Coupling to drivetrain and motor-generators

A variable speed power take-off is chosen due to its

improved ﬂexibility and efﬁciencies across a wider

range of operating conditions (Vasudevan et al. 2021).

The proposed system uses direct-drive transmissions

Figure 2: Modelling Domain for CFD comparison, including hub, struts and runners. (Fahlbeck et al. 2022b)

coupling the two runners to their individual motor-

generators. Neglecting ﬂexibility in the drivetrain

components, the angular velocities can be assumed

constant along the driveshaft between runners and

motor-generators. This allows to model each drive-

train as an individual rigid body with an equivalent

rotational inertia to account for the different rotating

parts leading to Eq. (13) and Eq. (14) (Leithead and

Connor 2000).

J1

dω1

dt=τh1 −τg1 −Df1ω1(13)

J2

dω2

dt=τh2 −τg2 −Df2ω2(14)

Here we have J1,2as the rotational inertias, ω1,2as

the angular velocities, τh1,2as hydraulic torques, τg1,2

as generator torques and Df1, 2 as a viscous damp-

ing torque coefﬁcient to account for torque losses.

The conduit model is coupled to both of these driv-

etrains via the hydraulic torques determined by ﬂow

rate, pressure drop across the individual runners h1,2,

runner efﬁciencies η1,2, ﬂuid density ρand their re-

spective angular velocities as shown in Eq. (15).

In return the angular velocities of both runners

combined with the ﬂow rate determine the pressure

drop across them as well as their efﬁciencies illus-

trated in Eq. (16) and Eq. (17). This relationship is

determined through the aforementioned characterisa-

tion of the runners. Such a characterisation can be

based on a range of CFD simulations or experimen-

tal results of the particular rotor design under steady-

state conditions. By doing a multi-variant regression

on such data, the pressure drop across, as well as the

efﬁciency of both rotors, can be expressed as a func-

tion of ﬂow rate and both angular velocities.

τh1,2 =ρgQh1,2η1,2

ω1,2

(15)

h1,2=f(Q, ω1, ω2)(16)

η1,2=f(Q, ω1, ω2)(17)

The governor controlling the angular velocities of

the runners is coupled through the generator torques.

If an additional control variable is required, a valve

that is able to regulate the ﬂow from the conduits to

the runners can be added to the system.

3 RESULTS

Following, the results of two scenarios, applied to the

model outlined in the previous section, are presented.

The methodology and setup are explained before the

sensitivity using varying node densities for the ﬁnite

difference method are compared. Lastly the results are

compared to CFD simulations.

3.1 Methodology & system properties

The setup and initial conditions for the results used

for comparing the model and CFD simulations are

based on a scaled down version of the system with

a runner diameter of 27.6 cm. On both sides of the

pump-turbines, draft tubes increase the pipe diameter

to 50 cm connecting the upper and lower reservoir.

The static head difference between these reservoirs is

6.45 m. Since the model results are compared with the

results of CFD simulations done by Fahlbeck et al.

(2022b), the same domain is used for the numerical

model. This domain is shown in ﬁgure 2.

Aside from the initial conditions of pressure and

ﬂow rate across the conduit, the main input to the

model are the static heads at the upper and lower

reservoir. These are based on the static head differ-

ence expected in the lab. Major and minor head losses

outside of the domain are included. These consist of

entrance and exit losses from the lower and upper

reservoir, a pipe bend, a ﬁxed and a variable valve. For

both scenarios the ﬁxed and variable valve are consid-

ered fully open. Additionally the major losses for an

additional 1 m of pipe upstream of the pump-turbine

and 15.5 m downstream of it are applied. Coefﬁcients

are chosen to match the CFD simulations. The param-

eters used for the simulations are shown in table 1.

Table 1: Model parameters used for the simulations.

Static head upper reservoir Hures 9.7 m

Static head lower reservoir Hlres 3.25 m

Pressure wave velocity a1200 m/s

Surface roughness e0.05 mm

Unsteady loss coefﬁcient k0.04 m/s2

Minor loss coefﬁcients

Entrance 0.45 -

Exit 1 -

Bend 0.2 -

Fixed Valve (fully open) 0.4 -

Variable Valve (fully open) 0.39 -

To compare the model against the CFD results and

ensure that no tuning of parameters is required for

individual cases to match, two scenarios are anal-

ysed. Between these cases no changes are made to the

model setup. The ﬁrst is a start-up sequence and the

second a change of operating point. The CFD simu-

lations were done with both a high- and low-ﬁdelity

model with one order of magnitude difference in num-

ber of mesh cells. The comparison is based on the

results of the high-ﬁdelity model. The methodology

and boundaries used for the CFD simulations are de-

scribed in further detail by Fahlbeck et al. (2021) and

Fahlbeck et al. (2022a).

3.2 Start-up sequence

To start up the system in pump mode, the chosen case

accelerates the runners from an initial 916 RPM to

their ﬁnal operating point at 1502 RPM over a period

of 3 s. At this initial angular velocity the net head pro-

duced by the pump-turbine matches the gross head of

the system resulting in zero ﬂow. The angular veloc-

ity of the two runners for the sequence is shown in

ﬁgure 3.

Figure 3: Angular velocity during start-up.

To determine the required node density, this se-

quence is ﬁrst simulated with 20, 40 and 60 nodes.

The resulting conduit ﬂow rate for modelling the sys-

tem with these varying node densities can be found

in ﬁgure 4. There is no relevant difference between

the 40 and 60 node model. When reduced to 20

nodes, minor differences in the dynamics are notice-

able. However, in steady state all solutions converge.

The 20 node model takes about 28 % of the computa-

tional time to solve compared to the 60 node model.

For all further results the 40 node model is used. This

results in a spatial distance between nodes of around

13.3 cm. Together with a pressure wave velocity of

1200 m/s the simulation time step is chosen at about

1.1×10−4s.

The comparison of ﬂow rates during the start-up

sequence between the 40 node model and CFD re-

sults is shown in ﬁgure 5. At the ﬁnal operating points

the results are closely matched with a difference of

only 1.3 %. However, the ﬂow rate of the CFD sim-

ulation is slightly more stable in steady state. At the

initial acceleration of runner two and the consequent

increase in pump head over the RPT, the ﬂow rate

in the proposed model reacts slower compared to the

CFD results. This marginally slower reaction time to

changes in the pump head is also visible after runner

Figure 4: Flow rate for varying node density.

two reaches its ﬁnal angular velocity and before run-

ner one is accelerated. After the acceleration of runner

one, the ﬂow rate of the model overshoots before con-

verging.

Figure 5: Flow rate and pressure head over the computational

domain of model and CFD simulation - start up sequence.

The pressure head over the domain is shown in the

same ﬁgure. The head in the CFD results clearly rises

faster, reaches a higher maximum during the acceler-

ation of runner one and remains higher in steady state.

At the ﬁnal operating point the head over the CFD do-

main reaches around 7.4 m compared to 7.16 m over

the proposed model. This reﬂects a 3.4 % difference.

Since the ﬁnal ﬂow rates and the static heads are

similar for both results, the overall losses should be

roughly equivalent. However, the reduced head over

the model domain indicates that the losses outside of

the domain are slightly lower compared to the CFD

and the losses within the domain slightly higher. The

slower response of the model ﬂow rate to changes

in pump head could also be caused by these higher

steady or unsteady losses within the domain. Inaccu-

racies may be introduced through the use of equiva-

lent friction factors and cross-sections along the con-

duit as well as the use of a static pressure wave veloc-

ity.

3.3 Change of operating point

To ensure consistent and repeatable modelling results

for varying scenarios and operating conditions, a sec-

ond case is compared. This second case simulates a

rapid change between operating points. This particu-

lar scenario starts at the ﬁnal operating point of the

start-up sequence, before reducing the angular veloc-

ity of runner two down to 1129 RPM as shown in ﬁg-

ure 6. This corresponds with a sudden reduction in

power by about 22 % over a period of 1 s.

Figure 6: Angular velocity during change of operating point.

Figure 7: Flow rate and pressure head over the computational do-

main of model and CFD simulation - change of operating point.

The resulting ﬂow rate and pressure head over the

domain from the model and CFD simulation can be

found in ﬁgure 7. The ﬂow rate in the model starts

at a lower operating point and overshoots after the de-

crease in angular velocity of runner two and the corre-

sponding reduction in pump head. It reacts marginally

faster than in the CFD results. This further supports

the conclusion drawn from the ﬁrst case that the dif-

ference in dynamic reaction may be caused by slightly

overestimated losses within the domain. Aligned with

the ﬁrst case the pressure head over the domain is

about 2.6 % higher in the CFD results.

After runner two reaches the ﬁnal operating point,

the ﬂow rate of the CFD simulation stabilises while

the ﬂow rate in the model keeps increasing resulting in

a difference of about 6.2 % at the ﬁnal operating point.

Such a divergence over time is most probably caused

by changes in the pump head. Since the head is deter-

mined through the runner characterisation, the inaccu-

racy in the model is likely introduced by a mismatch

between characterisation and actual pump head.

4 CONCLUSIONS

A system model to investigate the dynamics and com-

ponent interaction of a low-head pumped hydro stor-

age plant has been proposed. While using the model

compared to CFD simulations can decrease signiﬁ-

cantly the required computational resources, a com-

promise in the results accuracy is expected. One of

the major differences is that the model is based on

a one dimensional approach. This means that veloc-

ity and pressure values are averaged in the cross-

sections perpendicular to the ﬂow. Consequently, lo-

calised pressure variations are not covered which are

crucial when predicting effects such as cavitation. Ad-

ditionally non-axial ﬂuid velocities are not included

potentially leading to inaccurate loss approximations.

The comparison of the model results using varying

node densities has shown that, for the setup used in

the simulations, no further improvements to accuracy

can be achieved beyond 40 nodes and the consequent

spatial distance of around 13.3 cm. The comparison

of the results to CFD simulations demonstrated that a

simpliﬁed one dimensional model can produce satis-

factory results covering the relevant dynamics of the

system. In steady state the resulting ﬂow rates and

pressure heads of the model are within a small de-

viation of the CFD results.

While there can be improvements made to bet-

ter cover the losses within the conduit and the run-

ner characterisation, overall the results between the

proposed model and CFD simulations are closely

matched. This enables the more efﬁcient model to be

used to investigate system dynamics for varying com-

ponents and operating conditions. To further verify

the results an experimental validation should be con-

ducted.

ACKNOWLEDGEMENTS

This research is part of a project that has received

funding from the European Union’s Horizon 2020 re-

search and innovation programme under grant agree-

ment No. 883553.

REFERENCES

Adamkowski, A. (2003). Analysis of transient ﬂow in pipes with

expanding or contracting sections. Journal of Fluids Engi-

neering, Transactions of the ASME 125(4), 716–722.

Benito, J. J., F. Ure ˜

na, & L. Gavete (2001, 12). Inﬂuence of sev-

eral factors in the generalized ﬁnite difference method. Ap-

plied Mathematical Modelling 25(12), 1039–1053.

Chaudhry, M. H. (2014). Applied hydraulic transients.

Fahlbeck, J., H. Nilsson, & S. Salehi (2021). Flow Character-

istics of Preliminary Shutdown and Startup Sequences for

a Model Counter-Rotating Pump-Turbine. Energies 14(12),

3593.

Fahlbeck, J., H. Nilsson, & S. Salehi (2022a, 1). A Head Loss

Pressure Boundary Condition for Hydraulic Systems. Open-

FOAM Journal 2, 1–12.

Fahlbeck, J., H. Nilsson, & S. Salehi (2022b). Evaluation of

startup time for a model contra-rotating pump-turbine in

pump-mode. IOP Conference Series: Earth and Environmen-

tal Science.

Ghidaoui, M. S. (2004, 6). On the fundamental equations of wa-

ter hammer. Urban Water Journal 1(2), 71–83.

Ghidaoui, M. S., M. Zhao, D. A. McInnis, & D. H. Axworthy

(2005, 1). A Review of Water Hammer Theory and Practice.

Applied Mechanics Reviews 58(1), 49–76.

Hoffstaedt, J. P., D. P. Truijen, J. Fahlbeck, L. H. Gans,

M. Qudaih, A. J. Laguna, J. D. De Kooning, K. Stockman,

H. Nilsson, P. T. Storli, B. Engel, M. Marence, & J. D.

Bricker (2022, 4). Low-head pumped hydro storage: A re-

view of applicable technologies for design, grid integration,

control and modelling. Renewable and Sustainable Energy

Reviews 158.

Leithead, W. E. & B. Connor (2000). Control of variable speed

wind turbines: Dynamic models. International Journal of

Control 73(13), 1173–1188.

Mohanpurkar, M., A. Ouroua, R. Hovsapian, Y. Luo, M. Singh,

E. Muljadi, V. Gevorgian, & P. Donalek (2018). Real-time

co-simulation of adjustable-speed pumped storage hydro

for transient stability analysis. Electric Power Systems Re-

search 154, 276–286.

Qudaih, M., B. Engel, D. Truijen, J. De Kooning, K. Stock-

man, J. Hoffst¨

adt, A. Jarquin-Laguna, R. Ansorena Ruiz,

N. Goseberg, J. Bricker, J. Fahlbeck, H. Nilsson, L. Bossi,

M. Joseph, & M. Zangeneh (2020). The contribution of low-

head pumped hydro storage to a successful energy transition.

In Proceedings of the Virtual 19th Wind Integration Work-

shop, pp. 8.

REN21 (2021). Renewables 2021 Global Status Report.

Riasi, A., M. Raisee Dehkordi, & A. Nourbakhsh (2010, 06).

Simulation of transient ﬂow in hydroelectric power plants us-

ing unsteady friction. Strojniski Vestnik 56.

Sharma, J. D. & A. Kumar (2014). Development and Implemen-

tation of Non- Linear Hydro Turbine Model with Elastic Ef-

fect of Water Column and Surge Tank. International Journal

of Electrical and Electronics Research 2(4), 234–243.

Stecki, J. S. & D. C. Davis (1986). Fluid transmission lines-

distributed parameter models Part 1: a review of the state of

the art. Proc. Inst. Mech. Engrs. Part a 200(A4, 1986), 215–

228.

Vasudevan, K. R., V. K. Ramachandaramurthy, G. Venugopal,

J. B. Ekanayake, & S. K. Tiong (2021). Variable speed

pumped hydro storage: A review of converters, controls and

energy management strategies. Renewable and Sustainable

Energy Reviews 135, 110156.