![Principle view of bladed pump-turbine configurations, note that the term ''centrifugal'' refers to both the radial-and mixed-flow. The drawing is based on principles shown in [40-42,46].](https://www.researchgate.net/profile/Antonio-Jarquin-Laguna/publication/358277555/figure/fig2/AS:1119008241790978@1643803763686/Principle-view-of-bladed-pump-turbine-configurations-note-that-the-term-centrifugal_Q320.jpg)
![Principle view of non-conventional pump-turbine configurations. The drawing is based on principles showed in [45,55,56].](https://www.researchgate.net/profile/Antonio-Jarquin-Laguna/publication/358277555/figure/fig3/AS:1119008241786885@1643803763797/Principle-view-of-non-conventional-pump-turbine-configurations-The-drawing-is-based-on_Q320.jpg)
![Simplified block diagram for synthetic electrical inertia control [80,81]. Here, í µí»¥f is the deviation of system frequency, ROCOF is the rate of change of frequency, J is the virtual inertia control constant, í µí»¥í µí± imitate is the active power of the converter, and í µí»¥í µí± inertia is the emulated virtual inertia power that could be imitated into the system.](https://www.researchgate.net/profile/Antonio-Jarquin-Laguna/publication/358277555/figure/fig4/AS:1119008241795073@1643803763807/Simplified-block-diagram-for-synthetic-electrical-inertia-control-80-81-Here-i-if_Q320.jpg)
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Renewable and Sustainable Energy Reviews 158 (2022) 112119
1364-0321/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at ScienceDirect
Renewable and Sustainable Energy Reviews
journal homepage: www.elsevier.com/locate/rser
Low-head pumped hydro storage: A review of applicable technologies for
design, grid integration, control and modelling
J.P. Hoffstaedt a,∗, D.P.K. Truijenb, J. Fahlbeck c, L.H.A. Gans d, M. Qudaih e, A.J. Laguna a,
J.D.M. De Kooning b, K. Stockman b, H. Nilsson c, P.-T. Storli d, B. Engel e, M. Marence f,
J.D. Bricker g,h
aFaculty of Mechanical, Maritime and Materials Engineering, Department of Maritime and Transport Technology, Delft University of Technology, Mekelweg
2, 2628 CD Delft, The Netherlands
bDepartment of Electromechanical Systems & Metal Engineering, Ghent University & FlandersMake@UGent - Corelab EEDT-MP, Sint-Martens-Latemlaan
2B, 8500 Kortrijk, Belgium
cDepartment of Mechanics and Maritime Sciences, Division of Fluid Dynamics, Chalmers University of Technology, 412 96 Gothenburg, Sweden
dDepartment of Energy and Process Engineering, Waterpower Laboratory, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
eElenia Institute for High Voltage Technology and Power Systems, Technische Universität Braunschweig, Schleinitzstraße 23, 38106 Braunschweig, Germany
fIHE Delft Institute for Water Education, Westvest 7, 2611 AX Delft, The Netherlands
gDepartment of Hydraulic Engineering, Hydraulic Structures and Flood Risk, Delft University of Technology, The Netherlands
hDepartment of Civil and Environmental Engineering, University of Michigan, 2350 Hayward, Ann Arbor, MI 48109-2125, USA
ARTICLE INFO
Keywords:
Low-head pumped hydro storage
Energy storage
Grid stability
Renewables integration
Energy transition
Reversible pump-turbine
ABSTRACT
To counteract a potential reduction in grid stability caused by a rapidly growing share of intermittent
renewable energy sources within our electrical grids, large scale deployment of energy storage will become
indispensable. Pumped hydro storage is widely regarded as the most cost-effective option for this. However,
its application is traditionally limited to certain topographic features. Expanding its operating range to low-
head scenarios could unlock the potential of widespread deployment in regions where so far it has not yet
been feasible. This review aims at giving a multi-disciplinary insight on technologies that are applicable
for low-head (2-30 m) pumped hydro storage, in terms of design, grid integration, control, and modelling.
A general overview and the historical development of pumped hydro storage are presented and trends for
further innovation and a shift towards application in low-head scenarios are identified. Key drivers for
future deployment and the technological and economic challenges to do so are discussed. Based on these
challenges, technologies in the field of pumped hydro storage are reviewed and specifically analysed regarding
their fitness for low-head application. This is done for pump and turbine design and configuration, electric
machines and control, as well as modelling. Further aspects regarding grid integration are discussed. Among
conventional machines, it is found that, for high-flow low-head application, axial flow pump-turbines with
variable speed drives are the most suitable. Machines such as Archimedes screws, counter-rotating and rotary
positive displacement reversible pump-turbines have potential to emerge as innovative solutions. Coupled axial
flux permanent magnet synchronous motor-generators are the most promising electric machines. To ensure grid
stability, grid-forming control alongside bulk energy storage with capabilities of providing synthetic inertia next
to other ancillary services are required.
Abbreviations: ADRC, Active Distribution Rejection Control; AF-PMSM, Axial Flux Permanent Magnet Synchronous Machine; ANN, Artificial Neural
Network; AS, Ancillary Services; CAES, Compressed Air Energy Storage; CRPT, Counter-Rotating Pump-Turbine; DSO, Distribution System Operator; DSSR,
Double-Stator Single-Rotor; DTC, Direct Torque Control; EIA, Energy Information Administration; ESHA, European Small Hydropower Association; ESOEI,
Energy Storage On Energy Invested; ESS, Energy Storage System; FOC, Field Oriented Control; IRES, Intermittent Renewable Energy Source; LCOS, Levelised
Cost Of Storage; MEPT, Maximum Efficiency Point Tracking; MMD, Modular Machine Drive; MPC, Model Predictive Control; MPPT, Maximum Power Point
Tracking; MTPA, Maximum Torque Per Ampere; PAT, Pump As Turbine; PHS, Pumped Hydro Storage; PLL, Phase Locked Loop; PM, Permanent Magnet; PMSM,
Permanent Magnet Synchronous Machine; PTO, Power Take-Off; PWM, Pulse-Width Modulation; RPT, Reversible Pump-Turbine; SSDR, Single-Stator
Double-Rotor; SSSR, Single-Stator Single-Rotor; SVM, Space Vector Modulation; TSO, Transmission System Operator
∗Corresponding author.
E-mail address: J.P.Hoffstaedt@tudelft.nl (J.P. Hoffstaedt).
https://doi.org/10.1016/j.rser.2022.112119
Received 8 September 2021; Received in revised form 17 December 2021; Accepted 9 January 2022
Renewable and Sustainable Energy Reviews 158 (2022) 112119
2
J.P. Hoffstaedt et al.
1. Introduction
In a global effort to reduce greenhouse gas emissions, renewables
are now the second biggest contributor to the world-wide electricity
mix, claiming a total share of 29% in 2020 [1]. Although hydropower
takes the largest share within that mix of renewables, solar photo-
voltaics and wind generation experience steep average annual growth
rates of 36.5% and 23%, respectively, since 1990 [2]. Both of these
technologies, however, significantly differ in their generation char-
acteristics when compared to traditional thermal power plants. This
trend towards an increase in intermittent generation, coupled with
a reduction in spinning reserves, could undermine grid stability. To
counteract these effects, grid-scale deployment of energy storage is
indispensable.
There are complementary approaches to balance demand and sup-
ply in an electricity grid, such as an increase in flexible generation,
demand management, or exporting and importing electricity. Nonethe-
less, at certain penetration levels of renewables, to reduce the risk of
grid instability, a heterogeneous pool of storage solutions is needed.
A wide variety of such storage technologies – including capacitors,
flywheels, electro-chemical batteries, compressed air energy storage
(CAES), molten-salt or hydrogen storage – is available to balance the
grid in the timescale from seconds up to seasonal variations. Crucial
factors for large-scale balancing include energy and power capacity as
well as fast response times while maintaining high efficiencies. Aside
from fulfilling these criteria, the major driver towards commercial
deployment is the levelised cost of storage (LCOS); leading in this are
pumped hydro storage (PHS) and CAES [3]. An alternative approach is
based on the so-called energy stored on energy invested (ESOEI), which
gives an estimate of the relation between the stored energy during the
lifetime of a system and the energy required to construct the system.
Also for this metric, PHS and CAES are, by far, in the lead [4].
Pumped hydro storage is a mature and well-known technology that
has been used since the beginning of the 20th century. In 2020, it
contributed with 90.3% of the world’s energy storage capacity [5].
However, while some regions reach the limits of economically viable
PHS that can be implemented, others lack entirely the necessary to-
pographic features. Traditional PHS relies on high heads to realise the
expected power and storage capacity. Most of the plants produce in the
order of 1000–1500 MW of power, with round-trip efficiencies which
are commonly in the range of 70%–85% [6].
Aside from its use to store energy, hydropower is regarded as the
foremost renewable generation method when it comes to flexibility
and improving grid stability. Due to the proven advantages of hydro-
electric power generation, wide-ranging research efforts have focused
on conceptual adaptations and technological advancements utilising
low- and ultra-low-head scenarios. Some of these technologies, such as
wastewater, run-of-river hydropower, or tidal barrages have seen pro-
totyping and commercial deployment. However, theoretical attention
and practical implementation towards low-head PHS has been limited.
Fig. 1 shows a conceptual drawing of what such a system may consist
of when deploying a reversible pump-turbine coupled to a motor-
generator that is connected to the grid via an AC-DC-AC converter for
variable speed operation.
The lack of attention on low-head PHS can be partly explained
through high levelised cost of storage (LCOS) caused by extensive civil
structures, enlarged machinery, lower round-trip efficiencies, and lim-
ited flexibility to provide ancillary services (AS). The predicted increase
in demand for energy balancing and AS in the upcoming decades will
likely justify increased LCOS. Additionally, technological advancements
could significantly contribute to a reduction in LCOS. Addressing the
technological challenges and overcoming economic barriers of low-
head PHS could unlock the potential of integrating large-scale energy
storage into the grids of regions where it has not been feasible so far.
For the given reasons, research and development towards shifting
the operating range of PHS to low heads is scarce. Using a multi-
disciplinary approach, the main goal of this research is to review
and analyse technologies based on their applicability for low-head
utilisation. First, an overview of PHS and its historical development is
given. Based on this, recent trends leading to further innovation in the
field are identified, and the potential and necessity of storage technolo-
gies are discussed. Finally, technological and economic challenges are
explored, and the key advancements that could contribute to economic
and technical viability are isolated. Building on this, in the major tech-
nological fields – pump-turbine design and configuration, control and
electric machinery, as well as modelling – the most promising technolo-
gies are compared and their fitness for low-head application is assessed.
Additionally, implications of grid integration are discussed, including
further elaboration on the significance of integrating large-scale energy
storage, such as low-head PHS into world-wide grids.
2. Overview and historical development of pumped hydro storage
Pumped hydro storage is an amended concept to conventional
hydropower as it cannot only extract, but also store energy. This is
achieved by converting electrical to potential energy and vice versa in
the form of pumping and releasing water between a lower and a higher
reservoir. The energy conversion occurs by using pumps and turbines
either combined in a reversible (binary set) or separate configuration
(ternary and quaternary sets). The power of such a system, as well as
the amount of energy that can be extracted or stored, is proportional
to the product of head and water flow or volume, respectively. Hence,
a higher head results in a reduced flow for a given desired power and
smaller reservoirs for a given storage capacity. It does not, therefore
just correlate with scaled-down reservoirs but also smaller remaining
civil structures and machinery, historically leading to reduced cost and
a significant economic advantage of utilising high-head differences [7].
Of today’s bulk energy storage integrated into the world-wide grids,
over 90% is comprised of PHS of which the vast majority are high-head
applications. According to the International Hydropower Association,
in 2019, the global installed capacity reached 158 GW with the biggest
contributors being China making up 30.3 GW of the share, Japan
27.6 GW, and the United States 22.9 GW [8]. Fig. 2 shows the distribu-
tion of global storage capacity that is operational, under construction,
planned, and announced as of 2021.
In comparison, the next largest contributors to bulk energy storage
are electro-chemical battery storage – rapidly growing with a total
capacity of 14.2 GW – and thermal storage with 2.9 GW in 2020 [5].
To explain the historic market dominance of PHS and understand
recent trends, several factors have to be taken into account. Pumped
hydro storage utilising reversible pump-turbines has been available as
a mature and cost-effective solution for the better part of a century
with an estimated energy based capital cost of 5–100 $/kWh [10]. To-
day, compressed air energy storage is considered mature and reliable,
offering similarly low capital cost between 2–50 $/kWh, and electro-
chemical batteries offer high energy density with higher costs, and
experience drastic growth while the impact of hydrogen-based storage
in the energy transition is largely expected to be substantial [10].
However, PHS‘s dominance is not only due to its historic lead but
can also be attributed to its technical, economic, and sustainability
advantages. These include high efficiencies, large achievable capacities,
and long lifetimes. Compared to rapidly expanding battery storage that
can be used wherever it is most needed, one clear advantage is this
durability. It is currently assumed that a battery system will last around
15–20 years, but on the other hand, the oldest hydropower plant in
Norway has been operating for over 120 years [11,12]. Prolonged
lifetimes are one factor improving the sustainability of PHS compared
to other storage solutions. Others include maturity, low capital and
operating cost, as well as low energy and carbon dioxide density.
Based on these and other factors regarding economic, performance,
technological, and environmental considerations, Ren et al. ranked PHS
as the most sustainable storage technology [13].
Renewable and Sustainable Energy Reviews 158 (2022) 112119
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J.P. Hoffstaedt et al.
Fig. 1. Schematic showing a low-Head PHS concept and its main components.
Fig. 2. Global PHS Capacity [9].
Further advantages of PHS include suitability for long-term storage
– since hardly any storage losses occur other than seepage and evap-
oration – and quick availability due to short switch-on and switch-off
times. With these factors ensuring a significant share within a heteroge-
neous pool of storage technologies, one major disadvantage of PHS has
historically been its topographic constraints. A switch from river-based
to closed-loop off-river systems could overcome some of the constraints
and increase the potential for deployment [14,15]. Nonetheless, regions
with flat topographies still do not offer viable sites.
2.1. Early deployment and progression in the 𝟐𝟎th century
Not long after hydropower began to generate electricity, the first
small-scale PHS plants were constructed in the mountainous regions
of central Europe in the beginning of the 20th century. Initially using
separate pumps and turbines, combined reversible pump-turbines have
become the norm since the middle of the 20th century [6]. Experiencing
a major boom in Europe, parts of Asia, and North America, a large
portion of today‘s installed PHS capacity was constructed in the 1960s,
1970s, and 1980s; in most countries, this occurred alongside rapidly in-
creasing nuclear power. The gained flexibility that PHS plants provided
allowed them to match a varying demand with the baseload generation
of nuclear power plants. An example where this was particularly rele-
vant is Japan due to its lack of interconnections to other countries as
well as their strong strategy towards nuclear energy.
In the United States, another reason for the growing capacity of
PHS during that period was the energy crisis in the 1970s, leading
to an increased cost of fossil fuels allowing PHS to grow as a substi-
tute for peak balancing [16]. After that period, development slowed
down in most regions with the major exception of China. Its rapidly
growing economy and correlated energy demand largely satisfied by
non-flexible coal plants required major energy storage.
Renewable and Sustainable Energy Reviews 158 (2022) 112119
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J.P. Hoffstaedt et al.
Up until this point, pump-turbines were coupled to fixed speed
motor-generators. The next significant development occurred in the
1990s when variable speed operation was introduced in Japan. The
ability to adjust the angular velocity of the runners allowed for higher
efficiencies under changing conditions, reduced the switching time
between pump and turbine mode, and facilitated higher ramp rates and
quicker response times [17].
2.2. Recent trends
After an initial reduction of PHS deployment around the turn of
the millennium, the rapidly growing share of intermittent renewable
energy sources (IRES) in the last couple of decades sparked new interest
in sustainable flexible generation as well as large-scale energy storage
solutions. This caused increasing attention towards the rehabilitation
of old hydropower plants and an expansion of PHS [18]. While PHS
experienced a much longer development process than competitive tech-
nologies and could hence be considered mature, two major trends can
be identified pushing further innovation in the field.
The first one is derived from the change in grid characteristics
caused by a reduction in spinning reserves. A growing number of
converter coupled renewables raise the necessity for external provision
of AS. To provide these using PHS, research efforts focus on devel-
oping improved control and machinery but also novel concepts, such
as hybrid storage solutions. Examples of such concepts could be the
coupling of conventional PHS with flywheels for frequency control or
supercapacitors providing virtual inertia [19]. Hybrid storage solutions
incorporating PHS, such as hybrid pumped and battery storage, are also
particularly suited for off-grid applications [20].
The second major trend is expanding the operating range and
application. One of the most limiting factors in the potential use of
large-scale PHS has been the fact that not many locations could offer
economically viable deployment. These were traditionally mountainous
regions accessing water with enough space to construct extensive civil
structures. There is a large potential in Europe to deploy further mini
and small hydropower plants to counteract the effects of higher renew-
able penetration levels. However, this does not apply to countries with
flat topographies, such as Denmark, the Netherlands, or Belgium [21].
Additionally, to achieve the balancing capabilities of pumped storage
systems, larger plants typically provide better economies of scale.
Suitable locations for such are rare in Europe and some countries like
Japan are considered to have used nearly all available sites [22]. This
limited availability of appropriate locations drives the development of
new approaches. Examples for a promising change of approach are
underwater PHS or gravity energy storage.
The former is a recently developed and tested concept based on
submerging a hollow sphere offshore and using the static pressure
difference for energy storage. The surrounding sea acts as the upper
reservoir and the sphere as the lower which can be filled to generate
electricity or emptied to store it. Initial model-scale tests have been
successful; it is a freely scalable technology without issues regarding
land use and considered cost competitive with PHS and compressed
air storage [23]. Using seawater in general for PHS is so far an un-
common practice, but has been investigated as a solution for isolated
grids [24]. If technical, environmental, and economic challenges are
overcome, utilising seawater could be another promising expansion of
PHS’s potential deployment.
The latter similarly decouples the fundamental principle of PHS
from its topographic restrictions. Storage is done via gravitational
potential energy. However, energy is stored or extracted respectively
by moving a piston of large mass up and down using water powered by
a pump-turbine for conversion. While still under development, initial
economic evaluations show it to have a potentially attractive LCOS
compared to other storage technologies [25].
An alternative that is not less promising and will potentially suit
both these trends is to extend the operating range of conventional PHS
to low and ultra low-head applications, including the potential use of
seawater, while improving its capability to provide AS. If technological
advancements allow for economic viability, large-scale low-head PHS
could be integrated in regions where PHS so far was not a feasible
solution.
Later trends for PHS show the usage of ternary units. With ternary
units, a separate pump and turbine are connected on a single shaft to an
electric machine that can work either as a motor or a generator [26].
This configuration presents a very flexible and fast response range,
shows higher efficiencies than reversible machines, and can utilise
hydraulic short circuits for optimal power in- or outtake [27,28].
The major drawback with ternary units is that they requires higher
investment and maintenance costs compared to a reversible unit [28].
In a low-head scenario, the increase in investment cost would be even
greater since a high-power, low-head machine needs to be large in
order to handle a high flow rate. Thus, it is suggested as a less attractive
alternative for low-head PHS.
2.3. Potential of deployment and scalability in Europe
Resulting from the rapid transition that grids are experiencing
worldwide, the need for energy storage is evident. However, there are
a variety of factors influencing the actual storage demand and its ex-
pected progression during the coming decades. First and foremost, this
is the growth in intermittent and converter coupled renewables. While
a direct correlation between renewable penetration levels and storage
demand can be assumed, mitigating factors such as improved genera-
tion forecasting and the continuous development of renewables able to
provide AS will allow for later deployment of energy storage. Further
factors to consider include the flexibility of remaining generators in
the grids and the emerging need for additional operating reserves,
improved demand management, as well as further grid expansion and
interconnection.
Bearing these factors in mind, it becomes clear that storage demand
will heavily depend on individual grid characteristics and may vary
in different regions. Based on Germany as an example, additional
short-term storage can be expected at renewable shares between 40%
and 60% and long-term storage between 60% and 80%. Above 80%
and towards a fully renewable generation, bulk energy storage on all
timescales is not only required in order to avoid extensive renewable
energy curtailing, ensure grid stability and power quality, but will be a
cost-effective solution in the GW range [29]. In less flexible grids, for
example utilising large-scale nuclear power to cover the base load, the
need for extensive storage will be reached at much lower renewable
levels.
An update to the European Green Deal has raised the ambition to
reduce greenhouse gas emission by 55% until 2030 compared to the
standard of 1990 paving the way for a carbon neutral energy supply by
2050. Consequently, the share of intermittent renewables will need to
increase faster. Recent estimates see a growth towards 70% renewable
power generation in 2030 [30].
Depending on the flexibility of this share of renewables in different
regions, a rapid increase in demand for storage and the provision of
AS can be expected with PHS being a promising candidate to fill the
gap. For countries with a flat topography, economically viable low-
head PHS could bear a huge potential to cover the growing demand.
This is especially relevant if a large coastline is available, opening up
the possibility for seawater application. Coastal applications also come
with the additional benefit of proximity to large-scale IRES, such as
offshore wind farms.
Renewable and Sustainable Energy Reviews 158 (2022) 112119
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J.P. Hoffstaedt et al.
2.4. Technological and economic challenges
Low-head PHS has not yet seen deployment on a significant scale
within our grids. This is largely due to the increased upfront cost
required. While highly dependent on the individual project and site,
the major contributor to the initial CAPEX of PHS projects in general
are civil structures, including the reservoir, penstock, and lining [31].
Due to larger masses of water being stored in the reservoir and flowing
through the penstock when it comes to low-head applications, their
contribution to the overall economic viability can only be assumed to
be significant. All aspects regarding civil components as well as detailed
economic analyses of low-head PHS systems are, however, outside of
the scope of this review.
Low-head PHS would be most competitive utilising a storage ca-
pacity able to provide balancing in the timescale of hours to days.
This places it in the middle between lithium-ion batteries appropri-
ate for shorter and hydrogen storage appropriate for longer periods.
The LCOS of new high-head PHS systems ranges from 50 e/MWh to
80 e/MWh [32]. Initially low-head plants may not be able to compete
with this. However, changing demand characteristics of the electricity
markets, as well as further development and improvement of techno-
logical aspects, significantly influence economic viability and thereby
the potential of large-scale deployment. The increase in renewables in
world-wide grids will lead to rising demands, not just for short- and
long-term balancing but also the provision of AS increasing the value
of both. Additional revenue from the provision AS could hence increase
economic viability.
Further drivers making PHS economically more attractive are grow-
ing interconnections to other grids opening up additional markets
as well as technical advances such as higher efficiencies across a
broader operating range [22]. Technological progression can help fa-
cilitate these drivers. A reduction of switching times between pump
and turbine mode together with higher power ramp rates will allow
for enhanced capabilities to provide AS as well as maximise balancing.
Aside from regulatory changes, such as carbon taxation, electricity
price margins have been identified as one of the major drivers towards
PHS utilisation. Improved round-trip efficiencies directly correlate with
higher revenues for the operator and therefore result in increased
utilisation [33].
Based on these challenges, three main areas can be identified where
significant progress could contribute to making low-head PHS techni-
cally and economically competitive. These are pump-turbine design and
configuration, grid integration, and electrical machines and control.
Research in these fields will be discussed in the chapters following.
Additionally, modelling approaches that may aid the development are
compared.
3. Pump-turbine design and configuration for low-head pumped
hydro storage
The choices when selecting the type of reversible pump-turbine
(RPT) unit, or evaluating using a pump as turbine (PAT), are governed
by a number of factors. The first thing to evaluate is the power of the
hydropower plant, which is a function of head and flow rate and the
general formula is given by Eq. (1).
𝑃=𝜌𝑔𝐻 𝑄𝜂 (1)
Here, 𝜌is the density of water, 𝑔is the gravity acceleration, 𝐻is the
head, 𝑄is the volumetric flow rate, and 𝜂is the overall efficiency of
the power plant. The gravity acceleration and water density can be
regarded as constant. The equation shows that if the head is low, the
flow rate must be large in order to produce high power [34]. With
a large flow rate, the diameter of pipelines and the runner need to
be large as well to limit the flow velocity, and thus hydraulic losses
in the system. High-head conditions are usually preferable to build
pump storage hydropower plants. However, low-head solutions with
high volumetric flow rate are also regarded as having great potential
to unleash new opportunities for pumped hydro storage [35].
The definition of low-head is not unanimous among different coun-
tries and researchers. For example, the U.S. Energy Information Admin-
istration (EIA) considers low-head when the head is less than 30 metre
and Okot [36] classifies it as when 5< 𝐻 < 15 metre. In this work, the
European Small Hydropower Association (ESHA) classification defines
low-head, and states that low-head hydropower plants have a head of
2-30 metre [37].
The overall efficiency of a low-head power plant is more sensitive
to head losses than a high-head alternative, and low-head PHS requires
that the pipelines are short to be economically feasible [38]. This is
because head losses are proportional to the pipeline length and the
flow velocity squared, which is a further incentive for not using ternary
units in a low-head case since they require more pipelines and would
thus decrease the plant‘s overall efficiency. With the higher flow rate
of high-power low-head PHS, larger reservoirs are required to store the
same amount of energy as a corresponding high-head application [34].
This is because the energy storage capacity is a function of the water
mass and head. Apart from that, other conditions such as the type of
machine (radial-, mixed-, or axial-flow), operation (variable or fixed
speed), and reservoir configuration may apply when choosing the best
reversible pump-turbine configuration [39]. Chapallaz et al. [40] stated
that, in practice, almost any hydro pump can also be used as a turbine.
The reverse is, however, not the case. As an example, impulse turbines
(Pelton or Turgo) cannot be used as pumps.
The design and characteristics of any hydro pump and turbine
are determined by its conditions of operation. In turbomachinery, the
specific speed is one key parameter to select the most appropriate
reversible pump-turbine or using a pump as turbine (PAT). In this
paper, it is defined in accordance with Dixon and Hall [41] as Eq. (2),
and Table 1 shows ranges of specific speeds for various machines.
𝛺s=𝛺𝑄1∕2
(𝑔𝐻 )3∕4 (2)
Here, 𝛺is the runner rotational speed in rad/s, 𝑄is the volumetric
flow rate in m3/s, and 𝐻is the head in metre. Stepanoff [42] explained
in 1948 that a higher specific speed results in a smaller, and thus
cheaper, machine. With a higher flow rate, the blade design differs
significantly, as illustrated in Fig. 3. On the other hand, machines with
low rotational speeds and small shear forces (e.g. Archimedes screw and
positive displacement machines) are more fish-friendly [43,44]. Radial-
or mixed-flow machines are preferable for pumps with a specific speed
of 𝛺s<2.7, and as the specific speed increases (2.6< 𝛺s<11.6), an
axial configuration is more suitable [45].
Carravetta et al. [46] postulate that axial-flow pumps can be used
as PAT for heads between 1–5 m and flow rates up to 1000 l/s. They
also claim that mixed-flow PATs can be used for heads in the region
of 5–15 m and flow rates of 50–150 l/s. Bogenrieder [47] stated that
radial pump-turbines are suitable to use for heads that are above 60 me-
tre, with a power exceeding 50 MW. Typically, radial- or mixed-flow
machines work best for high heads and low flow rates. For exam-
ple, regular Francis-like pump-turbines (mixed-flow) are the common
choice when it comes to mid- to high-head applications, but the head
variations at low-head operation would greatly affect efficiency [48].
Mixed-flow machines can be used as low-head PHS if the flow rate is
low. However, according to Eq. (1), this implies that the power will also
be low. Multiple machines could be used in parallel to increase the total
power. Breeze [48] suggests that a Deriaz, mixed-flow machine can be
used for heads between 20–100 m. This is because its design is closer
to an axial machine compared to a conventional Francis-like pump-
turbine and the Deriaz design also presents adjustable blades [48,49].
Breeze further expresses the necessity of variable speed drives to extend
the operational region at high efficiency.
The reason why an axial machine is preferable in a low-head
application is that it allows for a higher flow rate, which is necessary
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Fig. 3. Principle view of bladed pump-turbine configurations, note that the term ‘‘centrifugal’’ refers to both the radial- and mixed-flow. The drawing is based on principles shown
in [40–42,46].
Table 1
Ranges of specific speed for various machines [45].
Technology Specific speed 𝛺𝑠
Axiala2.6–11.6
Mixed 0.6–2.7
Radial 0.1–0.8
Archimedes screwb0.03–0.39
Positive displacementb0.01–0.13
aCRPT is classified as an axial machine.
bValues should be regarded only as a reference number, since it is not common to
indicate a specific speed for these machines.
for a machine with high power at low heads. An axial machine also
allows for cheaper civil structures. In turbine mode, the runner rotates
due to the torque that is generated by the flow-induced runner blade
pressure and suction sides. The electric generator extracts power by
a balancing counteracting torque at the particular rotational speed.
In pump mode, an electric motor adds power to the runner in the
form of torque at the particular rotational speed. A flow is developed
due to the rotating runner blade pressure and suction sides, causing
a balancing counteracting torque. The pressure change is in an axial
machine primarily due to the change of relative flow velocity [45].
This is because the tangential velocity of the runner and the cross-
sectional area are constant along a streamline in an axial machine. In
a centrifugal machine, the flow must change direction from axial to
radial (pump mode), or radial to axial (turbine mode), as shown in
Fig. 3. The principles for the head rise in a centrifugal machine are
here described in pump mode for brevity. As the flow goes through
the machine, the cross-sectional area and the tangential velocity of
the runner increase with the radius through the machine. The absolute
flow velocity will decrease as the cross-sectional area increases, due to
continuity. According to Bernoulli’s principle, the static pressure will
increase with the change of absolute velocity squared [50]. The main
cause of the static pressure rise is, however, due to centrifugal effects
caused by the increase of the runner’s tangential velocity, and passage
diffusion, due to a reduction in the relative flow velocity, through the
machine [45]. The result is that the exit blade velocity needs to be
small in order to limit the pressure rise in a low-head application. This
means that the machine needs to be small and that the entrance-to-
exit diameters decrease with the decreasing head [51]. The smaller size
further limits the flow rate and thus the power.
In general, pump-turbines are worse at part-load conditions com-
pared to a pure pump or turbine since the pump-turbine design is
often a trade-off to reach acceptable performance at design condi-
tions [52,53]. Delgado et al. [54] reported that it is hard to predict
part-load performance for PATs, especially in turbine mode since pump
manufacturers usually do not supply any data of this. Stepanoff [42]
stated that centrifugal machines have preferable efficiency as a function
of flow rate; however, axial machines have a flatter efficiency curve
as a function of head. This further suggests that an axial machine
is preferable in a low-head scenario due to the fact that part-load
operations will be less influenced by the large variation in head of a
low-head PHS application.
Lately, axial-flow pump-turbines with two runners, rotating in op-
posite direction from one another, have been proposed as an alternative
for low-head PHS. They are usually referred to as counter-rotating
pump-turbines (CRPT) due to the rotation of the individual runners,
as illustrated in Fig. 4. According to Furukawa [55], the advantages of
those machines are that they can be of smaller size, have a more stable
head-flow rate characteristic curve, and have a wider range of high
efficiency with individual speed control of the runners when compared
to a single runner axial machine. Several numerical studies predict that
a well designed low-head counter-rotating pump-turbine may achieve
efficiencies of up to 80%–90% in both pump and turbine mode [56–58].
Fahlbeck et al. [59] showed numerical results for a prototype counter-
rotating pump-turbine in pump mode with a peak efficiency of 91%,
heads up to 12 metre, flow rates between 60–160 m3/s, and a maximum
power of almost 14 MW.
Additional non-conventional machines have also been studied as
low-head PHS. The Archimedes screw, depicted in Fig. 4, is a viable
option for heads between 2–10 m, discharge ranges up to 15 m3/s,
and power output of up to 355 kW [36,43,60]. The Archimedes screw
enables lower installation and maintenance costs compared to other
conventional pump-turbines and can reach efficiencies of up to 90%
in turbine mode [61,62]. An additional benefit is that the Archimedes
screw presents better conditions for fish-friendliness when compared to
conventional bladed pump-turbines [43,61,63].
Positive displacement (PD) pumps are usually chosen when the
system requires low specific speeds [45]. Some PD pumps can also
represent a good alternative when reversible flows must be taken into
account, thus resembling a PAT [64]. Positive displacement pumps are
self-priming, typically produce low flow rates, can handle big variations
in head without significantly changing their efficiency, and are often
regarded as a good choice for viscous fluids or fluids with the presence
of solids or precipitates that need to be handled [45,50]. Rotary positive
displacement machines have already been studied as micro hydro
turbines in water supply pipelines with pressures up to 5 bar (hydraulic
head equivalent to 51 metre) and presented efficiencies between 60%–
80% [65–68]. From all the available PD alternatives, the lobe and gear
pump configurations – illustrated in Fig. 4 – are the most suitable
options to handle reversible flow. Given the low specific speed, PD
pumps could most likely be regarded as a fish-friendly technology [44].
On the other hand, only the lobe design seems to handle fish and solid
without extra mitigation measures. A few small-scale projects have
tested PD RPTs [64]. However, further investigations and real-scale
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Fig. 4. Principle view of non-conventional pump-turbine configurations. The drawing is based on principles showed in [45,55,56].
prototypes are still needed to validate the use of PD RPTs in low-head
pumped storage application.
Pump-turbines in PHS applications can operate at fixed or vari-
able rotational speed. Variable speed machines take advantage of a
wider operating range at high efficiency and can thus produce power
in a wider spectrum [38,69]. Moreover, variable speed units ensure
greater penetration and bring more flexibility to PHS operations, es-
pecially for smaller machines [70]. Despite the technical advantages,
this technology is about 30% more expensive than fixed speed units.
Thus, the choice between the two speed control options relies on both
techno-economic and demand aspects [38,70].
4. Grid integration of energy storage systems
A reliable electrical power grid is a balanced system. As generation
and demand fluctuate perpetually, transmission system operators (TSO)
and distribution system operators (DSO) have to keep the system
balance everywhere in the electrical grid. This balance ensures that the
grid operates at its nominal frequency (50 or 60 Hz) and that voltage
and power load remain within a certain limit at all times. However, the
higher the penetration of intermittent renewable energy sources, the
more insecure this balance. Thus, the increasing penetration of IRES is
a challenge that TSO and DSO have to handle [71,72].
At the present time, power systems rely on conventional power
plants utilising synchronous generators contributing significantly to
the stabilisation of the electrical power system, using the rotating
masses in their generators (rotors). The synchronous generators keep
the frequency steady at its nominal value due to their large flywheel
masses and thereby assure system stability. In the case of generation
or load fluctuation leading to sudden grid frequency deviations, the
rotor’s combined inertia keeps the generators rotating and consequently
supports the grid stability [73]. On the contrary, not all IRES have large
rotating masses and most are integrated into the grid via converters,
subsequently decoupling the rotating masses from the grid frequency.
Therefore, they do not have any natural inertia (spinning reserve) and
thus operate in an entirely different way than synchronous generators.
As of today, the grid-connected converters for IRES follow the grid
frequency by using a phase locked loop (PLL). This tracks the grid
frequency in order to keep the IRES converters synchronised to the grid.
The PLL control concept is known as grid-following control [73,74].
To tackle the challenge of increasing IRES and decreasing natural
system inertia without affecting the system stability, two approaches
are feasible. The first is to maintain a minimum number of rotat-
ing machines. Among other purposes, the contribution of short-circuit
power and voltage support can provide the necessary inertia to the
transmission system in a case of disturbances in the grid [75,76].
The second solution is through IRES itself. This occurs by using the
capabilities of the power electronics, or energy storage systems (ESS),
to provide and ensure a stable grid frequency without any synchronous
rotating machines. For this purpose, a grid-forming control mode is cur-
rently being developed and tested in many research projects. Here, the
Fig. 5. Simplified block diagram for synthetic electrical inertia control [80,81]. Here,
𝛥f is the deviation of system frequency, ROCOF is the rate of change of frequency, J is
the virtual inertia control constant, 𝛥𝑃imitate is the active power of the converter, and
𝛥𝑃inertia is the emulated virtual inertia power that could be imitated into the system.
controlled converter acts as an AC voltage source with stated voltage,
phase, and frequency. By controlling the voltage magnitude and fre-
quency, the converter behaves very similar to a synchronous generator.
The fundamental difference between grid-following and grid-forming
is the way of synchronisation. By applying the swing Eqs. (3) and
(4) [77], the grid-forming control strategy calculates the voltage an-
gle and amplitude deviation, using current power transfer. It is thus
self-synchronising. Therefore, a converter using grid-forming control
coupled with an ESS is currently being discussed as a viable alternative
to imitate the synchronous generator‘s behaviour regarding frequency
control, especially its ability to provide synthetic electrical inertia [73,
74,78]. In power plants with rotating mass and consequent inertia that
are decoupled from the grid frequency, an additional control loop is
required that gives a power reference proportional to the derivative
of grid frequency. To provide the additional power requested by the
synthetic inertia, the plant may still rely on the physical inertia present
but due to its decoupled nature depends on said synthetic inertia
control.
𝑃m−𝑃e=𝐽 𝜔0
d𝜔
d𝑡(3)
𝜔=d𝜗
d𝑡(4)
Here, 𝑃mis the mechanical power, 𝑃eis the electrical power, 𝜔0is
the nominal angular frequency, 𝜔is the output angular frequency, 𝜗
is the rotation angle, and J is the total moment of inertia of the rotor
mass.
Fig. 5 shows a simplified block diagram for a synthetic electrical
inertia control system. As illustrated, ESS are needed along the grid-
forming control to provide the necessary synthetic electrical inertia.
This shows that ESS are an important factor in the energy transi-
tion and will play a key role in the future. Energy storage systems
will provide inertia for local grid stability as well as other necessary
AS, such as steady state voltage control, fast reactive current injec-
tions, short-circuit current, black start capability, and island operation
capability [79].
Moreover, ESS will also need to compensate for weather and sea-
sonal fluctuations in the power supply from IRES, specially from wind
and solar power. For all the previous reasons, ESS are becoming in-
creasingly important. New possibilities for medium and long-term ESS
with sufficient storage capacity and flexibility, in accordance with
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the respective requirements, are needed to meet the growing demand
from IRES. Low-head PHS system is a power generation system and
serves at the same time as an ESS. This makes the integration of
PHS (low-head or high-head) via grid-forming controlled converter a
vitally important milestone of the energy transition in order to provide
the necessary storage capacity needed for grid stability and flexibility.
The grid integration of low-head PHS via a grid-forming, controlled
converter will not only be of great significance for countries with flat
topographies such as Denmark, Belgium, and the Netherlands. It will
also be essential for countries with a high share of offshore wind energy
as these could enable the concept of energy islands.
5. Electric machines and control for low-head pumped hydro stor-
age
5.1. Electric machines
In traditional high-head, high-power PHS, synchronous machines
with excitation winding and direct grid connection are used. However,
doubly-fed induction machines have been adopted in Europe since
2006 for lower power applications. Doubly-fed induction machines
are coupled to a partially rated converter with rotor winding to in-
crease the operating range, which increases turbine efficiency at lower
speeds [82]. As can be seen from Eq. (2), RPT operation at low head
and high power reduces the nominal rotational speed for a fixed specific
speed. Therefore, the power take-off (PTO) in low-head PHS needs to
be designed to operate at high efficiency for low rotational speeds.
Furthermore, variable speed RPTs require a highly efficient PTO over
a wide operating range. Doubly-fed induction machines with a gearbox
were the classical choice for such low-speed applications. However,
with the recent decrease in cost of power electronics, permanent mag-
net synchronous machines (PMSM) with a fully rated converter are
opted for instead [83–90]. Advantages include a high power density,
high efficiency, and controllability over a wide operating range [91,
92]. Furthermore, PMSMs with a large pole number avert the use of
reduction gearing, which reduces energy losses and increases reliabil-
ity [93,94]. However, the increased cost of permanent magnets (PM)
and converter losses limits its application for high-power installations.
A more recent development in PMSMs is the axial flux PMSM
(AF-PMSM), which has a magnetic flux direction parallel to the axis
of rotation, in contrast to their radial counterparts. These disc-type
machines have a high diameter-to-length ratio, can accommodate high
pole numbers, and are suitable for high-torque low-speed applica-
tions [95–97]. They have a higher power density and use less core
iron, leading to a lower weight [96,98,99], which in turn results in a
higher torque-to-weight ratio. The possible topologies are single-stator
single-rotor (SSSR), double-stator single-rotor (DSSR), or single-stator
double-rotor (SSDR). Furthermore, different concepts can be differ-
entiated on the use of surface mounted or interior PMs, slotted or
slotless armature, presence or absence of stator core, concentrated or
distributed windings, etc. [100].
Single-stator single-rotor topologies [101] are simple in design and
compact. However, there is a strong imbalanced axial force between the
stator and rotor. Therefore, the rotor disc width needs to be increased
to avoid twisting [96]. Double-stator single-rotor topologies [102]
are a valuable alternative to SSDR topologies. Double-stator single-
rotor uses fewer PMs, but experiences more copper losses due to poor
winding utilisation [96]. A DSSR machine with integrated permanent
magnets has a high power-to-inertia ratio, since the rotor disc serves
no magnetic purpose and is eliminated [100]. The reduced inertia is
a significant benefit in a grid-supporting low-head PHS. In a slotted
stator AF-PMSM, cogging torque results from the interaction between
the PMs and the stator slots. This undesired torque can be significantly
reduced by changing the angle between both stators [103]. However,
this also reduces power output. Finally, SSDR is deemed the most
favourable AF-PMSM topology. Next to decreased copper losses, the use
of a stator yoke and the corresponding iron losses can be averted. This
can be achieved by using a north–south PM arrangement of the rotors.
Then, the flux path is completely axial, obviating the magnetic function
of the yoke. The single-stator double-rotor topology has already been
adopted in wind and tidal turbine applications [104,105]. An SSDR
with coreless stator maximises efficiency, while averting cogging torque
and torque ripple [106–108]. Since the flux path is axial, grain-oriented
material – which has greater magnetic permeability in one direction –
can be used in the stator slots. This results in significantly lower iron
losses compared to non-oriented material [109], while reducing PM use
compared to coreless alternatives [100].
Especially in high-voltage electric machines, the vast majority of oc-
curring faults are stator faults, followed by rotor and bearing
faults [110]. Therefore, AF-PMSMs with concentrated windings can
offer a significant advantage by adopting a Modular Machine Drive
(MMD) design. If a fault arises in one of the stator windings, the MMD
can compensate this with the other modules and remain functional
albeit the maximum power is reduced [111,112]. This fault-tolerant
design improves the reliability of the electric machine, which is a
considerable advantage for a low-head PHS system providing grid
support. The reliability can be further increased by means of condition
monitoring techniques and fault or anomaly detection methods [113,
114]. Thanks to the drastic increase in computational power in the past
years (both local and in the cloud), these techniques have become more
data-driven, relying on, e.g., machine learning [115,116], including
artificial neural networks [117], support vector machines [118], and
deep learning [119,120]. The use of digital twins for predictive main-
tenance of mechanical components [121] or the full drivetrain [122]
shows promising results and offer a perspective for the future of
condition monitoring [123]. These techniques can be applied on the
electric machine, and in extension on the whole drivetrain. Current,
voltage, magnetic flux, speed, temperature, and vibration signals can be
captured on the electric machine and serve as inputs for the condition
monitoring system.
It can be concluded that the PMSM is currently the most sensible
electric machine technology for modern low-head PHS due to its high
efficiency and direct-drive capability, although the use of rare earth
materials is a drawback. The principles of axial flux design, modularity
for fault tolerance and data-driven condition monitoring are likely to
play a role in the further improvement of the PMSM.
5.2. Torque and speed control
In variable speed PHS, the machine speed is altered to reach a
power setpoint as fast and precise as possible, both in pump and turbine
mode. Therefore, the machine torque must be precisely controlled.
Field oriented control (FOC) is a vector control method that has been
widely used in low-head micro-hydropower installations [83–89]. The
main advantage is an independent control of the machine torque, and
thus, highly dynamic performance. This is necessary in PHS to quickly
react to changes to the rapidly fluctuating grid frequency. The general
principle of FOC is to regulate the 𝑖dand 𝑖qcurrents in the rotating
reference frame. The electrical dynamics of a PMSM can be modelled
by Eqs. (5) and (6). Here, 𝛺𝑒𝛹PM is the back-EMF of the permanent
magnets. 𝑅is the stator resistance. 𝐿qand 𝐿dare the 𝑞and 𝑑axis
inductances, respectively. 𝛺𝑒𝐿𝑖 is the armature reaction EMF, through
which the 𝑞and 𝑑schemes are coupled.
𝑣d=𝑅 𝑖d+𝐿d
d𝑖d
d𝑡−𝛺e𝐿q𝑖q(5)
𝑣q=𝑅 𝑖q+𝐿q
d𝑖q
d𝑡+𝛺e(𝐿d𝑖d+𝛹PM)(6)
By regulating the 𝑑and 𝑞axis currents, the torque can be regulated as
shown in the general torque Eq. (7) of the PMSM.
𝑇=𝑝3
2𝛹PM𝑖q+ (𝐿d−𝐿q)𝑖d𝑖q(7)
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Fig. 6. Decoupled field oriented control of a PMSM with estimated back-EMF
feedforward.
Here, 𝑝is the pole pair number and 𝛹PM is the constant flux of the
permanent magnets. Fig. 6 shows the control scheme of a field oriented
controlled PMSM. On the bottom right, the stator currents are measured
and transformed to the rotating 𝑞,𝑑reference frame. These signals
are compared with the setpoints on the left and controlled by two PI
controllers. These controllers determine the duty ratios resulting in the
Pulse-Width Modulated (PWM) signals for the converter. In FOC, ̂
𝑖dis
set to 0. Eq. (7) shows that the machine torque is directly proportional
to 𝑖q, resulting in a highly dynamic control. To achieve decoupled
control of both currents, the coupling terms in Eq. (7) are used as a
feedforward. Furthermore, a back-EMF estimator can be implemented
in the 𝑞current control.
Although FOC is highly dynamic and easy to implement, setting
𝑖d= 0 is not the most efficient way to reach a desired torque setpoint
for a PMSM with saliency, like an interior magnet PMSM. Therefore,
maximum torque per ampere (MTPA) control can reduce copper losses
and increase overall efficiency in low-head hydropower applications.
The MTPA accomplishes this by minimising 𝑖s=𝑖2
q+𝑖2
dfor every
torque setpoint [124]. Applications with interior magnet PMSMs in
wind turbines found a reduction in Joule losses (up to 4.2%), while
maintaining a dynamic response to changing torque setpoints [124,
125].
The position sensor plays a critical role in FOC. However, a po-
sition sensor is costly and its signal can contain noise. Therefore,
saliency-based sensorless rotor position estimators [88,89,126,127] are
proposed for low-power systems, since they can increase reliability and
reduce cost [89]. For low rotational speed runners, as in low-head PHS,
the saliency-based approach is the most suitable [89]. Here, a high
pulse frequency is injected, while the current response, which depends
on the rotor magnetic flux position, is observed.
Active distribution rejection control (ADRC) is used in torque and
speed control to account for known and unknown electrical, hydrauli-
cal, or mechanical disturbances in the system, increasing performance
and robustness. Guo et al. [84] applies a first order ADRC for a
PMSM in a hydropower application, where the known disturbances are
mechanical friction and hydraulic torque. A second order state observer
is used to estimate the rotational speed and hydraulic torque. ADCR is
especially useful in low-head high-power PHS, since any change in the
system tubes has a significant influence on the head losses, because of
the high flow rate at low head.
Direct torque control (DTC) is an alternative control method to FOC.
In DTC, the electromagnetic torque and stator flux are controlled by
switching between a discrete number of stator voltage vectors, which
in turn form the stator flux vector interacting with the rotor flux.
Based on the torque and flux linkage reference and the current flux
vector position, a lookup table is consulted to select the optimal voltage
vector. If e.g. the torque must be increased, a voltage vector is selected
so that the angle between stator and rotor flux is increased. Fig. 7
visualises the control schematic. To find the torque and stator flux, an
Fig. 7. Control schematic of DTC.
estimator based on phase voltages and currents is used (bottom). These
estimated values are compared to torque and flux setpoints. Hysteresis
controllers then determine the proper voltage vector from a lookup
table, resulting in the switching signals. Direct torque control has a
slightly better torque response compared to FOC and does not require a
position sensor [128,129]. However, DTC relies on an accurate estima-
tor. Especially at low speeds, an estimator based on phase voltages and
currents cannot accurately estimate the stator flux [130] which makes
it less suitable for low-head PHS. Although some improved estimator
algorithms have been studied [130], this drawback is best averted by
using a position sensor in the estimator. Disadvantages of DTC include
variable switching frequency, high harmonic current distortion, and
torque ripple [128,129,131]. To achieve a smoother dynamic response
and thus less torque and flux ripple, space vector modulation (SVM) is
used instead of the lookup table [128,129,132].
5.3. Power control
In the power control of low-head PHS, the goal is to reach a
power setpoint as fast and efficiently as possible. Three main control
parameters are determined: the pump/turbine rotational speed 𝛺; the
inlet vane angle 𝛼; and the blade pitch 𝛽. An RPT with only 𝛺as
control parameter is defined as a non-regulated RPT. A single- and
double-regulated RPT further include, respectively inlet vane control,
and inlet vane and blade pitch control. In low-head PHS, a regulated
RPT is recommended, because it allows the RPT to be operated at high
efficiency in a large operating range of heads, flow rate, and power
setpoint.
5.3.1. Maximum power point tracking algorithms
Maximum power point tracking (MPPT)-based algorithms are used
to find the optimal speed setpoint for a certain power setpoint in tur-
bine mode. In a low-head turbine, this power setpoint is the maximum
available power, hence the name MPPT. In grid-supporting PHS, this
may not be the case, as the power setpoints depend on grid frequency.
Therefore, adjustments need to be made to the existing algorithms.
The MPPT algorithms can be divided into direct and indirect meth-
ods. Direct MPPT algorithms are based on iterative extremum-seeking
control algorithms. These algorithms require limited knowledge of the
system, but are inherently slow due to their iterative behaviour, making
them less suitable for grid-supporting PHS. However, they can still be
used in storage systems with lower dynamic requirements because of
their simplicity. Indirect methods are based on a model of the system,
making them more dynamic but less flexible. Most of the existing
MPPT control methods rely on flow rate measurement. However, a flow
rate sensor is costly and has a certain error. In low-head RPTs, the
accuracy can further decrease due to a non-uniform flow, a short intake,
and high turbulence [133]. To evade these drawbacks, Borkowski and
Dariusz [90] presented a flow rate estimator. The estimator is based on
an artificial neural network (ANN), which is trained by experimental
data.
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Among direct MPPT control methods, the perturb and observe
algorithm has been investigated for non-regulated low-head turbines.
The principle operation consists of altering or perturbing the rotational
speed 𝛺, i.e. accelerating or decelerating, and analysing the change in
output power 𝑃, measured at the electric machine or converter. If the
power has increased, the sign of d𝛺is maintained and the procedure
continues. Otherwise, d𝛺is reversed [83]. Eq. (8) shows how the speed
setpoint ̂
𝛺is altered after each iteration. Note that 𝛿(𝑡)implies the sign
of d𝛺.
̂
𝛺=∫𝑡𝑘−1+𝑇𝑠
𝑡𝑘−1
𝐾𝛿 (𝑡)d𝑡(8)
𝛿(𝑡) = sgn(𝑃𝑘−𝑃𝑘−1)sgn(𝛺𝑘−𝛺𝑘−1 )(9)
Inherent to this method is that the system will still perturb 𝛺when the
MPP is reached, resulting in an oscillation around the MPP. Step size
𝐾is an adaptive value that increases when the power is continuously
rising and decreases when the power is fluctuating [83]. However,
the dynamic behaviour of this method is not optimal. If 𝐾is too
low after oscillations and the MPP shifts, the dynamic response is
poor. To allow both dynamic response and minimal power fluctuation
around the MPP, 𝐾can be taken proportional to the power gradient
𝛥𝑃
𝛥𝛺 [134]. Due to the parabolic nature of the turbine characteristics,
𝐾is high when far away from the MPP and gradually decreases when
the MPP is neared. Note that using this gradient-based step size cannot
be used to reach a lower power setpoint ̂
𝑃. However, the step size
here can be proportional to ̂
𝑃−𝑃. In wind turbine applications, fuzzy
logic is recently used to find the value of 𝐾, where the perturbed
variable is the generator voltage, which is proportional to the generator
speed [135–137].
Gradient descent control is a direct maximum efficiency point track-
ing (MEPT) algorithm that allows multiple control variables, opposed
to the perturb and observe algorithm. However, to derive the efficiency,
an accurate flow sensor is necessary, which was discussed to be a
challenge in low-head PHS systems [133]. On every operating point,
the control variables are incremented with the direction of their partial
derivatives of efficiency at the current operating point, multiplied by a
step size 𝑘[138]. In Eq. (10),𝛼is the vane opening and 𝛽is the blade
pitch.
𝛥𝛼 =𝑘𝜕𝜂
𝜕𝛼 𝛥𝛽 =𝑘𝜕𝜂
𝜕𝛽 𝛥𝛺 =𝑘𝜕𝜂
𝜕𝛺 (10)
If the time constants of the control parameters are known, 𝑘can
be chosen differently for each control parameter. Furthermore, 𝑘can
be adaptive and defined by a line search algorithm at every itera-
tion [139]. Although this control algorithm shows great potential, any
disturbances on the gradient estimation due to measurement error
or mutual influence between control parameters has a great impact
on the convergence [138]. Therefore, a moving average filter and a
Kalman filter can, respectively, be used to increase robustness [90,140].
Furthermore, Borkowski [90] accounts for the time delay of flow rate
settlement after a change in turbine control parameter further reduce
risk of a non-converging control.
Indirect MPPT algorithms rely on prior knowledge of the system in
order to determine the optimal torque or speed reference to achieve a
power setpoint. Recently, this system knowledge is mostly captured in
the form of empirical equations, hill charts, or lookup tables, which are
derived from measurements or numerical analysis like computational
fluid dynamics. Márquez et al. [141] derived an empirical formula for
a propeller turbine, which is a modified Kaplan turbine, designed for
low-heads and low flow rates. Eq. (11) relates the non-regulated turbine
efficiency to flow rate and turbine speed.
𝜂ℎ(𝛺, 𝑄)=3.33 𝑄1
290
𝜆𝑖
+𝑄+ 0.78𝑒
−50
𝜆𝑖(11)
𝜆𝑖=1
(𝜆+ 0.089) − 0.0035−1
, 𝜆 =𝑅𝐴𝛺
𝑄
Although this model can be used in low-head control models, it is
important to note that flow rate Q is a function of head and rotational
speed 𝑄=𝑓(𝐻, 𝛺 )for a non-regulated RPT. Therefore, changing 𝛺will
affect flow rate 𝑄as well. Zhang et al. [142] proposes a polynomial
empirical equation for the efficiency of a turbine 𝜂ℎ(𝛺, 𝑄), where the
coefficients can be derived from experimental data. Borkowski and
Dariusz [143] used an ANN to compose and validate an efficiency
equation 𝜂ℎ(𝛺, 𝑄)together with a flow rate characteristic 𝑄(𝛺, 𝛼)for
a regulated turbine. The control system based on these characteristics
requires no flow rate sensing. However, the 𝑄characterisation is for a
constant head and the flow rate is approximated by a linear function of
speed. This limits its application under varying head at low rotational
speeds.
Similarly, ANN has also been used to form lookup tables [144].
Lookup tables can be constructed over a large operating range during
on-site measurements or by using an existing dataset. Pérez-Diaz and
Fraile-Ardanuy [144] use two ANNs to train the head and efficiency
for input parameters 𝑄,𝛺, and 𝛼. A possible application of the result-
ing lookup tables is to find reference ̂
𝛺and ̂𝛼 to reach the optimal
efficiency for a given head. In this control system, no flow sensor is
necessary, thus reducing cost and increasing reliability, especially for
low-head systems.
Hill charts define the relation between flow rate 𝑄, rotational speed
𝛺, inlet vane angle 𝛼, and efficiency 𝜂for a constant head 𝐻. Therefore,
if 𝛺and 𝛼are known, 𝑄and 𝜂can be read from the graph. Furthermore,
𝛼and 𝜂are plotted versus the unitary rotational speed 𝛺11 and unitary
flow rate 𝑄11 in Eq. (12), making hill charts scalable for different heads.
However, in a real system, the losses 𝐻L(𝑄)have to be taken into
account, making it difficult to estimate the net head across the turbine
without a flow rate sensor. Especially in a low-head high-power system,
where the flow rate is high, these losses have a significant influence on
the efficiency.
𝛺11 =𝛺 𝐷
𝐻
, 𝑄11 =𝑄
𝐷2𝐻
(12)
𝑄11 and 𝛺11 can also be compensated when the Reynolds number of the
real system differs from the design [145]. Fraile-Ardanuy et al. [146]
applied a hill chart to a control system in order to find the optimal
efficiency speed for given 𝛼and measured 𝑄. For a reduced-scale
RPT [147], a lookup table is trained based on measurements. The
lookup table is used to find ̂
𝛺for given measured 𝐻and ̂
𝑃. However,
the speed is controlled by 𝛼, while it was shown in the paper that
𝑄11 =𝑓(𝛼, 𝛺). However, the proposed control system is promising for
low-head hydropower if both 𝛺and 𝛼are controlled separately. Then,
the RPT could be controlled to reach ̂
𝑃at the highest efficiency for a
certain measured 𝐻.
One drawback of using turbine characteristics is that the electrical
machine and converter losses are not included. Therefore, the overall
MPP may differ from the turbine MPP [87]. De Kooning et al. [148]
found that the MPP displacement in wind turbines was greater for low
wind and thus lower rotational speeds. In direct MPPT methods, these
losses are included if the power is measured on the converter side. An-
other drawback of indirect MPPT methods is that they do not account
for system performance deterioration over a long time period. However,
reinforcement learning, as proposed for wind turbines [149,150], can
solve this problem at the cost of a higher real computational intensity.
5.3.2. Model predictive control
An important factor in RPT operation and control that is often
overlooked in traditional MPPT strategies is the transient effect of the
water supply system caused by a control action. The transient flow
equations are described in Section 6.1. Fang et al. [151] stated that
increasing the control action magnitude actually decreased the output
power, while the settling and maximum turbine pressure deviation
increased. Therefore, it can be seen how using an MPPT control that
does not account for these effects can have poor dynamic behaviour
Renewable and Sustainable Energy Reviews 158 (2022) 112119
11
J.P. Hoffstaedt et al.
when applied to a real system. In some studies on MPPT control, the
water inertia time 𝑇𝑤is incorporated as a time delay on the control
action [90] or as an extra mechanical inertia on the RPT [152]. How-
ever, this does not fully capture the transient effects. Therefore, model
predictive control (MPC) is applied to PHS systems [153–155]. In MPC,
a detailed model of the full PHS system, including hydraulic transients,
losses, and an RPT model, are used. Based on a certain operating state
setpoint, an internal optimisation algorithm simulates control actions
and observes the predicted outcomes of the model. The outcomes are
then given a cost value based on the power response. These predictions
are made for multiple future time samples. Each time sample, this
process is repeated. Therefore, MPC is an accurate control method
that can work on complex systems, at the cost of a significantly high
computational intensity. Furthermore, MPC can also incorporate system
constraints, such as maximum pressure deviation and mechanical rate
limits. Chaoshun et al. [153] proposed using a nonlinear MPC, which
includes the elastic water hammer effect in a high-head PHS plant.
Liang et al. [154] used MPC to define the optimal switching time
between pump and turbine mode for a multi-RPT PHS plant. However,
these studies did not include pressure constraints, which are especially
important in systems with long pipelines. The MPC for a 40 metre
PHS plant by Mennemann et al. [155] included this effect. MPC is
currently mostly investigated for high-head PHS. However, the benefits
of adapting MPC for low-head PHS could be substantial, because of the
potentially increased influence of transient effects, as described in Sec-
tion 6.1. For a dynamic system providing frequency support, the MPC’s
computational intensity increases even further, which might slow down
the optimisation algorithm. However, with the recent advancements
made in parallel computing with, e.g., multi-core processors (CPUs) and
many-core processors such as graphical processing units (GPUs), the
MPC process can be accelerated [156], making it suitable for complex
dynamic systems like low-head PHS.
6. Modelling of low-head systems
The overall objective of developing a model of a given system is
to have a representation of the real world. Since such a model will
always be a simplified depiction, it is crucial to weigh which aspects
are essential and what should be left out or simplified. In the case of
numerical models, this also helps to improve performance and reduce
the computational resources necessary. At the end, a well formulated
model allows to predict the behaviour of a system to a greater extent
and wider scenarios than experiments and interpolating empirical data.
These predictions are crucial in developing such systems to understand
performance and dynamics, aid optimisation, and can be required for
accurate control during operation. The mathematical models are typi-
cally derived from first principles, such as balance equations of mass,
energy, or momentum, but can also be based on phenomenological or
empirical observations or a mixture of both.
Models for high-head PHS are comprehensive and well researched
while attention to low-head PHS applications has been limited. Fun-
damentally, the same approaches can be used. There are, however,
differences in the relevance of individual model components. From a
hydrodynamic point of view, the major difference is a shift towards
higher flow and reduced head for a given power. The increase in the
mass flow rate of water may cause the system to be more prone to water
hammer effects. Cavitation is a further effect to consider when choosing
model components for a low-head scenario. Reaction turbines, such as
Francis or Kaplan turbines that are suitable for medium- and low-head
applications, are considered more susceptible to the effect [157].
The different relation between flow and head also affects turbo-
machinery and power take-off. The shift to a higher flow and lower
pressure at the machine side closer to the upper reservoir typically
results in lower angular velocity and higher torque at the runner and
motor-generator. This is due to an increased runner tip speed as a
consequence of enlarged machines. In combination with the likely use
of variable speed control which may cause even lower speeds at off-
design operation points, this may, for example, not just affect the choice
of motor-generator architecture but could also affect the drivetrain
losses. When choosing modelling approaches for individual system
components, considering these characteristics specific for low-head PHS
helps to cover the relevant aspects while also optimising performance.
6.1. Hydrodynamics
One of the most common approaches in PHS is to model the
penstock as a rigid conduit in addition to the consideration of water
being an incompressible fluid. A widespread approach making these
assumptions is based on the net force on the body of water which can be
given through both the rate of change of momentum and the differences
in pressure head to obtain the change in time of the volumetric flow
rate as shown in Eq. (13) [158–160].
𝐿d𝑄
d𝑡=𝐻−𝐻T−𝐻L𝐴𝑔 (13)
Here, Qis the volumetric flow rate through the conduit and turbine,
His the head over the body of water, 𝐻Tis the turbine head, 𝐻L
represents the head losses within the conduit, gis the gravitational
acceleration, Ais the conduit cross-sectional area, and Lis the conduit
length. The turbine head can be obtained either from empirical data
or physical models as a function of both its rotational speed and flow
rate, while the major and minor head losses are typically represented
through well known hydraulic models, such as the Darcy–Weisbach
formulation in combination with the Colebrook equation [50]. To
complete the conduit component of the system model, these equations
are typically coupled with equations relating to a governor, such as a
gate or guide vanes and mechanical power of the turbine as given in
Eq. (1).
Using the above mentioned combination of ordinary differential and
algebraic equations to model the water column as a rigid body is one
the simplest methods to cover the system dynamics. However, to accu-
rately depict transients in the system, such as travelling pressure waves,
an approach using coupled partial differential equations considering
compressibility and elasticity is required [161]. This could be partic-
ularly relevant in applications where enlarged mass flow rates of water
are subject to sudden changes of flow rates and heads, such as low-head
PHS. A commonly used 1-D approach considering these effects uses
the so-called, water hammer equations. These relate pressure head and
water velocity as a function of position and time as shown in Eqs. (14)
and (15) [162,163].
𝜕𝐻
𝜕𝑡 = −𝑈𝜕𝐻
𝜕𝑥 −𝑎2
𝑔
𝜕𝑈
𝜕𝑥 (14)
𝜕𝑈
𝜕𝑡 = −𝑈𝜕𝑈
𝜕𝑥 −𝑓 𝑈 𝑈
2𝐷−𝑔𝜕𝐻
𝜕𝑥 (15)
Here we have Has the pressure head, Uas water velocity, aas the
pressure wave velocity, gas gravitational acceleration, Das the conduit
diameter, and fas friction factor. If appropriate, simplifications can
be made neglecting velocity head or friction losses. The set of partial
differential equations can be solved either directly or by transforming
it first into a series of ordinary differential equations.
Comparisons of similar approaches have shown that treating the
conduit as rigid results in a reduction in computational resources neces-
sary and hence, decreased simulation time. However, if the underlying
scenario requires, higher accuracy can be achieved when considering
elasticity and compressibility effects [163,164].
Aside from travelling pressure waves, another effect that may be
of higher relevance in a low-head high-flow system is cavitation. The
inception of cavitation is dependent on the amount and type of particles
in the water allowing for nuclei to sustain [165]. Low-head PHS is
a promising candidate for seawater applications in coastal regions. In
such, breaking waves mixing particles from the seabed with the salty
water could increase the risk for cavitation to occur. Its likelihood is
Renewable and Sustainable Energy Reviews 158 (2022) 112119
12
J.P. Hoffstaedt et al.
also increased when pump-turbines work at off-design conditions as a
consequence of variable speed operation.
This formation of vapour bubbles occurs when the local refer-
ence pressure in the fluid reaches its vapour pressure. Fundamental
numerical estimates for the likelihood of cavitation occurrence use dif-
ferent forms of a dimensionless cavitation parameter, such as Thoma‘s
cavitation number shown in Eq. (16) [166].
𝜎=𝑝r−𝑝v(𝑇)
𝛥𝑝 (16)
Such cavitation numbers characterise how close the local reference
pressure is to the vapour pressure of the fluid. It is calculated from
the reference pressure 𝑝r, the vapour pressure at the given temperature
𝑝v(𝑇), and the characteristic system pressure difference 𝛥𝑝. Approaches
using various forms of the cavitation number have shown widespread
use in a variety of hydrodynamic applications. It has been found,
however, that studies giving too much emphasis to it, result in poor
repeatability and inconsistency between them. This is due to a wide
variety of definitions of the cavitation number as well as the neglect
of other factors, such as the influence of geometry, flow velocity, or
fluid temperature [167]. More accurate approaches typically include
representations of the dynamics of the vapour bubble cluster. While
computationally more intensive, these allow to model growth and
collapse of the nuclei based on the Rayleigh–Plesset equation derived
from the conservation of mass allowing to solve for the time-dependent
vapour bubble radius [168,169].
6.2. Power take-off
Variable speed operation of PHS does not just enable to work at
improved efficiency under varying conditions but also improves the ca-
pability to provide AS. When modelling newly developed low-head PHS
systems, this should be considered. For variable speed systems in low-
head PHS as well as related and comparable wind power generation, a
variety of power take-off architectures and controls are available. Com-
monly used are models representing doubly-fed induction or permanent
magnet synchronous motor-generators, respectively, in combination
with drivetrain models of the change in angular velocity based on
torque balance and inertia [161,170,171]. To model the drivetrain, the
simplest model consider a lumped rigid body approach with a rigid
shaft such that all rotating masses and hence rotational inertias can
be added together, leading to Eq. (17).
𝐽d𝜔
d𝑡=𝜏h−𝜏g−𝐷f𝜔(17)
This ordinary differential equation relates the change in angular ve-
locity 𝜔and rotational mass moment of inertia of the system Jto
the balance of hydraulic torque 𝜏h, generator torque 𝜏g, as well as
friction typically represented as a viscous damping torque 𝐷f𝜔. Typical
implementations modelling the electrical dynamics of motor-generators
use space-vector representation with the d-q frame of reference. An
example for such an approach for a PMSM can be found in Eqs. (5)
and (6) described in Section 5.2.
A further point of interest to modelling the PTO of low-head PHS
in combination with variable speed operation is a potential shift to
higher Joule and reduced iron losses. The changing loss characteristics
could affect control and supporting models when tracking optimal
operating point to extract maximum power as shown on the example
of wind turbines [172]. Effects that are potentially less relevant for
low-head applications are the influence of cogging torque and resulting
speed ripple. The shift towards lower angular velocity and increased
torque for a given power means cogging will be a smaller fraction of
the total torque. Additionally, larger diameters of the rotating mass
lead to increased rotational inertia. An increase here correlates with
a reduction in speed ripple [173]. This becomes clear when including
a cogging torque in Eq. (17).
7. Conclusion
Due to the rapid rise of intermittent renewable energy sources,
penetration levels will exceed what can be compensated for by alter-
native stability measures, and large-scale integration of energy storage
will become imperative. This increase in demand for short- and long-
term balancing and the provision of ancillary services will contribute
to novel systems turning into cost-effective solutions. While pumped
hydro storage is a promising candidate to improve grid stability, its
limitations in deployability call for a conceptual adaptation. Shift-
ing the operating range from traditional high-head towards low-head
applications could pave the way to utilise PHS in regions where so
far it had not been feasible. Further technological advancements can
significantly contribute to enhancing its capability to improve grid
stability while also making it cost competitive. Based on the lack of
research on low-head PHS, this review discusses challenges and the
potential of low-head PHS while giving an overview of pumped storage
technologies and their applicability to low-head applications. The main
outcomes are the following:
•In a low-head context, the choice of pump-turbine design is highly
dependent on the flow rate of the system. Axial flow pump-
turbines, with variable speed drives, are the most suitable solution
for high flow rates which leads to higher power outputs. On the
other hand, other designs, such as Archimedes screw or rotary
positive displacement configurations, can be beneficial at lower
flow rates and micro- or small-scale locations.
•The discussion on grid integration has shown that, to compensate
for an increase in intermittent generation and a reduction in spin-
ning reserves, a combination of grid-forming control alongside
bulk energy storage is necessary. To ensure grid stability, such
systems will need to provide synthetic inertia next to other an-
cillary services, namely steady state voltage control, fast reactive
current injections, short circuit currents, black start, and island
operation capability.
•For the power take-off, axial flux PMSMs are the most promising
electric machines for low-head PHS due to their high efficiency,
high power density, and suitability for high-torque-low-speed
operation. The machine torque can be controlled to achieve a
speed setpoint by either field oriented control or direct torque
control, with the latter having a slightly better torque response if
a position sensor is used, but increasing torque ripple. Active dis-
tribution rejection control can be used to complement the torque
and speed control, increasing performance and robustness. To
derive the speed setpoint, MPPT algorithms based on RPT models
are suitable for low-head PHS because of their short response time
and steady power output. However, it is important to include
the whole system with its losses to have precise control. Model
predictive control is a computationally intense control method
that can account for transient effects in complex systems, making
it a valuable option for low-head PHS.
•When modelling low-head PHS, the same fundamental approaches
of traditional PHS can be used. However, the change in system
characteristics being a shift to larger masses of water and reduced
head requires more attention on certain model components. Mod-
elling hydrodynamics in more detail allows to cover transients
such as water hammer and estimate the risk of cavitation. Paying
further attention to changing motor-generator dynamics can help
to accurately predict performance and improve control.
There are considerable opportunities for further research to improve
low-head pumped storage technology and facilitate economic viability.
Firstly, a detailed economic analysis incorporating a predicted increase
in revenue from energy arbitrage and the provision of AS combined
with improved control strategies optimised for these may serve as a
further proof of concept. Additionally, modelling and simulation efforts
integrating the proposed components and analysing performance on
Renewable and Sustainable Energy Reviews 158 (2022) 112119
13
J.P. Hoffstaedt et al.
a system level can help to estimate technical potential for round-trip
efficiencies, mode-switching times, and power ramp rates. Finally, a
step from such theoretical results to prototyping and implementation
would attract attention of stakeholders and pave the way for large-scale
deployment. With these steps taken, low-head PHS has the potential to
be a significant facilitator for the ongoing energy transition.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgements
This research is part of a project that has received funding from the
European Union’s Horizon 2020 research and innovation programme
under grant agreement No. 883553. The authors would like to thank
the International Hydropower Association for providing us with Fig. 2.
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