SANDIA REPORT
SAND2022-12375
Printed September, 2022
Prepared by
Sandia National Laboratories
Albuquerque, New Mexico 87185
Livermore, California 94550
Simulink Modeling and Dynamic Study of
Fixed-Speed, Variable-Speed, and Ternary
Pumped Storage Hydropower
Miguel Jimenez-Aparicio, Felipe Wilches-Bernal, Rachid Darbali-Zamora, Thad
Haines, David A. Schoenwald, S. M. Shafiul Alam, Vahan Gevorgian,
Weihang Yan
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2
Simulink Modeling and Dynamic Study of
Fixed-Speed, Variable-Speed, and Ternary
Pumped Storage Hydropower
Miguel Jimenez-Aparicio
1*
, Felipe Wilches-Bernal
1
, Rachid Darbali-Zamora
1
, Thad Haines
1
,
David A. Schoenwald
1
, S. M. Shafiul Alam
2
, Vahan Gevorgian
3
, Weihang Yan
3
1
Sandia National Laboratories, Albuquerque, NM 87185, USA
2
Idaho National Laboratory, Idaho Falls, ID 83415, USA
3
National Renewable Energy Laboratory, Golden, CO 80401, USA
ABSTRACT
Pumped Storage Hydropower (PSH) is one of the most popular energy storage technologies in the
world. It uses an upper reservoir to store water which can be later used during high-demand. In the
United States, most of the energy storage capability actually corresponds to PSH. Moreover, PSH
also brings multiple benefits to grid operation.
This report presents the Simulink models of three common PSH technologies: Fixed-Speed (FS),
Variable-Speed (VS), and Ternary (T)-PSH. These models are available to the general public on this
GitHub repository
1
, which contains the MATLAB model initialization files, the Simulink model
files, and supplementary MATLAB code used to obtain the figures in this work.
For each PSH model, an introductory description of the model components and other relevant
functionalities are provided. For further information regarding the models and the initialization
parameters, the reader is referred to the shared files in the repository. This report also presents
the dynamic behavior of each model. The response of such models to a load event is analyzed
and matched with each model’s features. A custom IEEE 39 bus case is employed for the FS and
T-PSH simulations, while the VS-PSH is simulated on a simplified three-bus test system due to the
computational complexity of the model. For the T-PSH, the steady-state and the switching between
several operating modes are also studied in this work.
SAND2022-12375
*
Send correspondence [email protected].
1
See:https://github.com/sandialabs/Simulink_PumpedStorageHydropower.
3
ACKNOWLEDGMENT
This research was supported by the US Department of Energy (DOE) Water Power Technologies
Office (WPTO) under the Grid Modernization Laboratory Consortium (GMLC) program.
Thanks to the entire FlexPower team for their collaboration during the development of the models.
4
CONTENTS
1. Introduction9
2. Fixed-Speed PSH10
2.1. Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2. Simulation: Load event for the FS-PSH in generating mode . . . . . . . . . . . . . . . . . . . . 11
2.3. Simulation: Load event for the FS-PSH in pumping mode . . . . . . . . . . . . . . . . . . . . . 12
3. Variable-Speed PSH14
3.1. Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2. Simulation: Load event for the VS-PSH during generating mode . . . . . . . . . . . . . . . . 16
3.3. Simulation: Load event for the VS-PSH during pumping mode . . . . . . . . . . . . . . . . . 18
4. Ternary-PSH21
4.1. Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2. Simulation: Steady-state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3. Simulation: Load Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4. Simulation: Mode switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5. Conclusions33
Bibliography34
5
LIST OF FIGURES
Figure 2-1. FS-PSH diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 2-2. FS-PSH location in the IEEE 39 bus system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 2-3. FS-PSH response to load event during generating mode . . . . . . . . . . . . . . . . . . . . 12
Figure 2-4. FS-PSH response to load event during pumping mode . . . . . . . . . . . . . . . . . . . . . 13
Figure 3-1. VS-PSH system diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Figure 3-2. VS-PSH location in the simplified system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 3-3. VS-PSH response to load event during generating mode . . . . . . . . . . . . . . . . . . . . 17
Figure 3-4. VS-PSH response to load event during generating mode (Cont.) . . . . . . . . . . . . . 18
Figure 3-5. VS-PSH response to load event during pumping mode . . . . . . . . . . . . . . . . . . . . . 19
Figure 3-6. VS-PSH response to load event during pumping mode (Cont.). . . . . . . . . . . . . . . 20
Figure 4-1. T-PSH schematic during generating, pumping and HSC operating modes . . . . . 22
Figure 4-2. T-PSH system diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Figure 4-3. T-PSH response to load event during generating mode . . . . . . . . . . . . . . . . . . . . . 24
Figure 4-4. T-PSH response to load event during generating mode (Cont.) . . . . . . . . . . . . . . . 25
Figure 4-5. T-PSH response to load event during pumping mode . . . . . . . . . . . . . . . . . . . . . . . 26
Figure 4-6. T-PSH response to load event during pumping mode (Cont.) . . . . . . . . . . . . . . . . 27
Figure 4-7. T-PSH response to load event during HSC mode . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Figure 4-8. T-PSH response to load event during HSC mode (Cont.) . . . . . . . . . . . . . . . . . . . 29
Figure 4-9. T-PSH response to mode switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 4-10. T-PSH response to mode switching (Cont.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6
LIST OF TABLES
Table 0-1. Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Table 4-1. Steady-state T-PSH behavior results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7
NOMENCLATURE
Table 0-1.Acronyms
Abbreviation Definition
PSHPumped Storage Hydropower
FS-PSHFixed-Speed Pumped Storage Hydropower
VS-PSHVariable-Speed Pumped Storage Hydropower
T-PSHTernary Pumped Storage Hydropower
DFIGDoubly-Fed Induction Generator
GSCGrid-Side Converter
RSCRotor-Side Converter
DCDirect Current
HSCHydraulic Short Circuit
p.u.Per Unit
푃
푅푒 푓
Active power setpoint
퐻Head
퐾
퐷
Power distribution factor
푃
푀푒푐ℎ
Mechanical active power
푃
푂푢푡
Overall active output power
8
1.INTRODUCTION
Pumped Storage Hydropower (PSH) is a mature hydro technology whose first use dates back to the
1890s. PSH plants’ service to the grid is important in many aspects: they can provide frequency
regulation, load leveling, black-start capabilities and increased generating capacity [1]. PSH plants
can work either “open-loop”, with a naturally flowing mass of water as a lower reservoir, or in
“closed-loop” configuration in two independent reservoirs. According to [2], PSH plants accounted
for a 93% of utility-scale energy storage in the United States (US) in 2021. All PSH plants can
work in two basic different operating modes: either generating mode - providing active power - or
pumping mode - absorbing active power.
The most common type of PSH is the Fixed-Speed (FS)-PSH: simple and widely employed, it can
provide frequency regulation or spinning reserve in generating mode. All of the PSH plants in
the US correspond to this type of technology [1]. More recently developed, the Variable-Speed
(VS)-PSH extends the capabilities of FS-PSH thanks to power electronics. Although its initial cost
is higher, VS-PSH can provide frequency regulation in both generating and pumping modes, its
operation modes are more flexible, and the potential revenue is higher [3]. Finally, Ternary (T)-PSH
units provide an even faster switching between generating and pumping modes, bringing more
flexibility in case that it is needed.
Three different models: a FS-PSH, a VS-PSH and a T-PSH, have been developed for Simscape, the
Simulink environment for developing physical systems. The goal of this report is to document and
introduce the developed models, and to show their dynamic response to a load event. For simulation
purposes, the FS-PSH and T-PSH models are integrated into the IEEE 39 bus system [4]. The
system is modified to include the FS-PSH and T-PSH. However, due to the demanding computation
requirements for the VS-PSH, it has been simulated in a simplified three-bus system.
The motivation for explaining and sharing these PSH models resides on the lack of PSH state-space
models that are publicly available. The distribution of these models aim to fuel and inspire research
on the PSH integration into the grid. The models are publicly available on this GitHub repository
1
.
If used, please cite this report
2
.
1
See:https://github.com/sandialabs/Simulink_PumpedStorageHydropower.
2
M. Jimenez-Aparicio et al., “Simulink Modeling and Dynamic Study of Fixed-Speed, Variable-Speed, and Ternary
Pumped Storage Hydropower,” Sandia Technical Report, September 2022.
9
2.FIXED-SPEED PSH
2.1.Model description
A Fixed-Speed (FS), or “conventional”, hydropower plant consists of a synchronous machine or an
induction generator that works at synchronous speed. It is a mature and reliable technology, and
the vast majority of PSH in the world are FS-PSH [5]. The cost is significantly lower than other
more advanced (and more complex) PSH technologies. The model presented in this report is based
on a synchronous machine. For this reason, it requires a governor for frequency regulation. The
elements in the developed Simulink model are:
1.A setpoint control, which calculates the gate opening command based on the deviation between
the actual output power and the selected power reference. The gate’s opening ranges between
[0.05, 0.5] p.u. The setpoint control is only used during generating mode.
2.A governor, which further modifies the gate opening to correct the frequency deviation. The
governor setpoint is added to the gate opening command previously calculated in the setpoint
control. The governor is only used during generating mode, so frequency-droop control
adjustments can be only observed in this operating mode.
3. A turbine model, used for generating mode simulations [6].
4. A voltage regulator and exciter, based on the IEEE type AC1A excitation system model.
5.
A 3-phase, 125 MVA, 18 kV synchronous machine modeled in the D-Q rotor reference frame.
As a PSH, the hydropower plant works as a pump as well. However, the pumping mode doesn’t
use any regulator or control. In pumping mode, the synchronous machine is set to work at nominal
power. The fact that the pump is operating at constant load prevents the FS-PSH to provide frequency
regulation or spinning reserve [7]. Regarding the output power constraints, a FS-PSH plant can
typically operate in the range from 0.4 to 1 p.u. while in generating mode. For pumping mode, the
lower limit is set to -1 p.u. [8]. The FS-PSH block structure is detailed in Fig. 2-1. Note that there is
no control for the pumping mode.
The two use cases that are presented below show the model response to a load event (or load pulse),
which corresponds to a 300 MW load being connected at푡=130seconds, and being disconnected
at푡=220seconds. Both the FS-PSH model and the aforementioned load are located at bus 2 in the
IEEE 39 bus system, as it can be observed in Fig. 2-2. Both generating and pumping modes for the
FS-PSH are analyzed. The system is at steady state before the load connection.
10
(a)FS-PSH diagram in generating mode
(b)FS-PSH diagram in pumping mode
Figure 2-1.FS-PSH diagram
Figure 2-2.FS-PSH location in the IEEE 39 bus system
2.2.Simulation: Load event for the FS-PSH in generating mode
In this simulation, the power reference setpoint for generating mode is푃
푅푒 푓
= 100 MW, which
matches the FS-PSH output power that can be observed in Fig. 2-3. The load event makes the
governor to vary its output to cancel the frequency deviation, and a slight transient can be seen in the
turbine gate opening. Eventually, this modifies the power output of the FS-PSH as well. A zoom in
into the FS-PSH output active power dynamic around the setpoint at the time of the load connection
is provided. However, neither the frequency-droop control nor the change in the FS-PSH output are
as fast as other resources, and that is the reason why the magnitude of the response is relatively
small. It is also noticeable the “opposite" reaction typically associated to hydro models at the start
of the load pulse. This can be seen on the gate opening: the response to a load increase should be
produce more power, which is the opposite of what actually happens in the beginning.
11
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
(e)Gate opening(f)Rotor angular speed
Figure 2-3.FS-PSH response to load event during generating mode
2.3.Simulation: Load event for the FS-PSH in pumping mode
As opposed to the generating mode, the FS-PSH only works at nominal power during pumping
mode, which is equal to absorbing 125 MW as it can be seen in Fig. 2-4. The FS-PSH doesn’t have
any frequency-droop control or set-point control. The transient in the output active power is due to
12
changes in the mechanical speed, and it comes back to the reference shortly after the load pulse as
the generation imbalance is addressed by other resources. In this mode, the gate opening (of the
turbine) variable is not applicable, and therefore it is not shown.
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
(e)Rotor angular speed
Figure 2-4.FS-PSH response to load event during pumping mode
13
3.VARIABLE-SPEED PSH
3.1.Model description
Variable-Speed (VS)-PSH, also known as “Adjustable-Speed” PSH, merges power electronics and a
conventional hydro-power plant to deliver an increased flexibility in the operation with more relaxed
output constraints. Similarly to the FS-PSH design, the VS-PSH output power constraints during
generating mode range from 0.4 to 1 p.u., but VS-PSH pumping operation is increased from a single
setpoint at nominal power to a broader operation from -0.7 to -1 p.u. [8]. This technology has been
largely researched in Type III wind turbines since the 1990s [9,10].
Some of the benefits of VS-PSH are their ability to provide grid stability and frequency regulation
in any operating mode. This is still an emerging technology, and just a few plants of this type have
been commissioned in the world [5]. From a economic point of view, VS-PSH can potentially
increase the revenue compared to FS-PSH [7].
The type of induction machine known as Doubly-Fed Induction Generator (DFIG) is the current
standard in VS-PSH. Generally speaking, a DFIG is a wound rotor induction machine that can be
used at variable speed operation within a certain range of the synchronous speed [11]. This is
achieved thanks to a back-to-back converter located in parallel to the induction generator. One side
of the converter is connected to the grid, while the other side is connected to the rotor. The Rotor
Side Converter (RSC) can inject current with varying frequencies in order to achieve the desired
frequency in the stator [5]. The power is transferred to the grid in two different paths: On the one
hand, the majority of the provided power is the DFIG stator output. On the other hand, some power
is provided by the Grid-Side Converter (GSC). There is a trade-off between the stator output power
and the total provided power, which implies a larger GSC contribution in order to achieve a larger
output power. The direction and magnitude of the rotor power depends on the rotor angular speed,
which eventually depend on the operating mode. A typical slip for a plant of this type is±10%, but
it can go up to±30% [5]. The rotor angular speed휔is optimized to achieve an efficient turbine
operation, and it can be calculated with a linear relationship as detailed in (3.1):
휔(푃
푅푒 푓
, 퐻)=1.25(푃
푅푒 푓
−0.8)−0.25(퐻−0.8)−0.05(3.1)
where푃
푅푒 푓
is the power setpoint and퐻is the head (the difference in height between the hydro
intake and the discharge points) [12].
The VS-PSH model has the following elements:
•A 3-phase, 300 MVA, and 18 kV wound rotor induction generator, implemented as a DFIG.
14
•A GSC, implemented as an averaged model. The power injection/ extraction to the DC link is
modeled as a current source.
•A RSC, following the same design as the GSC.
•A DC link, consisting of a large capacitor, which interfaces both the RSC and GSC.
•A gate optimizer block, which implements the expression in(3.1). The gates have an operating
range between [0.075, 1.2] p.u., and a maximum speed of 0.1 p.u./second.
•A governor, which calculates the gate opening to achieve the requested power reference, and
which provides frequency regulation in both generating and pumping modes.
The VS-PSH high-level diagram can be seen in Fig. 3-1.
Figure 3-1.VS-PSH system diagram
The simulation of the VS-PSH requires a multi-step initialization process in which several key
components are progressively turned on prior to reaching a steady state. The 5-step process is
detailed as follows. The initialization is the same for both generating and pumping modes.
1.GSC initialization (at푡=2seconds). The GSC and associated controls are fully turned
on. The GSC control aims to maintain the DC link voltage at 40 kV, but the voltage is still
artificially kept at that level by a voltage supply source. Therefore, the GSC is not actively
regulating at this time and the output power is zero. The rotor angular speed is stable at 1 p.u.,
as it is controlled by an initialization control that aims to reach a predefined speed reference.
2.The voltage source that bypasses the DC link prior to this step, and keeps the voltage stable at
40 kV, is removed (at푡=3seconds). At this moment, the GSC starts to regulate. The GSC
output power is still zero because the DC link voltage is stable.
15
3.Partial initialization of RSC (at푡=4seconds). The connection of the RSC with the DC link
is established, but the RSC controls are still turned off.
4.Total initialization of RSC (at푡=5seconds). The RSC controls are activated, and the rotor
reference output current is controlled to deliver the required output power. The stator starts to
generate or absorb power, and the rotor angular speed reference is now set at a 1.15 p.u. as the
speed limits are updated. A transient to achieve such rotor speed begins.
5.The VS-PSH governor is turned on (at푡=10seconds). The angular speed control is replaced
by the governor, which takes into account the physical model of the hydro plant. The power
electronics devices are fully engaged, and some power is either generated or drawn from the
grid by the GSC. The steady state is finally achieved around푡=30seconds.
The dynamics of developed model are tested on a simplified three-bus system, which is composed
of the VS-PSH, a 50 MW load and an infinite voltage source, as shown in Fig. 3-2. To produce the
load event, which is a 10 second load pulse, an extra load of 50 MW is switched on. The load event
occurs once the system has been initialized, at푡=35seconds, and it lasts until푡=45seconds. As a
disclaimer, this model is extremely expensive both in computing power and memory requirements.
Just a fraction of all the variables can be saved for later analysis, and the total simulation time is
limited. The test system has to be simplified for the same reason. In order to achieve stability in
more complex systems, additional modifications of the controls or the interface may be required.
Figure 3-2.VS-PSH location in the simplified system
Two use cases are presented below: the load events during generating and pumping modes. The
recorded variables are the VS-PSH outputs (active and reactive power, voltage and current), as well
as the DFIG stator and GSC active and reactive power in order to visualize the operation of the plant.
However, in this work, the voltage source unfortunately hides most of the dynamics.
3.2.Simulation: Load event for the VS-PSH during generating mode
During generating mode, the VS-PSH outputs a total of 235 MW. Although푃
푅푒 푓
=1, the optimizer
in(3.1)determines a lower power setpoint (around 0.7 p.u.). Most of the active power comes from
16
the stator, approximately 210 MW, and the remaining 25 MW comes from the GSC. The rotor speed
is around 1.14 p.u., and the output reactive power is oscillating around 0 Mvar. The GSC effectively
maintains the DC link voltage around 40 kV. The transients during the load event are small because
of the low system inertia (the infinite voltage source handles most of the perturbation), but it can be
appreciated how there is an effect on the VS-PSH behavior.
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
(e)Gate opening(f)Rotor angular speed
Figure 3-3.VS-PSH response to load event during generating mode
17
(a)Output active power(b)Output reactive power
(c)Stator active power(d)Stator reactive power
(e)GSC active power(f)GSC reactive power
Figure 3-4.VS-PSH response to load event during generating mode (Cont.)
3.3.Simulation: Load event for the VS-PSH during pumping mode
The dynamics are similar to the generating mode. This time, the VS-PSH is absorbing power. In
particular, the GSC absorbs around 35 MW, while the DFIG stator absorbs between 205 to 210 MW.
This gives a total of 240 MW absorbed by the VS-PSH as a whole.
18
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
(e)DC link voltage(f)Rotor angular speed
Figure 3-5.VS-PSH response to load event during pumping mode
19
(a)Output active power(b)Output reactive power
(c)Stator active power(d)Stator reactive power
(e)GSC active power(f)GSC reactive power
Figure 3-6.VS-PSH response to load event during pumping mode (Cont.)
20
4.TERNARY-PSH
4.1.Model description
T-PSH plants are equipped with separated turbine and pump units. Both elements have rotating
shafts aligned on the same axis, which is connected by a clutch. Depending on the operating mode,
the turbine, the pump and their respective valves may be active or not. The schematics for each
mode can be observed in Figure 4-1. During generating mode, only the clutch C1 is engaged to
transfer mechanical power to the generator. The turbine valve is open, while the pump valve is
closed. On the contrary, only clutch C2 is engaged during pumping mode. The pump valve is open
while the turbine valve is closed. Finally, during Hydraulic Short Circuit (HSC) mode both clutches
C1 and C2 are engaged, both turbine and pump valves are open, and the shared axis spins at the
same angular speed [13].
As the axis always spins in the same direction, the change from one mode to another takes just a few
seconds. It mainly depends on the action of the clutches and the valves. In [14], the required time
for switching between generating and pumping modes in the T-PSH is compared to those in the
FS and VS-PSH plants. The results show that T-PSH is by far the fastest technology. The mode
switching in the T-PSH model is analyzed later as a separate experiment.
However, a standard T-PSH unit would only provide frequency regulation in generating mode (it
essentially resembles a FS-PSH) [1]. In order to provide frequency regulation while pumping, there
is a third operating mode, HSC mode, in which both the turbine and pump work in a closed loop.
The pump absorbs more energy than what the turbine can produce so, overall, the T-PSH has a
certain pumping behavior during HSC mode [6].
Another advantage of the T-PSH is that this technology also offers an increased flexibility in the
power setpoint in both generating and pumping modes. Any power reference from 0.3 p.u. to 1 p.u.
(in generating mode), -1 p.u. (pumping mode) or from -0.6 p.u. to 0 p.u. (in HSC mode) can be
achieved [8].
The elements in the T-PSH model, which can be observed in Fig. 4-2, are:
1.A power distribution block, which calculates the turbine and pump power setpoints depending
on the operating mode. These setpoints vary over time in the “mode switching” experiment.
The flags that manage the switching between transfer functions are calculated here as well.
2.A governor, which calculates the turbine and pump gate opening. In pumping case, this is
just a simple arithmetic operation. During a generating case, the turbine gate reference is
represented by a transfer function. In addition, this gate reference is sensitive to frequency
variations during the generating mode.
21
(a)Generating mode(b)HSC mode
(c)Pumping mode
Figure 4-1.T-PSH schematic during generating, pumping and HSC operating modes
3.A pump and turbine gate models, which have an operating range between [0, 1] p.u., and a
maximum gate opening/closing speed of 0.05 p.u./second.
4.
Identical turbine and pump models [14]. There is a flag that determines if the penstock is
shared or not in the head to flow conversion matrix. The combined output of the turbine and
the pump is the generator’s mechanical input.
5. A voltage regulator and exciter, based on the IEEE type AC1A excitation system model.
6.A 3-phase, 320 MVA, 18 kV synchronous machine modeled in the D-Q rotor reference frame.
22
Figure 4-2.T-PSH system diagram
It is important to note that the mode switching experiment in a state-space based simulator, such as
Simulink, requires considering all the different modes at the same time. For this reason, several trans-
fer functions are defined in the model, and each one of them represents the corresponding operating
mode. When a mode switch occurs, the new mode’s transfer function must be reinitialized.
4.2.Simulation: Steady-state
For the T-PSH, the analysis of the steady-state becomes relevant to understand the plant’s behavior
in different modes. In Table 4-1, the distribution factor퐾
퐷
, the mechanical power푃
푀푒푐ℎ
for
both turbine and pump, and the overall T-PSH output power푃
푂푢푡
are shown for each of the three
considered operating modes. All quantities are in p.u., and퐾
퐷
is in the range of [0, 1].
Table 4-1.Steady-state T-PSH behavior results
Mode퐾
퐷
Turbine퐾
퐷
Pump푃
푀푒푐ℎ
Turbine푃
푀푒푐ℎ
Pump푃
푂푢푡
Generating100.800.8
Pumping010-0.9-0.9
HSC0.40.60.34-0.54-0.2
During HSC mode, the system works in a closed-loop where the turbine and pump are both working.
The system is inherently lossy and, therefore, the amount of power absorbed by the pump from the
grid is larger than the power generated by the turbine. This explains the slight pumping behavior of
the T-PSH during HSC mode.
4.3.Simulation: Load Event
The dynamics of developed model are tested on the custom IEEE 39 bus system. To produce the
power imbalance event, a load of 300 MW is connected to the system. The load is connected in
the same bus as the T-PSH plant. The set-up for this experiment is identical as the one depicted in
23
Fig. 2-2. The load event occurs once the system has been fully initialized, at푡=130seconds, and it
lasts until푡=220seconds.
As can be seen in Figs. 4-3, 4-4, 4-7 and 4-8, the T-PSH has frequency regulation only during
the generating and the HSC modes. The turbine gate value increases due to the governor action,
which increases the amount of mechanical power provided by the turbine, and eventually leads to
an increase of the overall active power provided by the T-PSH. In the generating mode, the overall
reactive power output remains fairly constant after an initial transient, although for the HSC mode it
does change. Both the pump gate value and the pump mechanical power remain constant as there
is no frequency-droop control in that element. Looking at the T-PSH current output it is possible
to see that it increases due to the load event during the generating mode, which is the expected
behavior. However, during the HSC mode, the current magnitude decreases instead. The reason for
this behavior is that the T-PSH is working as a pump, but when the power increase is needed, its
behavior starts to be closer to a turbine. Therefore, the amount of absorbed current decreases.
For the case of the pumping mode, the T-PSH doesn’t provide any frequency regulation capabilities.
The pump, which is the main element that is engaged in this period, doesn’t have a frequency droop
control. For the turbine, it is disabled in this operating mode. As it is shown in Figs. 4-5 and 4-6,
both pump and turbine gate values are constant.
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
Figure 4-3.T-PSH response to load event during generating mode
24
(a)Pump mechanical power(b)Pump gate value
(c)Turbine mechanical power(d)Turbine gate value
Figure 4-4.T-PSH response to load event during generating mode (Cont.)
25
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
Figure 4-5.T-PSH response to load event during pumping mode
26
(a)Pump mechanical power(b)Pump gate value
(c)Turbine mechanical power(d)Turbine gate value
Figure 4-6.T-PSH response to load event during pumping mode (Cont.)
27
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
Figure 4-7.T-PSH response to load event during HSC mode
28
(a)Pump mechanical power(b)Pump gate value
(c)Turbine mechanical power(d)Turbine gate value
Figure 4-8.T-PSH response to load event during HSC mode (Cont.)
29
4.4.Simulation: Mode switching
The “mode switching” experiment shows the T-PSH behavior during three different events:
1. Generating mode to Pumping mode ( at푡=10seconds).
2. Pumping mode to HSC mode ( at푡=35seconds).
3. HSC mode to Generating mode ( at푡=150seconds).
Results are shown in Figs. 4-9 and 4-10. Regarding changes in the pump, they always occur at
maximum speed. The pump governor changes its output immediately when a mode switch occurs.
However, the gate opening is adjusted according to its speed limit. For the turbine, its governor is
not as fast. According to [14], not all mode switchings occur at the same speed. The switching
between generating to pumping mode occurs at maximum speed, as it just depends on the action
of the valve. The situation is similar to change between pumping to HSC. However, the change
from HSC to generating is remarkably slower. In Simulink, this is modeled in the following way:
for fast transients (generating to pumping, and pumping to HSC), the turbine governor is just the
static gain of the transfer function. Then, the setpoint change is immediate and the overall dynamics
just depend on the gate velocity. Afterwards, once the switching is over, the steady-state transfer
function kicks in to model the dynamic behavior of the plant. The transfer function is reinitialized
to start directly on steady-state. On the other hand, for slow transients (such as HSC to generating),
the entire transfer function is employed. For this experiment,푃
푅푒 푓
=0.5is employed. The HSC
operating mode can be clearly observed as an operating mode between generating and pumping, but
more leaned towards the last one.
As for the switching times, the model is well aligned with [14]. The first switch (Generating mode
to Pumping mode) is performed in about 10 seconds. The second switch (Pumping mode to HSC
mode) takes around 30 seconds. Finally, the third switch is approximately in the new setpoint in
around 100 seconds, although the turbine is still slowly moving towards the new steady state.
30
(a)Output active power(b)Output reactive power
(c)Output voltage(d)Output current
Figure 4-9.T-PSH response to mode switching
31
(a)Pump mechanical power(b)Pump gate value
(c)Turbine mechanical power(d)Turbine gate value
Figure 4-10.T-PSH response to mode switching (Cont.)
32
5.CONCLUSIONS
This report introduces three Pumped Storage Hydropower technologies models: Fixed-Speed (FS),
Variable-Speed (VS) and Ternary (T). The models are developed in Simulink, and they are publicly
available on this repository
1
. Please, cite this report
2
if the models are employed.
An introductory description and the dynamic analysis for a load event of these models are presented.
The output of each model matches their expected behavior. The FS-PSH achieves frequency
regulation during generating mode only, although the effect of the frequency-droop control on the
overall response is light. The VS-PSH, on the other hand, achieves frequency regulation during both
generating and pumping modes thanks to the rotor speed regulation with power electronics. The
operating range is increased in relation to FS-PSH in both generating and pumping modes. Finally,
the T-PSH also achieves frequency regulation during generating and Hydraulic Short Circuit modes
thanks to its design and the action of the clutches. For this technology, there is a total flexibility
in generating and pumping operating modes. In addition, for the T-PSH, the steady-state, and the
behavior during mode switching are also analyzed. The model correctly includes the fast switching
speed among some of the operating modes.
1
See:https://github.com/sandialabs/Simulink_PumpedStorageHydropower.
2
M. Jimenez-Aparicio et al., “Simulink Modeling and Dynamic Study of Fixed-Speed, Variable-Speed, and Ternary
Pumped Storage Hydropower,” Sandia Technical Report, September 2022.
33
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[14]Z. Dong,Dynamic Model Development and System Study of Ternary Pumped Storage
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35
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