Conference PaperPDF Available

On Modelling and Sizing a Supercapacitor Energy Storage For Power System Frequency Control

Authors:

Abstract

In this paper, we explore the issues of sizing, modelling and controlling a supercapacitor ESS (SESS) for power system applications. We give an overview of different supercapacitor models used in literature. We present a simple method for sizing a SESS taking into account a realistic supercapacitor model, calculate the energy yield and voltage profile, and give insight into supercapacitor characteristics that may cause issues if not modelled adequately.
Sizing a supercapacitor energy storage for power
system applications
Matej Krpan
Department of Energy and Power Systems
Faculty of Electrical Engineering and Computing
University of Zagreb
Zagreb, Croatia
Email: matej.krpan@fer.hr
Igor Kuzle
Department of Energy and Power Systems
Faculty of Electrical Engineering and Computing
University of Zagreb
Zagreb, Croatia
Email: igor.kuzle@fer.hr
Abstract—In this paper, we explore the issues of sizing,
modelling and controlling a supercapacitor ESS (SESS) for power
system applications. We give an overview of different superca-
pacitor models used in literature. We present a simple method
for sizing a SESS taking into account a realistic supercapacitor
model, calculate the energy yield and voltage profile, and give
insight into supercapacitor characteristics that may cause issues
if not modelled adequately.
Index Terms—power system dynamics, power system simu-
lation, power system modelling, supercapacitor, ultracapacitor,
frequency control
I. INTRODUCTION
The increasing penetration of variable renewable energy
sources (RES) connected to the grid through an inverter
interface brings issues of frequency stability due to the de-
coupling effect of inverters [1]. Thus, a lot of research effort
has been given in the recent years to improve the frequency
stability of power systems in the presence of high share of
inverter-interfaced generation (IIG): participation of variable-
speed wind turbines and solar PV plants in frequency control
[2]–[5], using energy storage devices for frequency control
services [6], [7], generally controlling voltage-source converter
(VSC) based devices in virtual synchronous/induction gener-
ator schemes [8] and demand response.
Supercapacitors (SC), ultracapacitors (UC) or electric
double-layer capacitors (EDLC) are a type of electrostatic
energy storage device in which the energy is stored in the
electric field between the electrodes. They are characterized by
high power density and low energy density, i.e. they are good
for short term power support. For grid applications, they can be
used as a standalone system or in combination with batteries
since their characteristics are complementary. Unlike batter-
ies and flywheels, supercapacitors can withstand significantly
more charging/discharging cycles and have smaller operation
The work of the authors is a part of the H2020 project CROSSBOW
CROSS BOrder management of variable renewable energies and storage units
enabling a transnational Wholesale market (Grant No. 773430). This document
has been produced with the financial assistance of the European Union. The
contents of this document are the sole responsibility of authors and can under
no circumstances be regarded as reflecting the position of the European Union.
This work has been supported in part by the Croatian Science Foundation
under the project WINDLIPS - WIND energy integration in Low Inertia Power
System (grant No. PAR-02-2017-03).
Csc
+
uC
+
usc(t)
(a)
Rs
+
uRs
isc
Csc
+
uC
+
usc(t)
(b)
Rs
+
uRs
isc
Csc(uC)
+
uC
C1(uC)
+
uC1
R1(uC)
Cn(uC)
+
uC5
Rn(uC)
+
usc(t)
(c)
Fig. 1. Common supercapacitor models: (a) ideal model; (b) nonideal model;
(c) realistic model.
& maintenance costs since there are no moving parts and
no electrochemical reactions [9]. There are many applications
of supercapacitor technology, e.g. in electric vehicles [10],
for power smoothing intermittent RES [11], for improving
fault ride through [12] or for power system frequency control
applications [6], [13]–[15].
These papers usually model the SC/UC too ideally, neglect-
ing the voltage-dependent characteristics of a SC cell. This
paper aims to discuss various characteristics of a superca-
pacitor and the implications of those characteristics, compare
different models and give insight into sizing and controlling a
SC/UC/EDLC ESS in the context of power system applications
(oriented towards frequency control).
II. IMPLICATIONS OF SUPERCAPACITOR MODELLING
In the power system applications literature, the SC is
modelled either as an ideal capacitor or a constant capacitance
behind an equivalent series resistance (Fig. 1(a) and Fig. 1(b),
respectively). However, a realistic model of a SC obtained by
experimental work [16]–[18] is shown in Fig. 1(c).
The ideal model neglects the equivalent series resistance
(ESR) which will cause a voltage drop across it during charg-
ing and discharging process, and therefore the error in voltage
measurement as well as energy dissipation. Although usually
small (between 0.1 mand 100 mbased on datasheets of
commercial cells) it can have an impact on the bank efficiency
especially when connecting cells in series and parallel to form
a bigger supercapacitor. Note that the voltage one can measure
is the total voltage including ESR, not the voltage across the
actual capacitive element so the state-of-energy (SoE) must
be measured in open-circuit, i.e. when the capacitor is neither
charging nor discharging.
Furthermore, what both ideal and nonideal models neglect
is the fact that the capacitance Csc varies non-linearly with
the SC voltage [16]–[18] for DC applications (the SC is not
subject to periodic AC). However, for practical purposes the
relationship is linear enough that it can be approximated by
a linear relationship. This means that the stored energy also
varies with the voltage and this might have to be considered
when sizing a SC bank. Furthermore, this means that the
voltage dynamics will also be different as the SC is charging
or discharging.
The realistic model shown in Fig. 1(c) has been ex-
perimentally identified using procedures such as impedance
spectroscopy and charge/discharge tests and validated against
various real supercapacitor cells in [16]–[18]. This model
only shows the first branch which describes the fast dynamic
behaviour in the time scale of several tens of seconds. Parallel
RC branches and leakage current branch are neglected because
those phenomena are much slower (lasting from several min-
utes to several weeks). Although these phenomena are impor-
tant when investigating the performance of the supercapacitor
over tens of days, they are not important in the context of
relatively fast charge/discharge for fast frequency control
The important characteristics of the realistic SC model can
be summarized as follows:
Basically all of the SC capacitance comes from Csc;
Series combination of parallel branches Rs
1Cs
1Rs
nCs
n
is actually an infinite series of these parallel groups.
However, it has been shown in [18] that five groups
are sufficient to obtain an accurate model. These parallel
groups model the porosity of the electrodes;
Capacitance Csc and elements Rs
k,Cs
kare dependent on
uC(t). This dependence is nonlinear hence the model
has the time-varying parameters. That is why an ideal
capacitor representation used in many papers in the past
may not always be appropriate.
Electrical parameters of the realistic model are calculated
according to (1)–(4) [18].
Csc(uC) = C0+kvuC(t)(1)
Cs
k=1
2Csc, k {1...n}(2)
Rs
k=2τ(uC)
k2π2Csc
(3)
τ(uC)3Csc(Rdc Rs),(4)
C0is the ultracapacitor capacitance at 0 V and kvis a con-
stant expressed in F/V; τ(uC)is a time constant approximated
by (4); Rdc is the resistance experimentally obtained at very
low frequencies; Rsis the equivalent series resistance (ESR)
determined at very high frequency.
Voltage and current dynamics of ideal and nonideal model
are described by (5), while the energy stored in steady-state
(uC=Usc) is calculated by (6). Then, for constant discharging
power (replacing isc from (5) with P/uCand solving for
uC), voltage decay time profile (7) is obtained [6], where tis
discharging time and uC0is the initial SC voltage.
isc =Csc
duC
dt (5)
Eid =1
2CscU2
sc (6)
uC(t) = ru2
C02P t
Csc
(7)
However, for a realistic SC model, (5) is equal to (8) [18].
Then, the steady-state stored energy can be calculated by
integrating uCisc to arrive to (9). Voltage decay profile is
then given in the implicit form (10).
isc = (C0+kvuC)duC
dt (8)
Ereal =1
2C0U2
sc +1
3kvU3
sc (9)
2kvu3
C(t)+3C0u2
C(t)=2kvu3
C0+ 3C0u2
C06P t (10)
According to literature [17], [18], the ratio of (minimum)
capacitance at 0 V C0and (maximum) capacitance at rated
voltage Ur,C0
C0+kvUrcan range between 50% and 80%,
although an example of a datasheet of modern cells [19] puts
it around 80%. Based on (6) and (9), the absolute and relative
errors in stored energy can be expressed by (11) and (12),
respectively.
E=Eid Ereal =U2
sc
6[3(Csc C0)2kvUsc](11)
eE=E
Ereal
×100% (12)
To calculate error in stored energy, three different volt-
age dependent characteristics of a realistic SC were used,
differing in the magnitude of voltage dependent capacitance
(C0/Cmax = 0.6—black curves, C0/Cmax = 0.8—blue
curves, C0/Cmax = 0.95—red curves)—see Table I. For
each SC characteristic, three ideal/nonideal models were used
differing in the capacitance value: minimum (Cmin =C0),
average (Cavg =Cmin+Cmax
2) and maximum (Cmax =
C0+kvUr). The SC module consists of 370 cells in series
with rated voltage of 2.7 V each. Note that the equivalent
capacitance of Nsidentical cells in series can be calculated
by (13).
Ceqv =C0
Ns
+kv
N2
s
uC(t)(13)
0 200 400 600 800 1000
Voltage [V]
-40
-20
0
20
40
60
80
Relative error in energy [%]
Fig. 2. Relative error in stored energy for different models
TABLE I
SUP ERC APACI TO R MOD EL S WIT H DIFF ER ENT V OLTAGE D EPE NDE NT
CHARACTERISTICS USED FOR ENERGY ERROR CALCULATIONS
Model C0[F] kv[F/V] Cmax [F] Ur[V]
C0
Cmax
= 0.62160 533.3 3600 2.7
C0
Cmax
= 0.83000 222.2 3600 2.7
C0
Cmax
= 0.95 3420 66.7 3600 2.7
The relative error in stored energy when ideal/nonideal
model is used relative to the realistic model is shown in Fig.
2. Firstly, it can be observed that the smaller the voltage-
dependent capacitance the better the ideal/nonideal models
represent the SC in terms of stored energy.
For 40% voltage-dependent capacitance, the error ranges
between: 15% and 60% when maximum capacitance is used,
8% and 30% when average capacitance is used and 30%
and 2% when minimum capacitance is used.
For 20% voltage-dependent capacitance, the error ranges
between: 6% and 20% when maximum capacitance is used,
3% and 10% when average capacitance is used and 12%
and 0% when minimum capacitance is used.
For 5% voltage-dependent capacitance, the errors for all
cases are inside ±5%.
Hence, one should be careful when modelling a SC with a
constant capacitance models because the actual stored energy
may vary significantly depending on the actual cell in question,
i.e. how much the capacitance is truly constant. The issues of
sizing are dealt with in the next section.
Voltage discharge profiles of a realistic, nonideal and ideal
models for different discharge powers are shown in Fig. 3(a).
This figure shows the 20% voltage dependent capacitance
model with ideal/nonideal models with average capacitance
representation. The SCs are discharged to 10% rated voltage. It
can be observed that the nonideal model accurately represents
the realistic model in this case, while ideal model has a slightly
longer constant power discharge time (between 2% and 15%
depending on the discharge power). However, these differ-
ences may be much more significant depending on the actual
TABLE II
MINIMUM DISCHARGE EFFICIENCY FOR DIFFERENT MODELS
Model Discharge power [MW]
0.1 1 2
Realistic 87% 45% 33%
Nonideal 90% 53% 39%
Ideal 100% 100% 100%
cell characteristics, initial voltage and discharge power. Fig.
3(b) illustrates this by showing the voltage discharge profiles
(constant 0.5 MW discharge power) for a 40% variable ca-
pacitance for different ideal/nonideal representations differing
in capacitance value. For the nonideal model, discharge time
difference relative to the realistic model varies between 30%
(minimum capacitance) and 17% (maximum capacitance). For
the ideal model, this difference is between 27% (minimum
capacitance) and 20% (maximum capacitance). In this case,
the average capacitance was the again the most precise in
terms of voltage dynamics (7% for nonideal model, 3%
for ideal model).
Notice that the nonideal and realistic models will have the
voltage bounce back effect due to the ESR: the measured
voltage is smaller than the actual capacitor voltage because
of the voltage drop on the ESR during discharging.
The issue with constant power discharging is that the current
increases as voltage decreases which will increase losses on
the ESR. ESR increases when the cells are connected in series,
thus when designing a SC bank for high-voltage high-power
applications, a certain number of strings must be connected in
parallel for two reasons:
1) to decrease the ESR;
2) to reduce the current that flows through each string.
Those two reasons will reduce the power losses and increase
efficiency. Efficiency (14) curves are shown in Fig. 3(c).
The higher the depth of discharge, the bigger the losses due
to higher current demand. Moreover, for the same depth of
discharge, higher discharge power results in bigger losses also
due to higher current demand for the same voltage. Minimum
achieved efficiencies are shown in Table II. They correspond
to the maximum depth-of-discharge which is in this case 90%.
Realistic and nonideal model have the same ESR, but the
difference arises from the series combination of parallel RC
groups (Fig. 1(c)). The ideal model has 100% efficiency in all
cases because it has no losses as it is an ideal capacitor.
(t) = uC(t)
usc(t)(14)
III. SUP ER CA PACITOR B AN K SI ZI NG
In this section, it will be shown how to size a SC bank
for constant power operation for frequency control services
by taking into account realistic characteristics of a SC cell.
The procedure is based on methodology in [20].
0 2 4 6 8 10
Time [s]
0
200
400
600
800
1000
Voltage [V]
Realistic
Nonideal
Ideal
Realistic
Nonideal
Ideal
Realistic
Nonideal
Ideal
(a)
0 2 4 6 8 10 12
Time [s]
0
200
400
600
800
1000
Voltage [V]
(b)
102103104105
Discharge current [A]
30
40
50
60
70
80
90
100
Efficiency [%]
(c)
Fig. 3. Impact of modelling on supercapacitor performance: (a) voltage profile
for various discharge powers; (b) voltage profile for various ideal/nonideal
model capacitance values (solid black line is the realistic model); (c) discharge
efficiency for various discharge powers
Although the complete voltage range of a SC (from 0V
to rated) can be exploited, for constant power operation this
is not possible since the current would tend towards infinity.
Considering an ideal capacitor (6), 75% of energy is used
between rated voltage and half the rated voltage (15).
E0.5
Emax
=
1
2CUmax
22
1
2CU 2
max
=1
4(15)
For a realistic super capacitor, eq. (15) changes to (16).
E0.5
Emax
=1
4
1
2C0+1
2
kv
3Umax
1
2C0+kv
3Umax
<1
4(16)
This means that a realistic SC will use slightly more energy
between some arbitrary voltage value and rated voltage than
the equivalent ideal model. Therefore, it is not necessary
to have a deep depth of discharge which increases current
and losses. Approximately 84% of energy is used between
40%Umax and Umax, and 91% between 30% Umax and Umax .
When sizing a storage for frequency support services, the
design parameters are rated power Pand duration of rated
power t. Consider a 1 MW/30 s SESS. DC voltage range
must be appropriately chosen to deliver the required power.
The DC-DC converter must then be able to operate in that
voltage range and be able to withstand the maximum current.
For this power, an appropriate voltage range is 5001000 Vdc.
The first approximation of sizing is done using a nonideal rep-
resentation. First, minimum, maximum and average currents
are calculated:
Imin =P
Vmax
= 1000 A (17)
Imax =P
Vmin
= 2000 A (18)
Iavg =Imax +Imin
2= 1500 A (19)
Since the ESR is unknown, in first approximation it can
be estimated using a RC time constant τRC =RC 1s ac-
cording to commercial datasheets. Linearizing circuit equation
from Fig. 1(b), total voltage change is equal to:
usc = uRs+ uC
=Iavg Rs+Iavg
t
C(20)
=Iavg
C(τRC + t)
Solving for Cand substituting usc =Vmax Vmin:
C=Iavg
Vmax Vmin
(τRC + t)(21)
=1500
1000 500(1 + 30) = 93 F=Ceqv
Rated cell voltage of a SC is between 2.5 and 3 V on
average. Considering a 2.7 V cell, to obtain 1000 V DC, it
will require Ns= 1000/2.7370 cells in series. If we have
only one string (Np= 1), the required cell capacitance would
be Ccell =Ceqv Ns= 34410 F. Obviously, such a cell doesn’t
exist but this capacitance can be obtained by connecting cells
in parallel. For Np= 10, average cell capacitance is:
Ccell Ceqv
Ns
Np
= 93370
10 = 3441 F (22)
ESR of a such a cell is around 0.29 m[19] which means
the equivalent ESR is:
Reqv Rs
Ns
Np
= 0.29 ·103370
10 10.7m(23)
Since there are effectively 10 strings in parallel, each string
will carry only a tenth of power, i.e. a tenth of total current
therefore the losses on ESR are reduced by a factor of 100.
Considering a 20% voltage-dependent capacitance, kvand C0
can be approximated from (24) and (25) and they are equal to
283.2 F/V and 3058.7 F, respectively.
Ccell =Cavg =C0+kv
Umax
2(24)
C0
C0+kvUmax
= 0.8(25)
0 10 20 30 40
Time [s]
0
0.2
0.4
0.6
0.8
1
Power [MW]
(a)
0 10 20 30 40
Time [s]
400
500
600
700
800
900
1000
Voltage [V]
(b)
0 10 20 30 40
Time [s]
94
95
96
97
98
99
100
101
Efficiency [%]
(c)
0 10 20 30 40
Time [s]
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
ESR losses [p.u. of rated power]
(d)
Fig. 4. Performance test of SESS design: (a) power; (b) voltage; (c) discharge
efficiency; (d) ESR losses.
Now this SC bank can be simulated with a realistic model
to test the performance. Results are shown in Fig. 4. This SC
bank can sustain the rated power output for 35 seconds
which is a 16% margin of error compared to requested 30 s
(Fig. 4(a)). This power is discharged between the 0.5Umax
and Umax which can be measured at the SC bank terminals
(Fig. 4(b)). Discharging efficiency is between 94% and 98.5%
(Fig. 4(c)), while ESR losses are between 0.01 p.u. and 0.045
p.u. (Fig. 4(d)) which is satisfactory.
The presented design procedure can be applied iteratively
until satisfactory performance is achieved or if a larger margin
for error is needed due to variable capacitance (e.g. 30%
variable capacitance). The benefit of the presented method is
that it is quite straightforward to do, even by hand, and it is
based on a few simple assumptions and data that is easy to
obtain from datasheets. Simulation on a realistic model then
serves as a performance test for first approximation after which
the process can be repeated iteratively until desired accuracy
is achieved.
IV. CONCLUSION
In this paper, we have discussed the supercapacitor char-
acteristics and how different modelling approaches have an
impact on predicted SC performance:
variable capacitance of the SC cell can have significant
impact on the amount of energy stored and therefore on
the voltage dynamics during charging/discharging;
SC cells are very low voltage devices which need to be
connected in series for high-voltage application. How-
ever, this increases losses so a balance has to be achieved
with parallel strings to reduce losses;
constant power operation can be achieved only for a
limited voltage range due to current limitations—around
75% of energy can be utilized between half the rated
voltage and rated voltage.
Finally, a simple iterative procedure for sizing a SESS has been
presented which uses model simplifications for approximation
and realistic model simulation for testing the performance.
REFERENCES
[1] F. Milano, F. D¨
orfler et al., “Foundations and challenges of low-inertia
systems (invited paper), in 2018 Power Systems Computation Confer-
ence (PSCC), June 2018, pp. 1–25, doi: 10.23919/PSCC.2018.8450880.
[2] M. Krpan and I. Kuzle, “Towards the new low-order system frequency
response model of power systems with high penetration of variable-
speed wind turbine generators,” in 2018 IEEE Power Energy Society
General Meeting (PESGM), Aug 2018, pp. 1–5.
[3] M. Dreidy, H. Mokhlis, and S. Mekhilef, “Inertia response and frequency
control techniques for renewable energy sources: A review, Renewable
and Sustainable Energy Reviews, vol. 69, pp. 144 155, 2017.
[4] M. Krpan and I. Kuzle, “Introducing low-order system frequency re-
sponse modelling of a future power system with high penetration of
wind power plants with frequency support capabilities, IET Renewable
Power Generation, vol. 12, pp. 1453–1461, October 2018.
[5] M. Krpan and I. Kuzle, “Dynamic characteristics of virtual inertial
response provision by dfig-based wind turbines,” Electr. Power Syst.
Res., vol. 178, p. 106005, 2020.
[6] J. Kim, V. Gevorgian et al., “Supercapacitor to provide ancillary services
with control coordination,” IEEE Trans. Ind. Appl., vol. 55, no. 5, pp.
5119–5127, Sep. 2019.
[7] D. Peralta, C. Ca ˜
nizares, and K. Bhattacharya, “Practical modeling of
flywheel energy storage for primary frequency control in power grids,
in 2018 IEEE Power Energy Society General Meeting (PESGM), Aug
2018, pp. 1–5.
[8] U. Markovic, P. Aristidou, and G. Hug, “Virtual induction machine
strategy for converters in power systems with low rotational inertia,”
August 2017.
[9] X. Luo, J. Wang et al., “Overview of current development in electrical
energy storage technologies and the application potential in power
system operation,” Applied Energy, vol. 137, pp. 511–536, jan 2015.
[10] A. Tahri, H. E. Fadil et al., “Management of fuel cell power and
supercapacitor state-of-charge for electric vehicles, Electr. Power Syst.
Res., vol. 160, pp. 89 98, 2018.
[11] T. Zhou and W. Sun, “Optimization of battery–supercapacitor hybrid
energy storage station in wind/solar generation system,” IEEE Transac-
tions on Sustainable Energy, vol. 5, no. 2, pp. 408–415, April 2014.
[12] S. I. Gkavanoudis and C. S. Demoulias, “A combined fault ride-through
and power smoothing control method for full-converter wind turbines
employing supercapacitor energy storage system, Electr. Power Syst.
Res., vol. 106, pp. 62 72, 2014.
[13] L. Sigrist, I. Egido et al., “Sizing and controller setting of ultracapacitors
for frequency stability enhancement of small isolated power systems,
IEEE Trans. Power Syst., vol. 30, no. 4, pp. 2130–2138, July 2015.
[14] J. Cao, W. Du et al., “Optimal sizing and control strategies for hybrid
storage system as limited by grid frequency deviations, IEEE Trans.
Power Syst., vol. 33, no. 5, pp. 5486–5495, Sep. 2018.
[15] M. Krpan and I. Kuzle, “Coordinated control of an ultracapacitor
bank and a variable-speed wind turbine generator for inertial response
provision during low and above rated wind speeds, in 2019 IEEE
Sustainable Power and Energy Conference (iSPEC), Nov 2019, pp.
1693–1698.
[16] S. Buller, E. Karden et al., “Modeling the dynamic behavior of superca-
pacitors using impedance spectroscopy, IEEE Trans. Ind. Appl., vol. 38,
no. 6, pp. 1622–1626, Nov 2002.
[17] R. Faranda, M. Gallina, and D. T. Son, A new simplified model of
double-layer capacitors,” in 2007 International Conference on Clean
Electrical Power, May 2007, pp. 706–710.
[18] V. Musolino, L. Piegari, and E. Tironi, “New full-frequency-range super-
capacitor model with easy identification procedure,” IEEE Transactions
on Industrial Electronics, vol. 60, no. 1, pp. 112–120, Jan 2013.
[19] Maxwell Technologies, “2.7v 650-3000f ultracapacitor cells, 2019,
datasheet.
[20] Maxwell Technologies, “Maxwell technologies R
BOOSTCAP R
ultracapacitor
cell sizing,” 2009, applications note.
... The authors of [23] address different aspects of SC models and propose small-and large-signal models for simulation and control, based on a first-order RC model. The same model is used in [24] to discuss SC module selection and design. Krpan et al.,in [25], compare the stored energy and discharge profiles of ideal and realistic SC models. ...
Article
Supercapacitors are a promising technology for addressing the challenges faced by power systems with an increasing share of inverter-based resources. Due to their unique characteristics, supercapacitors can provide ancillary services to the grid. Understanding the behavior of supercapacitors under various conditions is crucial. Therefore, modeling and analysis are of significant interest in the research of supercapacitors for a wide range of applications. This article provides a brief overview of supercapacitor technology and presents a systematic review of five equivalent circuit models of supercapacitors.
Article
Full-text available
Power converter technology partially or fully electrically decouples the wind energy source from the grid which results in the decrease of system inertia. However, when those units participate in virtual inertial response their electromechanical dynamics become coupled to the grid electromechanical modes. To date, there were no comprehensive studies on how do different elements and parameters of a wind energy conversion system (WECS) impact its virtual inertial response provision. This is important from the standpoint of understanding the expected wind farm response during frequency containment process as well as from the standpoint of developing better inertial response controllers. In this paper we have investigated how do operating point, line-side and machine-side converter, phase-locked loop and pitch angle control impact the inertial response of the total power controlled type III WECS (DFIG) which is one of the most common wind turbine topologies used today. We show that the operating point, pitch angle control and outer loop of the machine-side converter have a visible impact on strength of the inertial response, while other elements do not and some can even be neglected in inertial response studies.
Conference Paper
Full-text available
In the recent years, frequency support from converter-connected wind power generation has been a hot topic in the field of power system dynamics and control. At the same time, the share of wind generation in the power systems worldwide has significantly risen. Therefore, it is necessary to discuss a new approach to low-order system frequency response (SFR) modelling of power systems. In this paper, a new low-order SFR model of a power system with high penetration of wind power generation is proposed by taking into account the different operating regimes of variable-speed wind turbine generators (VSWTGs). The results are compared to the nonlinear transient stability dynamic models to show that the low-order model adequately describes the nonlinear model. The proposed model can be used (e.g. by researchers, students or power system operators) to qualitatively simulate power system frequency behaviour for different operating scenarios.
Conference Paper
Full-text available
The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy resources. This transition involves the major challenge of substituting synchronous machines and their well-known dynamics and controllers with power electronics-interfaced generation whose regulation and interaction with the rest of the system is yet to be fully understood. In this article, we review the challenges of such low-inertia power systems, and survey the solutions that have been put forward thus far. We strive to concisely summarize the laid-out scientific foundations as well as the practical experiences of industrial and academic demonstration projects. We touch upon the topics of power system stability, modeling, and control, and we particularly focus on the role of frequency, inertia, as well as control of power converters and from the demand-side.
Article
Full-text available
Wind power generation has reached a significant share in power systems worldwide and will continue to increase. As the converter-connected generation reduces the grid inertia, more and more interest has been given to exploiting the kinetic energy and controllability of variable-speed wind turbine generators (VSWTGs) for frequency support. Consequently, the grid frequency dynamics are changing. Thus, it is necessary to include the frequency response of wind power plants in the system frequency response (SFR) model. In this paper, a novel approach to low-order SFR modelling of a future power system with a high share of frequency-support-capable VSWTGs has been presented. Low-order model of VSWTGs with primary frequency response and natural inertial response has been developed considering different wind turbine operating regimes and compared to the nonlinear model for validation. Low-order model has been presented in a symbolic transfer function form. Model accuracy has been discussed and the impact of VSWTG parameters on frequency response has been analysed. The developed model facilitates studying power system frequency dynamics by avoiding the need for modelling complex VSWTG systems, while retaining a satisfying level of accuracy.
Conference Paper
Full-text available
This paper presents a novel comprehensive control strategy for grid-connected Voltage Source Converters (VSCs) in power systems with low rotational inertia. The proposed model is based on emulating the physical properties of an Induction Machine (IM) and taking advantage of its inherent grid-friendly properties, i.e. self-synchronization, virtual inertia, power and frequency oscillation damping. For that purpose, a detailed mathematical model of the IM’s working principles is derived, which includes the possibility of obtaining the unknown grid frequency without a dedicated synchronization unit, but rather via processing the voltage and current magnitude measurements at the converter output. This eliminates the need for an inherently nonlinear phase-locked loop, characteristic for virtual synchronous machines, while simultaneously preserving the synchronization and damping properties of a conventional electrical machine. Several case studies are presented that validate the mathematical principles of the proposed model and conclusions on VSC performance are drawn.
Article
This paper proposes a dynamic frequency support scheme of a supercapacitor energy storage system (SCESS) in coordination with run-of-the-river (ROR) -based pumped storage hydropower (PSH) to enhance the short-term frequency stability in a power system that has a high penetration of renewable energy. To achieve this, the proposed coordinated frequency controller (CFC) enables the SCESS and PSH plant to provide the frequency response. The CFC scheme employs a dynamic droop characteristic in parallel with an integral controller and a distribution function. The dynamic droop characteristic determines the power production for frequency regulation employing a variable gain, which varies with the total capacity of the frequency control units and magnitude of the system frequency error with time; the gain increases with the frequency error, and thereby arresting the frequency nadir at a higher level than in conventional droop characteristic. In addition, the distribution function dispatches the power from the dynamic droop and integral controller to the control units in proportion to their headrooms; furthermore, the distribution function considers a sudden loss of generation from a SCESS by its operational constraint during the frequency support. Thus, the proposed dynamic frequency support scheme can enhance the short-term frequency stability for a frequency event.
Article
Frequency deviation of power systems caused by grid-connected wind power fluctuations is one of the key factors which restrains the increase of wind penetration level. This paper examines a combined wind and hybrid energy storage system (HESS, supercapacitor and battery) to smooth wind power fluctuations without wind spillage. A fuzzy based wind-HESS system (FWHS) controller is proposed to suppress the wind power fluctuations. The proposed controller takes full advantage of the complimentary characteristics of the supercapacitor and battery with the supercapacitor and battery in charge of high and middle frequency components of wind fluctuations respectively. The efficient state of change (SoC) operation is considered. A differential evolution (DE) based optimal sizing method for wind-HESS systems is introduced to evaluate the minimum capacity of HESS as being limited by grid frequency deviation. The efficiency of the proposed scheme in the paper for wind-HESS system is evaluated by an real Chinese power system.