Electric Power Systems Research 58 (2001) 179– 185
www.elsevier.com/locate/epsr
Battery energy storage for load frequency control of an
interconnected power system
S.K. Aditya, D. Das *
Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India
Received 1 May 1999; accepted 16 February 2001
Abstract
This paper deals with load frequency control of an interconnected reheat thermal system considering battery energy storage
(BES) system. Area control error (ACE) is used for the control of BES system. Time domain simulations are used to study the
performance of the power system and BES system. Results reveal that BES meets sudden requirements of real power load and
very effective in reducing the peak deviations of frequency and tie-power and also reduces the steady state values of time error
and inadvertent interchange accumulations. © 2001 Elsevier Science B.V. All rights reserved.
Keywords: Load frequency control; Battery energy storage system; Power generation control
1. Introduction
A lot of work reported in the literatures to improve
the performance of load frequency control (LFC). One
alternative to improve the performance of LFC is the
introduction of storage facilities during peak load period and specially a battery energy storage (BES) facility. Since BES can provide fast active power
compensation, it also can be used to improve the
performance of load frequency control. BES also improves the reliability of supply during peak load periods. Storage facilities possess additional dynamic
benefits such as load leveling, spinning reserve, area
regulation, long line stabilization, power factor correction and black start capability. Some of these applications have been successfully demonstrated at a 17 MW
BES facility in Berlin [1] and 10 MW/40 MWh Chino
facility in Southern California [2]. Kottick et al. [3]
have studied the effect of a 30 MW battery on the
frequency regulation in the Israeli isolated power system. Their study was performed on a single area model
representing the whole power system and containing a
first order transfer function that represented the BES
performance. However, they have not considered the
effect of generation rate constraints on dynamic performances. Lu et al. [4] have studied the effect of battery
energy storage system on two area reheat thermal system considering conventional tie-line bias control strategy. Their study reveals that a BES with simple control
can effectively reduce frequency and tie-line power oscillations following sudden small load disturbances.
However, they have considered generation rate constraint (GRC) of 10%/min for reheat type unit, but
modern reheat type units have GRCs of 3%/min [5].
In this paper, an incremental BES model is proposed.
The effect of BES on two area interconnected reheat
thermal system is studied considering conventional tieline bias control strategy. A GRC of 3% per min is
considered for reheat type units to obtain realistic
responses. The results show that with the use of BES,
the dynamic performance of LFC can greatly improve
the overshoots of frequency deviations, tie-power deviation and reduce the steady state values of time error
and inadvertent interchange accumulations.
2. BES model
* Corresponding author.
E-mail address: [email protected] (D. Das).
A schematic description of a BES plant is given in
Fig. 1. The main components of the BES facility are, an
0378-7796/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.
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S.K. Aditya, D. Das / Electric Power Systems Research 58 (2001) 179–185
180
Fig. 1. Schematic description of a BES plant.
Fig. 2. Equivalent circuit of BES.
equivalent battery composed of parallel/series connected battery cells, a 12-pulse cascaded bridge circuit
connected to a Y/D −Y transformer and a control
scheme. The ideal no load maximum d.c. voltage of the
12-pulse converter is expressed as [6],
Edo =Edo1 +Edo2 =
6
6
Et
y
(1)
where Et is the line to neutral r.m.s. voltage.
The equivalent circuit of the BES can be represented
as a converter connected to an equivalent battery as
shown in Fig. 2. In the battery equivalent circuit [7],
Eboc is battery open circuit voltage; Eb is battery overvoltage; rbt, connecting resistance; and rbs stands for
internal resistance.
The terminal voltage of the equivalent battery is
obtained from,
Ebt = Edo cos h o −RcIbes
3
6
6
Et(cos h o1 +cos h o2 ) − XcoIbes
(2)
y
y
o
where, h i is firing delay angle of converter i; Xco stands
for commutating reactance; Ibes is d.c. current flowing
=
into battery; rb denotes overvoltage resistance; cb is
overvoltage capacitance; rbp is self discharge resistance;
cbp stands for battery capacitance.
From equivalent circuit of BES (Fig. 2), we can write
the expression of d.c. current flowing into the battery as
Ibes =
(Ebt − Eboc − Eb)
(rbt + rbs)
(3)
According to the converter circuit analysis active and
reactive power absorbed by the BES system are [6],
Pbes =
3
6
EtIbes(cos h o1 + cos h o2 )
y
(4)
3
6
EtIbes(sin h o1 + sin h o2 )
y
(5)
Qbes =
There are two control strategies (i) P–Q modulation
and (ii) P-modulation. But only incremental active
power is considered in load frequency control and
hence we select P-modulation in this paper.
For P-modulation h o1 = − h o2 = h o. Therefore,
Pbes =
6
6
EtIbes cos h o = (Edo cos h)Ibes
y
Fig. 3. Block diagram of incremental BES model.
(6)
S.K. Aditya, D. Das / Electric Power Systems Research 58 (2001) 179–185
181
Fig. 5. Plot of J vs. KI without considering BES system.
is to respond the system disturbance. Therefore, we
assume,
Fig. 4. Block diagram of LFC with BES.
E ocoDIbes + I obesDEp = 0
ƒDEp = −
and
Qbes = 0
(7)
Let us assume,
Eco = Edo cos h
E oco
Edo cos h o
DI
=
−
DIbes
bes
I obes
I obes
From Eqs. (12) and (13) we get,
DPbes = I obesDEd
o
(8)
where, Eco = d.c. voltage without overlap.
From Eqs. (6) and (8) we get,
Pbes = EcoIbes
(9)
Linearizing Eq. (9), we get the incremental BES
power as,
DPbes = E ocoDIbes +I obesDEco
(10)
For BES system constant current operating mode is
the most efficient but for the sake of LFC we adjust the
firing angle h o, that is DEco to the BES in constant
power mode.
Let us decompose DEco into two components, that is,
DEco =DEp + DEd
(11)
From Eqs. (10) and (11) we get,
DPbes = E ocoDIbes +I obesDEp +I obesDEd
(12)
Second term of Eq. (12) I obesDEp is to compensate the
power deviation caused by DIbes and third term I obesDEd
(14)
Then the use of BES in LFC is obtained by a
damping signal DEd.
DEd =
Kbes
DSignal
1+ STbes
(15)
where Kbes and Tbes are the control loop gain and the
measurement device time constant, respectively. The
Dsignal is useful feedback from the power system in
order to provide damping effect.
Energy is released from BES system during peak load
period, that is discharging mode. For the operation of
BES in discharging mode we can use the ignition angle
i o(i o = y− h o) for the converter and the power consumption of the BES is
Pbes =
6
6
EtIbes cos i o,
y
i o = y− h o
ƒPbes = − EdoIbes cos h o = − EcoIbes
DF1 (Hz)
DF2 (Hz)
DPtie1 (pu MW)
(16)
The similar result in discharging mode is obtained as
DPbes = − I obesDEd
(17)
Table 1
Peak deviations and settling time of DF1, DF2 and DPtie1 with and without considering BES system for 1% step load disturbance in area-1
Without BES
(13)
BES+ACE feedback
Peak deviation
Settling time (s)
Peak deviation
Settling time (s)
−0.12404 (100%)
−0.12219 (100%)
−0.00969 (100%)
150
150
150
−0.03176 (25.6%)
−0.02894 (23.7%)
−0.00528 (54.5%)
50
50
50
S.K. Aditya, D. Das / Electric Power Systems Research 58 (2001) 179–185
182
Fig. 6. Responses of power system with and without BES for 1% step load increase in area-1. BES is under discharging mode.
In general,
DPbes =(sign)I
DEd
o
bes
Eb = E ob + DEb
(18)
When sign=1, battery is in charging mode and when
sign = −1, battery is in discharging mode.
Now battery overvoltage capacitive current can also
be written as,
Icb =cb
d
(E )
dt b
(19)
If there is a deviation in battery current, then the
battery overvoltage capacitive current (Icb) and voltage
(Eb) will also deviate from their initial values. Therefore, we can write,
Icb =I ocb + DIcb
and
(20)
(21)
From Eqs. (19)–(21) we get,
d
1
(DEb)= (I ocb + DIcb)
(22)
dt
cb
In Fig. 2, current through overvoltage capacitance
can be written as,
rb
Icb =
I
(23)
(rb + Xcb) bes
Therefore,
rb
I ocb =
I obes
(24)
(rb + Xcb)
and also from Eq. (23),
rb
DIcb =
(25)
DI
(rb + Xcb) bes
S.K. Aditya, D. Das / Electric Power Systems Research 58 (2001) 179–185
183
both the areas are taken as input signal (Dsignal1 =
ACE1 and Dsignal2 = ACE2) to BES system. When
BES system is used in both the areas, the complete
system is 15th order.
In this paper a 10 MW/40 MW h BES system is
applied [8]. Parameters of the two area reheat thermal
system and the BES system are given in Appendix A.
The computer programs are developed in FORTRAN-77. Time domain simulations are conducted
with a fourth-order Runge–Kutta method.
4. Generation rate constraint (GRC)
Fig. 7. Random load pattern applied to two area interconnected
reheat thermal system.
we get,
d From Eqs. (22),
rb (24) and (25),
(DEb)=
(DIbes +I obes)
dt
cb(rb + Xcb)
(26)
d
rb
(DEb)=
(DI +I 0bes)
dt
cb(rb +Xcb ) bes
After simplifying Eq. (26), we get
DEb =
rb
(DI +I obes)
(1+STb) bes
(27)
(28)
Tb =rbcb
(29)
Tbp =rbpcbp
(30)
Time error and inadvertent interchange accumulations of area i are given as,
1
60
&
Dfi dt
(33)
Ii = DPtiei dt
(34)
&
where mi and Ii are the time error and inadvertent
interchange accumulations of area i.
From Eq. (3), we also can write,
DEbt − DEb − DEboc
(rbt + rbs)
(32)
5. Time error and inadvertent interchange accumulations
mi =
where,
DIbes =
DPgi (k)= DPgi (k−1)9 rgDt
where, rg = 3% per min=0.0005 pu MW/s.
Similarly, we obtain,
rbp
DEboc =
(DI +I obes)
(1+STbp) bes
In a power system having steam power plant generation can only change at a specified constant rate.
Rate limits are imposed to avoid wide variations of
process variables like temperatures, pressure, etc. for
the safety of the equipments.
To explore this aspect, a GRC of 3% per min is
considered. At each integration time interval of Dt,
the generation rate is checked for its magnitude and
sign. In case generation rate exceeds the maximum
specified rate rg, the generation is constrained through
the relationship,
(31)
Now using Eqs. (13), (18), (27), (28) and (31) battery incremental block diagram is drawn in Fig. 3.
3. Studied system
6. Controller model
Emphasis has been laid on conventional integral
controller. The integral control law is described as
&
Ui (t)= − KIi ACEi (t)dt
In order to study the effect of the BES, a digital
computer model for LFC of a two area reheat thermal system, and the BES in both the areas is shown
in Fig. 4. Conventional area control errors (ACE) in
(35)
where, KIi is the integral gain setting of area i and
ACEi = Bi Dfi + DPtiei = ACE of area i and Bi is the
frequency bias setting of area i.
S.K. Aditya, D. Das / Electric Power Systems Research 58 (2001) 179–185
184
Fig. 8. Responses of power system with and without BES for random load disturbance in area-1. BES is under discharging mode.
7. Optimization of integral controller gain setting using
integral squared error (ISE) technique
Integral squared error (ISE) technique is used for
obtaining the gain settings of integral controllers with
and without BES system. A performance index,
J=
&
disturbance in area-1 for obtaining the optimum value
of integral gain setting with BES system. It was found
that with BES system KI =KIopt = 0.12 and Jopt =
0.00169.
8. Dynamic responses with and without BES system
(ACE21 +ACE22)dt
(36)
0
is minimized for 1% step load disturbance in area-1 for
obtaining the optimum values of integral gain setting KI
(for two equal area system KI1 =KI2 =KI). Fig. 5 shows
the plot of J versus KI without BES system. From Fig.
5, it is seen that KI = KIopt =0.015 and Jopt =0.05083.
Similarly, when ACE feedback is used for BES system
(Dsignal1 =ACE1 and Dsignal2 =ACE2), the same performance index (Eq. (36)) is minimized for 1% step load
Battery energy storage system will operate in discharging mode during peak load period and will be in charging
mode during off peak hours. Therefore, only discharging
mode behavior of BES is examined on LFC loop. Fig.
6 shows the dynamic responses for 1% step load disturbance in area-1 with and without BES system considering
conventional ACE. From Fig. 6 and Table 1, it is clearly
seen that with the use of BES system, there is considerable reduction in peak deviations of DF1, DF2, and DPtie1
S.K. Aditya, D. Das / Electric Power Systems Research 58 (2001) 179–185
and settling time is very less. Fig. 6 also reveals that
BES system has eliminated the tie power oscillations.
Time error and inadvertent interchange accumulations
are also shown in Fig. 6. It is seen that BES system
is capable of reducing the steady state values of time
error and inadvertent interchange accumulations.
Battery output power deviations DPbes1 and DPbes2 are
also shown in Fig. 6.
The dynamic behavior of the two area reheat
thermal system with and without considering BES
system under random load changes are also studied.
Fig. 7 shows the random load pattern of power
system. The loads are random both in magnitude and
duration. The random loads are generated by using a
subroutine to generate random numbers, which are
then multiplied by appropriate scale factors to yield
the desired ranges of magnitude and duration of
loading.
Fig. 8 shows the dynamic responses for random
load disturbances in area-1 with and without
considering BES system. It is clearly seen from
Fig. 8, that the BES system provides very good
damping even in presence of a random load
variation.
9. Conclusions
A comprehensive mathematical model of BES system
has been developed for investigating its application in
load frequency control. Analysis reveals that the use of
ACE for the control of BES substantially reduces the
peak deviations of frequency and tie-line power and
reduce the steady state values of time error and inadvertent interchange accumulations. Responses of the
power system under random load changes have also
been studied with and without considering BES system.
It was found that the BES system is capable of improving the system dynamic performance even under the
random load disturbance. It can be concluded that the
application of BES system to load frequency control of
interconnected power system will provide great improvement in system dynamic performance.
.
185
Appendix A
Data for power system
f= 60 Hz, Pr1 = Pr2 = 1000 MW, Kp1 = Kp2 =120
Hz/pu MW, Tp1 = Tp2 = 20.0 s, Kr1 = Kr2 = 0.5, Tr1 =
Tr2 = 10.0 s, Tg1 = Tg2 = 0.08 s, Tt1 = Tt2 = 0.3 s, R1 =
R2 = 2.4 Hz/pu MW, B1 = B2 = 0.425 pu MW/Hz.
BES (10 MW/40 MW h) [8 –10]
Battery voltage=1755–2925 V d.c., cbp = 52597 F,
rbp= 10 kV, cb = 1 F, rb = 0.001 V, rbt = 0.0167 V,
rbs = 0.013 V, Xco = 0.0274 V, I obes = 4.426 kA, Kbes =
100 kV/pu MW (ACE feedback), Tbes = 0.026 s, h o =
15°, i o = 25°.
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