1
Decoupled Power Controller for Inverter-interfaced
Distributed Generation System
C. V. Dobariya, Student Member, IEEE and S. A. Khaparde, Senior Member, IEEE
Abstract— This paper introduces concept of decoupled power
controller for tracking load demand of an inverter-interfaced
distributed generation (DG) system. The approach suggested in
the paper uses reference frame theory to decouple quadrature
axis and direct axis currents. As compared to the power-frequency
droop based controller, the proposed controller design involves exact mathematical formulation in terms of quadrature and direct
axis powers. It also relinquishes forced relationship between the
DG variables like power and frequency. The controller has been
simulated using MATLAB/SIMULINK for single DG feeding a
three phase balanced load. Step changes in quadrature axis and
direct axis load are simulated to illustrate the performance of
the controller. Results showing response of the DG controller to
the load change are presented and discussed in the paper.
Index Terms— Distributed generation, load tracking, reference
frame theory.
N OMENCLATURE
C
E abc
eabc
ed∗
eq∗
eqd0
I abc
id∗
iq∗
iqd0
L
R
r
V abc
v abc
v qd0
w
wb
xl
DC link capacitance in F
Inverter terminal voltages in V
Inverter terminal voltages in pu
Direct axis inverter voltage reference
Quadrature axis inverter voltage reference
pu inverter terminal voltages in synchronously rotating
reference frame
Phase currents in A
Direct axis current reference
Quadrature axis current reference
pu currents in synchronously rotating reference frame
Filter inductance in H
Filter resistance in ohms
Filter resistance in pu
Load terminal voltages in V
Load terminal voltages in pu
pu load voltages in synchronously rotating reference
frame
Speed of reference frame in rad/s
Base frequency of the system in rad/s
Filter reactance in pu
I. I NTRODUCTION
L
OCAL power generation will be playing an important
role in the power industry in coming decades to supply
electrical and thermal requirements. Currently, 35 % of total
US industrial electric power is met by on-site generation. A
study by the Electric Power Research Institute (EPRI) indicates
C. V. Dobariya and S. A. Khaparde are with Electrical Engineering
Department at Indian Institute of Technology Bombay, Mumbai, India. (email:
[email protected], [email protected])
that, as much as 25 % of the new generation coming online by
the year 2010
will be of distributed kind. The Natural Gas
Foundation concluded that, this figure could be as high as
30 % [1]. Even though penetration of such local generators is
small today, it has been estimated that, within a decade, their
market will exceed $60 billion a year [2].
An individual DG as an energy supplier can lead to
few problems along with solving many other problems. For
instance, a stand-alone DG system may solve problem of
electrification, but it may raise issues related to reliability and
power quality. This is because, most of the DGs are either
inertia-less (e.g. photo voltaic cell, fuel cell, etc.) or have
very small inertia (e.g. microturbine). Such fragile generators
generally show poor performance in load tracking as compared
to the large central generators. For example, a microturbine
requires about 10 seconds interval for 50 % change in the
power output. A fuel cell requires about 10 seconds interval for
15 % change in power output. It also requires a recovery period
of few minutes to establish equilibrium before it can provide
another step change in power output [3], [4]. The storage
devices like battery, ultra-capacitor, flywheel, and superconducting magnetic energy storage (SMES) can be considered
as virtual inertia for DGs in fast load tracking scheme. Similar
schemes can also be implemented by operating two or more
DGs in parallel (e.g. wind-diesel). The combination of DGs
and/or storage devices is generally referred as hybrid DG.
As compared to an individual DG operation, the master-slave
control for a hybrid DG results into improved performance in
feeding sensitive loads.
Main concerns in the area of DG include control of active and reactive power, and grid integration issues. The
concept of active and reactive power control for a DG is
suggested by many researchers. Published literature [1], [4]–
[8] has suggested a power-frequency droop based approach
to control active and reactive power of a stand-alone system.
The suggested method works satisfactorily with linear loads.
While feeding sensitive loads, one or more DGs and/or storage
devices may be operated in parallel. This raises issue of power
sharing between the parallel generators. The power sharing
between inverters is adversely affected by change in network
parameters. Tuladhar et. al [9] explain control strategy for
parallel inverter in the presence of variable line impedance.
The method performs satisfactorily for linear as well as nonlinear loads. In [10], Macken has suggested and demonstrated
controllers based on an effective communication network. He
recommended current controlled voltage source inverter (VSI)
for grid-connected operation and voltage controlled VSI for
stand-alone operation of a DG.
1-4244-1298-6/07/$25.00 ©2007 IEEE.
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2
This paper introduces a new approach to control power
dispatch of an inverter-interfaced DG. The concept of the
design introduced here is examined for a stand-alone DG
system. It can also be extended to grid-connected and MicroGrid mode of operations with minor modifications related to
control signals. The controller design is based on the reference
frame theory. Conventional power-frequency droop based controllers involve approximation in mathematical formulation of
active and reactive power (i.e. assumption of purely inductive
network). The proposed controller works on the principle of
direct and quadrature axis power control, which is based on
exact mathematical formulation. The principle has been widely
used for induction motor drive applications. Application of
similar approach for power system has been reported in [11]
to control static VAR compensator. However, this principle has
not been applied to control inverter-interfaced DGs. In addition
to explanation of basic principle, the mathematical derivation
and the simulation of DG controller are also discussed here.
The inverter model is simplified so as to illustrate the basic
working principle of the controller. Simulation results using
MATLAB/SIMULINK for balanced direct and quadrature
power demands are subsequently presented.
The organization of the paper is as follows. Section II
explains general philosophy and shortcomings of the conventional approach of controlling DGs. Mathematical formulation
of proposed controllers and basic control strategy is also
presented in the same section. Section III describes simulation
results and controller performance. Section IV concludes the
paper.
II. D ESIGN OF C ONTROLLERS
The design of power-frequency droop based controllers for
control of active and reactive power dispatch of a distributed
energy resource has been proposed in [1], [4]–[8]. Such controllers dispatch power based on the value of local frequency.
Hence, they require only local information for operation. Such
a scheme works on the assumption that,
P =
EV
sin( δ)
Xl
(1)
and
V 2 − EV cos( δ)
(2)
Xl
where, the power angle δ is the phase angle between load
terminal voltage V and inverter terminal voltage E, and Xl is
the system reactance.
Many a times, power extraction from location specific DGs
like wind etc., require long transmission lines. In case the
load is located at remote end, bulk power transfer may result
into the power angle δ exceeding 30 °. Hence, the assumption
of linear relationship between power dispatch and δ does not
hold true. Therefore, on such instances, the power-frequency
droop based controller will loose the faithful operation ability.
Furthermore, when connected to an LV distribution network,
the conventional controller may not be able to control the
power dispatches accurately. This is because, an LV distribution network is characterized by obtrusive system resistance.
Q=
Vdc
DG
E
abc
R
L
R
L
R
L
C
V
abc
L
O
A
D
Inverter
Converter
Fig. 1.
Schematic of stand-alone DG feeding a load
Predominant effect of resistance on such a network may
adversely affect the effectiveness of power control algorithms
of the conventional controller. Therefore, a DG system should
be equipped with more robust power controller.
In conventional generation systems, speed of the turbine/generator and the power output are naturally related
quantities. Hence, power-frequency droop based controllers
become effective in dispatching active and reactive power for
such systems. In a DG, with the inverter at the output stage,
the natural relationship between power and generator speed
no longer exists. The frequency of the output voltage of an
inverter can be set to any value. In power-frequency droop
based controllers, this relationship is enforced by modifying
PWM signals. In proposed approach of the controller design,
this enforced relationship is avoided. Further sections provide
design approach of the proposed controller.
A. Inverter terminal voltage control
Assume a DG feeding a balanced three phase load as shown
in Fig. 1. The DG considered here is a high frequency AC
power generator (e.g. microturbine). Such a DG would require
AC-DC-AC converters to produce useful AC power. The DC
power generators (e.g. fuel cell, PV cell, etc.) require only
DC-AC converter.
In simplified model, the terminal voltages of an inverter are
expressed as a function of modulation index (k) and DC link
voltage (Vdc ). So, we have two degrees of freedom (although
each has its own range of operation) to control the terminal
voltage of an inverter. Usually, the valid voltage variation range
is 1 ± 0 .03 per unit [12]. The strategy adopted for the controller
is to first adjust k until its upper limit (say 0 .9) is reached.
Once the upper limit of k is hit, the inverter terminal voltages
are regulated by changing Vdc .
In simplified model of an inverter, terminal voltages can be
expressed as,
Ea =
Eb =
(3)
kVdc cosθ
kVdc cos( θ −
2π
)
3
(4)
2π
)
(5)
3
From Fig. 1, the inverter terminal voltages can be expressed
as,
Ec =
E abc =
kVdc cos( θ +
V abc + [R]I abc + [L]
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d abc
I
dt
(6)
3
where, E abc , V abc , and I abc are column vectors of three phase
quantities, and [R] and [L] are diagonal matrices of R and L
respectively.
By using synchronously rotating reference frame transformation as described in appendix, we can write (6) in per unit
form in q, d, 0 variables as,
r
i
q*
+
−
PI
r.wb
xl
+
w.xl
wb
+
+
*
eq
vq
vd
− [xl ]−1 [r]ωb − ω[ K]) iqd0 + [xl ]−1 ωb ( eqd0 − v qd0 )
(7)
where, [r] and [xl ] are diagonal matrices of r and xl respectively, and
⎡
⎤
0 1 0
⎦
[ K] = ⎣ − 1 0 0
0 0 0
*
id
G1 + G2
(8)
−
PI
Fig. 2.
K∗ =
( eq ∗ )
G1 =
[xl ]−1 [r]ωb ( iqd0
− ω[ K] iqd0 − [xl ]−1 [r]ωb iqd0
− iqd0 )
(9)
+ [xl ]−1 ωb ( eqd0 − v qd0 )
(10)
From (8), two fold observations are evident. First observation is, if by some action, the term G2 is reduced to zero, the
decoupled control of iq and id currents can be achieved. One
of the ways to accomplish this lies in modifying the inverter
terminal voltages to eliminate the term G2 in steady state. By
equating (10) to zero, reference inverter terminal voltages can
be derived as,
∗
ω
) [x ][ K] iqd0 + [r]iqd0 ∗
(11)
ωb l
The other observation is, with only G1 term in (7), the iq
and id currents are the functions of their respective reference
values. This results into decoupled control of quadrature and
direct axis currents. In addition to that, upon passing the term
∗
iqd0 − iqd0 from a proportional and integral (PI) controller,
the currents will always settle to their respective reference
value in steady state. Thus, by properly coordinating controls
between the reference currents and the inverter voltages, iq
and id currents at the output terminal of inverter can be
controlled independently. The controller schematic diagram
corresponding to this logic is shown in Fig. 2.
eqd0
∗
=
v qd0 + (
B. DC link voltage (Vdc ) control
The DC link transfers the energy of the generator to the
inverter. Accurate control of the Vdc ensures proper operation
of the inverter switches. According to the proposed operating
strategy, whenever k hits the upper limit, Vdc changes to
regulate E abc within the specified limits. For this purpose,
reference value of Vdc is calculated from modulation index
reference K ∗ (obtained from reference inverter terminal voltages) and value of k such that,
*
ed
2
+(
∗ 2
ed )
(12)
and
K∗ =
∗
+
+
Controller schematic diagram
where,
G2 =
r.wb
xl
r
For the purpose of load tracking, (7) can be rewritten as,
d qd0
i
=
dt
+
−
d qd0
i
=(
dt
w.xl
wb
kVdc
(13)
Vdc stays at its reference value until k hits the cap value
(i.e. 0 .9 here), and after that, Vdc gets updated by (13). The
new value of Vdc is obtained by modifying capacitor charging
current Ic to the required value.
1
Vdc =
(14)
Ic dt
C
The value of Ic has to be maintained by modifying fuel
supply setting of DC generator like fuel cell, etc. In case of
AC generator, a rectifier is required to generate Vdc . In this
case, current setting of AC generator is modified to supply
required Ic .
In case of hybrid DG system, whenever master DG is unable
to supply power, i.e., in case of transient and overloading
conditions, slave DG can supply additional Ic to maintain
required Vdc . By maintaining proper DC link voltage, a DG
would be able to supply active power. Depending upon the
loading, the demanded reactive power can be generated by
switching of the inverter, and limited by the inverter rating.
The regulation of Vdc will need model of a particular DG.
Hence, Vdc regulation technique varies depending upon the
type of DG. Renewable DGs like wind and PV cell need
more attention to maintain Vdc which establishes unidirectional
power flow.
C. Frequency control
Frequency of the inverter can be set to any value. In contrast with the power-frequency droop based method, proposed
control strategy does not allow the frequency to vary from
its standard value. This is of crucial importance for frequency
linked instruments like digital clock, etc. In stand-alone mode,
the reference frequency can be set to 50 Hz or 60 Hz. The
frequency of the inverter can be set to the grid frequency while
operating in conjunction with utility grid. A phase locked loop
(PLL) can be employed to track and settle the frequency to
its reference value. Design of PLL suggested in [13] and [14]
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4
Initialization
Block
Vdc
k
abc to qd0
1
m
V
0
q
q
V
d
V
V
d
V
0
V
abc
Phase
K*
k
Vdc
k
K*
Vdc
Vdc controller
k
q*
I
d*
I
Load voltages
Alpha
+
+
E
abc
Phase
Inverter
DG controller
q
Vdc
Refenece I
Reference I
−
+
Fig. 3.
(E
d
abc
abc
−V
)
I
abc
Load currents
MATLAB/SIMULINK implementation of the controller
is able to work in variable frequency environment. It is not
discussed here for brevity.
D. Fault current control
It is much easier to handle total power dispatch in terms
of direct axis and quadrature axis powers rather than active
and reactive power. The concept is also useful in fault current
limiting applications of the inverter. For the stand-alone application of DG, as soon as the faulty condition is detected, the
DG has to stop feeding the fault. For this purpose of reducing
fault current to zero value, the reference load current signals
to the controller are set to zero. Thus, even upon maintaining
terminal voltages within the acceptable range, load current can
be reduced to zero.
E. Power control in integrated mode of operation
Integrated mode of a DG implies its operation in conjunction with either a utility grid or a MicroGrid. The difference
between the stand-alone operation and the integrated operation
lies in generating the reference signals, i.e. power, voltage, etc.
In a stand-alone mode, a DG controller receives signals from
local measurements. Whereas in integrated mode, these signals
are derived from the network measurements of a MicroGrid
or a utility grid. In a MicroGrid, the central controller decides
the dispatches of every generator, and conveys information
regarding the same to each controller. However, when a DG
is connected to a utility grid, the generation of the reference
signals becomes a policy matter. Irrespective of the method
involved (e.g. economic dispatch, etc.) in the reference signals
generation, the proposed controller can follow the load signals,
as it deals with magnitude of the reference signals.
III. S IMULATION R ESULTS
To evaluate the response of the controller, consider a standalone DG system feeding a balanced three phase load as shown
in Fig. 1. Equivalent MATLAB/SIMULINK model is shown in
Fig. 3. The system is simulated in pu quantities and works on
50 Hz frequency. The design parameters of the DG controller
mainly involve series inductance and resistance of the filter
connected at the output stage of the inverter. For simplicity of
analysis, reference load voltages are set to 1 pu with 0 phase
angle delay. Reference current signals are obtained by passing
measured load currents signals through synchronously rotating
reference frame. In the model, the reference load signals are
represented as step change blocks. The output of the DG
controller is the magnitude and phase angle references for
inverter terminal voltages, which are achieved by modifying
values of k and Vdc . The Vdc controller block controls and
modifies value of Vdc and k as per requirement. At the starting
of the simulation, values of k and Vdc are set by initialization
block.
Results of the change in quadrature axis and direct axis
current at 0 .2 second are shown here. Quadrature axis current
is increased from initial value of 0 pu to 0 .8 pu at 0 .2 second.
At the same time the direct axis current is also changed from
− 0 .5 (leading power) to 0 .5 (lagging power).
Change in reference load currents and the response of
the controller are shown in Fig. 4 and Fig. 5. It can be
observed that, the quadrature and direct axis powers settle to
their respective reference values in steady state. Since current
limiters are not modeled, current spikes can be observed in
transient period. Fig. 6 shows generated three phase load
current. Variation in the values of Vdc and k are shown in
Fig. 7 and Fig. 8 respectively. It can be observed that, once
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5
1.6
1.5
DG power
Load demand
1.4
1
Phase currents Ia, Ib and Ic in pu
Quadrature axis power in pu
1.2
1
0.8
0.6
0.4
0.2
0
0.5
0
−0.5
−1
Ia
−0.2
−0.4
0
−1.5
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Ib
Ic
0.5
time in seconds
−2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
time in seconds
Fig. 4.
Quadrature axis power control
Fig. 6.
Phase currents
1.2
DG power
Load demand
1
1.135
1.13
0.6
0.4
Vdc in pu
Direct axis power in pu
0.8
0.2
0
1.125
1.12
−0.2
−0.4
1.115
−0.6
−0.8
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
time in seconds
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
time in seconds
Fig. 5.
Direct axis power control
Fig. 7.
k hits the upper limit of 0 .9, inverter terminal voltages are
maintained within the limits by modifying reference value of
Vdc . Variation in Vdc , since not large, can be easily obtained
by modifying reference value of capacitor charging current Ic .
Change in the value of Vdc also indicates the change in active
power demand of the system. The switch over from leading
power to lagging power can be observed in Fig. 9.
IV. C ONCLUSION
Design of power controller will play a key role in the
successful implementation of the DG technologies. This paper
provides an analytical background and generalized framework
of new power control strategy for an inverter-interfaced DG.
The design of the controller uses reference frame theory to effectively decouple quadrature and direct axis load currents. As
compared to the power-frequency droop method, the proposed
approach is more robust in terms of mathematical formulation,
as it does not involve any approximation. The results presented
here indicate that, the decoupled controller is able to dispatch
quadrature and direct axis powers accurately. However, the
response time can be decreased further by optimal selection
of PI controller gains. Moreover, implementation of proper
current controlled PWM method can reduce the spikes in the
currents in real time. The current work presents analysis of
DC link voltage
stand-alone system, and can be extended to grid-connected
mode of operation and unbalanced loading condition.
A PPENDIX
Several transformation matrices are suggested by different
researchers for various types of analysis. The orthogonal transformation has the fundamental disadvantage of maintaining
unit-to-unit relationship between abc and qd0 variables [15].
Here, the q axis leads the d axis as shown in Fig. 10. Hence,
the transformation matrix used in the analysis is defined as
[16],
⎤
⎡
cosθ
sinθ
1
[ T ] = ⎣ cos( θ − 2 3 π ) sin( θ − 2 3 π ) 1 ⎦
cos( θ + 2 3 π ) sin( θ + 2 3 π ) 1
such that,
f abc = [
T ] f qd0
where,
θ=
0
t
ω( ξ) dξ + θ(0)
where, ξ is the dummy variable of integration.
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(15)
6
b
0.9
Modulation index k
q
θ
0.895
a
0.89
d
c
0.885
0
Fig. 10.
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Reference frame axis
0.5
time in seconds
Fig. 8.
[6] M. S. Illindala, “Vector control of PWM VSI based distributed resources
in a microgrid,” Ph.D. dissertation, University of Wisconsin-Madison,
Wisconsin, USA, 2005.
[7] P. Piagi, “Microgrid control,” Ph.D. dissertation, University of
Wisconsin-Madison, Wisconsin, USA, 2005.
[8] A. Hajimiragha, “Generation control in small isolated power systems,”
Master’s thesis, Royal Institute of Technology, Cambridge, 2005.
[9] A. Tuladhar, H. Jin, T. Unger, and K. Mauch, “Control of parallel
inverters in distributed AC power systems with consideration of line
impedance effect,” IEEE Trans. Ind. Applicat., vol. 36, no. 1, pp. 131–
138, Jan. 2000.
[10] K. J. P. Macken, “Control of inverter-based distributed generation used
to provide premium power quality,” in Proc. 53 th Annual IEEE Power
Electronics Specialists Conference, Aachen, Germany, 2004, pp. 3188–
3194.
[11] C. Schauder and H. Mehta, “Vector analysis and control of the advanced
static var compensators,” in Proc. Institution of Electrical Engineers-C,
vol. 140, no. 4, July 1993, pp. 299–306.
[12] R. G. Yadav, A. Roy, S. A. Khaparde, and P. Pentayya, “India’s fast
growing power sector: From regional development to growth of a
national grid,” IEEE Power Energy Mag., pp. 39–48, July 2005.
[13] M. Karimi-Ghartemani and M. R. Iravani, “A method for synchronization of power electronic converters in polluted and variable-frequency
environments,” IEEE Trans. Power Syst., vol. 17, no. 2, pp. 617–622,
Apr. 2002.
[14] ——, “A nonlinear adaptive filter for online signal analysis in power
systems: Applications,” IEEE Trans. Power Delivery, vol. 19, no. 3, pp.
1263–1270, Aug. 2004.
[15] P. Kundur, Power System Stability and Control. New-York: McGrawHill, Inc., 1994.
[16] P. C. Krause, Analysis of Electric Machinery. New-York: McGraw-Hill,
Inc., 1987.
Modulation index
1.5
Phase "a" voltage and currents in pu
1
0.5
0
−0.5
−1
Phase "a" voltage
−1.5
Phase "a" current
−2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
time in seconds
Fig. 9.
Phase “a” voltage and current
The inverse transformation matrix is defined as,
[ T ] −1 =
⎡
cosθ
2⎣
sinθ
3
1
cos( θ −
sin( θ −
2
2
such that,
f qd0 = [
1
2 π
3 )
2 π
3 )
T ] −1 f abc
cos( θ +
sin( θ +
1
2 π
3 )
2 π
3 )
⎤
⎦
2
(16)
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C. V. Dobariya (S’05 ) received B. E. degree from Nirma Institute of
Technology, Ahmedabad, India in the year 20
. Currently, he is working
towards his M. Tech. degree at Electrical Engineering Department, Indian
Institute of Technology Bombay, India. His research area includes analysis
and control of Distributed Generation and MicroGrid.
S. A. Khaparde (M’87 , SM’91 ) is Professor, Department of Electrical Engineering, Indian Institute of Technology Bombay, India. He is member of Advisory Committee of Maharashtra Electricity Regulatory Commission (MERC).
He is on editorial board of International Journal of Emerging Electric Power
Systems (IJEEPS). He has co-authored books on Computational Methods for
Large Sparse Power System Analysis: An Object Oriented Approach, as well
as, Transformer Engineering, published by Kluwer Academic Publishers and
Marcel Dekker, respectively. His research area includes Distributed Generation
and power system restructuring.
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