Hybrid control of multiple inverters in an island-mode distribution system
ABSTRACT Inverter-interfaced distributed generation offers the possibility of introducing power quality functions such as suppression of harmonic distortion. However, the traditional voltage- and frequency-droop methods of achieving load sharing work on average values and do not address waveform quality. This paper proposes a hybrid scheme for an island-mode system with many inverters. Inverters in close proximity operate in master-salve mode whereas load sharing between distant groups uses frequency droop. Communication between inverters is used where it can improve performance but not where such links are impractical. The master inverter uses repetitive voltage control at the common node to suppress harmonic distortion. Slave inverters within a group also use repetitive control but in current mode. The performance has been assessed through simulation.
Conference Proceeding: A survey of control methods for three-phase inverters in parallel connection[show abstract] [hide abstract]
ABSTRACT: This paper critically compares existing control methods for paralleling voltage source converters and applies these to three-phase power inverters. Three existing and one new control topologies are presented, and their properties are discussed in terms of a variety of balanced and unbalanced communication demands, synchronisation and robustness. The domains in which the control takes place are discussed and the boundaries for their application are statedPower Electronics and Variable Speed Drives, 2000. Eighth International Conference on (IEE Conf. Publ. No. 475); 02/2000
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ABSTRACT: The parallel operation of static inverters is, in a large amount of cases, the appropriate solution to achieve the high power required by some applications or to improve power system reliability. The limited inverter capacity obliges to parallel the individual units to obtain the nominal load power. In UPS systems, there are situations where a high reliability/availability is required by critical loads. Parallel redundancy appears an immediate solution to satisfy this requirement. This paper presents a control system for parallel operation of nonredundant UPSs based on current control. The relative phase between the inverters is constant. Simulation results as well as experimental studies are presented. The overall control system is implemented on a simple and low cost platformIndustrial Electronics, Control, and Instrumentation, 1995., Proceedings of the 1995 IEEE IECON 21st International Conference on; 12/1995
Article: Parallel processing inverter system[show abstract] [hide abstract]
ABSTRACT: A novel method of instantaneous voltage and power balance control of a parallel processing inverter system is proposed. It consists of a high-speed switching PWM (pulsewidth modulated) inverter with an instantaneous current minor loop controller, a voltage major loop controller, and a power balance controller. This system realizes the following functions with only one inverter: constant AC output voltage control with reactive power control, active filtering to absorb load current harmonics, DC voltage and current control as AC-to-DC converter, and uninterruptible power supply (UPS) for stand-alone operation. This system covers a wide application range, including UPS systems, new energy systems, and active filters with voltage control functionsIEEE Transactions on Power Electronics 08/1991; · 4.08 Impact Factor
Hybrid Control of Multiple Inverters in an Island-Mode Distribution System
J. Liang, T.C. Green, G. Weiss and Q.-C. Zhong
Imperial College London,
South Kensington Campus
London SW7 2AZ, U.K.
Abstract – Inverter-interfaced distributed generation offers the
possibility of introducing power quality functions such as
suppression of harmonic distortion. However, the traditional
voltage- and frequency-droop methods of achieving load sharing
work on average values and do not address waveform quality.
This paper proposes a hybrid scheme for an island-mode system
with many inverters. Inverters in close proximity operate in
master-salve mode whereas load sharing between distant groups
uses frequency droop. Communication between inverters is used
where it can improve performance but not where such links are
impractical. The master inverter uses repetitive voltage control at
the common node to suppress harmonic distortion. Slave
inverters within a group also use repetitive control but in current
mode. The performance has been assessed through simulation.
Keywords: island-mode distribution system, distributed
generation, repetitive control, H∞ control
Distributed generation (DG) is of increasing importance as
new forms of generation and new ownership of generation is
encouraged by policy makers and market opportunities .
Many of the newer forms of generation need power electronic
based interfaces. Photo-voltaic arrays and fuel cells require DC
to AC inverters. Variable speed wind-turbines require AC to
DC to AC conversion as do high speed gas-turbine driven
An inverter has a quite different characteristic to a
conventional electrical machine. Power export and waveform
quality can be controlled with a relatively high bandwidth in
an inverter. Indeed, control is necessary since an inverter has
little short-time overload rating and close sharing must be
enforced. Further, the inverter will have at least an inductive
filter. This filter will have been chosen to present a high
impedance to current emissions from the inverter at the
switching frequency. However, this filter will still have a
relatively large impedance to low-order harmonic distortion
and so harmonic currents drawn by a non-linear load will
cause voltage distortion to appear across this filter which will
be common to other loads in the vicinity.
An electrical machine, on the other hand, has a power export
that is controlled with modest bandwidth and waveform
quality is set at design stage by the winding configuration. A
low source impedance is used to ensure that fault current can
be supplied (to clear faults) and to avoid harmonic current
causing large harmonic voltage drops.
When the distributed generators are exporting into a large,
strong grid then power export from a small DG unit can be set
at will. In an island situation (a physical island or de-
synchronisation because of a problem in a main grid) there
is a need to match load and supply and provide a
mechanism for sharing load between generating sets. For
traditional electrical machines this is achieved through a
governor (or control) setting that has a defined frequency
droop as a function of real power supplied and a voltage
droop with reactive power. For an inverter-interfaced
system, it would be attractive, from a control point of view,
to distribute reference signals to all of the inverters to ensure
that the desired power matching and power sharing was
There have been several proposals for parallel operation of
inverters in application areas such as UPS [2,9] and
photovoltaic power supply system . For inverters in close
proximity there are methods such as: central mode, master-
slave mode and distributed logic mode . The close
proximity has allowed control signals to be communicated
There are communication-based sharing and control
methods using a PLL to provide synchronisation and
communication to provide sharing [5, 6]. Communication
has the potential to provide a better degree of control; better
in terms of response to load changes and better in terms of
providing low distortion. However, with DG units spread
over some physical distance
communication links with a degree of robustness that is not
thought to be practical or economic at present.
To avoid communication, the frequency droop method has
been adapted for inverter use [7, 8, 9]. The common system
frequency is used to indicate the degree of load on the
system. Some low bandwidth communication may well be
used to supplement the system so that the load sharing can
be adjusted (by setting the parameters of the droop
characteristic) and to allow generators scheduled.
Communication should be used to whatever extent is
practicable in a given environment. Thus, inverters
connected to the same node of a distribution system could
have inter-inverter communication of demand signals to
provide rapid response sharing and suppression of harmonic
distortion. But the impracticality of communication between
inverters at remote nodes is recognised and the sharing
between these groups is accomplished through more
traditional means. Thus a hybrid control scheme can be
developed that uses as much of the potential of the inverter
as can be realised.
this would require
610-7803-7754-0/03/$17.00 ©2003 IEEE
Figure 1 A multi-inverter system with inverters arranged in groups.
This paper will develop and test a hybrid, hierarchical, control
scheme. It will employ droop characteristics between inverter
groups and master-slave current sharing within groups. An
inverter group is defined as those inverters connected to the
same distribution system node. Within the group, voltage
control will operate in a high bandwidth loop so that good
waveform quality is ensured. The loop will be designed to be
robust to disturbances and plant uncertainty.
II A MULTIPLE INVERTER SYSTEM
Figure 1 illustrates the proposed arrangement of inverter groups
with three groups, A, B and C. Group A is shown in detail. It
consists of a master inverter and a number of slave inverters.
The distinction between master and slave only applies to the
control function allocated to the inverter. Technologically, the
inverters are identical. Because the inverters of a group are
physically close and connected to a common node, they can
not all have control of their output voltage. Instead, one
inverter is allowed to control the node voltage and is
designated the master. This task need not be allocated to the
same inverter at all times. The other inverters operate as slaves
that inject current into the common node in order to take a
share of the power generation.
III CONTROL SYSTEM DESIGN
A. Inter-Group Power Control
Inter-group power control is achieved through a droop
characteristics. A conventional droop method is described as:
where ω0 is the nominal (full load) frequency, V0 the
nominal voltage amplitude and P0i & Q0i are the total real
and reactive power rating of inverters at node i.
To provide equal (per unit) sharing, the slopes mi and ni are
chosen to match the frequency and voltage differences
between zero and full load for each node:
The droop characteristic provides voltage references for the
inverters in phasor form which are converted to
instantaneous voltage references in the normal way.
The conventional scheme will provide equal sharing of
power generation between inverter groups but this may not
be the best solution for the distribution system. Part of the
rational for DG is that loads can be supplied by local
generation and losses through distribution networks reduced.
The proposal here is to modify the droop characteristic such
that generation is increased at nodes with a large local load
so that power exchanges through the distribution system are
reduced from those that would occur with a conventional
droop. The slope is modified according to a second,
additional, droop based on the local load. If the local load
increases, the slope is decreased giving rise to great power
generation at the node concerned for a given deviation of
system frequency from its nominal value.
Common Inverter Bus
Inverter Group Node
and Local Load
Figure 2 An inverter group comprising one master and several slaves connected to a common node.
B. Intra-Group Power Control
Inverters within a group share a common voltage node and are
connected to it by an inductance. The inductance allows the
current between the voltage source inverter and the voltage
node to be controlled and also forms part of the filter to
attenuate switching frequency current emissions. The filter is
formed with the capacitor at the node. The electrical
connections of the inverters and filters are shown in figure 2.
Only one element can have control of the node voltage and so
one inverter is designated as the master and operates with a
voltage control loop. The voltage controller acts to follow the
references set by the inter-group power controller. The intra-
group power sharing is assured by making other inverters at
the node slaves to the master. For this the overall output
current is measured and each slave is controlled to provide a
proportion of this.
C. Voltage Controller Design
Good dynamic control of voltage in a three-phase system is
often achieved by controlling in a rotating reference frame. A
key advantage is that positive sequence fundamental frequency
voltage and current terms appear stationary once transformed
and therefore a PI controller can reduce the steady-state error
to zero. However, negative sequence terms (arising from
unbalance) appear as a double frequency term and completely
eliminating error in this term is not possible. Similarly, a
standard PI controller may not sufficiently suppress harmonic
terms. Since both unbalance and distortion are to be expected
in a distribution system, control in a rotating reference frame
may not be the best option.
For unbalanced systems, a controller with a high gain at
fundamental frequency operating in a stationary reference
frame can be used. This controller will ensure that phase
voltages remain balanced even when unbalanced currents
are drawn through significant impedance. The gain can be
formed by a second order transfer function:
Although this second order function provides the gain
necessary to provide good tracking of the fundamental term,
it does not provide good rejection properties at harmonic
frequencies. For this repetitive control can be used.
Repetitive control offers good tracking performance for
periodic references and good rejection of periodic
The schematic diagram of figure 1 includes within the local
control loops for voltage and current an internal model
block in order to implement repetitive control. The internal
model operates on the error term and provides a series of
poles-pairs at multiples of a chosen frequency. The first
several pole-pairs are close to the imaginary axis but at
higher multiples the poles-pairs are brought into the left
half-plane. The internal model can be implemented from a
delay element (equal to the period of concern) in a positive
feedback loop. Including a low pass filter in the loop
provides the necessary shift to the left of the higher poles.
Figure 3 shows the arrangement of the control-loop and the
( ) sW
Figure 3 A repetitive control system, including internal model, for control of
voltage of master inverter.
The delay element is in fact chosen to provide a delay of just
less than the period of interest. Here a delay of τ=19.9 ms was
chosen (50 Hz system) with a first order low-pass filter.
The plant, PV, is a state-space representation of the plant
shown in figure 2.
The voltage tracking error is defined as
The state-space model (AV, BV, CV, DV) was obtained in the
normal way. The inductors were modelled with both series and
parallel internal resistance to include core losses and properly
characterise them at harmonic frequencies. The linear portion
of the local load is included in the plant but subject to
uncertainty. The non-linear portion of the local load is treated
as a disturbance current.
The controller, CV, that stabilises this loop must be robust to
disturbance and plant uncertainty. For this reason the H∞
design procedure is used to design the controller . An
augmented plant model,
, is formed, figure 4. This has an
exogenous input, w~and an external output, z~. An additional
input, vand scaling parameter, ξ are introduced. The low-pass
feature of W(s) results in a small output voltage error in the
low frequency range. W2(s) is chosen as a high-pass filter so as
to reduce control gain in the high frequency range so that the
The standard H∞ problem for
compensator such that the H∞ norm of the transfer function
from w~to z~,
H∞ norm of the transfer function from a to b,
is to find a stabilizing
wz T ~
, is smaller than a given bound and the
be smaller than 1. Moreover,
is minimized so as to obtain a small steady-state error. The
standard H∞ design tools in the Matlab toolbox were used to
choose a stabilizing compensator CV to meet these criteria.
( ) sW
( ) sW2
Figure 4 The standard H∞ problem for the repetitive control system.
D. Current Controller Design
Design of the controller for the current controlled inverters
follows a similar procedure as for the voltage controlled
case. The plant, PI, shown in figure 2, includes a feed-
forward term for the node voltage, vO. It is considered that
this term will not, in practice, be a perfect representation of
the node voltage and so a disturbance voltage, vd is included
in the model. The current tracking error is defined as
and the state-space model of the plant is
The H∞ design method is again applied to an augmented
plant model and a stabilising controller found.
IV SIMULATION STUDY
The proposed hybrid control system was assessed through a
series of time-step simulation
PSCAD/EMTDC. Two inverter groups were modelled each
with 3 inverters. Node A was composed of identical 30 kVA
inverters (to give a total power rating of 90 kVA) and node
B had similar inverters but with ratings of 15 kVA (a total
rating of 45 kVA). An interconnection line was placed
between the two nodes and a set of local loads provided at
each node. The switching frequency was chosen as 20 kHz.
A four wire LC filter was formed at each node. The filter
inductors are modelled with a series winding resistance and
a parallel core loss resistance. The load has a linear element
(star connected resistors) and a non-linear element (an
uncontrolled diode rectifier and resistor).. The system is
shown in figure 5.
Figure 5 Circuit diagram of complete distribution system model (note capacitances are in µF)
The full load frequency was set to 50Hz and the no-load
frequency to 50.05Hz. The example simulation shown here
used a load of 39kW at Node A and a load of 36 kW at Node B.
The load at Node B was increased to 60kW after 0.8s. Figure 6
shows the frequencies of the two nodes converge to 50.022Hz
after 0.7s and then, after the load increases, they fall to
0 0.51 1.5
Figure 6 Frequencies at the two inverter group nodes at start-up and
following the switching in of additional load.
Figure 7 shows how the power generation is shared between
the two inverter groups. With conventional sharing, group A
should provide twice the power because it has twice the
capacity of group B but here the sharing has been modified to
reduce the power exchange between nodes. There is an 11 kW
exchange through the line. When the local load at node B
increases by 24 kW, it would be expected under
conventional sharing that ⅔rd of that increase would be met
by a transfer from group A but in fact the modified sharing
means most of the increase is met locally and the transfer
only increases by 11 kW.
0 0.51 1.5
Real Power (kW)
Figure 7 Inverter-group real power output and power flow through the
Figure 8 shows that the total harmonic distortion (2nd to 31st
harmonics) at both nodes is kept below 0.5%. During the
start-up period the distortion caused by the non-linear loads
is apparent but as the internal model builds up a history of
the voltage error the voltage distortion is reduced.
Following the increase in load, there is a period of
readjustment. The currents supplied by each inverter group
are non-sinusoidal and rich in harmonics as shown in figure
9. However, that the power exchange between nodes occurs
with undistorted current because the node voltages are free of
distortion. Figure 10 shows that the slave inverters, under
repetitive control, accurately track the current reference
obtained from the load current and provide their share of both
fundamental and harmonic current.
00.2 0.40.60.81 1.21.4
Voltage THD (%)
Figure 8 Voltage waveform distortion
Figure 9 Inverter output current and interconnection line current
Figure 10 Current sharing and tracking performance
A hybrid control system has been proposed for an island-mode
distribution system containing many inverters, some in close
proximity and some not. The key features are that inter-group
power sharing avoids communication links by using droop
characteristics. These droop characteristics have been
modified so that local loads are predominantly met by local
generation and reaming load is shared in proportion to
power rating. Sharing between inverters in close proximity
and connected to a common node is achieved through a
master-slave arrangement. To provide good tracking of the
current sharing reference in terms of both fundamental and
harmonic current, repetitive control has been used.
Repetitive control has also been used in master inverter to
provide low distortion voltage waveforms at the common
node even in the presence of substantial non-linear local
load. A simulation study, using EMTDC, has shown that the
control system achieves good power quality and satisfactory
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This work was supported by the EPSRC (www.epsrc.ac.uk)
on grant number GR/N38190/1