Abstract A microgrid can be used in

Abstract
— In
order to regulate current and voltage of the inverters connected to renewable
energy units in a microgrid, a predictive control technique is used. This
control technique uses a state-space model of the inverters used in the microgrid.
The proposed microgrid is analyzed during grid-connection and
grid-disconnection using MATLAB. It can be seen from the simulation studies that,
with this control method, inverters connected to DG units can effectively
operate thereby providing required voltage and current under different conditions.

Index
Terms —
Distributed generation, predictive control, grid-connected, stand-alone  

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I.     INTRODUCTION

Microgrid
is a low-voltage distribution network with distributed generations (DGs) such
as solar photovoltaics (PVs), microturbines and fuel cells together with power
converters, energy storage devices, and customer loads. A microgrid can be used
in a military base station for improving reliability and security of power
supply during grid failures and other emergency situations. There is an
increased penetration of DGs in the power grid. These DGs
provide variable DC or AC output voltage and thus require inverters or
rectifiers to interface them with the microgrid 1.

Inverter control has been widely applied
in microgrids, energy storage systems and uninterruptible power supplies
(UPSs). Several control methods such as linear, sliding mode, artificial
intelligence and predictive control have been used for the control of inverters
in microgrids operating under various conditions 2, 3. Predictive control
has been gaining increased attention in recent years due to its significant
advantages over other classical control methods. The main principle of
predictive control is the use of a system model in order to predict the future
behavior of the controlled variables. Then the controller uses this information
to obtain the optimal control input, based on a predefined optimization of a
cost function. Several predictive control methods, namely deadbeat control, generalized
predictive control (GPC) and model-based predictive control or simply model
predictive control (MPC) are available 4.

A microgrid is able to operate efficiently under both grid-connected
(GC) as well as stand-alone (SA) conditions. So an effective control method is
needed to provide the desired voltage and power to the load under both these
conditions. In
GC condition, inverter voltage cannot be regulated as inverter is tied to the
grid voltage and frequency. In this condition, the inverter current is controlled
to inject a preset amount of power into the grid 5. In SA condition, the
inverter output voltage is controlled to provide the required power to the load
6. In this paper, a control method called model predictive control (MPC) is
used to control the output voltage and real and reactive power of the inverter.
A state-space model of the inverter is used to predict the future behavior of
the variables such as voltage and current. The main advantages that make MPC suitable
for the control of inverters are:

 

·        
Easy inclusion of non-linearities in the model as inverters are
generally non-linear systems with a finite number of switching devices and simple
treatment of constraints, such as maximum output voltage of the inverter,
maximum current etc.

 

·        
No need of any modulator and gate drive signals as the inverter
switching signals are generated directly by the controller itself.

 

One
disadvantage of using MPC is the need of huge number of calculations. However
with the advent of faster and powerful computers, there has been an increase in
the application of this method. In 7-11, MPC is used to control an inverter
but the different modes of operation of the inverter in a microgrid such as GC
and SA modes have not been addressed.

Different
from other methods, a new state-space model based MPC approach is used in this
paper to regulate the inverter during its different modes of operation. Finally
simulation studies are conducted on the proposed microgrid to test the
effectiveness of its operation during GC mode as well as SA mode. As this
microgrid can be used in both GC and SC modes, it is useful for military base
stations during grid emergencies and failures. 
  

                                                                                                                                                 
II.    SYSTEM DESCRIPTION

The
proposed microgrid system comprises a PV array as the main DG unit, which is
connected in parallel to the dc side of the DG inverter through a dc/dc boost converter.
Vdc  is the value of the DC link
voltage of the DG inverter. A lithium ion storage battery, which is used to
back up the intermittent generation of the PV array, is also connected to the
dc side of the DG inverter through a bidirectional dc/dc buck-boost converter. There
are two semiconductor switches in each of the three legs of the three-phase
inverter shown in Fig. 1. An LC filter is connected to each phase of the
inverter, where L and C represent the inductance and capacitance of the filter
respectively. R represents the inverter power loss resistance. The inverter
along with the filter is connected to a load as well as the utility grid. In Fig.
1, RL and LL are the resistance and inductance of the
load respectively.

The
inverter is connected to an LC filter to smoothen the inverter output currents.
The currents flowing through the filter in each phase are represented by ia,
ib and ic. The output currents of the inverter in each of
the three phases are represented by iDG,a, iDG,b
and iDG,c. The currents supplied by the grid in each of the
three phases are represented by iGa, iGb and iGc
respectively. The load currents in each of the three phases are represented by
iLa, iLb and iLc. Voltages across the load in
each of the three phases are represented by VLa, VLb and
VLc.

In
case of a fault in the grid, a circuit breaker (CB) is used to disconnect the
microgrid from the utility grid. The microgrid is now operated in the islanded
mode. Under GC condition, the currents – iDG,a, iDG,b and
iDG,c are regulated to their specified reference values in order to
provide a preset power to the load. So the inverter and grid can share the load
demand during the GC condition.

During
SA operation, the inverter in the microgrid is required to supply for all the
load power demand. So under the SA condition, the inverter can regulate its
output voltage across the load in each of the three phases as shown in Fig. 1. This
is done in order to provide the required amount of reliable power to the load.
The switches (S1, S2, S3, S4, S5
and S6) of the inverter have two operating states and can be defined
as follows:

                                                       (1)

where i = 1, 2, 3, 4, 5, 6.

The
switching states of the semiconductor switches are controlled separately in
each of the three phases. Here we assume a balanced three-phase system. The
filter and load impedances remains the same in all the three phases of the
system. There are mainly two modes of operation of a microgrid, namely GC and
SA modes of operation. In GC mode, the grid as well as the DG supplies the
required power to the load. Hence it is necessary to develop a suitable control
strategy to control the output power of the DG during this mode. During the transition
from GC to SA mode, the DG can respond effectively with minimum delay to switch
over from GC to SA mode. In SA mode, the DG can regulate the load voltage to
provide the required real and reactive power to the load.

In
the proposed microgrid, an RL load is considered.  The proposed control method can also be
applied to the same microgrid with purely resistive load as well. The load
voltage, the inverter output current, real and reactive power and also the real
and reactive power consumed by the load are analyzed in the GC mode first. Then
the load voltage and inverter output current are analyzed during the transition
from GC to SA mode. In addition, the real and reactive power consumed by the
load is also analyzed during SA mode. 

                                                                                                                      
III.   INVERTER MODELLING AND
CONTROL

A microgrid should be
able to provide its load with specified voltage, current and power during both
GC and SA modes. Thus effective strategies are developed in this paper to
control the DG inverter during both GC and SA modes.

 

A.   
Control of Inverter During GC Mode

When
the microgrid is connected to the grid, the microgrid voltage and frequency is
tied to that of the utility grid and thus remains fixed. In order to make the
inverter in the microgrid provide specified power to the load, the output
current of the inverter needs to be controlled. This mode of inverter operation
is called Current Control Mode (CCM). The single-phase equivalent circuit of
the inverter based microgrid in the GC mode is shown in Fig. 2. By applying
Kirchhoff’s law to the single phase equivalent circuit, the following equations
are obtained:

                                                             (2)

                                                                     (3)

Euler difference method is applied to (2) and (3) to derive the
augmented form of the discrete state-space model as follows:

                         (4)

                                                                         (5)

where 

 

 

xc(k) is the state vector, yc(k) is the output vector, ?uc(k) is the incremental change in the switching state input vector, Ts is the discrete sampling
time period, k is the sampling
instant, xc(k+1) is the state vector at the sampling
instant k+1 and yc(k+1) is the
output vector at the sampling instant k+1.
Ac, Bc, Cc
and Dc are the different
matrices used in the state-space model. By using the state-space model, MPC is
used to control the output current of the inverter in GC mode.     

B.   
Control of Inverter During SA Mode

When the grid is disconnected, the
load voltage is disturbed. This will affect the operation of the microgrid. The
load voltage needs to be maintained at the required nominal value to ensure the
reliable operation of the load. Thus the inverter controller is made to switch
over from GC mode to SA mode of operation to maintain the load voltage
constant. As a result, the DG inverter is operated to maintain the required
load voltage and thereby supply the required power to the load. This mode of
operation of the inverter is called Voltage Control Mode (VCM). The single-phase
equivalent circuit of the inverter based microgrid in the SA mode is shown in
Fig. 3. Since the grid is disconnected during SA mode, it is not shown in Fig. 3.
By applying Kirchhoff’s law to the single phase equivalent circuit, the following
equations are obtained:

                                                              (6)

                                                                          (7)

Due to high sampling
frequency, it can be assumed that

                                                                                       (8)

Then, Euler difference method is used to derive the   discrete time state space model as follows:

                                                       (9)

                                                                          (10)

where

;

 

X (k), U (k) and Y (k) are the state,
input and output vectors respectively. Ad,
Bd and Cd are the different matrices
used in the state-space. By using the state-space model, MPC is used to control
the output current of the inverter in GC mode.  
 

 

                                                                                                                                                
IV.   SIMULATION STUDIES

MATLAB/Simulink
is used to simulate the microgrid for two test cases. The microgrid is operated
under GC mode in the first test case. In the first test case, DG needs to
provide the required amount of power to the load. When the grid is disconnected
from the microgrid, there should be a smooth transition from GC to SA mode to minimize any
sudden voltage change across the load 12. Both the test cases are explained
as follows:

A.   
GC mode

In the GC mode, the
desired amount of real and reactive power to be provided by the DG to the load
is set as the reference values. The inverter output voltage is same as the grid
voltage in the GC mode. Since the three-phase microgrid is assumed to be a
balanced system, the output currents in each phase of the inverter remain the
same. The parameters used in the simulation are given in Table I.

TABLE I.            
PARAMETERS OF THE PROPOSED
SYSTEM

Parameters

Value

DC source voltage

Vdc
= 325.2 V

Inverter power loss resistance

R = 0.001 ?

Filter inductance

L = 1.2 mH

Filter capacitance

C = 20 ?F

Load resistance

RL = 10 ?

Load inductance

LL = 10 mH

Sampling period

Ts = 0.5 ?s

Frequency

f=50 Hz

 

The values of reference
real and reactive power output/phase of the inverter chosen are: P=1000 W; Q= 1000 VAr. The total three-phase real and reactive power output
of the inverter is 3000 W and 3000 VAr respectively. Power factor and reference
output current/phase of the inverter are calculated as follows:

Power factor (pf) = = cos45° =
0.707           

Reference Output current/phase =
1.414×P/ (230×pf) = 8.3 A (peak)

 

As shown in Fig. 4, the value of the reference real power output
of the three-phase inverter is maintained at 3000 W. In Fig. 5, it is seen that
the value of the reference reactive power output of the three-phase inverter is
maintained at 3000 VAr.

 

Figure 4: Real
power output waveforms.

Figure 5: Reactive
power output waveforms.

 

B.   
Transition from GC to SA mode

 

Initially the microgrid
operates in GC mode. At t= 0.035s, the grid is disconnected. As shown in Figs. 6 and 7, MPC ensures a
rapid transition of the microgrid from GC to SA mode, except for minor
transient disturbances in load voltage and inverter output current for a very
short time duration of about 0.005s.

 

After this transient period, the load voltage and inverter output
current attains a steady state value. The output current of the inverter
increases to 31.03 A (peak) in SA mode, as shown in Fig. 7.

 

The amplitude of the reference output voltage of the inverter is
maintained at 325.2 V (peak) in SA mode as shown in Fig. 6, to ensure the required
power delivery to the load. Thus the microgrid is capable of stable and
reliable operation both in GC as well as in SA mode. This ensures continuous
and reliable supply of power even during grid failures.

 

Figure 6: Three-phase
load voltage.

Figure 7:
Three-phase inverter output current.

 

                                                                                                                                                               
V.    CONCLUSION

A new state-space model
based MPC approach has been proposed for the control of a three-phase inverter,
which is connected to a DG in the proposed microgid. The microgrid is tested
under both GC and SA modes of operation. The proposed MPC makes use of the
model of the inverter to control parameters like voltage, current and power of
the DG. The simulation results have shown that the proposed approach achieves
good performance on both current-reference tracking in GC mode and
voltage-reference tracking in SA mode. With the help of the newly developed
control strategy, the proposed microgrid is able to operate efficiently and
accurately during both GC and SA modes. Thus, this microgrid can be operated even
during grid emergencies and failures, which is an
essential requirement in military base stations, built for ensuring national
security. To
reduce the transient disturbances in the load voltage and improve the load
voltage profile during the transition from GC to SA mode, the use of battery
energy storage system on the ac side of the DG inverter can be considered,
which will have a scope for future research.    

 

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Figure
1.