 Open Access
 Total Downloads : 19
 Authors : K.Rameshkumar, A.Sakthivel, P.Vijayakumar
 Paper ID : IJERTCONV2IS06010
 Volume & Issue : RTIA – 2014 (Volume 2 – Issue 06)
 Published (First Online): 30072018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Predictive Current Control Strategy for Voltage Source Inverter
Predictive Current Control Strategy for Voltage Source Inverter

ameshkumar1, A.Sakthivel2 ,Member, IEEE, A.Senthilkumar4, Member, IEEE
1, 2, 4 Department of Electrical and Electronics Engineering, Dr.Mahalingam College of Engineering and Technology, Pollachi, India
1 rameshvel.k@gmail.com, 2ersakthi@yahoo.com,
3asenthil@drmcet.ac.in
AbstractWhile the classical control techniques for three phase twolevel threeleg inverters are based on pulse width modulation or 3D space vector modulation, this paper presents a Finite Control Set Model Predictive Control (FCS MPC) strategy for a twolevel threeleg voltage source inverter with resistive inductive load. The Model Predictive Control method chooses a switching state that minimizes the error between the output currents and their references. Firstly the performance of the proposed predictive control method is compared with pulse width modulation control. Secondly the performance of controller is analyzed with various conditions is carried out. The proposed controller offers excellent reference tracking with less current harmonic distortion for all conditions. The proposed system's performance is investigated using a MATLAB simulation model.
Keywords Model predictive control (MPC), voltage source inverter, Current control, Pulsewidth modulation (PWM)

INTRODUCTION
Voltage source converters have been extensively studied in the last decades in most industrial sectors for many applications. By considering the increasing energy demands and power quality and efficiency, a control and power conversion using power electronics have become an important topic today. Nowadays, MPC control scheme has been applied for current control of ActiveFrontEnd Rectifier[10],[11], Distributed Generation Systems[12], Active Filters and Power Conditioning[5],[13],[14], Non
P.Vijayakumar3
3 Department of Electronics and Communication Engineering, Kathir College of Engineering, Coimbatore, India
4vijay_p6@hotmail.com
powerful and robustness of the proposed control method are evaluated through simulations results. This paper is organized as follows. In Section II, the mathematical model of the converterload system is presented, followed by the explanation of the proposed control strategy in Section III. In Section IV, simulation results are presented. Finally in Section V appropriate conclusions are drawn.

POWER CONVERTER MODEL
Fig. 1. Voltage source inverter power circuit.
A. Voltage Source Inverter Model
The power circuit of the converter considered in this work is shown in Fig. 1. It has been selected for a clear analysis of a predictive control strategy with RLLoad. It is a three leg two level inverter operated by switching S1, S2
,S3, S4, S5and S6.The inverter consisting of two pairs of complementary controlled switches in each leg(S1, S4), (S2, S5) and (S3, S6). The switching states of converter are determined by the gating signals Sa, Sb, and Sc as follows:
Conventional Renewable Energy[15],[16], uninterruptible
S 1 if S1 on
and
S 4 off
power supplies (UPS)[4], drives[17],[18] and power factor correction [9]. This control scheme predicts the future load
a
0
if S1
off
and
S 4 on
(1)
current behavior for each valid switching state of the converter, in terms of the measured load current and predicted load voltages.
The predictions are evaluated with a cost function that minimizes the error between the predicted currents and their
S
1 if S on
S 2
b
0 if S 2 off
1 if S 3 on
and and
and
S 5 off
S 5 on
S 6 off
(2)
0
references at the end of each sampling period.This has been applied for the controlling of power converters due to the advantages, like fast dynamic response, easy inclusion of
c
if S 3
off
and
S 6 on
(3)
nonlinearities and constraints of the system, and the flexibility to include other system requirements in the
and it can be expressed in vectorial form by
2 2
controller [2],[7].The classical current control techniques for a three leg two level VSI use PI controller and a modulation stage (PWM or SVM) to generate the gating signals. In the FCSMPC takes the advantages of direct application of the control action to the converter without using modulator
S
where a e j 2 / 3
(Sa aSb a
3
Sc )
(4)
stage. Compared with the Classic Linear PIPWM the MPC offers manyadvantages such as good reference tracking and minimum output distortion [1],[2],[5],[6].In this paper, the
The output voltages space vectors generated by the
inverter are defined by
Fig.3.Model predictive current control block diagram.
2
v Ri L di
dt
(10)
v (VaN VbN VcN ) 3
(5)
where R is the load resistance L is the load inductance, v
where N , N and N are the phase to neutral voltages of the inverter . Then the load voltage vector V can be related to the switching state vector S by
is the voltage generated by the inverter.

MODEL PREDICTIVE CURRENT CONTROL
Then
v Vdc S
v 2 V (Sa aSb a 2
3 dc
(or)
Sc )
(6)
(7)

The Control Strategy
The proposed predictive current control scheme is shown in Fig. 3.It uses the system model to predict the future behavior of the variables to be controlled. The quality function or cost function or error between the reference and predicted values is calculated. The switching state that minimizes g is selected and applied during the next sampling
v 2 V (Si [1 a
i 3 dc
a 2 ])
(8)
period.
It consisting of five main steps as follows[5]:
where vi
is the voltage vector generated by the switching

Measurements:The predictive model requires supply voltage and load currents at instant of k. In this system
states Si with = 0, 7.
By evaluating each of the switching states in (8), eight voltage vectors ( v0 v7 ) can be generated by the inverter resulted in only seven different voltage vectors because v0 and v7 produce the same zero voltage vector , that means a threephase twolevel voltage source converter can deliver
only 7 different voltage vectors, although there are 8
different switching combinations, as it can be seen in Fig. 2.
supply voltage is known and constant, when we go for other applications, supply voltage measurement is needed example APF. For this reason one voltage sensor and three current sensors is needed.

References calculation:Based upon on the application the current references are generated. In this system a simple modelling and control the inverter. So that the references are user defined. By changing the reference it can be used for any applications.

Extrapolation:For sufficiently small sampling time,
example TS
is less than 20Âµs no extrapolation is needed. In
that case take approximation as
i* (k 1) i* (k)
(11)
0
When sampling time
0
TS is greater than 20Âµs the
following fourthorder extrapolation can be used:
i* (k 1) 4i* (k) 6i* (k 1) 4i* (k 2) i* (k 3)
0 0 0
0 0
(12)

PredictiveModel: A discretetime form of the load current
p>Fig. 2. Voltage vectors generated by the inverter.
for a sampling time
TS can be used to predict the future


Load Model
In a balanced threephase load, the current can be defined as a space vector by
value of load current by using measurement of load current and supply voltage at the sampling instant k.
di
2
Approximating the derivative by
2 dt
i 3 (ia aib a
ic )
(9)
di i(k) i(k 1)
The load current dynamics can be expressed by vector equation
dt TS
(13)
Substituting equation (13) in equation (10) the following expression as
i(k) i(k 1)
B. MPC Algorithm
v Ri L
TS
Then the load current at instant k as
1
(14)
In general, the control algorithm can be summarized to the following steps [6].

Measure the load currents.

Predict the load currents for the next sampling instant
i(k)
RTS
L [Li(k 1) TS v(k)]
(15)
for all the possible switching states.

Evaluate the cost function for each prediction.
Shifting the discretetime one step forward in the future load current can be determined by

Optimal switching state is selected which minimizes thecost function.
i(k 1)
1
RTS L
[Li(k) TS v(k 1)](16)

Apply the new switching state.

The optimal voltage vector is selected which minimizes the cost function and the switching state associated to the
where R and L are the load resistance and inductance,
respectively is the sampling time, i(k) is the measured load current, and v(k+1) is the inverter predicted voltage is the decision variable to be calculated by the controller.
5) Cost function or quality function optimization:The error between the reference current and the measured load current at the next sampling instant can be expressed as follows
selected voltage vector is set to the gating signals.


SIMULATION RESULTS
In this simulation two types of cases are considered. In the first case the Inverter controlled by the two different current control methods have been carried out, and in second case using Model Predictive Current Control method the simulations are carried out during non
g i* (k 1) i(k 1)
(17)
sinusoidal reference and input frequency variation in order to assess the performance of the proposed predictive
where, i* (k 1) is the reference current vector and i(k 1) is predictive load current vector. Furthermore, (17) can be expressed in stationary frame as follows
method.The Simulations are carried out using MATLAB/Simulink. The fig 4 and 5 denoting the matlab simulink model of the PIPWM and MPC controller based voltage source inverter
*
g i (k 1) i
where i (k 1) and
(k i (k 1) i (k (18)
*
i (k 1) are the real and imaginary

Comparison with PIPWM Control
A comparison of the proposed predictive current control with Classic Linear PIPWMcontrol is presented in Figs. 6
parts of the predicted current vector and i * (k 1) ,
i * (k 1) are the real and imaginary parts of the reference
current vector respectively. In this work, the absolute error is used for computational simplicity. Other quality functions such as error squared could also to be used that can be expressed as follows
and 7. Here, the amplitude of reference current is reduced from 13 A to 5.2 A at instant 0.015 (s),while keeping the amplitude current fixed. This is done to assess the decoupling capability of the current control loop. PI with PWM current control, shown in Fig. 6(a), presents slower dynamic response and some noticeable coupling effects between and.In the response of the proposed predictive current control, for the same test, is shown in Fig.7(a).Its
g (i
* (k 1) i
(k 1))2 (i
* (k 1) i
(k 1))2
(19)
dynamic response is as fast than linear PIPWM and no coupling effects between and .In Fig. 6(b) and Fig. 7(b) denoting the corresponding load voltages.
Finally the corresponding switching state is given to the
inverter.
Fig . 4. Inverter controlled by PIPWM controller Simulink diagram.
Fig. 5.Inverter controlled by MPC controller Simulink diagram.
Table.1 Simulation Parameters
Variables
Values
Supply voltage Resistance Inductance
PWM carrier frequency
Sampling time Reference current
100V
0.5 ohm 10mH
2kHz 20e6
13 A
Fig. 6.Classic Linear PIPWM step on . a) Ref, Load and ) currents. b) load voltage.
Fig. 7. MPC step on . a) Ref, Load ( and .) currents. b) load voltage.

Performance of MPC for Various Conditions

Analysis with input frequency variations
In this analysis the Reference frequency F = (5020 70)Hz , Ref current (Ia,Ib,Ic) =13A and load Ra = Rb = Rc
= 0.5ohm ; La = Lb = Lc = 10mH;
Fig.8 Simulation result with input frequency variations
In the fig.8 shows that good reference tracking with frequency variations and fast response is observed.

Analysis with Non sinusoidal reference

In this the seventh harmonic reference with amplitude and frequency are 10 A at 50 Hz, respectively. The loads are the same as of the input frequency variations earlier.
Fig .9 .Simulation results with seventh harmonic injected sinusoidal reference currents for Ts= 20s
The results is indicated in Fig.9 where a good tracking of the load current to its reference is observed, which demonstrates that this control strategy can be applied effectively in a twolevel threeleg converter operating as an active lter.


CONCLUSION

In this paper the FSMPC for twolevel voltage source inverters were studied. The control technique does not need to use modulator. The control algorithm has been evaluated with two different cases through simulation results. It has been noticed that the control algorithm provides very good current tracking behavior. First of all, when the step change in the amplitude of the reference, the simulation results shows that the predictive control method has fast dynamic response with inherent decoupling between iand i. Secondly, the simulation results show the good performances of the current tracking ability in various conditions such as input frequency variations and non sinusoidal references.
Finally the Simulation results show that FSMPC strategy gives very good performance under these conditions. In further research on predictive control is to analyze the performance of various condition such as load variations and sampling frequency variations.
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