An Improved Hysteresis Band based FCS MPC for Grid-connected

Three Phase Inverter

Hendi Purnata

, Galih Mustiko Aji

, Afrizal Abdi Musafiq

and Purwiyanto

Department of Electronics Engineering, State Polytechnic of Cilacap, Indonesia

Keywords: Optimization, FCS MPC, Inverter, Hysteresis Band.

Abstract: The Indonesian government has begun to promote the use of non-oil and gas alternative energy. Optimizing

renewable energy technology is a priority for system implementation. One method to overcome modulation

in one computational stage is by using a Finite control set – predictive control model (FCS MPC) compared

to traditional controllers such as PID, SPWM. This method is very challenging to find the optimal, especially

in the field of prediction that considers far into the future. FCS MPC in this method provides the latest

discovery by adding a hysteresis band to produce a better current. The results of research on optimization of

renewable energy technology apply with direct current response system of 882.7 Volts with a steady-state

error of 2 %. The optimal current has been obtained from the hysteresis band of 0.2 bands. On switching on

the inverter, the second vector voltage or g2 is 0.47or this vector value is used for switching on the inverter.

FCS MPC has been implemented to a two-level converter system, then the need for a filter circuit to produce

a sine wave like a pure sine wave generated by a generator.

1 INTRODUCTION

Indonesia has large renewable energy capabilities

such as hydropower, geothermal, wind, solar,

oceanic, or biomass. Sources of power generation

such as nuclear and fossil fuels depend on the

depletion of natural resources and the process of

generating electricity can damage the environment.

The right choice to be sustainable is to use renewable

energy because it has decent economic potential and

is environmentally friendly (Secretariat General Of

The National Energy Board Koutl Oo, n.d.).

The Indonesian government is starting to flock to

apply non-fossil renewable energy. The solution is

expected to be able to maintain the stock of energy

resources in Indonesia. Based on the National Energy

Policy (KEN), in 2025 Indonesia can use energy

sources with a composition of 77% fossil and the

remaining 23% from new and renewable energy. The

government reaffirmed in Law No. 25 of 2000 on

PROPERNAS (National Development Program) that

this policy is the main program to increase the use of

renewable energy. To achieve the National

https://orcid.org/0000-0003-2047-816X

https://orcid.org/0000-0002-1582-9597

https://orcid.org/0000-0002-8241-1000

Development Planning, the experts must be from

within the country, so that human resources can know

and implement the National Development Plan (iesr,

2019). Converter technology on renewable energy is

a special topic in this research, which focuses on the

energy results obtained from power electronics

devices, namely converters. Some of the problems

raised following previous studies look at the

problems, methods to the results obtained in previous

studies. The study (Lyu, Ma, Yan, 2020) explained

that MPC was introduced as a controller that can look

ahead or predict and take advantage of low

frequencies in switching and can manipulate system

stability. MPC can also overcome flux and torque

ripples. FCS-MPC is used to control power electronic

devices. The basic concept of this method is to predict

the system when switching then evaluate the cost

function which will be the optimal value and applied

to the next control. In the study (Vazquez et al, 2014)

applying FCS-MPC which is easier than conventional

controllers because this system is online to determine

the optimization value. Some of the advantages of

control in this study are the response generated is

748

Purnata, H., Mustiko Aji, G., Abdi Musaﬁq, A. and Purwiyanto, .

An Improved Hysteresis Band based FCS MPC for Grid-connected Three Phase Inverter.

DOI: 10.5220/0010952900003260

In Proceedings of the 4th International Conference on Applied Science and Technology on Engineering Science (iCAST-ES 2021), pages 748-755

ISBN: 978-989-758-615-6; ISSN: 2975-8246

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

dynamic, does not have a modular, fast response and

can overcome non-linear systems.

In addition, the problem in the output converter is

in the switching which results in harmonics. In this

study (Gendrin, Gauthier, Lin-Sh, 2016, p-5487),

overcoming network-connected switching using a

direct power control (DPC) sequence with a constant

frequency. Research (Zhang et al, 2017), the constant

switching frequency can be overcome but by using

large calculations and complex methods. Research

(Tarisciotti et al, 2014) made an FCS-MPC scheme to

overcome switching to get a constant frequency.

To get a good FCS-MPC computation, the

computation requires implementation time beyond

the switching of the phase-locked loop (PLL) and

maximum power tracking. To overcome this

limitation there is a modulated MPC (M2MPC) by

utilizing a constant switching frequency (Tarisciotti

et al, 2014) (Zhang et al, 2016) (Yang et al, 2017).

M2MPC is designed to control three-phase active

rectifiers by using seven levels of H-Bridge cascade

and using a matrix converter, therefore the

computational burden of using this method is very

large.

In the study (Guo et al, 2017) FCS-MPC using

commutation so that the current network can be

balanced. Efficiency in the form of a reduction in the

form of sectors on the inverter, other than in the

network can be used for speed control on a permanent

motor synchronous machine (PMSM) based on

torque and flux control. In this control, the order in

the inverter switching table is not considered (Nadour

et al. 2020).

Research by (Ali, 2021) (Purnata, 2017) combines

the hysteresis band and svpwm methods for current

and voltage improvement. Current improvement

utilizes the hysteresis band method while SVPWM

uses the voltage improvement method.

From some of the studies above, researchers have

an idea to apply FCS MPC to a converter connected

to the grid. This system is added a hysteresis band to

produce a current limit that is more optimal than the

ratio of the current value of idq.

2 MODELLING OF THE FCS

MPC WITH GRID

2.1 FCS MPC

Model Predictive Control (MPC) or predictive

control system is included in the design concept of

process model-based controllers, where the process

model is used explicitly to design controllers by

minimizing a criterion function. The underlying idea

for each type of MPC is (Wang et al, 2012). The FCS

MPC block diagram can be seen in Figure 1:

Figure 1: above is a setting using FCS MPC by

utilizing the optimization of the cost function from

the calculation between the reference and the current

prediction. The cost function equation can be shown

in the equation below:

𝑔𝑖



∗



𝑘1



𝑖



𝒑



𝑘1



𝑖



∗



𝑘1



𝑖



𝒑



𝑘1





(1)

Figure 1: Block Diagram System FCS MPC.

𝑣



𝑖



Inverter

DC/AC

Filter

Grid

𝑣



𝑣



∗

𝑒



𝑖



∗

𝑖



∗

𝑣



𝑣



𝑖







𝑖







𝑘  1

𝑆



Cost Function

Optimization

redictive

ode

abc/dq

𝜃

An Improved Hysteresis Band based FCS MPC for Grid-connected Three Phase Inverter

749

Where 𝑖



𝒑



𝑘1



and 𝑖



𝒑



𝑘1



is part of the real

and imaginary in the prediction model. 𝑖



∗



𝑘1



and

𝑖



∗



𝑘1



is the current reference. The output signal

from the inverter corresponds to the generated DC

voltage and the state of the switching signal 𝑆



,𝑆



and 𝑆



. The converter uses a two-level converter in

which there are 6 sectors and 8 vectors following the

equation below:

𝑆







1 𝑗𝑖𝑘𝑎 𝑡𝑜𝑝 𝑠𝑤𝑖𝑡𝑐ℎ 𝑚𝑒𝑛𝑖𝑛𝑔𝑔𝑎𝑙𝑘𝑎𝑛  𝑡ℎ 𝑖𝑠 𝑂𝑁

0 𝑗𝑖𝑘𝑎 𝑏𝑜𝑡𝑡𝑜𝑚 𝑠𝑤𝑖𝑡𝑐ℎ 𝑚𝑒𝑛𝑖𝑛𝑔𝑔𝑎𝑙𝑘𝑎𝑛  𝑡ℎ 𝑖𝑠 𝑂𝐹𝐹

The value at the output voltage is defined as

𝑣



𝑆



𝑣



𝑣



𝑆



𝑣



𝑣



𝑆



𝑣



(2)

Where 𝑣



is a DC voltage source. Taking into

account the unitary vector 𝑎𝑒

/









𝑗



3/2

which represents a phase shift of 120°, The

output voltage on the grid can be defined as

𝑣

𝑣



𝒂𝑣



𝒂

𝟐

𝑣





(3)

Where 𝑣



,𝑣



and 𝑣



are the phase-to-neutral

(N) voltages in the inverter. The possible

combinations of the gate signal in the inverter,

namely 𝑆



,𝑆



and 𝑆



, there are eight possible

according to the table below

Table 1: Switching States Voltage Vector.

𝑆



𝑆



𝑆



Voltage Vector v

0 0 0



0

1 0 0





𝑣



1 1 0





𝑣



𝑗

√

𝑣



0 1 0





𝑣



𝑗

√

𝑣



0 1 1





𝑣



0 0 1





𝑣



𝑗

√

𝑣



1 0 1





𝑣



𝑗

√

𝑣



1 1 1



0

Figure 2: voltage with real and imaginary axes.

2.2 Grid Model

The three-phase axis with the X and Y coordinate

systems showing the fixed axis and the rotating axis.

The mathematical model on the grid will be shown in

the image and equation below.

Figure 3: Grid Model.

𝑣



𝑣



cos



𝜔.𝑡



(4)

𝑣



𝑣



cos𝜔.𝑡 

2𝜋



(5)

𝑣



𝑣



cos𝜔.𝑡 

4𝜋



(6)

Where 𝑣



is the amplitude at the phase voltage

and is the angular frequency. The three-phase

currents in this system are shown in the following

equation:

𝑖



𝑖



cos



𝜔.𝑡  𝜑



(7)



→𝑔





→𝑔



,

→𝑔

,



→𝑔





→𝑔





→𝑔





→𝑔



iCAST-ES 2021 - International Conference on Applied Science and Technology on Engineering Science

750

𝑖



𝑖



cos𝜔.𝑡 

2𝜋

𝜑

(8)

𝑖



𝑖



cos



𝜔.𝑡 

4𝜋

𝜑



(9)

Where 𝑖



is the amplitude of the phase current

and is the phase voltage and current. From the

symmetrical form, the line-to-line voltage can be

defined as

This section must be in one column.

𝑣



𝑣



𝑣



(10)

𝑣



𝑣



𝑣



(11)

𝑣



𝑣



𝑣



(12)

The number of neutrals at current 𝑖



𝑖



𝑖



𝑖



𝑖



(13)

In the case of the neutral current balance is zero

(𝑖



0) then the above equation can be simplified to:

𝑖



𝑖



𝑖



0

(14)

𝑣



𝑣



𝑣



0

(15)

Figure 4: Flow Diagram Implementation FCS MPC.

Startup

Measure i(k)

Back Emf estimation

(

.23

)

t = inf

𝑥𝑥1

Predictive

model

(

.16-21

)

Hysteresis Current

Controller (eq.22)

Evaluation cost

function(eq.1)

Optimal vector v(k)

end

sampling

An Improved Hysteresis Band based FCS MPC for Grid-connected Three Phase Inverter

751

The power flow in the grid converter can be

controlled by improving the DC-link voltage with a

constant limit.

3 PROPOSED SYSTEM

The model that will be implemented in this study is

as shown in the image below, for determining the cost

function, following equation (1). The following is an

explanation for predicting the incoming current and

providing a hysteresis band before entering the cost

function

Figure 5: Block Diagram Proposed System.

The reference current for short time (K+1) in the

current prediction block is following the equation

below in equations (16) and (17) while the current

(k+2) in equations (18) and (19). In addition to the

current reference, the current prediction current (k+1)

is shown in equations (20) and (21)

𝑖



∗



𝑘1



3𝑖



∗



𝑘



3𝑖



∗



𝑘1



3𝑖



∗



𝑘2



(16)

𝑖



∗



𝑘1



3𝑖



∗



𝑘



3𝑖



∗



𝑘1



3𝑖



∗



𝑘2



(17)

𝑖



∗



𝑘2



3𝑖



∗



𝑘1



3𝑖



∗



𝑘



3𝑖



∗



𝑘1



(18)

𝑖



∗



𝑘2



3𝑖



∗



𝑘1



3𝑖



∗



𝑘



3𝑖



∗



𝑘1



(19)

𝑖







𝑘1



3𝑖





𝑘



3𝑖





𝑘1



3𝑖





𝑘2



(20)

𝑖







𝑘1



3𝑖





𝑘



3𝑖





𝑘1



3𝑖





𝑘2



(21)

After knowing the current prediction, the use of

Hysteresis Current Controller is a comparison

between the current prediction and the previous

current and by giving a band of 0.2 bands. The

equation for determining the band before entering

into optimization is

𝑖



𝑖



𝑖







(22)

The optimization used is to determine a vector that

is truly optimal. To obtain the optimal vector, it is

assumed that the input to the grid is a sinusoidal wave

with a fixed amplitude and a fixed frequency. Vector

can be seen from the equation below:

𝑅𝑖𝐿

𝑑𝑖

𝑑𝑡

e

(23)

where v is the vector voltage generated from the

inverter, 𝑖 is the current flowing to the grid and e is

the vector for the back emf. All switching states at

𝑣𝑘 with current current 𝑖𝑘 are compared with

subsequent current 𝑖𝑘1 with estimates at

𝑖



𝑘  1.

4 SIMULATION RESULT

Matlab/Simulink programming is used to

demonstrate the application using the FCS MPC

method. The simulation results obtained with

parameters such as the following table:

Table 2: System Parameter.

Parameter Unit Value

DC Voltage 𝑣



900 V

Converter Side Inductor 𝐿



20 mH

Grid Side Inductor 𝐿



1.6 mH

Filter Capacitor 𝐶 65.25 𝜇𝐹

Capacitor Resistance 𝑅



5Ω

The first simulation result is to know the 𝑣



the converter system. 𝑣



affects the result of the

generated system.

Figure 6: 𝑉



Figure 6: above is a 𝑣



response with a generated

or reference voltage of 900 𝑉𝑜𝑙𝑡𝑠, the voltage read is

882.7 𝑉𝑜𝑙𝑡𝑠. In the picture there is a steady state error

of 18 𝑉𝑜𝑙𝑡𝑠 or 2%. The power demand from the DC

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Time (s)

100

200

300

400

500

600

700

800

900

1000

Vdc

Refferensi

Actual Current

0.01056

909.5

0.0756

900

0.07591

882.7

Optimalisation

of cost function

Hysteresis Band

Current Controller

Predictive

Model

𝑠



𝑠



𝑠



𝑖

∗

𝑘

𝑖





𝑘 1

𝑖



iCAST-ES 2021 - International Conference on Applied Science and Technology on Engineering Science

752

Link input is very influential for the process in the

converter system.

Figure 7: Response 𝑖



actual and 𝑖



𝑟𝑒𝑓𝑓.

Figure 8: Response 𝑖



actual and 𝑖



𝑟𝑒𝑓𝑓.

Figure: 7 and 8 above are currents from 𝑖



then

enter the range of the upper and lower bands on the

hysteresis band. The use of the hysteresis band on 𝑖



here is to get the optimal value before entering the

switching system and getting the cost function value.

Table 3: Cost Function.

Volta

e vecto

Cost function





𝑔





0,55



𝑔



0,76



𝑔



0,47



𝑔



0,65



𝑔



1,27



𝑔



1,45



𝑔



0,37

In the table above, the vector 𝑔



0.47 is said to

be the lowest value or optimal value for the cost

function. There are 8 voltage vectors that produce

current to get the cost function value. The lowest

value 𝑔



0.47 above is the value that will be used

in the inverter.

Figure 9: 𝑖



Predictive.

In Figure 9 above, there are still ripples generated

from back emf or caused by dynamic loads. The result

of the flow above is an evaluation of the value of the

cost function. The value of the cost function will be

processed on switching on the inverter.

Figure 10: 𝑣



,𝑣



and 𝑣



output inverter.

Specialization for implementation on FCS MPC

using Two levels. Figure 10 above is the result of

switching generated by the converter obtained from

the cost function. The generated voltage is 600 Volts.

The above wave is not pure sine but the result of some

switching obtained. After getting the sine signal, the

LC filter is given to make it a pure sine signal.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Time (s)

0.96

0.97

0.98

0.99

1.01

1.02

1.03

Hysteresis Id idref

Upper Band

id actual

id ref

Lower Band

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Time (s)

-0.02

-0.015

-0.01

-0.005

0.005

0.01

0.015

0.02

0.025

Hyesteresis Iq Iq ref

Upper Band

iq ref

Lower Band

An Improved Hysteresis Band based FCS MPC for Grid-connected Three Phase Inverter

753

Figure 11: 𝑣



Output Grid.

The picture above is the final result of this

research which is obtained from the filter and will be

inserted into the transformer to be processed into the

grid system or for use. The generated voltage

amplitude is 600 Volts.

5 CONCLUSIONS

The FCS MPC which is implemented in the inverter

is successfully used by obtaining the cost function.

This system can be implemented on a renewable

energy system in the form of wind, sunlight from a

DC source or an AC source. This optimization

renewable energy technology can be applied. The

power demand from the DC Link input is very

influential for the process in the converter system, the

system can run well starting from the input dc voltage

of 882.7 volts with a steady state error of 2%. The 𝑖



current is processed to produce an optimal current by

utilizing the hysteresis band of 0.2 band. On

switching on the inverter, the second vector voltage

or 𝑔



is 0.47 vector value which is used for switching

on the inverter. FCS MPC can be applied to a two

level converter system, the results obtained are a

voltage of 600 volts. The need for a filter circuit to

produce a sine wave like a pure sine wave generated

by a generator.

ACKNOWLEDGEMENTS

The author acknowledgements State Polytechnic of

Cilacap for supporting the author’s internal research

with the DIPA funding. The author thanks

colleagues who support and assist research directly.

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An Improved Hysteresis Band based FCS MPC for Grid-connected Three Phase Inverter

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