A Five-Level H-Bridge STATCOM for an Off-Grid PV Solar

Research ArticleA Five-Level H-Bridge STATCOM for an Off-Grid PV SolarFarm under Two Controllers PI and PIλ-MPC Hybrid

Onur Ozdal Mengi

Department of Energy Systems Engineering, Engineering Faculty, Giresun University, 28100 Giresun, Turkey

Correspondence should be addressed to Onur Ozdal Mengi; [email protected]

Received 6 December 2017; Revised 1 February 2018; Accepted 20 February 2018; Published 4 April 2018

Academic Editor: Mahmoud M. El-Nahass

Copyright © 2018 Onur Ozdal Mengi. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Investigations were presented in order to eliminate the reactive power on microgrid loads fed by an off-grid and mid-powerphotovoltaic solar energy system (PVSES) with a static synchronous compensator (STATCOM) device. The electric network isspecifically characterized by P-Q loads, ambient temperature, and widely variable solar radiation levels. Two main innovationsare developed. Firstly, the STATCOM apparatus is a 5-level H-bridge inverter with capacitances as load and must totallycompensates the reactive power in the network load. Secondly, this compensation is controlled by a set of fractional PI (PIλ)and model predictive control (MPC) hybrid. The efficiencies of these controllers were compared with classical PI controllers.Large simulations, without and with reactive power compensation, in steady and transient states, are carried out to underlinethe merits of the presented works, by performing in the MATLAB-Simulink environment.

1. Introduction

The sun warms our planet with the resulting energy releasedfrom nuclear explosions taken place within itself and makesour planet a place to live for people, animals, and plants. Thesun, which is our source of life along with the rapid progressof technology, now also serves as an energy source. Photo-voltaic solar cells are systems that convert solar energy fromsunlight into electricity and thus produce electricity. Solarcells come together to form panels, and the panels cometogether to form PVSESs [1]. The solar panels generate DCvoltage at the output. The DC voltage and power obtainedfrom the solar panels are used to feed either DC loads orAC loads by converting it to AC voltage via an inverter. Var-ious solar cell production techniques and materials havebeen developed. There are many solar panels made ofnumerous materials such as amorphous silicon, copperindium gallium selenide, and cadmium telluride [2]. Thecosts and efficiencies of these panels are quite different.Nowadays, solar cells yielding 35% of efficiency have beenproduced [3].

Large scale applications have become more economicalwith the development of solar panel production techniques,

the increase in production, and also the increase in panelpower values and yields [4]. As a result of these, large powerplants have been begun to build from large scale photovoltaicsolar panels [5]. These power plants are on-grid or off-grid[6]. In off-grid PVSESs, compensation must be applied tothe system for reducing harmonics caused by the loadshaving reactive power and preventing injecting of thereactive power from the source [7, 8]. There are many differ-ent compensation techniques. Among them, voltage sourceconverter- (VSC-) based compensators are the Static VARCompensator (SVC), STATCOM,ThyristorControlled SeriesCompensator (TCSC), Static Synchronous Series Compensa-tor (SSSC), and Unified Power Flow Controller (UPFC) [9].STATCOMs are one of the dynamic systems capable of doingthis [10, 11]. STATCOMs are able to do compensation byappropriately switching the reactive power generated bycapacitors. In general, IGBT, thyristor, and transistor areused for switching. These components are switched by tech-niques such as PulseWidthModulation (PWM) and Sinusoi-dal Pulse Width Modulation (SPWM) [12]. There aredifferent topologies in the inner structure of the STATCOM.These systems, which are usually multilevel inverters, areswitched by appropriate control techniques. Current source,

HindawiInternational Journal of PhotoenergyVolume 2018, Article ID 4030214, 14 pageshttps://doi.org/10.1155/2018/4030214

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voltage source, impedance source, quasi impedance sourceinverters, and multilevel inverters are commonly used [13].These inverters are controlled by using classical andadvanced control methods such as a PID controller [14],fuzzy logic controllers [15], fractional PID [16], artificialneural networks [17], vector control methods [18], modelpredictive control [19], and genetic algorithms [20].

The innovation carried out by this study is the implemen-tation of a five-level H inverter for the STATCOM converter(including 24 IGBT-s transistors). In addition, this deviceallows eliminating the load reactive powers, to regulate thenetwork voltage by increasing its efficiency and reducing har-monics contained in the electric network. The plant is fed byan off-grid photovoltaic solar power generation system, and

the STATCOM converter is controlled by PIλ and MPC.The efficiency of the obtained advanced control structurewas compared using classical PI controllers. The voltageson loads were tried to keep constant at a value of380V/50Hz with a classical 2-level three-phase voltage. Ithas been tried to create challenging conditions by continu-ously changing the loads, ambient temperature, and the solarirradiation level. In this environment, the performances ofthe controllers were tested and the contribution of theadvanced control techniques was addressed by comparingthe results obtained. All of the simulation was performed inthe MATLAB/Simulink environment.

This paper is organized in four sections. Section 1 con-tains the introduction. The STATCOMdevice and controllers

1

2

25

1 2 40

Filter

Filter

iload

ist

Vst

C1

C2

C3

C4

C5

C6

PI𝜆controller

VPV

VPV

Loads

Couplinginductance

Cascaded 5-levelH-bridgeSTATCOM

40 × 25 = 1000 solar panels

Vgrid

2-level inverter

Vgrid

PWMS1...S6

e

−+380 V

Mechanicalswitches

R S T

u v w

T11

T12 T14

T13

T15

T16 T18

T17

T21

T22 T24

T23

T25

T26 T28

T27

T31

T32 T34

T33

T35

T36 T38

T37

T1

T2

T3

T4

T5

T6

1

2

3

MPC-PI𝜆controller

Figure 1: PVSES with a STATCOM device.

2 International Journal of Photoenergy

are described in Section 2. Section 3 presents simulationresults. The last section gives some remarks and conclusion.

2. Materials and Methods

The overall scheme of the proposed PVSES and STATCOMsystem was given in Figure 1. The system consisted of solarpanels, filters, inverters, loads, measuring components, anda STATCOM device.

The solar panels contained 25 parallel branches and 40panels in each branch. The PV solar panels’ output filterhas a 6.5μF capacitor. The voltage obtained from thesepanels was converted to 380V/50Hz AC voltage through a2-level inverter before passing from a filter. The two-levelinverter output filter consisted of a 22μF capacitor and2mH inductance. This inverter is switched using PI control-lers, and carrier frequency is 2 kHz.

The STATCOM device consisted of 5-level H-bridgeIGBTs, capacitors, and a control unit. These controllers herewere used to control the capacitor voltages and IGBTs.Capacitor voltage was controlled by PIλ, and IGBTs werecontrolled by MPC. The STATCOM device was connectedto point of common coupling (PCC) via a coupling induc-tance. Different resistive and motor loads were used as loads.

2.1. PV System. Photovoltaic solar cells are semiconductorcomponents that turn solar light to electrical energy. Thereare different equivalent circuit models. The equivalent cir-cuit model with one diode of a solar panel is seen inFigure 2 [21, 22].

The output voltage of the PV cell is as in (1) [23].

VPV = Nλln ISC − IPV +MI0

MI0−

NM

RsIPV 1

Descriptions of the variables used here are seen inTable 1.

2.2. STATCOM Device. A STATCOM is a parallel-connectedstatic synchronous compensator. The STATCOM is aFACTS device that continuously supplies reactive power toor injects reactive power from the system that it is connected.STATCOM has important features such as having a fastresponse time and fewer space requirements and showingvery good dynamic characteristic under different operatingconditions [24].

The active and reactive power exchanges between theSTATCOM and the system are given by (2).

Pst =V stV sXst

sin δ,

Qst =V sXst

V s −V st cos δ2

V s is system voltage, V st is STATCOM voltage, and δ isthe phase angle between V st and V s. Xst is reactance betweenthe STATCOM and the system. Lst is an inductive part ofthe Xst.

The basic structure of the STATCOM device is shown inFigure 3.

The values of the passive elements of the STATCOM arecalculated in (3) and (4).

Cdc =2 · IRMS

ω · ΔVpp1 − sin arccos Mmaxπ

4 3

Ist

Couplinginductor

VSI

DCcapacitor

Point of commoncoupling

Con

trolle

r

Vst

VDC

Xst

Figure 3: Basic structure of the STATCOM device.

Table 1: The descriptions for the PV cell.

Expression Definition Unit

VPV Cell output voltage V

IPHPhotocurrent, function of irradiation level,

and junction of temperatureA

IPV Cell output current A

ISC Cell short-circuit current A

I0 Reverse saturation current A

RS Series resistance of the cell ΩN Series cells per string

λConstant coefficient and depends upon

the cell material

M Parallel strings

Diode

IPV

VPV

RS

IPH

Figure 2: Equivalent circuit model of a PV solar cell.

3International Journal of Photoenergy

IRMS is the RMS value of the system current, ΔVpp is peakto peak variation of the three-phase system voltage, Mmax isthe maximum value of the modulation index.

VDC8f s nLevel − 1 ΔIr

≤ L ≤V st −V sI load fωIst

4

VDC is DC voltage of the STATCOM, f s is PWM fre-quency, ΔIr is current ripple, V st is VSI voltage, V s is systemvoltage, Iload f is the fundamental harmonic component ofthe load current, ω is angular velocity, Ist is the RMS valueof VSI output current, and nLevel is the number of the inverterlevel [25, 26].

In this study, the five-level H-bridge STATCOM device isused. The reason of this, 3-level inverters give lower qualityresults and 7-level inverters have much more complicatedresults because of using too much IGBTs.

2.3. STATCOM Device Control Structure with a Classical PIController.Various structures for the STATCOM device con-trol are used in literature. One of them is the indirect currentcontrol method [26]. In this method, generally, classical PIcontrollers are used. This control structure is shown inFigure 4.

In Figure 4, I load q is defined as the reactive component ofload current.

2.4. Fractional PID Controller (PIλDμ). PIλDμ controllersare advanced controllers that can give better results thanclassical PI controllers. They are widely used becausethey are able to adjust more precisely than PID

controllers. The best knowns are the descriptions ofCaputo, Grunwald-Letkinov, and Reimann-Liouville [27,28]. The PIλDμ controller general block diagram is shownin Figure 5.

System output, C(s), is as seen in (5).

C s = U sE s = KP +

K Isλ

+ KDsμ 5

Here, λ and μ ≥ 0. λ is the order of integration,and μ is the order of the differentiator. KP, KI, andKD are the PID controller gains. U(s) and E(s) arethe control and error signals, respectively. In this study,PIλDμ controller software was performed by FOMCONtoolbox [29].

2.5. Model Predictive Controller (MPC). MPC is a controltechnique designed on the basis of the prediction ofbehavior of the systems in the next step. It is aimed atestimating the next possible switching states and providingthe selection of switching that minimizes the error overthe existing states. To achieve this, a correct model ofthe system has to be revealed. At each sampling time,the control of a particular topology defines a cost functionthat is minimized as an optimization problem. The generalapplication of MPC in the STATCOM device is as shownin Figure 6.

MPC generally consists of two groups: finite controlset MPC and continuous control set MPC. They aredivided into two groups among themselves. Finite controlset MPC is divided into optimal switching vector MPC

VDC_ref

Istd_refPI PI

PI SPW

M

Istq_refIload_q

VDC

STATCOMcurrent

abcdq

abc

dq

Istd Istq

Vstd_ref

Vstq_ref

+−

+−

+

−

+−

−−

𝜔Lst𝜔Lst

Figure 4: General block diagram of an indirect current controller.

Systemoutput

KP

uG(s)

VDC e 1/S𝜆

PI𝜆D𝜇

S𝜇

KI

KD

++++−

Figure 5: General block diagram of a PIλDμ controller.


and optimal switching sequence MPC, and continuouscontrol set MPC is divided into generalized predictive con-trol and explicit MPC. In the simulation, an optimalswitching vector MPC technique was used because it doesnot need a modulator and fixed switching frequency, it isintuitive, and it can perform online optimization [30].The predictive control technique can be used easily inmultilevel STATCOM applications.

For multilevel STATCOMs, the AC side equality is asin (6).

Vabcs = Lst

ddt

iabcst + Rstiabcst + Vabc

st 6

Minimizationof cost

functionPredictive

model

40 × 25 = 1000 solar panels

2-levels inverter

Filter

Filter380 V

LoadsISTATCOMref

PI𝜆D𝜇

STATCOM

VC1

VC2

S1...S6

VPV

Vgrid

Vgrid

VDC

VDC, ref = 200 V

e d dq0wt abc

dq0 to abcabc to dq0q

0

dq0

abcabc wt

PLL

wt

iload

Vgrid

ist

Sk

Z−1

S(k + 1)

ist(k + 1)

VDC

Lst Rst

e

PWMPI𝜆controller

+

++

1/6+

++

Vc1

Vc2

Vc3

Vc4

Vc5

Vc6

KP

KI

KDS𝜇

1/S𝜆−++++

VPV

−+

Figure 6: Block diagram of MPC for the STATCOM device.

Table 2: Photovoltaic solar panel parameters.

Value Unit

Open-circuit voltage 36.3 V

Short-circuit current 7.84A

Maximum power 213.15W

Voltage at maximum power point 29V

Current at maximum power point 7.35Α

Temperature coefficient of short-circuit current 0.102%/deg.C

Temperature coefficient of open-circuit voltage −0.36%/deg.CSerial resistance 0.39 ohm

Diode saturation current 2.92e-10A

Diode ideality factor 0.98


If iabcst is extracted and discretized from (6), its next valuecan be computed from (7).

iabcst k + 1 = 1 − TsRstLst

iabcst k + TsLst

Vabcs k − Vabc

st k

7

Here, Ts is the sampling time. k expresses the currentstates of the variables. k+1 is used to predict the futurebehavior of the system. Rst is a coupling resistor, Lst is acoupling inductance, iabcst is 3-phase STATCOM current,Vabc

s is 3-phase grid voltage, and Vabcst is 3-phase STAT-

COM voltage.A cost function should then be used. This cost function

should evaluate the all possible switching combinations,choose the option minimizing cost function, and apply it inthe next step. The cost function used to minimize the currenterror is as in (8) [31].

g = iabc,refst k + 1 − iabcst k + 1 8

3. Results and Discussion

Firstly, the installed system was run without the STATCOMdevice. What happened in this case was investigated. Then,the STATCOM device with a PI controller and finally thePIλ-MPC hybrid controller were used, and their results wereshown. In all the simulations, the total power of the pho-tovoltaic solar panels and the system used in PVSES werekept same.

3.1. Data of PV Panels. The solar panels are commerciallyavailable and have the characteristics as defined in Table 2.The passive elements of the STATCOM device consist of4700μF capacitors and of coupling inductance with 56mΩand 12mH [32]. In Figure 7 are shown the exploitationcurves of each panel and the set of panels (40 in series and25 in parallel).

Figure 7 and Table 2 define the data used in commercialPV panels.

Also, in all the simulations, the ambient temperature leveland solar irradiation level were changed according toFigure 8.

3.2. Simulation Results and Discussion.Here, the PV filter hasa 6.5 μF capacitor. The voltage obtained from these panelswas converted to RMS phase-to-phase voltage 380V under50HzAC voltage through a 2-level inverter before passingfrom a filter. This filter consists of a 22 μF capacitor and2mH inductance. The system sampling time is 5 μs. PVpanel output voltage changes between 1200V and 1350V,and output current changes up to 150A.

The installed system was tested using variable loads,according to Table 3 for their connection and disconnectiontimes.

In addition, during the time simulation (between 0 and1 s), ambient solar irradiation and temperature change asshown in Figure 8.

3.2.1. Case 1: Installation without the STATCOM Device(Mechanical Switch Open). The two-level inverter is switchedusing PI controllers, and carrier frequency is 2 kHz, involving

200

150

100

Curr

ent (

A)

50

00 500 1000

Voltage (V)1500

(a)

Pow

er (W

)

2.5

2

1.5

1

0.5

00 500 1000

Voltage (V)1500

×105

(b)

8

6

4

Curr

ent (

A)

2

00 10 20 30

Voltage (V)40

(c)

Pow

er (W

)

200

250

50

100

150

00 10 20 30

Voltage (V)40

(d)

Figure 7: (a) Total PVSES output V-I diagram, (b) total PVSES output V-P diagram, (c) a photovoltaic solar panel V-I diagram, (d) aphotovoltaic solar panel V-P diagram.


a pulse width modulation principle. In the absence of theSTATCOM device, the compensation of reactive power can-not not be performed. The graphs obtained in this case areshown in Figure 9.

Figure 9 shows that the reactive power taken by the loadcannot be compensated when there is no STATCOM devicein the system. The same reactive power was present on theload and the grid side.

In Figure 9, change in the voltage amplitude on the loadsis shown. PI controllers kept the load voltage constant at380V. Here, 2-level IGBTs inverters were used. PI controllersthat set the load voltage were also set to KP = 0.5, KI = 100.These values were found by different simulations work onthis system. The controller could hold magnificently theRMS phase-to-phase load voltage constant at 380V. Thechange was around ±5V.

As shown in this figure, the dispersion of RMS phase-to-phase voltage is very negligible: around 1V/380V and aftersudden changes of load, we notice: for Δ2 =−5V; for Δ3 =+5.8V; Δ5 =−1V. And the disturbance duration are lesser25ms.

3.2.2. Case 2: STATCOM with a PI Controller. The resultsobtained when an indirect current control method with PIcontrollers were used to control both the VDC voltage andthe switching signals are shown in Figures 10 and 11. Theambient conditions and also the constant change in loadsforced the system. PI controllers used in an indirect currentcontrol method were set to KP = 5 and KI = 40. For PI con-trollers that adjust the load voltage, KP = 0.5 and KI = 100were also taken. This value is the same as the values used inthe case without the STATCOM device.

Figure 10 shows the switching states belonging to a phasewhen the STATCOMwith a PI controller is enabled. The firsttwo graphs show the switchings of IGBTs on the firstH-bridge (triggers of T11 and T12) and the other two onthe second H-bridge (triggers of T15 and T16). While twoIGBTs on each bridge were switched, the opposite way ofthe switchings was sent to the other two.

Figure 12 shows the efficiency of the STATCOM device.The reactive power compensation was performed success-fully. The reactive power take from the grid was zero.

Also, Figure 12 shows change in the tension on loads.Although PI controllers had a high overshoot value, they keptthe load voltage at 380 quite well. The PI controller constantswere KP = 0.5 and KI = 100. These values are deduced by trialand error.

As shown in this figure, overshoot is too bad. This valuereach 465V. So, ΔVO is +85V. Nevertheless, ΔV2 and ΔV3are negligible. Between t2 and t3, the reactive power residueis approximately +300VAr.

In Figure 13, each DC capacitor voltage VDC in theSTATCOM device were kept at 200V and the capacitorvoltage on H-bridge converter is perfectly balanced. Thisunderlines that the more the controllers efficiently operate,the compensation action is more performing.

Table 3: Loads used in the system and times that they entered thecircuit.

Load type Value Commutation times (s)

R +50 kW t1 = 0: connection

RL +10 kW/+10 kVAr t2 = 0.3: connection

RL −10 kW/−10kVAr t3 = 0.45: disconnection

R +5 kW t4 = 0.6: connection

L +5 kVAr t5 = 0.8: connection

1010Sx (W/m2)

Tx (°C)

Time (S)

1000990980970960950940

252423222120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 8: Ambient solar irradiation level and temperature changes.


Figure 11 shows FFT analysis of the PVSES system out-put voltage and current. For the phase-to-neutral voltage,the shape is perfectly sinusoidal and the module gap differ-ence is lesser than 1%.

3.2.3. Case 3: STATCOM with a PIλ-MPC Hybrid Controller.The results obtained in using PIλ-MPC hybrid controllers tocontrol both VDC voltage and switching signals are shown inFigures 14 and 15. Here, VDC voltage was controlled by PIλ

and the switching signals in a 24 IGBTs 5-level STATCOMdevice were controlled by MPC. Both ambient conditionsand loads are constantly changing.

The switching states belonging to a phase when theSTATCOM device with a PIλ-MPC hybrid controller isenabled are shown in Figure 14 (the first two graphs:triggers of T11 and T12, and the other two: triggers of

T15 and T16). The switching signals are different thanin the case using PI controllers. These signals took randomlyin the time scale.

Figure 16 shows the efficiency of the STATCOM devicewith a PIλ-MPC hybrid controller. The reactive power com-pensation was performed successfully. The reactive powertaken from the grid was zero. The fluctuation was less thanin the case using a PI controller.

This figure shows change in the voltage on loads. Over-shoot and settling time values were better than PI controllers.For PIλ controllers that adjust the load voltage, KP = 0.5,KI = 100, and λ=1.2 were taken. As shown in this figure,overshoot is very low. This value reach 384V. So, ΔVOis +4V. But, sudden load changes like at ΔV2, ΔV3, andΔV5 are important. Despite the change in voltage on theload, the reactive power is well compensated. At this time,

t2 t2 t2 t2

ΔV2

ΔV3

ΔV2

ΔV3

×104

6543210

0 0.1 0.2 0.3 0.4 0.5

Load powers

0.6 0.7 0.8 0.9 1

×104

6

4

2

0

390

388

386

384

382

380

Vlo

ad (V

)

378

376

374

372

370

0 0.1 0.2 0.3 0.4 0.5

Grid powers

0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5Time (s)

0.6 0.7 0.8 0.9 1

Active power (P)Reactive power (VAr)

ΔV5

Figure 9: Active, reactive power, and load voltage states on the system.


1

0.5

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.36

0

1

0.5

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.360

1

0.5

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.360

10.5

0.35 0.351 0.352 0.353 0.354 0.355Time (s)

0.356 0.357 0.358 0.359 0.360

Figure 10: Switchings belonging to a phase when the STATCOM device with a PI controller is enabled.

200

2

1.5

1

0.5

00 10 20 30 40 50

Harmonic order

Fundamental (50 Hz) = 309.9, THD = 5.05%

60 70 80 90 100

Signal

FFT analysis

−200

0

0.6 0.61 0.62 0.63 0.64 0.65Time (s)

FFT window: 5 of 35.55 cycles of selected signal

0.66 0.67 0.68 0.69

Sign

al m

ag.

Mag

(% o

f fun

dam

enta

l)

(a) Voltage FFT analysis

SignalFFT window: 5 of 35.55 cycles of selected signal

0.6 0.61 0.62 0.63 0.64 0.65Time (s)

0.66 0.67 0.68 0.69

2

1.5

1

0.5

00 10 20 30 40 50

Harmonic order


60 70 80 90 100

FFT analysis

Mag

(% o

f fun

dam

enta

l)

100

−50−100

500

Sign

al m

ag.

(b) Current FFT analysis

Figure 11: FFT analysis of phase to neutral voltage and line current on the electric network of the system.


reactive power on the system is approximately +50VAr.This is a too low value.

Figure 17 shows that the capacitor voltages in theSTATCOM device are kept at 200V. Both settlingtime and overshoot values were much better than thecase using a PI controller. Also, the fluctuations inthe load changes were less. Here, the PIλ-type control-ler was used. In PIλ controllers used both in the set-ting of voltage on load and in the controlling of VDCvoltage in the STATCOM, controller parameters areKP = 5, KI = 40, ve λ=1.2 were taken.

Figure 15 underlines the good results shown in Figure 11(the same values about the modulus of phase-to-neutral andits THD).

t2 t3 t4 t5

ΔVO

ΔV2

ΔV3

×104

×104

6

4

2

0

6

8

4

2

0

460

440

420

400Vlo

ad (V

)

380

360

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5

Grid powers

Load powers

0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5Time (s)

0.6 0.7 0.8 0.9 1

Active power (W)Reactive power (VAr)

Figure 12: Reactive power compensation when the STATCOM device with a PI controller is enabled and voltage change on loads.

240220200180160

Vdc (

V)

140120100

800 0.1 0.2 0.3 0.4 0.5

Time (s)0.6 0.7 0.8 0.9 1

Figure 13: Capacitor voltage control in the STATCOM device witha PI-controller.


Time (s)

0

1

0.5

0

1

0.5

0

1

0.5

0

10.5

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.36

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.36

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.36

0.35 0.351 0.352 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.36

Figure 14: Switchings belonging to a phase when the PIλ-MPC hybrid controller is enabled.


Time (s)0.6

−200

0

Sign

al m

ag.

Signal

FFT analysis

200

0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69


Mag

(% o

f fun

dam

enta

l)

Harmonic order0

0

0.5

1

1.5

2

10 20 30 40 50 60 70 9080 100

(a) Voltage FFT analysis


Time (s)0.6

−50−100

0

Sign

al m

ag.

50100

0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69


Mag

(% o

f fun

dam

enta

l)

Harmonic order0

0

0.5

1

1.5

2

2.5

10 20 30 40 50 60 70 9080 100

Signal

FFT analysis

(b) Current FFT analysis

Figure 15: FFT analysis of a PVSES system.


4. Conclusion

In the study, the performance of the STATCOM device usinga PIλ-MPC hybrid controller has been investigated and com-pared with the version using a PI-type controller to eliminatethe reactive power on loads fed by off-grid solar panels. Thesystem was forced by constantly changing the ambienttemperature and the solar irradiation level as well as theloads, and the efficiencies of the controllers were tried tobe shown meanwhile.

In the system, VDC voltage was controlled by PIλ and theswitching signals in a 24 IGBTs 5-level STATCOM devicewere controlled by MPC. The most important reason for thisis that PID-type controllers can be placed everywhere com-fortably, while it is necessary to use detailed mathematical

equations for designing MPCs. This makes MPCs difficultto design. However, the controllers with different PID typescan be placed easily everywhere that errors are in. MPC con-trols the switching signals in the STATCOM device. It worksmore efficiently because it chose the right and the best onefrom the switching possibilities. VDC voltage was controlledby PIλ that is able to adjust more precisely than PI. By com-bining these two controllers, a hybrid controller was created.

The comparison of STATCOM device results obtainedfrom PI and PIλ-MPC controllers shows that PIλ VDC over-shoot parameters are better than PI because PIλ overshootis 213V and PI overshoot is 230V. Similarly, the reactivepower overshoot value for a PI controller is 70 kVAr. ButMPC has no overshoot. PIλ load voltage overshoot is 384V;PI controller load voltage overshoot is 465V.

7 × 104

× 104

6543210

6

4

2

0

390

ΔVO

ΔV2

ΔV3

ΔV5

388

386

384

382

380

Vlo

ad (V

)

378

376

374

372

370

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Active power (W)Reactive power (VAr)

1

0 0.1 0.2 0.3 0.4 0.5

Grid powers

Load powers

0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3

t2 t3 t4 t5

0.4 0.5Time (s)

0.6 0.7 0.8 0.9 1

Figure 16: Reactive power compensation when the STATCOM device with a PIλ-MPC hybrid controller is enabled and load voltage change.


PIλ VDC settling times are better than those of PI. The PIλ

settling time is 0.1ms, and the PI settling time is 0.3ms forthe steady state. The reactive power settling time is 0.02msfor a PI controller and MPC is approximately 0ms, andfinally, the load voltage settling time is 0.05ms for a PIcontroller and 0.02ms for a PIλ controller.

If we compare steady state errors, PIλ and PI controllersare equal for the VDC steady state error parameter and loadvoltage steady state error parameter. VDC steady state erroris 0 in both PI and PIλ controllers. The load voltage steadystate error change range is ±6V in both PI and PIλ control-lers. But reactive power steady state error is better thanMPC. MPC steady state error is 50VAr, and the PI controllervalue is 300VAr.

The results of the FFT analysis show that the PIλ-MPCcontroller is better than the PI controller. Total harmonicdistortion of the PIλ-MPC controller is 4.94% for voltageanalysis and 4.17% for current analysis, and then PI control-ler FFT analysis for voltage is 5.05% and current is 4.18%.

As mentioned in the previous paragraph, the reactivepower compensation performed very well and the error rateswere very weak. The overshoot values of PI controllers werehigher than those of PIλ-MPC hybrid controllers. Also, thesettling time values were shorter on the PIλ-MPC hybrid con-troller. In general, the performance of the PIλ-MPC hybridcontroller is much better than those of PI controllers.

Conflicts of Interest

The author declares that they have no conflicts of interest.

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Time (s)0

190

195

200

Vdc (

V)

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A Five-Level H-Bridge STATCOM for an Off-Grid PV Solar