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Novel Maximum Power Point Tracking with Classical Cascaded

Voltage and Current Loops for Photovoltaic Systems

M.Fazeli, P.Igic, P.Holland, R.P.Lewis, Z.Zhou

College of Engineering, Swansea University,Swansea SA2 8PP, UK, Email:m.fazeli@swansea.ac.uk

Keywords: Maximum Power Point, Photovoltaic.

Abstract

Almost all of the Maximum Power Point Tracking (MPPT)

methods for photovoltaic (PV) systems are based on

searching algorithms. Searching algorithms require relativelycomplex control schemes and reduce the speed and accuracy

of the MPPT method. This paper proposes a novel MPPTmethod which aims to circumvent traditional searching

algorithms thus increasing the speed and accuracy of the

response to varying irradiation levels. The method will be

validated through MATLAB-SIMULINK simulations.

1 Introduction

The global environmental, financial and political issues

necessitate the use of renewable resources to meet the fast

growth in energy demand. Among renewable resources, PVsystems have received considerable attentions and it is

expected that the penetration of PV energy generation will

increase steadily to become a significant proportion of totalenergy generation. One major issue with PV systems is that

its current-voltage (iPV-vPV) characteristics and hence its

maximum power vary according to the irradiation level (S).For a given S, there is only one maximum power:Pmax=ioptvoptwhere, iopt and vopt are the unique optimum PV current andvoltage for a given S. In order to increase the efficiency of thePV systems it is necessary to track the maximum power point

(MPP) as quickly and accurately as possible for varying S. Totrack the MPP either iPVor vPVshould be controlled to ioptorvopt, respectively. However, the voltage control is preferredsince the voltage at MPP is approximately constant for

different S while the current variation is much wider [1].

There are many MPPT methods introduced in papers. Themost common methods are briefly reviewed in the next

subsection:

1.1Review of MPPT methods

ThePerturb and Observe (P&O) andHill Climbing methods,which are probably the most common methods, are twodifferent ways to apply the same fundamental principal [2]. In

Hill Climbing a perturbation is applied on the duty cycle of

the PV converter while in P&O the perturbation is directly

applied on the operating voltage of the PV array. In both

methods, if the perturbation causes an increase of the output

power, the perturbation will continue in the same directionand if the output power decreases, the next perturbation will

be in the opposite direction. This will continue until the MPP

is reached then the system will oscillate around the MPP. It is

possible to reduce the perturbation size as approaching the

MPP in order to reduce the system oscillation [3].

The incremental conductance (IncCond) method utilizes thefact that dP/dVof a PV array is zero at the MPP, positive onthe left of the MPP and negative on the right. Thus, it can be

shown that I/-I/V I/-I/Von the left of

I/-I/V on the right [2]. Therefore, thereference PV voltage Vdc

*can be adjusted towards vopt.

The main disadvantage of P&O, Hill Climbing and IncCond

is their relatively slow responses due to the fact that they arebased on some sort of searching algorithm.

The Fractional Open Circuit Voltage uses the approximation

of voptk1VOCwhere VOCis the open circuit voltage of the PVarray. The Fractional Short Circuit Current is based on theapproximation of iopt2ISC where ISC is the short circuitcurrent of the PV array. The fact that there will be

periodically interruption on power supply in order to measure

VOC and ISC is the main disadvantage of these two methods.Moreover, the approximations are not quite accurate [2, 4].

There are also some other methods using, for example, fuzzy

logic or neural network method, which are relatively complexand expensive to apply.

This paper proposes a new and simple MPPT method using a

lookup table. Although lookup tables can be considered as a

searching algorithm, the method is much faster and simpler

than P&O, Hill Climbing and IncCond. Moreover, the method

uses a simple DC/DC boost converter with classical cascaded

voltage and current loops which is relatively simple and

cheap. This method does not address the issue of partial

shading and the paper assumes a uniform irradiance.

However, as far as the authors are aware, there is no MPPT

method that can track the real maximum power in partial

shading situations without an additional algorithm. The

method proposed in this paper can be augmented with all the

methods explained in literature to address the partial shading

issue. Furthermore, due to the relatively simpler and cheaper

equipments required in this method, the method seems to be a

proper option for parallel-connected PV system which is a

good structure to minimise the effects of partial shading [5,

6].

2 Control scheme

The PV system studied in this paper and the proposed control

structure is shown in Figure 1. The PV array consists of NPparallel connected strings ofNSseries connected cells.

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Vout-VFWLookup Table

NS ~

Grid

vPV*

vPV

VFW

Vout

L RiPV iL

iC

NP

T

-PI

-

iPV

PI

iL* -

iL

-/ PWM

1

0 Diopt

vopt

iPV

DC/DC boost converter

DC/AC

C

1

2

3

4

PVV

Figure 1. Proposed control structure for the PV system

A MOSFET-based DC/DC boost converter is used to control

the DC-link voltage of the PV array vPV to vopt as S and/ortemperature T changes. The lookup provides the referencevoltage for the DC-link of the PV array. The output voltage ofthe DC/DC converter is kept constant by the DC/AC

converter which transfers the generated solar energy to the

grid. This section consists of three subsections. The first

briefly explains the PV model used in the paper, the second

discusses the lookup table and the last subsection explains thecontrol loops of the DC/DC converter. The simulation results

are provided in section 3.

2.1 PV module model

The mathematical model of PV array is described by (1) [7]:

1exp

S

dcrsPphPPV

kTAN

qvININi

(1)

where Irs is the reverse saturation current of a p-n junction(1.2 10

-7A), qis the unit electric charge (1.60210

-19C), kis

-23 J/K), T is the p-n junctiontemperature (Kelvin), A is the ideally factor (1.92) and Iph ,

which is the short circuit current of one string of the PV

panel, is a function of Tand S [7]:

rTscrph TTkIS

I

100

(2)

where Tr is the cell reference temperature (300 K), KT is

temperature coefficient (0.0017 A/K), Iscr is the short circuitcurrent of one PV cell at the reference temperature (8.03 A)

and Sis the solar irradiation level normalised to 1 kW/m2[7].

2.2 Choosing the reference DC-link voltage

Considering a PV array composing of NP=1500 and NS=176cells [7], the PPV-iPVcharacteristics of the PV array is shownin Figure 2. Figure 2 shows thatPmax790.77iopt, which means

that vopt an accurate enoughapproximation, especially for lower S, as shown in Figure 2.

y = 790.77x

0

2000

4000

6000

8000

10000

0 2 4 6 8 10 12 14

PV current (A)

PVpower(W)

S=0.1 kW/m^2

S=0.25 kW/m^2

S=0.5 kW/m^2

S=0.75 kW/m^2

S=1 kW/m^2

Figure 2.PPV-iPVcharacteristics for differentSand T=25

C

Figure 3 illustrates the vPV-iPVcharacteristics of the PV arrayand shows that:

dcibiaiv op top top top t 23

(3)

y = 0.1488x3- 4.3249x

2+ 47.163x + 600.89

0

100

200

300

400

500

600

700

800

900

1000

0 2 4 6 8 10 12 14PV current (A)

PVvoltage(V

S=0.1 S=0.25 S=0.5 S=0.75 S=1 kW/m^2

Figure 3. vPV-iPVcharacteristics for differentSand T=25

C

Assuming that the DC/DC converter controls vPV to voptveryquickly, ipv=ioptand hence, (3) can be rewritten as:

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dcibiaiv PVPVPVPV 23*

(4)

For a given solar array, the coefficients a,b,canddare also afunction of Tas shown in Figure 4.

630

680

730

780

830

880

0 2 4 6 8 10 12 14

PV optimum current (A)

PVoptimumvoltage(

T=15

T=30

T=45

T=60

Figure 4. vopt-ioptcharacteristics of PV array for different T(Celsius)

Figure 4 illustrates that as Tvaries, equation (4) also changes.However, as it can be seen, the variation of (4) is not

significant compared to that of the T. Therefore, it seems

accurate enough to store the coefficients of (4) for each 5-

10C. Obviously, interpolation can also be used to further

reduce the error. Knowing the vPV-iPVcharacteristics of a PVarray (which is usually provided by manufacturer), it is

possible to form (4) for different Tand sore it in the lookup

table. If the characteristics of the PV module is not provided

by the manufacturer, paper [8] proposes some adjustments in

order to match the mathematical model of PV array with thatof the practical one. The current paper assumes that the vPV-iPV characteristics of the PV module is available and uses

for a given T. The coefficients a,b,canddalso change asNSand/or NP change. It can be shown that NP has almost noeffect on voptand neither doesNSon iopt. Therefore, equations(5) and (6) can be used to adjust the lookup table for a new

number of parallel 'PN and series

'SN connected solar cells:

P

Pop top t

N

Nii

''

(5)

S

Sop top t

N

Nvv

''

(6)

Therefore, assuming that lookup table of the PV module

(NPNS) is available, there are two approaches to apply themethod for the PV array ofNP

NS

solar cells:

1. Is to make the new vPV-iPVcharacteristics in order toform the new lookup table.

2. Is to use the available lookup table and adjust the

measured current and voltage according to (5) and

(6), respectively.

In this paper the second approach will be used and validated

through MATLAB/SIMULINK simulation. Obviously, this

will also validate the first approach as well.

2.3 Control of DC/DC converter

The control scheme of the DC/DC converter consists of an

inner current control loop and an outer voltage loop as shown

in Figure 5.

Inner Current Loop

PI Controller Plant

-

PlantPI Controller

-

vPV* vPV

iPV

-

s

ask vv iL*

s

ask cc

iPV

iL-

ic

sC

1

RsL

1

Figure 5. Control diagram of the DC/DC boost converter

Inner current loop

The current loop controls the inductance current iL byregulating the duty cycle D of the MOSFET. Over oneswitching period of the converter, one can write (see Figure

1) [9]:

)(1234 FWou t VVDDVV

(7)

where VFWis the forward voltage of the diode and Voutis theoutput voltage of the DC/DC converter which is kept constant

by the DC/AC converter.Using and considering (7), one can write the

control plant as:

sLRsLR

VVDVI

VVDdt

diLRiv

FWou tPVL

FWou tL

LPV

0

(8)

Thus, as shown in Figure 1,Dwould be:

FWou t

PV

VV

VD

(9)

The duty cycle is then used to generate the PWM signal for

the MOSFET. As discussed in section 2.2, vPV is almostconstant around MPP. Therefore, in (9) an approximation of

vPV( PVV see Figure 1) will be quite sufficient. It is noted that

(9) is a compensation term and is used to reduce the transient

error, in fact the system can work without that.

Outer voltage loop

The voltage loop controls the voltage across the PV array.

The control plant is:

sCI

V

dt

dvCi

C

PV

PV

C

1

(10)

The voltage loop also provides the reference inductance

current for the current loop using :

LCPV iii (11)

It is noted that the bandwidth of the outer voltage loop must

be 5-10 times slower than that of the inner current loop.

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Figure 6. MPPT for step change solar irradiance: (a) PV output power depicted on PPV-iPVcharacteristics (b) PV output power vs time forS=0.1,0.25, 0.5, 0.75, 1kW/m2

3 Simulation results

Let consider a PV module consisting of NP=44 and NS=100solar cells. Assuming that the vPV-iPVcharacteristics of the PVmodule is known, equation (4) is formed for S=0.1, 0.3, 0.7and 1kW/m

2

336.40921.12747.4666.0 23* PVPVPVPV iiiv

(12)

Considering a PV array composing of 4 strings of parallelconnect PV module with each string has 15 series connected

PV modules, the total PV array has NP=176 and NS

=1500

solar cells. In order to adjust (12) for the PV array (using (5)

and (6)), the measured iPVis multiplied by 0.25(=44/176) andthe output vPV

*is multiplied by 15 (=1500/100). As discussed

in section 2.2, an alternative approach is to find the vPV-iPVcharacteristics of the total PV array (i.e.NS

NP

) and form (4)

for the new arrangement directly (i.e. Figure 3).

The system parameters are .The switching frequency of the boost converter is 50 kHz and

the bandwidth frequencies of the voltage and current loops

are 15Hz and 150Hz. In order to keep the system simpler, the

output capacitor, DC/AC converter and the grid is replaced bya DC voltage source (950v). This section considers two

scenarios: in the first scenario Svaries in step changes whilein the second a real measured Sis applied. The temperature isassumed constant at 30

C.

3.1 Step change in solar irradiance

Figure 6 illustrates the output power of the PV array when Sincreases in four steps from 0.1 to 1kW/m

2. Figure 6.a shows

that the PV output power follows the MPP quite precisely and

Figure 6.b illustrates that the PV output power follows the

MPP quite fast.

3.2 Real solar irradiance

In order to be able to simulate the system with real solar

irradiance for a long time (e.g. several hours), it is needed to

replace the DC/DC converter with its equivalent average

(non-switching) model to reduce the simulation time:

Average model of DC/DC converterIt can be shown that over one switching cycle, the average

current to the DC/AC converter isDiLand the average voltageacross the MOSFET from PV side is DVout (neglecting thediode forward voltage) [1, 9]:

Vout

vPV*

vPVVout

L RiPV iL

iC

-PI

-

iPV

PI

iL*

-iL

-/

1

0 D

C

1

2

3

4

PVV

DVout DiL

Figure 7. Large signal average model for DC/DC boost converter

Therefore, in Figure 7, which shows the average model for

the DC/DC boost converter, the MOSFET is replaced by a

variable DC voltage source of DVoutand the diode is replacedby a variable DC current source ofDiL(Dis the duty cycle ofthe converter)

hence its controllers are identical to the switching model.

Considering the same PV array as before, Figure 8 shows the

results with real solar irradiance variations. Figure 8-topshows the applied solar irradiance measured every second on

2/6/2011 at College of Engineering, Swansea University,Swansea, UK (at 51.6100 northern latitude and 3.9797

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western longitude). The reading starts at 5:40AM and

continues for almost 6 hours.

Figure 8. MPPT for real solar irradiance. Top: Per second solar

irradiance measured on 2/6/2011 at College of Engineering, Swansea

University, reading starts at 5:40AM. Bottom: PV output power

depicted onPPV-iPVcharacteristics

Figure 8-bottom illustrates that the PV array output power

follows the MPP very precisely.

4 Discussions and Conclusions

The paper proposes a new, simple and yet robust MPPT

method for PV systems. The method is faster and itsapplication is cheaper than similar methods. It has been

shown that using the method, the PV output power will

follow the MPP for fast (step change) and normal (real

measured) variations of solar irradiance. The main drawback

of the method is its dependency on temperature measurement.

If the measured temperature is not accurate, it can cause someerror. However, it was discussed that the variation of vopt is

not significant (compared to that of temperature) and the error

can be reduced using interpolation techniques.

Although the method does not address the issue of partialshading, it can be augmented with all available methods to

mitigate the problem. Moreover, due to its simplicity, the

method is a proper choice for parallel connected PV arrayswhich minimise the effects of partial shading.

Applying the method experimentally will be investigated in

future publications.

Acknowledgment

The financial support of the EU Convergence Programme is

acknowledged for this project.

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