Low-cost solar emulator for evaluation ofmaximum power point tracking methods

D.M.K. Schofield, M.P. Foster and D.A. Stone

Presented is a design for a solar photovoltaic (PV) emulator optimisedfor the cost-effective evaluation of solar-array maximum point tracking(MPPT) methods and their associated power converters. The systemdesign and component calculation methodology are reported with apractical comparison of the emulator output with measurements froman actual solar panel. Unlike previous work in this area the output ofthe emulator is compared with measurement from an actual PV array.The results show good agreement between the characteristics, demon-strating its suitability for the evaluation of static parameter based esti-mation and dynamic search based MPPT techniques.

Introduction: Owing to increasing pressure encouraging the exploita-tion of sustainable energy resources, coupled with increases in wirelesstechnologies including remote base stations and mesh networks, solarcell based power supply technologies are beginning to gain acceptanceas a viable solution. The low efficiency of current solar power supplytechnologies, without MPPT systems, can require a nominal capacityfor an installation which renders solar PV prohibitively expensive. Totest and evaluate such MPPT systems, a device which can replicatethe voltage-current characteristic of a real solar array is required, ineffect, a solar array emulator.

Some emulators are commercially available at significant cost due tobeing designed for greater power ratings than perhaps would be required(powers less than 100 W are considered in the proposed design).Similarly in previous literature [1, 2], systems are proposed to meetthe demands of satellite applications requiring far greater accuracy andpower ratings than is required for domestic applications.

Common methods of MPPT are the open circuit (O/C), short circuit(S/C) and perturb-and-observe (PO) methods [3]. To test O/C and S/Cmethods, adequate replication of the maximum power point location ineither current or voltage with respect to the O/C voltage and S/C currentmust be achieved. For dynamic search based methods, the slope of thepower curve from the emulator must be free from features such as dis-continuities and stationary points, points of inflexion, etc., that canlead such algorithms to behave erratically [4].

Design methodology: From the single diode model of a solar cellderived by Walker [5], shown in Fig. 1, (1) provides a mathematicalrelationship for the solar cell (or array) terminal voltage and current:

Iterm = Isol − Isat expVterm

VT

( )+ 1

( )(1)

where Iterm is the measured current at the terminals; Isol is the current dueto incident solar radiation; Isat is the saturation current of the equivalentinternal diode; VT is the thermal voltage of the equivalent internal diode:and Vterm is the measured terminal voltage.

IsolIdiode

Vterm

Iterm

Fig. 1 Single diode model of solar cell [5]

Given the nonlinear dependence of Iterm on Vterm a high-bandwidthcontrol loop is required to maintain stability when testing switchedmode power supply based MPPT owing to the existence of ripplecurrent. Although it is possible to implement (1) using a microprocessor,the high switching frequency (.20 kHz) of the MPPT imposes tightsampling constraints on the emulator [6], therefore analogue circuitsare commonly employed. The exponential term in (1) leads to instabilityproblems as the MPP is approached, this issue is mitigated via manipu-lation to make Vterm the dependent variable:

Vterm = VT lnIsol − Iterm

Isat+ 1

( )(2)

The essential sub-circuits for the emulator (Fig. 2) intuitively follow (2)such that the inputs to the circuit are proportional to the variables in the

ELECTRONICS LETTERS 3rd February 2011 Vol. 4

equation, the current due to insolation (Vsol / Isol) and output loadcurrent (V / Iterm). Vterm is the output voltage of the circuit.

VDC

DIODE

R2R4

R1

R3

Vsol

Vi

V1

V2

V2

V3

V3

R5

R8

R10

Vi

V1

Vo

Io

A1

A2

A4

D

R16

R12 R13load

A3

Fig. 2 Simplified circuit diagram of solar emulator

Relating the circuit to (2), an opamp configured as a differentialamplifier performs the subtraction of Isol and Iterm (by operating on vol-tages proportional to these currents), and the division by Isat is achievedby setting the final gain of this amplifier proportional to Isat. Opamp A2then applies the logarithmic function. Resistances R8 and R10 provide adegree of flexibility to compensate for small changes in the parametersof D and provide a finite gain in the case where the diode is reversebiased. Opamp A3 acts as an inverting half wave precision rectifierwith unity gain employed to invert the negative signal for the poweramplifier A4 that provides both voltage gain to compensate for thedifference between the thermal voltage of D and the solar arraythermal voltage and current gain for the output.

The closed loop DC relationship between the output voltage andcurrent is shown by (3) given in terms of the output terminal voltageand current to be matched to an arbitrary solar array curve and circuitcomponents. The emulator component values are found by using anumerical solver to curve fit the solar cell characteristics (3) given thesolar cell parameters, thermal voltage and saturation current, and illumi-nation level:

0 = VtD lnG1Vsol − G2(R16Iterm)

IsatD+ Vterm

1 + R13

R12

( )⎛⎜⎜⎝

⎞⎟⎟⎠a2 + 1

⎛⎜⎜⎝

⎞⎟⎟⎠

+ R10(G1Vsol − G2(R16Iterm)) + a1Vterm

1 + R13

R12

( )⎛⎜⎜⎝

⎞⎟⎟⎠

(3)

where

G1 = R3

R4R5

R4 + R2

R1 + R3

( )G2 = R2

R5R4a1 = R10

R5− 1a2 = 1

R8IsatD

The diode parameters are open to a certain degree of flexibility in that thevalues used for the thermal voltage VtD and saturation current IsatD canbe varied by series and parallel combinations of diodes. Successfulresults were obtained here by using a series string of eight 1N4148diodes to increase the thermal voltage such that a greater signalvoltage is produced at the output of the logarithmic amplifier.

Results and conclusion: Fig. 3 shows the current-voltage characteristicsobtained from the characterisation of a nominally 12 W thin film siliconsolar cell and the emulator configured as described above. Fig. 4 presentspower against array voltage demonstrating the relationship between MPPand O/C voltage. The position of the maximum power point is located at17 V for both curves with a 2.5% error in the location of the maximumpower point with respect to current. Although there is a 5.4% error in theactual maximum power level and 3.4% error in the open circuit voltagesthe emulator captures the characteristic shape. In previous work on this

7 No. 3

subject [1, 2] there is no direct comparison of the emulator output to areal solar panel, as they are focused on the matching of an ideal equation.However, it can be shown that if the MPP is calculated based on eitherthe S/C current or O/C voltage (by means of a constant ratio) the errorin the location of the MPP with respect to either of these values deter-mined from the emulator will be less than 5%.

0 5 10 15 20 250

0.05

0.10

0.15

0.20

0.25

0.30

voltage, V

curr

ent,

A

realemulator

Fig. 3 Voltage-current relationship for solar emulator

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

pow

er, W

realemulator

0 5 10 15 20 25voltage, V

Fig. 4 Voltage-power curve for solar emulator

ELECTRON

# The Institution of Engineering and Technology 201118 October 2010doi: 10.1049/el.2010.2930One or more of the Figures in this Letter are available in colour online.

D.M.K. Schofield, M.P. Foster and D.A. Stone (Department ofElectronic and Electrical Engineering, The University of Sheffield, SirFrederick Mappin Building, Mappin Street, Sheffield, S1 3JD, UnitedKingdom)

E-mail: m.p.foster@sheffield.ac.uk

References

1 Kui, W., Yongdong, L., Jianye, R., and Min, S.: ‘Design andimplementation of a solar array simulator’. Int. Conf. on ElectricalMachines and Systems, (ICEMS 2008), Wuhan, China, October 2008,pp. 2633–2636

2 Marenholtz, P.E.: ‘Programmable solar array simulator’, IEEE Trans.Aerosp. Electron. Syst., 1966, 2, (6), pp. 104–107

3 Hohm, D.P., and Ropp, M.E.: ‘Comparative study of maximum powerpoint tracking algorithms using an experimental, programmable,maximum power point tracking test bed’. Conference Record of 28thIEEE Photovoltaic Specialists Conf., Anchorage, AK, USA, 2000,pp. 1699–1702

4 Armstrong, S., Lee, C.K., and Hurley, W.G.: ‘Investigation of theharmonic response of a photovoltaic system with a solar emulator’.2005 European Conf. on Power Electronics and Applications, Dresden,Germany, 2005, p. 8

5 Walker, G.: ‘Evaluating MPPT converter topologies using a Matlab PVmodel’, J. Electr. Electron. Eng., 2001, 21, (1), pp. 49–55

6 Dolan, D., Durago, J., Crowfoot, J., and Taufik, : ‘Simulation of aphotovoltaic emulator’. North American Power Symp. (NAPS),Arlington, TX, USA, 2010, pp. 1–7

ICS LETTERS 3rd February 2011 Vol. 47 No. 3