Field Measurements of Transient Effects In

Photovoltaic Panels and its Importance in the

Design of Maximum Power Point Trackers

Rodrigo J. Serna lIlt, Brandon J. Pierquet+, Juan Santiago§, and Robert C.N. Pilawa-Podgurskit

t Derartment of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801 Department of Electrical Engineering, University of Washington, Seattle, WA 98195

§ Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Abstract-This paper describes the implementation of an ex­perimental setup to capture the dynamic behavior of photo voltaic (PV) modules at significantly higher sample rates than what has previously been done. The data helps guide the design of maximum power point tracker (MPPT) algorithms, particularly as it pertains to tracking speed and accuracy. We present data that illustrates the dynamic behavior of PV modules for various cloud coverage and weather situations. In addition, we perform analysis on the collected data to illustrate the frequency of rapid transient changes in PV output power due to fast moving clouds and other sources of shading, all of which are essential for evaluating the speed/accuracy trade-off in any MPPT converter.

I. INTRODUCTION

The continued cost reductions realized by photovoltaic (PV)

panel manufacturers have helped bring down the cost of solar PV installations substantially, and has brought us considerably

closer to the ultimate target of grid parity. As PV panel prices

continue to decrease however, the balance of system (BOS) costs begin to have more significance. Excluding labor, the

inverter, or other power conversion circuitry, becomes the next natural target for reducing system costs. To capture the

maximum power from a PV cell or module, power electronics

circuitry is used to interface with the load, commonly the electric grid, or an energy storage device such as a battery.

This is achieved using dc-ac and dc-dc converters, as shown in

Fig. l. The ability of the power conversion stage to continually track the maximum power point improves the cumulative

energy capture from the source.

To illustrate the properties of a PV cell (or collection of

cells), Fig. 2 shows the current-voltage (I-V) characteristics of

a typical solar panel, as well as the corresponding power versus

voltage characteristics of the same panel, while operating

at a nominal full-sun level. The function of the maximum power point tracker (MPPT) is to operate the PV panel at

this maximum power point, irrespective of the voltage of the

load. This is typically accomplished with intelligent circuitry controlling a dc-dc converter (in the case of a charge con­

troller), or an inverter. A thorough review of various methods for accomplishing this power point tracking is presented in

[1]. Common to most methods is their ability to continually

Solar Panel MPPT-based Charge Controller

IIIII � Ba""y

Solar Panel MPPT-based Inverter

1 1111� Grid

Fig. 1. Schematic illustration of the two most common applications of maximum power point trackers (MPPTs)

1.4 1.2

� 1.01------i-----'-----.;.... C 0.8 � 0.6 u 0.4

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0.2 o.oo=-----:------: '::-----:'=-------!:'::-'

20,-----,----,-----,----"

15

� 10 �

°o�----:------:'::-----:'=-------!:'::-'

Fig. 2. I· V and p. V curve of BP SX320M solar panel used in this work, under full sun.

track the MPP as it moves due to changes in insolation and

temperature.

Various methods [2]-[4] have been proposed to achieve high speed tracking to maintain operation at the MPP, despite

rapidly changing conditions. Ideally, one would like to operate

978-1-4673-4355-8/13/$3l.00 ©2013 IEEE 3005

(a) (b)

Fig. 3. Figures showing (a) block level schematic of the experimental setup, and (b) photograph of the experimental setup on the roof of Everitt Laboratory.

as close to the MPP as possible when conditions are not changing (steady-state), and to quickly follow the MPP as it

moves due to transient events such as cloud shading. However,

it is generally the case that there exists a trade-off between tracking speed and steady-state accuracy, and it is difficult

to achieve both in a practical implementation. Fundamentally,

accurate steady-state operation requires high precision voltage and current sensing as well as high resolution duty cycle con­

trol of the power converter. It is well-known that to measure a signal with high precision, sampling frequency is typically

reduced. The simplest example of this is the averaging of

many samples to achieve a measurement of higher resolution than each individual measurement [5], [6]. Likewise, high­

resolution duty cycle control can be obtained in the digital

domain by the use of PWM dithering or more advanced techniques such as Sigma-Delta PWM converters [7]. Both of

these solutions contain a similar trade-off between resolution

and transient response.

The question for any engineer designing the MPPT as part

of a PV system is how to choose the balance between tracking

speed and steady-state accuracy. Since the goal is always to extract the maximum amount of energy from the PV system

over time, the decision of what balance is appropriate requires a good model of the dynamic behavior of a PV panel under

real world conditions. More specifically, the designer must

know how fast and how far the MPP is moving during typical transient events, as well as how often these transient events

occurs. Armed with such data, the designer can then make

an informed decision about what tracking speed is suitable in

order to maximize the total energy extracted from the system

over time.

Despite the inherent value of this data, very limited ex­perimental results exist in the literature to guide the design

of MPPTs. Most field-measurements of PV installations have

focused on the measurement systems themselves [8], or in­vestigated data on a daily or seasonal time frame [9]-[12],

with measuring rates that are too slow to be of practical use in the design of MPPT converters. It is our hope that the

data presented here will be useful to any power electronics

MPP and Vmpp Over Day [11/16/2012]

Fig. 4. Plot of power versus time for sunny day (top) and MPP voltage for the same time (bottom).

engineer tasked with designing an MPPT as part of a PV system. Previous work on MPPT implementations that focus

on fast dynamic response [2], [4], [13], [14] have used seem­

ingly arbitrary irradiance transient rates without any reference to experimental data. It is therefore also our hope that by

providing extensive statistical analysis of experimental data,

we can stimulate a discussion regarding the trade-off between tracking speed and steady-state accuracy in MPPTs.

The paper is organized as follows: Section II provides

information about the experimental setup we used to capture our data, inculding the relevant captured data. Section III

provides key design insights obtained from our analysis, and Section IV summarizes the conclusions of this paper.

II. EXPERIMENTAL SETUP AND RESULTS

The experimental setup used to obtain current-voltage mea­

surements can be seen in Fig. 3, which is located on the roof of Everitt Laboratory at the University of Illinois at

Urbana-Champaign. The apparatus contains a weather resistant

3006

M PP and Vmpp Over Day [11/23/2012] vmpp Over Day [11/23/2012]

��[ � o� � � � � � � � � � � � # � # � � � � , � � � � Time of Day

_20r-__ � __ ,-__ �V�m�O�v�e�rD�a�y� __ ,-�� __ _

e:.. 19

Time of Day Time of Day

Fig. 5. Plot of power versus time for a day with fast-moving clouds, together with a zoomed-in section to help visualize the changes.

enclosure for instrumentation, and two coplanar 36-cell PV modules (BP part number SX320M). One module is connected

to an Agilent 34410A meter, which captures high frequency

transients in the solar irradiance by measuring changes in Isc at a rate of 5000 readings per second. The second module

is connected to a programmable four-quadrant voltage source

(Keithley 2420 SourceMeter), to measure the changes in the module characteristics due to temperature, clouds, or shadows.

Both instruments are controlled by a Netbook, and the Keithley

SourceMeter is controlled through a GPIB interface, while the high bandwidth data of the Agilent meter is transmitted

over an Ethernet cable, as illustrated in Fig. 3. The data is automatically backed-up nightly over Ethernet to a server

housed in a secure location.

To consistently capture the current-voltage relationship of the module, the voltage source is programmed to perform

continuous voltage sweeps, while measuring the current at each point. The sweep include an open circuit voltage (Voc) measurement, a short circuit current (lsc) measurement, and

an evenly distributed set of voltages centered around the maximum-power voltage. After each sweep, the maximum

power voltage (V M P p) is extracted from the data, and used

to update the center-point for the next voltage sweep. This

dynamic adjustment of the center-point of the sweep reduces

measurements outside of the range of interest, providing a

relatively high temporal resolution as compared to existing literature [9]-[12]. For the data presented here, 100 hundred

points were sampled in a ±2 V window around the previous

Vmpp, for a voltage resolution of 40 mY. Each sweep (includ­ing samples of Isc and Voc takes 3.9 seconds). Data is collected

continuously throughough the day, to ensure the capture of the low-light time periods around the sun rise and set.

Shown in Figs. 4 and 5 are measurements taken on two

separate days during late Autumn, representing one day with uniform sun and one day with continually passing clouds.

These two days represent opposing sides of a typical speed and accuracy trade-off. To understand the variability and trends of

the module power and its constituent parameters, two values

____ i

+

n v

Fig. 6. Equivalent circuit model of a PY cell [1].

are extracted from each current-voltage sweep: the maximum

power output of the PV module (Pmpp), and the corresponding voltage at this point (Vmpp). It can be observed that even with

large variances in output power, the corresponding voltage

magnitude remains comparatively stable. Consequently Isc tracks the dynamics of P mpp' since changes in irradiance have

much larger influence on the module output current than its

voltage. The changes in Vmpp due to cloud cover, while less pronounced than changes in power, can still be observed, as

shown in the inset of Fig. 5.

To ensure adequate resolution of the peak-power location

from the measured data, each sweep is fit to the standard

implicit formula [1]

. _ �tviC' V + iRs z - Iph - Ise T -

R' (1)

sh

corresponding to the photovoltaic model in Fig. 6. The

known parameters of this model are such that: N is the number

of series-connected cells in the module, VT is the thermal

voltage, defined as kT where k is the Boltzmann constant, T q

is the measured temperature of the module, and q is the charge

of an electron in coulombs. A least-squares solver is used to calculate the remaining parameter values for Rs, Iph, Is, n,

and Rsh, which are the cell series resistance, photo-current,

diode dark-current, diode ideality factor, and the parallel shunt­resistance respectively. By creating this model representation

of each sweep, a higher resolution can be obtained near the peak-power voltage and current locations, and reducing the im­

pact of measurement noise. By compressing the characteristics

3007

0.9

0.8

l: .� Q 0.7

0.6

0.5

V MPP Rate of Change (VIs) IVMP� Rate of Change (VIs)

(a) (b)

Fig. 7. Histograms showing the (a) frequency distribution, and (b) cumulative distribution of Vmpp for the time period July 12th to October 4th.

of the module to a set of parameters, the information required

to adequately describe the measured sweep is significantly

reduced, which is beneficial as the sweep rates and monitoring duration have increased.

III. DESIGN IMPLICATIONS

While the change of panel power over time is an illustrative metric of the dynamic conditions under which a PV system

has to operate, it is not always the most significant behavior to be considered. Most MPPT implementations act by modulating

the voltage to locate the MPP [1]. As an example, consider the

operation of a simplified buck-mode PWM converter. In this case, the input-to-output voltage relationship is proportional to

the duty-cycle chosen, such that Vout = DVin. If this converter

is feeding a constant output voltage, such as a battery, then the duty-cycle will control the voltage imposed across the PV

module, minus any losses.

As the insolation on a module changes, so will its peak­power point. If the converter is initially operating at the MPP

of the module, with a duty-cycle that results in a voltage of VI, and then the insolation suddenly changes, the corresponding

panel I-V characteristics will change. The power converter will

no longer be operating at the optimal operating point, since the new MPP voltage is different than that of the previous

insolation level. The converter must respond by changing its

duty-cycle to appropriately match the new optimal voltage.

During the time between the change in power level and the

response of the converter, there is an effective reduction in

power output which can be expressed as !:lP = P2(Vmpp) -P2(Vd, where Vmpp represents the new MPP voltage, and P2 is the power as a function of voltage of the new insolation

level.

The ability of the converter to properly track changes in

the module output is dependent on a number of factors, such as measurement accuracy, duty-cycle resolution, and system

response - the trade-offs of which require understanding the

magnitude and rate-of-change of Vmpp. Fig. 5 illustrates the

transient nature of Vmpp during a time of fast-moving cloud

coverage. It is clear that there are periods of rapid change in addition to slow-moving variations.

To add visibility into this data, the rate of change of

the peak-power voltage, !:l Vmppl !:It, is investigated. The two charts in Fig. 7 represent these dynamics, as both a probability

distribution and cumulative distribution, for data captured

between July 12th and October 4th, 2012. This data allows comparison of the relative frequency of transient events, and

a clear way to understand the percentage of events that can be

tracked for a given response rate.

For example, if a given power converter hardware design

and MPPT algorithm have a response rate capable of tracking a 1 Vis change, the cumulative distribution plot of Fig. 7b illustrates that this system will be able to adequately track the

MPP voltage for 99.2% of events. Conversely, if the static !:l V characteristic for the system can only be held below 100 m V,

then this may impact up to 40% of the test cases.

Additionally, Fig. 9 shows the dynamics of the short-circuit current measurements, !:lIse I !:It, which provide a significantly

higher sampling rate than the full 1-V sweep data. To minimize

the effect of measurement noise, 1000 samples of the Ise data was averaged, giving an effective sampling rate of 5

Hz. It should be noted that if higher frequency transients

are expected, the effective sampling rate can be improved by

averaging fewer samples (at the cost of resolution). Owing to

the large volume of data captured by the Agilent meter, custom

Python software has been written to enable the averaging of long-term data in a reasonably short time period, through the

use of parallelization. Currently Amazon's EC2 service is used

to quickly process this data, but the software can be used on many different cloud services, if desired.

As can be expected, the measured probability density of

Fig. 9 has a much larger peak around 0 Als than the corre­

sponding peak around 0 Vis for the Vmpp measurement. This

3008

10' .------�--;>!L:...:..::=�-=::..:::::.+_--�--___,

Isc Rate of Change (Ns) IIscl Rate of Change (Ns)

(a) (b)

Fig. 8. Histograms showing the (a) frequency distribution, and (b) cumulative distribution of Isc for the time period July 12th to August 15th.

is due to the fact that conditions do not have time to change

substantially between the high frequency Isc measurements, and many samples will therefore be similar to the previous

measurements. The data of Fig. 9 is thus useful to visualize

the frequency at which very fast transient events occur in the insolation of the panel.

Finally, shown in Figures 9a and 9b are probability density

functions for a sunny day (corresponding to Fig. 4) and

a cloudy day (corresponding to Fig. 5), respectively. It is apparent from these plots that on days with fast-moving cloud

coverage, there are a much higher occurence of fast rate of

change transitions of Isc, which is to be expected. These plots

give a quantitative result that can be used in the design of

MPPT converters.

IV. CONCLUSIONS

We have presented a system measurement setup used for

capturing dynamic PV panel data of high temporal resolu­

tion. The captured data is useful in the design of MPPT converters, as it will guide the trade-off between tracking

speed and steady-state accuracy. In addition, we present a

statistical analysis of the dynamic behavior of PV panels, as well as provide design insights based on this data. Armed

with statistical parameters of the expected rate of changes

of the variable Vmpp and Isc, a system designer can choose the corresponding PWM resolution as well as voltage and

current sensing resolution and sampling speed to achieve the

objectives at minimum hardware cost.

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10'

10-1

10-2

l> .� 10-3 0

10-4

10.5

1.5

(a)

10'

10-1

10-2

� � 10-3 0

10.4

10-5

1.5

(b)

Fig. 9. Probability density functions of 6.Isc/6.t for (a) a sunny day (corre­sponding to Fig. 4) (b) a day with fast-moving cloud coverage (corresponding to Fig. 5).

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