Optimal design parameters for a PV array coupled to a DC motor via a DC-DC transformer

593

IEEE Transactionson Energy Conversion, Vol. 6,No.4, December 1991.

OPTIMAL DESIGN PARAMETERS FOR A PV ARRAY COUPLED TO A DC MOTOR VIA A DCDC TRANSFORMER M.M.Saied(SM) Y.A.Safar(NM)

A.A.Hana8 M) M.A.El-Gabaly(SM) M.G.Jaboori(St.M) KH.A.Yamin(NM)

Electrical & Computer Engineering Dept.,

A.M.Sharaf(SM)

University of Brunswick

Colleg of Engineering and Petroluem

Fredricton,

Kuwait University

Canada

P.O. Box 5969 13060 Safat. KUWAIT

ABSTRACT This paper presents a study of the optimal operathg parameters of a system comprising a source (PV Solar Array), electromechanical energy converter DC (Motor) driving a mechanical load. Unlike a battery, a PV m a y is a nonlinear DC source and its operation has to be carefully matched to that of its equivalent electrical load in order to extract the maximum available energy. Henceforth, the analysis and design procedure will include the addition of a variable DC-DC matching transformer placed between the array and the motor. It will be responsible for adjusting the load curve seen by the array to coincide with its maximum power point. The model takes into considerationthe effect of different temperature as well as insolation profiles along the year. The analysis procedure will guide the design of DC motors as well as variable DC transformers especially suited to be operated in conjunction with PV arrays. The procedure determines optimal motor constants (flux coefficient Ce* for a separately-excited motor [SPM] & M*, the mutual inductance of a series motor [SEMI) in relation to narrowest range of the DC transformer ratio variation (T*) which will lead to an improved overall design in terms of maximizing the total annual gross mechanical energy delivered to a load of a given torque-speed characteristic. Keywords: PV, DC-DC Transformer,Matching

I. INTRODUCTION The recent developments in the solid state industry accompanied by a parallel increase in energy prices and the environmental restrictions as well as the need for reliable sources of energy lead to the consideration and assessment of new sources of energy which can secure the needs of the public at the least impact on the environment. An important candidate is the photovoltaic source of energy, where the solar radiation is directly convened into electricitythat can either be residentially used as a local selfsufficient source or interconnected to available AC public grid. Since solar cells are expensive, nonlinear sources of energy, careful study of their characteristics and operating conditions provides a major step in the efficient utilization of the available solar energy. Cell characteristics(I-V) for various solar insolations at a constant temperature are shown in Fig.1 .Tracing the power versus voltage curves, superimposed on the (I-V) curves, clearly indicates a point of maximum power output given by (Im-Vm) at Pm=Vm*Im. This paper deals with the optimal design of a PV system, where the objective is to maximize the annual output mechanical energy represented by a mechanical load 91 WM 146-1 EC A paper recommended and approved by the IEEE Energy Development and Power Generation Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1991 Winter Meeting, New York, New York, February 3-7, 1991. Manuscript submitted July 6, 1990; made available for printing January 16, 1991.

-

U

+ c m L

L U 2

ZD L

L 4

PV

Array Yoltage

(VI

Fig. 1: Effect of Insolation on the I-V and P-V characteristics of Crystalline Silicon Solar Cells

coupled to a DC motor, which, in turn connected to the PV array via a power conditioner, better known as a DC-DC transformer or a DC-Chopper. The following operating conditions will be included in the simulation procedure of the PV system in Fig.(2) :

Fig. 2: System schemtic diagram

i)

various insolation levels

ii) temperature variation curves during dil :rent months (Fig.(3))

iii) two different motors (SPM & SEM) Jaded by two different mechanical loads (T, ,Tu) The paper will give the steady state analysis of the four following cases, SPM driving a centrifugal pumping load, SPM driving a constant load torque, SEM driving a centrifugal pumping load and finally SEM driving a constant load toque. The analysis includes DC-DC transformersworking at their optimal transformation ratios. The addition of DC transformers to PV systems as well as discrete switching control has been studied in [1,2,3] While the consideration of the optimum motor parameters was introduced in [4,5]. It is the intension of this work to combine the two criteria in the optimizationprocedure and arrive at optimum solution in terms of both design parameters (Ce & M) as well as control parameters (T). It is believed that the above procedure will be helpful to design

0885-8969/91$01.0001991 IEEE

594

For a typical 1 hp, 120 V, 9.2 A system [I], and TLcan either be TL1=B*02 (centrifugalpumping load) = 1.54 * lod 02 orT,= 4.2+ BO2387 * o (for load torque)

-

U

v

+-

(6)

(7)

As for the transformer, it enters the analysis as a ratio (T) represented by

E (Y

L

a U

T=-V Vm

3

m

L 4 L

Im

and

M

0

Bo

40

80

IW

IM

140

160

180

PV Array Voltage ( V I Fig. 3:

of temperature on the I-v characteristics of Crystalline Silicon Solar Cells Effect

engineers in identifyingoptimal design parameters and whether such Parameters comply with industry standards and acceptable operating conditions. Other Parameters are shown to be included in Table (I).

T=f

where T is equivalent to different switching configurations. Its selection represents a tradeoff between operation reliability and maximum energy utilization. The analysis pertinent to each of the considered four cases is presented in the following: Case (1): Steadv State Analvsis of a SPM Driving a Cetrifuval

Pumuine Load The case describes a system comprising a PV array connected to a SPM through a DC transformer where the motor is coupled to a pumping load. Solving equations (2),(3),(6),(8)and (9), the realtion that provides the transformation ratio needed to operate the PV array at (Im,Vm) is given by:

The system (as shown in Fig.2) consists of a PV array of Ns cells in series by Np strings in parallel and has the following (I-V) relation

IT)

Ns + Ns V = -I*Ra* -* 1 ~ ( 1 + Np A

with B, as given by equation (6).

and is connected to a DC motor that can either be a seperately excited motor (SPM) or a series motor (SEM) as shown below:

Solving the above equation for different values of Ce results in the followingplots:

1. (T vs. Ce) at constant insolation levels (Fig.(4)) 2. (%Power vs. Ce) at constant insolation levels, with each point

1. Seperately excited motor (SPM)

on the curve has been taken to correspond to the optimum transformation ratio, where:

V = I*Ra+Ce*o Te= Ce*I = TL

Mechanical Power * %Power = Elecmcal Power

2. Series motor (SEM)

V = I*(Ra+Rf) + Ce*w Te= M*I*= TL T a b l e ( I ):

where Maximum Electrical Power = Im * Vm, and the corresponding Mechanical Power = Im * Vm - ImZ * Ra, and R% : Percent Insolation

List of symbols

'V ARRAY jymbol

Indotion Laolr (20 to 1w atop 20)

Rated Value

17

Description

16

Ns NP

Rs Iph IO

324 Cells 16 Strings 0.05 ohm 0.756 Amp

0.45'10-3 Amp 13.66 1IV

14

Series resistance o f on cell CeIl photocurrent Cellreverse Satur8tiOn current q/AkT (Cell Constant)

13

la W

Ra Rf

La Lf M Ce J

120v 9.2 Amp 1500 rpm 1.5 ohm 0.7ohm 0.02 H 0.13 H 0.0675 H

0.621 V/rad/sec 0.02365Kgzlrnz

Terminal Voltage Armature Current Shafi Spced Armature Resistance Field resistance Anneture self-hductance Field self-ioducmce Mutual inductance F l u coefficient Moment of inertia

oad Data

B

p

12

0

11

p

10

$

9

Z

JOTOR DATA V

15

Cells in series Stnigs io prallel

1.54'10-4

N.m/(rad/sec)

Load Constant

B

g

7

!

6

C

'

S

4

3 2 1

0 0

2

4

6

8

10

nux Coaemsient (C3

Fig. 4: T r a n s f o m r Ratio as function of flux' Coefficient (Ce) with insolation as a parameter (20-100%)in steps of 20%

~

595

3. (%Energy vs. Ce) and each point on the curve is represented by a value of Ce and a corresponding optimal value for the transformation ratio (T), (Fig.(5)), where: %Energy =

Out ut Mechanical Energy ’Electrical Energy

Results for Fig.(4) show a linear relation between T and Ce at different insolation levels, with the slope of the curves increasing as insolation level increases. As for (T vs. R%) with Ce as a parameter, the relation is almost linear relation except for low insolation levels. And T changes from about 0.4 to about 1.7 which is fairly moderate. Fig.(S) depicts how as Ce is increased, the percent power is increased at very fast rate approaching the high 9 0 s at considerably low Ce (using T=T*). However, as Ce is increaesd still further (Ce>l) the improvement in P is insignificant. Fig.(7) illustrates for the two different mechanical loads, selecting Ce around the value of 0.9 results in percentage annual energy utilization higher than 90%. For the particular application considered, the optimum transformation ratio, T*, and the percentage energy utilization are related to the insolation ratio, R%, and electric flux coefficient, Ce, according to the following equations: T = 0.3*Ce + 0 . 3 0 3 * C e * m (13) %Energy = (1.541-0.695 Ce+.12*Ce2+.52 h(Ce))*100% (14)

Fig.@) shows the annual %Energy as a function of Ce for cases (1) & (2). At values of Ce below 0.8, the use of centrifugal pumps is superior to that of a volumetric one. IncreasingCe beyond the value of 0.8, both pumping loads can result in approximately the same energy utilization percentage. Similar to equations (13) and (14), the corresponding equations for this constant load torque are: T = -0.1724 Ce+0.0085 Ce R%+O.O757*Ce*R%*h(R%) (16) %Energy = 1.8267+0.53*Ce-1.404*Ce55+.33 *

rn

% (17)

Case (3): Steadv State Analvsis of a SEM Driving: a Centrifugal The case describes a system comprising a PV array connected to a SEM through a DC transformer where the motor is coupled to a pumping load. Solving eq.‘s (4),(5),(6),(8) and (9), the governing relation for (T vs. M) and accordingly %Power and %Energy is given by:

Solving the above 3rd order equation under different operqting conditions and taking the same steps of the analysis procedure as in cases (1&2), yields the followingresults: T = 0.00355*R% - 0.172*M+0.0133

* M*R%’.S ~

h(. R % ),

+0.321*(M*R%).55-.000422*R%*exp(M)

(19)

%Energy = (6.2+.478*M-5.652*M2.782*h(M))*l00 % (20)

0.1 0

Fig. 5:

03

05

C*tIifugOl Load

0.7

0.9

1.3

1.1

Flux Coofncient

1.5

1.7

1.9

0) +

Constant Torque

The relation of T and M with R% as a parameter is now nonlinear. And for O20%, the %Power utilized out of the array reaches 90% and higher. Fig.(6) shows that selecting the value of M higher than 0.2 results in percentage energy utilization, for both loads, of value higher than 90%. However, the required range of T that is needed for insolation ratio range from 20% to 100% is much wider than that corresponding to SPM motor case. This will result in switching reliability and maintenance problems.

The %Energy u t i l i z a t i o n of a SPM d r i v i n g c e n t r i f u g a l and constant torque loads as function of (Ce)

Case (2): Steadv State Analvsis of a SPM Driving a Constant Load Toque A

The case describes a system comprising a PV array connected to a SPM through a DC transformer where the motor is coupled to a volumetric load. Solving eq.’s (2),(3),(7),(8) and (9) the relation providing optimum transformation ratio for a SPM driving volumemc load is given by:

K

B

H

2 0 ‘

4.2 * Ce Im T2+(.002387 * Vm). T - % * (....0687)=O

(”)

The bahavior of T as a function of Ce is linear with a slope proportional to the percent insolation. Unlike the relation in case 1, the lines of (T vs. Ce) with R% as a parameter cover a wider range of T and for the same Ce, T is lower for case 1 than that in case 2, e.g. at Ce=2, T,=3.5 while T2=5. For T as a function of R% with Ce as a parameter, for case 1, T is changed by the order of twice its initial value as R% changes fron 20% to 100% whereas, a constant load torque requires a ten fold change in T as R% sweeps the insolation range. It is ,therefore,recommended to select a cetrifugal pumping load in conjunction with a SPM, that would result in a lower range of T, i.e., lower number of switchings in the DC transformer.

10

0.2

0

0.4

M W l IndustDM (U) 0

Fig. 6:

Cetdhqd Lmd

+

0.6

Constant T w u e

The %Energy u t i l i z a t i o n of a SEM driving c e n t r i f u g a l and constant torque loads as function of mutual inductance (M)

Case (4): Steadv State Analvsis of a SEM Driving a Constant Load Toraue. The case describes a system comprising a PV array connected to a SEM through a DC transformer where the motor is coupled to a

596

pumping load. Solving eq.'s (4),(5),(7),(8) and (9) gives the equation of the optimum T in relation to (Im,Vm) and M, given by:

important, is the resulting increase in the required transformation ratio range as temperature is changed as depicted by Fig.(8).

[g [

4.2*~ M Z *1m3 (21) T4- T2* - * Ra+Rf- .002387))- [.OO2387*Vm) The subseiuent disiussion is the resui(of \solving the a&ve 4* order equation. The relation between (T & M) with R% as a parameter is nonlinear, whilst T as a function of R% with M as a paramater is almost linear. The range of T required for this case is wider than that in case (3), an intermediatesituation between cases (l&2), where T for this case ranges from (.5 to 5) compared to (.5 to 3). Moreover, T changes a maximum of 6 times as R% changes from 20% to 100%insolation compared to half that number for case (3). Operational differences in the annual utilization of energy between cases (3&4) reach a 30% difference at M S . 0 1 and decrease to about 1% at M=0.28, as shown in Fig.(6). In accordance with eqns.(l9) and (20), the corresponding equations for this load are: I 1

ZM,(R%)~

'0.1

T=0.0305*R%-0.974*M+.2307*(M*R%) 0.0259*- exp(M)

+.107*exp(M)

(22) Fig. 8:

%Energy=(11.231+3.21*M-13.3465*M.=+1.537

% (23)

~

exp(M)

111. q

The objective of the above analysis is to identify ranges from which Ce and M are to be chosen, and then the corresponding change in T can be determined. Clearly, the narrowest ranges of T result in the least number of discretized values of switchings that would closely preserve the optimum energy utilizationcondition [1,2], maintaining the system reliability unaffected. For a %Energy of 90% and higher, the ranges are given in Table (IQ. Table (11): R e c m n d e d ranges o f Ce L M with t h e required Transformer r a t i o values

I

Motor

1

Ce

Load

I

10.56-0.8

1

t

I

M

T

I

I 0.6-1.6 10.13-0.3 10.55-2.4

I

I

0.78-1.0

0.3-2.3

I

I

0.7

0.9

1

1.1

I

1.3

I

I

1.5

1.7

Flux Coefficient (Ce) Effect of ambient temperature on transformer r a t i o as function of (Ce)

I I

1.9

the

Therefore, it is very crucial to consider the variations in ambient temperature as the discretized transformation ratio steps are to be selected. This is even more true for countries of severe weather conditions such as Kuwait. To describe the on-line switching scheme to be used to optimize the utilized energy, the case of SPM is considered for the two different pumping loads. Considering the value of Ce selected as 0.621, that result in utilized energy percentage of more than 90% with the narrowest range of T, the corresponding range of optimum transformation ratio is 0.67 < T < 1.16 for the centrifugal pumping load. While a Ce of 1 would require T between (0.133-1.33) for the volumetric load. Lower Limit

-R

1

-

1

I

0.2-0.4

I

0.5

I

SEM

T

I

IPurnping Load

Constant Torque Load

I

SPM

9

0.3

1 I

0.6-2.75

Measure VL, lL] I

Compute (PI) I Update index I

I Measure new VL, I

3 Reverse Direction

1

Compute (P2)

I

C=C+l

I

'

increment PI PP1 QetP2

L P I '0.1

1

I

I

0.3

0.5

0.7

0.9

Effect

of

I

1

1.3

1.5

1.7

1.9

tmrature

on

the

I

1.1

1

'

Pl -P2 GetP2

1

Flux Coefficient (Ce) Fia. I :

ambient

available p w e r as function of (ce)

Fig. 9:

Flowchart of t h e on-line search diagram using discrete switchinas f o r s e v e r a l s o l a r modules

For the centrifugal pumping load, two discrete values of T= 0.833 and 1 are selected to represent the corresponding continuous range whereas, for the volumetric pumping load, three discrete values of T= 0.467, 0.733 and 1 are selected. These discrete values of T would represent different series/parallel connections for the PVarray modules. Flowchart depicted in Fig.(9) shows the details of the on-line search based on measuring the load terminal voltage and current as sampled every 5 or 10 minutes. Representativedaily insolation curves for the months of January and July pertinent to real data of KUWAIT taking temperature effect into consideration are shown in Fig.(lO).

.BJ

KUWUT C M d i S w (Lobhxh 30)

1

100

Hours of effective i n s o l a t i o n

F i g . 1 2 : Ideal, continuous and discerte t r a c k i n g of a day i n January for t h e case of a SPM connected t o a constant torque load

a

U

T a b l e (111):Annual and m n t h l y energy u t i l i z a t i o n percentage using direct, continuous and discrete t r a c k i n g modes for both loads

2

0

0

Into.(Jul)

4

6

+

8

10

12

14

20

1.9

16

22

I

I

Volumetric

I

Pumniwo

1

HOW

Jon.

6

A

Tmp.(Jul)

JM.

Fig. 10: I n s o l a t i o n and temperature p r o f i l e s p e r t i n e n t t o January & J u l y i n t h e state of Kuwait To illustrate the outcome of the proposed on-line search, Fig.(ll) and (12) depict the evolution of the transformation ratio using the selected discrete values as compared to the continuously adjusted ratio for the incremental change in T by a step 0.01-0.02 Also, shown in the figures, the ideal transformation ratio pertinent to the representativeday of July and that of January.

a

L

I

I

I

I

I

,

12

, 18

Hours o f e f f e c t i v e i n s o l a t i o n Fig. 11: Ideal, continuous and discerte t r a c k i n g of a day i n J u l y for t h e case of a SPM connected t o a constant torque load Table (m) shows the percentage energy utilization pertinent to the months of July and January as well as the annual value for the cases of direct coupling, continuously adjusting the transformationratio T using AT=0.01-0.1 and sampling interval of 5 minutes. Also, the results for the case corresponding to discrete switching using only two or three steps are shown for two different sampling intervals of 5 and 10 minutes. It is clear from the shown results that using online search routine for the coarse transfornation ratio adjustment are near enough to that obtained using the f i e adjustmentsequence and

both schemes can result in superior annual energy utilization percentage of about 12% more for the volumemc load and about 9% more for the centrifugal load than the case of direct coupling. In order to increase the switching reliability, specific values of T a~ to be used, e.g., 1, 0.5, 0.25, I n , 1/6, .., etc. However, using these values for the selected Ce may result in low energy utilization. Therefore, higher value of Ce should be selected given these predetermined values of Ti to improve the energy utilization rate.

1. Using Ce and T as optimizingparameters, maximum energy can be delivered to the load through the separately-excited motor. And the same goes for the M and T for the series motor. 2. Beyond certain values of Ce and M the improvement is negligible. 3. SEM and SPM can have the same efficiency for different types of loads when all the optimization parameters are used. However, using SEM can result in much wider range of T for the same percentage of utilized energy. 4. The study has revealed the dramatic effect the change in the ambient temperature has on increasingthe range of T. Therefore, in countries as KUWAIT characterized by its severe weather conditions, a design trade-off between the value of Ce or M that optimize the percentage of annual energy utilization and the corresponding increase in the range of T that can result in increasing the number of required switchings that can adversely affect the system reliability should be considered. 5. On-line search algorithm has been devised to coarsly adjust the transformation ratio using preselected discrete values based on the continuous range of T comesponding to the value of Ce that results in energy utilization percentage higher than 90% with minimum range of T required to cover the whole insolation pattern. The results clearly demonstratethe effectiveness of such algorithm.

ACKNOWLEDGEMENT This study is supported by Kuwait University Research Grant No. ECE 040.

sa

REFERENCES [l]. Z. Zinger, A. Braunstein: " Dynamic Matching of a SolarElectrical (Photovoltaic) System, An Estimation of the Minimum Requirements on the Matching Systems". IEEE Transactions on Power Apparatus and Systems, Vol. PAS100, No. 3, March 1981, pp 1189-1192. [2]. Z. Zinger, A. Braunstein: " Optimum Operation of a Combined System of a Solar Cell Array and a DC Motor". IEEE Trans. on Power Apparatus and Systems, Vol. PAS100, NO. 3, March 1981, pp 1193-1197. [3]. J. Applebaum: " The Operation of Loads Powered by Seperate Sources or by a Common Source of Solar Cells". IEEE Trans. on Energy Conversion, Vol. 4, No. 3, Sept. 1989, pp 351-

357. [4]. M. M. Saied: " Matching of DC Motors to Photovoltaic Generators for Maximum Daily Gross Mechanical Energy". IEEE Trans. on Energy Conversion, Vol. 4, No. 3, Sept. 1988. [ 5 ] . M. M. Saied, M. G. Jaboori: " Optimal Solar Array Configuration and DC Motor Field Parameters for Maximum Annual Output Mechanical Energy". IEEE Trans. on Energy Conversion, Vol. 4, No. 3, Sept. 1989, pp 459-465.

Mohamed M. Saied (M80-SM84): Recieved his Ph.D. from the University of Aachen, West Germany, in 1974. From 1974 to 1983 he worked at the Universities of Assiut (Egypt) and Tripoli (Libya). Since 1983 he is working at Kuwait University, where he is currently a professor of Electrical Engineering.

Adel A. R. Hanafy (M'74): He is a professor of Control Engineering at Cairo University. Currently, Dr. Hanafy is a visiting professor at Kuwait University. His present work is on different industrial applications of control theory. Moustafa El-Gabaly (S'70, M74, SM81): He recieved the Ph.D. degree in Electrical Engineering from the University of Alberta, Canada, in 1974. In 1976, he joined the faculty of Electrical Engineering of Kuwait where he is currently a professor. His research area includes microwave and solid-state devices, photovoltaic energy conversion and photoelectronic properties of crystalline and amorphous semiconductors. Yousef A. Safa: Recieved his Ph.D. from Wayne State University in 1982. He is currently an assistant professor in Kuwait University in the power systems and high voltage department. His interests include high voltage transients on compensated lines. Monii Ghanim Jaboori (St. M86): Recieved B.Sc. in Electrical Engineering from Kuwait University Jan. 1988. Currently a fulltime master student and part-time research assistant. He has coauthored several papers and is planning to persue his career in the field of Power Electronics and Renewable Energy Sources. Khaled Abdul Raheim Yamin: Recieved B.Sc. in Electrical Engineering from Kuwait University Jun. 1988. Currently a fulltime research assistant. Planning to continue in the field of solidstate technology. Adel M. Sharaf (SM): Acquired his M.Sc. and Ph.D. degrees from the University of Manitoba, Canada in 1976 and 1979 respectively, and is a member of several professional societies. Currently a professor of electrical machines and power systems in the same university. His research interests include power systems, control, protection, modelling and motor drives.