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Anadolu University , Turkey September 22 nd 2008. Cost-effective PV sizing approaches; towards an Intelligent Building S. Kaplanis, E. Kaplani Mech. Engineering Dept., T.E.I. of Patra, Greece ABSTRACT.

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anadolu university turkey september 22 nd 2008

Anadolu University , TurkeySeptember 22nd 2008

Cost-effective PV sizing approaches; towards an Intelligent Building

S. Kaplanis, E. Kaplani

Mech. Engineering Dept., T.E.I. of Patra, Greece

  • This paper discusses a most cost-effective configuration of an S.A PV plant.
  • It describes and compares two new approaches which when combined may provide much more reliable and economic PV sizing and performance.
  • It outlines an evolution of PV sizing methodologies with an inbuilt level of intelligence to maximize the cost–effectiveness and the Performance Ratio, PR.
  • The issue of cost-effectiveness in S.A. PV plants has not received enough attention,
  • Apart from the requirement for maximizing the Yield, Yf, ( kWhe/kWp), on an annual basis for a PV plant , there is, also,

an increased concern about the reliability of the PV performance,

to meet the loads with a pre-determined confidence level, at the minimum possible installed Peak power.

According to the aforementioned issues, the design of a PV plant should have as objective to deliver a plant able enough to produce and deliver the right output at the minimum cost, with a small PBP and with a high Performance Ratio, PR.
  • The issue of reliability has introduced the concept of the period of energy autonomy of a PV plant, expressed in days, d.
The number of d days, increases when the fluctuations in solar radiation become larger.
  • The less the mean PSH value is, the higher is the d value.
  • The drawback of this conventional approach is the high cost, as both the Peak power to be installed and the Capacity of the Battery Storage System increase linearly with the number of the d days of the energy autonomy.
In addition, the Performance Ratio, PR, of such a PV plant decreases.
  • This implies a non-economic approach due to the high PBP or low IRR associated to this PV sizing methodology.
  • An outline of two new approaches is given which may serve either independently or coupled to each other towards a more cost-effective PV configuration, than the conventional methodology.
three approaches for a cost effective reliable sizing
  • 1st The static-conventional PV sizing methodology,
  • the main quantities:Peak Power, Pm, and Battery System Capacity, CL (Ah), are determined by the following formulae:
  • (1)
  • (2)
2nd The Statistical fluctuations model Introduced into PV sizing
  • In this approach, described analytically in our previous paper, it is necessary that the statistical fluctuations of the daily solar radiation are studied from the T.M.Y. data and are introduced into the PV sizing analysis.
For a monthly based sizing approach, the s.d., σΗm(nj), of the mean daily solar radiation on the horizontal for the representative day of the month, for which the PV plant is to be sized, is determined by the expression:
  • σ2Ηm(nj)=[σ2H(nj)1 + σ2H(nj)2 +…+ σ2H(nj)N]/N2 (3)
  • H(nj) is the global solar radiation at horizontal for the mean or the representative day of the month.
  • N is the number of years for which data are collected.
The standard deviation, (s.d), σ, of the data and especially of H(nj)1 , H(nj)2 etc, is determined by:
  • σ2Η(nj) = sqrt( Σ(Ηm(nj)–H(nj))2/ (N-1)) (4)

where, Ηm(nj) is the mean value of H(nj)1 , H(nj)2 etc.

  • The expected H(nj) values, through which PSH is determined, lie with a 95% confidence level, in the domain :

H(nj) Є [Hm(nj) ± 2* σ Η(nj) ] (5)

or when the PV plant is to be energy independent for d days, in the domain:

H(nj) Є [Hm(nj) ± 2*d*σ Η(nj)] (6a)

  • In the case the days are statistically correlated, the expression which holds in this case, is the following:

H(nj) Є [Hm(nj) ± 2*sqrt(d)*σΗ(nj) ] (6b)

The above expressions hold for a small number of d. The reason is that Hm(nj) changes with nj but slowly, so that for d up to 4-5 days the change of Hm(nj) is to be much less than the σ of the Hm(nj) .
  • Expressions (6a) and (6b) may provide the expected 95% energy deficit to occur for a period of d days.
  • The deficit for a time period of d days is estimated to be equal to:
  • 2* d * σ Η (nj) (7a)
If the sizing is to be based on the expected mean daily radiation for a specific day nj, within a group of d days, with a span of ±l days around the day nj, ie 2*l+1=d,

then, the expected energy deficit for that period is estimated by:

2*sqrt(d)*σ Η(nj) (7b)

  • This is true for the case when data for only the nj day are considered.
  • On the other hand, the deficit is equal to :
  • 2*d*σ Ηm(nj) (8)
Following this analysis, the Pm and CL values are determined by relationships derived in [8]:



A comparison of the first 2 approaches, as outlined, provides that for a given load, QL (Wh/day), the Pm and the CL, as determined by the statistical fluctuations model, are more cost-effective, compared to the conventional sizing methodology.
  • Results of this comparison are given in figs. 1,2 and 3.
  • A measure of the comparison is the ratio CR given by the capacity, CL, determined by the statistical fluctuations approach (2nd Approach), over the CL determined by the conventional approach (1st Approach),
Similarly, for Pm , the ratio of Pm(statistical) over Pm(conventional) is given by the same parameter, CR, as shown below.
The fluctuations of the solar radiation which are statistically interrelated cause a limited increase in Pm and CL,

while, the term d, introduced in eq(1) and (2), is higher than the correction term introduced in eq (11) and (12), as outlined above

This reasonable and limited increase in the Peak power contributes to a limited relative decrease in PR ,compared to the 1st approach.
  • This, in turn, leads to a smaller Pay Back Period, PBP, determined by:

PV plant Peak power compared with the conventional method vs d The solid line gives the results of the conventional method. The dashed line gives the results when Eq. 7a is used. The dotted line gives the results when Eq 8 is used, which is the usual case as the neighbouring days are inter-related in solar radiation..

The effect of PR values to PBP for different discount rate, I, values is presented in fig 4.
  • The curves of the discounted PBP were calculated for various discount rate values and with a buying rate 0.5 Euros / kWh.
  • For cases of S. A. PV plants and with a performance ratio less than 30%, PBP exceeds 20 years, ie a period very close to the life period of a PV plant, which implies that the system is not cost effective
As PR increases and takes values between 60 % and 80%, the PBP gets lower than 10 years. Such cases are in favour while in addition the discount rate value is no so crucial as it is for lower PR values.
  • The LCCA for such systems has to take into account along with the discount rate values the buying rate. CI, too.
  • The parametric analysis of the performance ratio for several economic conditions in a country is shown in fig 6. It is obvious that the less the performance ratio value is, the more the discount rate value influences PBP.
3rd Predictive management of a PV system. An Intelligent PV system coupled to Load Management
  • Although the 2nd approach provides much better results as far as cost-effective sizing is concerned, a new concept is developed that may further contribute to the increase of the Performance Ratio, PR.
  • A new approach is developed, which increases the utilizability of the system.
  • This approach may be either independently implemented or it may be associated with the 2nd approach, presented above.
It involves a higher level of intelligent management of the overall PV& Building system. This approach has the following characteristics:
  • 1. An inbuilt intelligence to manage the PV system. This is experienced when the PV system is equipped with the ability to predict the daily global solar radiation profile.
  • The prediction model introduces a stochastic factor, which takes into account the current hour I(h1;nj) measurement for the prediction of I(h1+1; nj) value at the next hour h2.

The model is based upon the following:

The predicted value of I(h2;nj) is based on the mean expected Im,pr(h2;17), with a new deviation value λ'· σI'

Ipr(h2;nj)=Im,pr(h2;nj)±λ'·σI' (17)

  • λ' is determined through a Gaussian sampling and is permitted to take, according to this model, values within the range λ±1.
  • The model determines the Ipr(h2;nj) value and compares it with the mean expected Im,pr(h2;nj), in order to give a prediction for next hour h3, and so on.
Fig. 6a,b provides such predicted solar radiation profiles where it is clear that the system may be able to predict deviations from the average solar radiation in a rather successful way.
current work
Current work
  • Currently working on improving the model considering 2-3 Intensity measurements at previous hours for the prediction of the Intensity value at next hours of the day.
  • (Imeas(h1;nj)-Im,exp(h1;nj)) /σI(1) = t1
  • (Imeas(h2;nj)-Im,exp(h2;nj)) /σI(2) = t2
  • (Imeas(h3;nj)-Im,exp(h3;nj)) /σI(3) = t3
  • I(h3;nj)=Im,exp(h3;nj)+ R*σI(3)+


  • I(h4;nj)=Im,exp(h4;nj)+ R*σI(4) +

(t2*σI(2) -t1*σI(1))*R1/4 +


This leads to the determination of the pragmatic energy to be delivered in a day by the PV plant.
  • 2. A data acquisition system, which is tailored to the model management parameters opted e.g. global solar radiation intensity, temperatures (indoor, outdoor), humidity, wind velocity.
  • 3. A micro-processor control unit
According to all these, the system takes the following configuration, which provides the topology of the communication network and its sub-networks.
  • The whole communication network is split in two basic parts: the sensors’ sub-network and the PC sub-network. The interface between them is the so called master node. The topology of the communication network and its sub-networks is drawn in fig. 7.

Fig 7. Communication Network topology with the two sub-networks. Sensors are the pyranometer to provide the global solar radiation, the thermocouples

Each sensor node includes a microcontroller (Microchip PIC16F786) that introduces the upper layer network control and management. A CAN controller (Microchip MCP2515) through SPI protocol is opted.
  • Several alternatives were examined for the implementation of the sensors’ sub-network, e.g. 802.11, 802.15.4, CAN, etc. Among them, the Controller Area Network (CAN) protocol – or CANbus, was found to fit best the technical and economical needs of the application.
The outlined M.S. associated to this PV generator, may face successfully cases where the conventional design or the statistical fluctuations model, may fail to meet the loads.
  • The whole PV + Building system equipped with the solar radiation prediction software and the load management system is intelligent enough to predict the daily PV energy.
  • If prediction is effective, it may shift some lower priority loads to next days, using a micro-processor system, using the following formula:
  • QL(Wh/day)=QL,crit+e1QL,1+e2QL,2+… (15)
QL,crit are the critical loads (Wh/day) which the PV-plant is permitted to fail to meet them by less than 1% of the annual time (87 hours/year).

Loads QL,1 , QL,2 , etc. are assigned importance weights e1, e2 , etc., respectively.

  • The system load management operation targets to satisfy the load requirements over a period of d days. Such a management policy described above increases obviously the PR value and improves the second approach when coupled with it.
  • From the analysis outlined, becomes clear that the study of the statistical solar energy fluctuations either on an hourly basis or on a daily, finally result in a sizing approach which is cost-effective and reliable, compared to the conventional one.
  • Accordingly, PR, relatively increases as the PV plant is not oversized and therefore power burning in the Power Conditioning Unit, due to over-production is limited.
  • This provides a PV system performance close to the nominal Yield value.
The dynamic 3rd approach based on an intelligent predictive management of the PV system, may be considered as an independent one, too.
  • However, it is more effective to couple it onto the Statistical approach. Then, there is a double effect to the PV sizing cost-effectiveness.
  • First, the size is more rational as statistical fluctuations introduced into the PV sizing may even decrease the power deficit.
  • Second, the energy performance of the PV plant may be predicted for any day, based on the software the plant is equipped.
Hence, for cases when the expected daily power is not adequate to meet the loads, some of them are to be shifted to next day or days, when there will be prediction from the morning hours that there will be sunny day.
  • This performance leads to design Intelligent Energy Buildings with Predictive performance and management.
further work
Further Work
  • Develop an improved version for the prediction of the hourly global solar radiation.

Work has already began with the predictions based on the 2 and 3 morning measurements as earlier presented and the first results look very promising.

  • Improve and expand the predictive loads management.
  • Add a version of remote management
  • The authors appreciate the contribution of the EPEAEK Programme of the Hellenic Ministry of Education and especially of ARCHIMIDES I programme
  • which has funded the ASETHLEN project. The paper presents partial results of this project.
  • A contribution from the E.C. FP 6 project CRISTAL is appreciated, too.

Thank You All

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