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Solar Energy 84 (2010) 1284–1293

Electricity storage for grid-connected household dwellingswith PV panels

Grietus Mulder a,*, Fjo De Ridder b, Daan Six a

a Vlaamse Instelling voor Technologisch Onderzoek, Unit Energy Technology, Mol, Belgiumb Vrije Universiteit Brussel, Belgium

Received 2 January 2010; received in revised form 3 April 2010; accepted 5 April 2010Available online 5 May 2010

Communicated by: Associate Editor Dr. Arturo Morales-Acevedo

Abstract

Classically electricity storage for PV panels is mostly designed for stand-alone applications. In contrast, we focus in this article onhouses connected to the grid with a small-scale storage to store a part of the solar power for postponed consumption within the dayor the next days. In this way the house owner becomes less dependent on the grid and does only pay for the net shortage of his energyproduction. Local storage solutions pave the way for many new applications like omitting over-voltage of the line and bridging periodsof power-line black-out. Since 2009 using self-consumption of PV energy is publicly encouraged in Germany, which can be realised byelectric storage.

This paper develops methods to determine the optimal storage size for grid-connected dwellings with PV panels. From measurementsin houses we were able to establish calculation rules for sizing the storage. Two situations for electricity storage are covered: – the storagesystem is an optimum to cover most of the electricity needs; – it is an optimum for covering the peak power need of a dwelling.

After these calculation rules a second step is needed to determine the size of the real battery. The article treats the aspects that shouldbe taken into consideration before buying a specific battery like lead–acid and lithium-ion batteries.� 2010 Elsevier Ltd. All rights reserved.

Keywords: Electric energy storage; Solar system; Batteries; Lead–acid battery; Lithium-ion battery; Smart grid

1. Introduction

Since the industrial age, we produced power and otherproducts in ever bigger constructions. Concerning powerproduction, this trend is turning. In the post-industrialage, our society strives to live more autarkic, causing thatpeople take actions to get grip on their own living situation.A beautiful example of this tendency is PV installations.The house owner becomes less dependent on the electricutility companies and is proud to fulfil part of his ownenergy need. The balance between solar energy productionand household electricity consumption is still obtained withthe help of the electricity grid. An overproduction in the

0038-092X/$ - see front matter � 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2010.04.005

* Corresponding author. Tel.: +32 14 33 58 59.E-mail address: Grietus.Mulder@vito.be (G. Mulder).

day is sent into the grid and a demand in the evening isdrawn from the electricity network. The grid is used as avirtual storage. A next step could be to store the producedelectric energy during the day for delayed consumption inthe night or the day after. In this way the house ownerbecomes yet less dependent on the grid and does onlypay for the net shortage of his energy production.

A logical counter argument is that storage is expensive.However, a second trend in our society is a fast increasingmarket share of hybrid cars. This has several advantages: amassive increase in batteries will take place in the futureresulting in lower prices and an additional market for usedbatteries will appear. Batteries of which capacity havedropped will be replaced in hybrid cars or these cars areabandoned. Many of these batteries can still be used fordomestic applications, where storage place is less critical

PV production and household consumption

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Fig. 1. A production profile of solar panels on a day in October and theconsumption profile of the household on the same day.

G. Mulder et al. / Solar Energy 84 (2010) 1284–1293 1285

(Les conclusions du groupe de travail sur les infrastructuresde recharge pour les vehicules electriques ou hybridesrechargeables, 2009). These two effects will make it possiblethat future households will start to install batteries to back-up their energy supply system.

Local storage solutions pave the way for many newapplications. Examples are: (i) over-voltage of the linedue to too many injecting inverters on the grid is omittedby storage; (ii) periods of power-line black-out can bebridged provided that the house is allowed to work inisland mode (Braun and Stetz, 2008). Other new businesscases can be identified: households that store their pro-duced energy may allow their electricity provider to switchthem off during periods of peak demand. In return theymay receive a discount or a payment. Moreover, the newrealm of possibilities are so-called smart grid applications(Hammons, 2008; Clastres et al., 2010). A house can inter-actively work with the grid and trade with the power mar-kets. Peak reduction and demand response can beestablished more thoroughly than without storage (Ibra-him et al., 2008; Jossen et al., 2004; Denholm and Margo-lis, 2007; Chicco and Mancarella, 2009). A dwelling caneven start to trade on energy markets on arbitrarymoments.

Since 2009 using domestic storage for self-consumptionof PV energy is encouraged in Germany. Traditionally,German owners of PV panels obtain a remuneration of0.43 €/kWh for feeding their electricity into the grid. How-ever, to encourage direct consumption, the owners of PVpanels (up to 30 kW) receive also an allowance of 0.25 €/kWh for the directly consumed electricity. (Auswirkungendes Direktverbrauchs von Strom aus Photovoltaikanlagen,2009). In this way it becomes more attractive to store thePV power than sending it into the grid and buying electric-ity back later.

Classically the storage for PV panels is mostly designedfor stand-alone applications (Jossen, 1994). This meansthat an amount of energy must be stored to fill at leastthe production gap of several days of very clouded weather.In practice this is between 3 and 20 days (Jossen, 1994;Markvart and Castaner, 2003; Haberlin, 2007; Diaf et al.,2007). The daily cycle of charge and discharge is thereforeonly a small variation on the total storage capacity, typi-cally between 2% and 30%.

In contrast, we focus in this article on small-scale stor-age to store a part of the solar power of one day for post-poned consumption within the day or the next days. If thedwelling is grid-connected a storage system should not nec-essarily cope with a long period of low solar energy produc-tion, as the grid is available as a back-up. Hence the sizingcriteria can be different from autonomous systems. Westudy storage for dwellings in connection with the grid,establishing new sizing methods. All calculations are basedon real measurements during a year in seven houses in Bel-gium with PV-panels.

We start this article with a characterisation of the solarproduction and household consumption in the next section.

In Section 3 we study why a storage system is bound to aneffective maximum size. In Section 4 several ways of dimen-sioning storage systems are studied. In this section calcula-tion rules are derived based on correlations withmeasurement data such as panel surface and dependenceon the electricity grid. In Section 5 generalised calculationrules are developed for the case that solar panels cover theelectricity (peak) demand. In Section 6 the repercussionsfor several battery systems are discussed. In Section 7 thetotal system integration is discussed.

Two situations for electricity storage are covered:

– the storage system is an optimum to cover most of theelectricity needs;

– it is an optimum for covering the peak power need of adwelling.

2. Production and consumption

This section gives an introduction in production andconsumption profiles for households with PV panels. Thisis necessary to understand the impact of small-scale batterysystems and the way they can be dimensioned.

A typical solar energy production profile during a day isshown in Fig. 1. The figure also includes the simultaneousconsumption of that dwelling. It is clear that consumptionand production do not take place at the same moment. Anintra-day storage can offer a solution.

Two important design criteria for storage systems arepower need, both for charge and discharge current, andstorage capacity. This paragraph studies the power needand responsiveness. The storage must be able to absorbthe full power of the PV panel, as the consumption canbe sometimes almost zero, according to Fig. 1. The solarpower change happens on seconds scale. Fig. 1 shows thatthe PV power can suddenly drop and be at full power againseveral seconds later. The household draws sometimes highpower during short periods due to e.g. water cookers orespresso machines. The power that flows into the storage

1286 G. Mulder et al. / Solar Energy 84 (2010) 1284–1293

or is drawn out of it, should be accepted like it is. The sec-ond design criterion, storage capacity, is much less precise.For our aim of short period (days) storage, there are nodesign rules yet in literature.

We have measured power fluxes in seven houses with PVpanels. Most of the houses have been measured during acomplete year, some of them only the first or the last halfof a calendar year. The measured AC power out of theinverter, the power to the grid and the power drawn fromthe grid is taken into account. From these data the dwell-ing’s consumption can be calculated. These can be used toplace a virtual storage in between and to calculate how thedependence on the grid changes. The measurements havebeen performed with a 5 min interval. An example of a mea-surement is shown in Fig. 2a for a week in April. Alreadyfrom this figure it can be deduced that production and con-sumption does not coincide for this dwelling as the produc-tion line and the energy to the grid line corresponds mostly.This offers the opportunity of installing a small storage.

Fig. 2b shows a typical consumption and productionprofile on month to month base during a year of one of

Production and grid depg p300300

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Fig. 2. (a) The measured data of a house for a week in April. It shows the proand out of the grid in red (a week consists of 2016 intervals of 5 min.). (b) Themonthly base.

the measured households. It can be seen that the solar pan-els hardly produce energy in the three deepest wintermonths and that consumption in those months rises,maybe due to an increased lighting demand. Whether thetotal production matches the consumption depends onthe amount of solar panels every household had installed,what is shown in Table 1. It appears that the productionfor none of the houses equals the consumption, with a largespread of the production–consumption ratio between 0.3and 0.8. It was a sunny year as four of the seven housesshow a higher production than the average prediction valueof 826 kWh/kWp (Suri et al., 2007).

Storage can be introduced in the measured data, absorb-ing the production surplus. It is a virtual storage, sincethere was no storage in the actual measured houses.Fig. 3 shows the influence of storage for the same houseand week as Fig. 2a. The green and red line (energy torespectively out of the grid) are almost disappeared, butnot completely. So, a small storage system can make thehouse occupant here almost independent of the grid, usinghis own solar electricity and shifting it over the day. The

endence during a weekg

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duced energy in Wh/5 min. in blue, the energy flowing to the grid in greenproduction and consumption profile for the same house during a year on

Table 1Characterisation of the seven houses under study, showing the PV panel data and the electric production and consumption data.

Lummen Olen Sint-Niklaas Antwerpen Arendonk Begijnendijk Blankenberge

Panel surface (m2) 16.7 9.3 9.3 20.7 12.9 7.6 16.4Installed power (kWp) 2.2 1.2 1.2 2.1 1.8 1.0 1.7Relative annual yield (kWh/kWp) 975 825 747 788 890 1001 999Annual solar production (kWh) 2107 996 897 1639 1 603 1021 1686Annual consumption (kWh) 2890 1234 1 671 3215 3905 2945 5134Production–consumption ratio (�) 0.7 0.8 0.5 0.5 0.4 0.3 0.3

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time (x 5 min)

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DemandDemand

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Storage levelStorage level

Fig. 3. Influence of a virtual storage on the grid dependence. The interaction with the grid (red and green) is confined.

G. Mulder et al. / Solar Energy 84 (2010) 1284–1293 1287

next section will deal with which storage size can still beeffective.

3. Limiting conditions for electric storage

The aim of our research is to design rules to dimension asmall, well-performing storage system. Classically, storagesystems in combination with solar panels are large systemsto bridge many-day periods. The daily cycle is merely asmall fluctuation of the storage level. For grid connectedstorage the size can be smaller because a daily dynamicsof the storage is sought for. The effectiveness of grid con-nected storage can be reflected in the amount of energy thatstill flows to and out of the grid. When a storage isincreased in size, from a certain size onwards, the energyflow to and out of the grid do not change anymore. Fromthat specific size on, also the energy absorbed by the stor-age does not alter anymore: it attains a plateau value. Toobtain insight in the reason and size of the storage plateauvalue, calculations have been performed on monthly basewith the measurement data of the seven houses.

The monthly solar energy production (see Fig. 2b) deter-mines the maximum useful size of storage system for eachmonth (provided that only energy from the PV installationcan flow into the battery). The reason why a plateau valueappears, lies in the limitation of the production: there is amaximum amount of energy that can flow to the battery.

In winter months the production is five times less than insummer months according to Fig. 2b. So, the energy thatcan flow towards the battery is much less than in summermonths leading to a low plateau value in January and ahigh plateau level in June. This is translated into a biggermaximum size of the battery in summer than in wintertimes.

It should be noticed that we look for a storage systemthat can make daily shifts of energy exchange and notthe classical approach of week shifts. From this vision, inthe summer a limitation on battery size can be derived fromthe energy that is still consumed from the grid. It makesless sense to store a lot of solar energy when it cannot beconsumed. Several criteria can be imagined: no energyfrom the grid or e.g. only 20% of the energy from the gridin comparison to the case without storage. The first crite-rion leads of course to a larger storage size than the second.

From above it is understood that the solar productiondefines a maximum storage size on monthly base and thatsize can be further reduced taking into account the monthlyconsumption pattern. Fig. 4 represents this graphically. Itshows the influence of an increase in storage size on theamount of energy flowing towards and coming out of thegrid. The plateau level is the maximum available energy.It clearly coincides with the energy towards the grid beingzero. It situates at the enormous value of 60 kWh. At20 kWh there was already no demand from the grid any-

Influence of (ideal) storage on electricity flows

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Fig. 4. Influence of the storage size on the electricity flows from andtowards the grid. The example is given from data of April. In this casetotal independence of the grid can be obtained by installing a large storagesystem.

Optimalisation size of ideal storage

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Fig. 5. The influence of storage of the energy flow to and from the grid.The line is a fit on the energy that flows into the storage. The dashed linerepresent the optimum storage size as defined by being the crossing of theinitial tangent line with the plateau value.

1288 G. Mulder et al. / Solar Energy 84 (2010) 1284–1293

more, resulting in an autarkic house for that month. The20% dependence criterion leads to a storage size of6 kWh: a substantial reduction.

The above calculation for every month leads to Table 2.If no size is given, it means that the consumption could notbe covered by the production. Only two months of the yearthe production is enough to cover the consumption in thisexemplary house. This low amount of months is in relationwith the fact that the dwelling cannot fulfil its yearly elec-tricity demand by its panels (see Table 1). Continuing the20% grid dependence assumption, half of the year thehousehold can be merely dependent on the grid for thisamount. From Table 2 it can be concluded that a 6 kWhsize is a kind of optimum to obtain a daily dynamic stor-age. It does not make a lot of sense to put more batteries,without increasing the PV installation. It is firstly due tothe PV energy production that the net energy from the gridis lowered. The batteries help for optimising the self-consumption.

4. Dimensioning electric storage and calculation rules

Although the previous section gives a clear insight in thelimiting factors for storage size on a monthly base, it is adifficult method to work with, as it requires an examinationfor each month and an estimation of the average or medianover all the months. It is much easier to work on a yearlybase while accepting the grid dependency: increasing thestorage size lowers the dependency on the grid but onlyto a certain degree. Fig. 5 shows the yearly calculationfor the reference house. The calculation has been per-

Table 2The storage size (in kWh) based respectively on plateau value due to a limited mgrid (if it occurs, only 2 months) and on 20% dependence of the grid (possible

January February March April May June

0% to grid 4 16 40 60 16 600% from grid 20 2420% from grid 6 8 4

formed up to a storage size of 10 kWh. Again, a plateauvalue is discernable. A plateau also implies that the slopedecreases to zero or that the first kWh’s of storage do havemost of the impact on the energy flows. To automate thecalculation of the optimum size, the optimum is chosenas the crossing of the tangent line at zero storage withthe plateau level. For our reference dwelling this situatesat 3000 Wh, as can be noticed in Fig. 5. If only the plateauvalue would have been taken or a fraction of it, it leads tolarge storage sizes that are not necessarily dynamically (i.e.to a large content) charged and discharged. The tangentline at zero storage has been added an indicator for thisdynamism.

Table 3 gives the result for all 7 measured dwellingstogether with characteristic ratios, being the production–consumption ratio and the simultaneity between instanta-neous consumed production and total production. Thereis a large variety between the optimum storage sizes, i.e.between 300 and 3000 Wh. The house with the lowest stor-age demand has a high simultaneity. This means thatalmost all produced solar energy is consumed at the sametime. Obviously, storage is hardly necessary in this case.Storage will hardly has an influence here on the energy thatcomes out of the grid neither. The number of virtual cyclesis also shown in Table 3. This is the ratio of total amount ofenergy that flows into the storage divided by the storagecapacity. This number is an indication of the storage use.

The same kind of calculation can also be performed forpeak loads. Here, somehow arbitrarily, peak load is definedas the energy need that is higher than twice the averageneed on a year base. It can be assumed that this ‘peak

onthly solar production (i.e. 0% to the grid), based on independence of thefor half of the year). These criteria decreases the storage size demand.

July August September October November December

60 26 18 12 4 4

6 6 6

Table 3Optimum storage size and characteristic ratios. The first two lines are based on the original measurement data. In the middle, the calculated optimumstorage size and its consequences are given. Below is the calculated optimum storage for peak load and its consequence on remaining peak demand.Simultaneity is defined as the ratio of instantaneous consumed production and total production.

Lummen Olen Sint-Niklaas Antwerpen Arendonk Begijnendijk Blankenberge

Production–consumption ratio (�) 0.73 0.81 0.54 0.51 0.41 0.35 0.33Simultaneity (�) 0.41 0.53 0.9 0.86 0.54 0.53 0.66Optimum storage (Wh) 3000 1500 300 900 1500 1100 1200Relative energy flow from grid (�) 0.57 0.5 0.92 0.86 0.84 0.87 0.92Relative energy flow to grid (�) 0.32 0.27 0.25 0.16 0.34 0.33 0.33Virtual cycles (�) 248 202 193 93 275 134 118Optimum storage for peak load (Wh) 1100 900 500 900 1500 1500 1500Relative peak demand (�) 0.5 0.2 0.7 0.65 0.65 0.69 0.74

G. Mulder et al. / Solar Energy 84 (2010) 1284–1293 1289

power’ is preferably taken from a storage. This represents acase that base load is less expensive than peak load, so thatthe peaks should be trimmed. The optimum storage capac-ity for this kind of application is given in the lower part ofTable 3. For half of the amount of dwellings, the resultseems to be comparable to the previously calculated opti-mum for total coverage of the energy need.

We want to know which variable describes in the bestway the needed storage size for a grid connected dwelling.Given the determined optimum storage sizes, correlationscan be established between measurement data and thestorage size. The correlations have been performed for:installed panel power, production yield, energy taken fromthe grid, energy flow to the grid, consumption, peakdemand, production–consumption ratio, simultaneity andcombinations of the complement of simultaneity with pro-duction and consumption.

Table 4 gives the result for the correlation factor. Totalcoverage means that energy from the storage is used tocover all electricity need (as long as the storage is notempty), and peak coverage means that energy from thestorage system is used for peak loads, which we definedas twice the yearly mean consumption.

The optimum storage size for all electricity demand cor-relates strongly with the measured energy flow to the grid,having an R2 of 0.9. The same correlation also exists withthe combination of simultaneity with production. In whichsimultaneity was defined as the ratio of instantaneous con-sumed production and total production. These correlationsare shown in Fig. 6a and b including the fit expressions.The fit formulae in both figures are almost the same. Thiscan be understood as (1-simultaneity) � production repre-sents the energy flowing into the grid.

Table 4Correlation between storage size and measurement data in terms of R2 based onload need.

Installed panel power Production yield Energy from

Total coverage 0.3 0.5 0Peak coverage 0 0.1 0.7

Production–consumption ratio Simultaneity

Total coverage 0.2 0.7Peak coverage 0.4 0.3

The optimum storage for peak load (i.e. above twice theaverage consumption) correlates well with peak demandand with the combination of simultaneity with consump-tion. These correlations are shown in Fig. 6c and d includ-ing the fit expressions. The expressions can be taken as acalculation rule for dimensioning storage for PV panels.Although, at first glance, the storage for total coverageand peak coverage seemed to be comparable, the correla-tions are strictly different.

As design rule for the storage size, the total energy sentinto the grid (known by measurement) or the complementof simultaneity multiplied by the yearly production can betaken and multiplied by 2.4 as shown by the fit in Fig. 6aand 6b. In case of covering peak demand, the design rulebecomes the measured peak demand multiplied by 0.83and adding 570 Wh, as shown by the fit in Fig. 6c or bythe complement of simultaneity multiplied by the yearlyconsumption multiplied by 2.4 and adding 570 Wh.

5. Calculation rules for consumption-matched panels

In the previous section strong correlations were foundbetween storage size and measurement data, resulting incalculation rules. The electricity produced by the installedPV panels did not match the consumption of the house-holds. Depending on the specific household, the PV panelscovered between 33% and 73% of the electric energy need.The installation costs of PV panels lower each year. Thisencourages house owners to install as many panels as tocover the total consumption, provided that the availablespace on the roof is large enough. In many European coun-tries a household should not produce more than its ownyearly consumption, in order not to fall in the category

linear fits in case of covering respectively all the energy need and the peak

the grid Energy flow to the grid Consumption Peak demand

0.9 0 N.A.0.2 0.6 0.8

(1-simultaneity) � production (1-simultaneity) � consumption

0.9 0.40.2 0.8

Correlation of storage size against energy towards grid

y = 2,331xR2 = 0,8947

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Fig. 6. The best correlations and fit expressions for storage size to cover all demand (a and b) and for storage size to cover peak load (c and d).

1290 G. Mulder et al. / Solar Energy 84 (2010) 1284–1293

of electricity production companies. Thus, an importantconsideration is: what if the panels would have beenmatched with the yearly total consumption? How will thisinfluence the correlation between storage size and data?

In this section the production can be scaled so that itmatches with the consumption on an annual base.

By matching production and consumption, also theamount of energy towards and out of the grid becomesequal, resulting into identical correlation factors. Table 5gives the result for the correlations. The same variablesare used as in Table 4.

Almost all parameters correlate now well except theratio of production and consumption (being fixed to onein the exercise, while the storage size varies) and simultane-ity. The decrease in correlation with simultaneity can beintuited as there should be an opposed relationshipbetween increasing panel size and simultaneity. Also, thecorrelations for total coverage and peak demand coveragehave become the same. That the correlation to productionyield is stronger than to installed panel power, may beexplained by the spread in relative annual yield (kWh/

kWp) as shown in Table 1. Fig. 7 gives the correlation datafor installed panel power and for the combination of simul-taneity and production yield. The correlation with panelpower is not the best one, however, it does not requiremeasurements.

The calculation rules for storage to cover all electricityneed are: panel power multiplied by 860 or (1-simultane-ity) � production multiplied by 1.2 and 400 Wh added.The calculation rules for storage to cover peak demandare: panel power multiplied by 350 and 350 added, or (1-simultaneity) � production multiplied by 0.5 and 500 Whadded.

6. Real batteries

All storage calculations in this article have been idea-lised in the sense that there are no losses and no limitationson power. For real battery systems at least four aspectsshould be considered: efficiency, voltage limitation, cyclelife and calendar life. The considered storage is ideal or ithas a 100% efficiency. It is important to do the calculation

Table 5Correlation between storage size and measurement data in terms of R2 based on linear fits if production and consumption are matched.

Installed panel power Production yield Energy from the grid Energy flow to the grid Consumption Peak demand

Total coverage 0.7 0.8 0.9 0.9 0.8 N.A.Peak coverage 0.7 0.8 0.9 0.9 0.8 0.7

Production–consumption ratio Simultaneity (1-simultaneity) � production (1-simultaneity) � consumption

Total coverage 0 0.4 0.8 0.8Peak coverage 0 0.4 0.9 0.9

Correlation storage size against panel power

y = 871,78x - 36,644R2 = 0,6981

y = 861,72xR2 = 0,698

0

1 000

2 000

3 000

4 000

5 000

6 000

stor

age

size

(Wh)

Correlation storage size against combination of simultaneity and production

y = 1,2237x + 366,27R2 = 0,8473

0

1 000

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6 000

stor

age

size

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Correlation storage size against panel power

y = 350,68x + 350,39R2 = 0,7316

0

500

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1 500

2 000

2 500

0.0 1.0 2.0 3.0 4.0 5.0 6.0

panel power (kWpeak)

stor

age

size

(Wh)

Correlation storage size against combination of simultaneity and production

y = 0,482x + 532,63R2 = 0,8514

0

500

1 000

1 500

2 000

2 500

0 1000 2000 3000 4000

(1-simultaneity) X production (kWh)

stor

age

size

(Wh)

0 1000 2000 3000 4000

(1-simultaneity) X production (kWh)0.0 1.0 2.0 3.0 4.0 5.0 6.0

panel power (kWpeak)

a

c d

b

Fig. 7. The correlations and fit expressions for storage size to cover all demand (a and b) and for storage size to cover peak load (c and d) both for installedpanel power and for the combination of the complement of simultaneity with production yield.

G. Mulder et al. / Solar Energy 84 (2010) 1284–1293 1291

with an idealised storage in order not to mix the input mea-surement data with various effects that take place in batter-ies and that are different from one battery chemistry to theother, and from one manufacturer to the other (Jossenet al., 2004; Josse and Weydanz, 2006). Broadly the effi-ciency is between 70% and 95%.

In reality, a battery has an efficiency between chargingand discharging due to a difference in voltage for bothactions. Also, any power converters between the solarpanel, the battery and the AC-grid have a limited efficiency.Moreover, batteries discharge by internal leakage currents.

The typical values are very different for the various batterytypes like lead–acid batteries and lithium-ion batteries. Val-ues are found in battery handbooks (Josse and Weydanz,2006; Garche, 2009).

The second phenomenon that was not taken intoaccount is that batteries may not absorb full power abovea state of charge of around 80%, because the battery shouldbe charged at a restrained voltage level in this area. Thecurrent and thus the power reduces quickly in this area.Charging up to 100% takes therefore a long time, indepen-dent of battery type. For lithium and nickel metal hydride

Fig. 8. A probable set-up of system integration.

1292 G. Mulder et al. / Solar Energy 84 (2010) 1284–1293

batteries this area of state of charge is sometimes omitted(Kelly et al., 2002; Wohlfahrt-Mehrens et al., 2004). Forlead–acid batteries, however, it is necessary to charge peri-odically up to 100%, at least once a month, in order to sup-press the so-called sulphating phenomenon that shortenslifetime drastically (Josse and Weydanz, 2006). It is the for-mation of lead sulphate at the electrodes when the batteryremains unused for a long time in deep discharge state. It isan insulator and thus prevents current flowing.

The third aspect is about cycling. If batteries are fullycharged and discharged like the ideal storage, they may liveonly for a hundred of cycles (Rosenkranz, 2003). It shouldbe asked to the manufacturer which sizing factor is neces-sary. Many lead–acid battery manufacturers state forexample that the battery should be five times oversized inorder to obtain 1000 cycles. For lithium it is less clear asmany sub-chemistries exist like lithium cobalt oxide orlithium iron phosphate and because there is an enormousprogress in this type of batteries going on. Some manufac-turers already state that a factor of 1.2 fulfils to obtain1000 cycles.

The fourth phenomenon for real batteries is calendarlife. They fail after some years even if they were kept atvoltage without cycling (Wohlfahrt-Mehrens et al., 2004;Broussely et al., 2001). No typical data can be given. It var-ies between a year and 10 years.

The number of possible cycles and calendar life deter-mines up to large extent the economic viability of batterypackages. At the moment many lead–acid batteries areused for PV applications (Haberlin, 2007) with a replace-ment every 5 years. Lithium batteries may have a longerlifetime with almost no sensitivity to cycles, while specificfuture cost levels are predicted that are four times less thannowadays (Kalhammer et al., 2007). If this becomes true itopens an epoch with storage in every house.

7. Peripheral equipment

In order to address the storage issue further this sectiongives an insight in setting up a storage system in combina-tion with PV panels. A probable set up is given in Fig. 8. Inaddition to the indispensable DC/AC inverter two DC/DCconverters are added. The arrangement creates a commonDC bus to the three devices. The addition of two conver-tors is important in order that the batteries do not fix thesolar panel voltage, preventing the panels to work at theoptimal voltage. The optimal voltage is normally main-tained by a so-called maximum power point tracker. Thiscan increase the power output by 20% in comparison witha fixed voltage (Haberlin, 2007). Another advantage is thatthe charging and discharging of the storage unit can becontrolled independently of the solar panels. Althoughthe AC/DC inverter is largely available on the market, itis not directly useful for our approach of self-consumptionof solar energy. The nowadays versions only come intoaction if the grid power has disappeared. That means thatthey work in islanding mode to deliver power to a limited,

independent network. The needed extension is a detectionof household demand while the complete system is still gridconnected. This can be obtained by implementing a currentsensor between the house and the distribution grid or bycurrent measurement information from a smart electricityconsumption meter. The control software of the invertershould be correspondingly adapted for our application ofself-consumption.

Converters and inverters have an efficiency in the rangeof 85–97%, dependent on the quality of the device butalso on the relative amount of power it delivers. TheDC/AC inverter is also needed in the classical case with-out storage and should therefore be omitted from the effi-ciency estimation of the battery application. Theeffectiveness is sensitive for the efficiencies as they aremultiplied. If less optimal equipment is used like two con-verters with 90% efficiency and a battery with 80% effi-ciency, this leads to 65% energy throughput. This meansthat a considerable amount of PV energy is lost in thechain. Considering however 95% efficiency for the DC/DC converter at partial load and a battery efficiency of90%, what is a valid value for lead–acid batteries at mod-erate current density, the overall effectiveness is 81%. Thisseems to be reasonably high to allow the addition of stor-age in combination with solar panels.

8. Conclusion

In this article measurement data of seven households inBelgium have been used to acquire relationships to dimen-sion storage packages for grid connected PV panel installa-tions. In contrast with the classic large storage sizes, theaim is here to find an optimal small size for being relativelywell independent from the grid, but not totally. The pack-age can be at least five times smaller than the classical ones,as there is no initial interest in bridging a period of severaldays or more without sunshine. Also, the PV panels do notnecessarily need to match or even be oversized compared tothe consumption.

It appears that a strong relationship exists between stor-age size and the amount of energy flowing to the grid. Thesame relation is found the product of the complement ofsimultaneity with production. The associated calculationrule is a factor 2,4 (�) between both variables. If the PV

G. Mulder et al. / Solar Energy 84 (2010) 1284–1293 1293

panels are matched with the consumption good relation-ships have been found for storage size as function of panelpower and of the combination of simultaneity with produc-tion. Also to cover peak demand, calculation rules havebeen determined.

Based on ideal storage a calculation has to be madetowards real storage systems. At least four items shouldbe taken into account for this, i.e. efficiency, voltage limita-tion, cycle life and calendar life. Manufacturers can givespecific information on these topics.

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