La Maison à Energie Minimum

4-Resistive Photovoltaïc

1.                      Introduction

Here a description of a domestic sanitary water   installation through an electric water heater   (accumulation)   , self-construction type, directly powered by a photovoltaic solar panel without any electronics; this installation operates satisfactorily since more than one year without any troubles (of course, only when it’s sunny!).

2.                      Basis and characteristics

The specificity of this installation is the simplicity of the design and the absence of maintenance in order to warrantee investment profitability; the electric current generated - 30V DC - is directly injected in the tank water heater electric resistance, the tank being used as energy accumulator; none electronics - none battery nor voltage regulator, none power supply - are necessary. The system is simply resistive type (Joule effect)   , fully static (none spare part under motion, therefore no wear and no maintenance.

For profitability reasons, this is a mandatory requirement; indeed, for a low power system (single panel type), electronics cost - even without batteries - would be 5 to 10 time panel cost! Moreover, electronics being subject to maintenance and scheduled replacement, this cost would completely annihilate the profitability of the system, profitability being also an operation main concern.

It is a national grid complementary installation only , who decrease electricity costs ; but it’s not possible to substitute it for the national grid , as there are not only pure resistive uses ( water heater or heating purposes ) as domestics apparatus or lighting , and of course all uses during no sun period ( 80 % of the time ).

Sanitary water heating is the best use , as it’s used also in summer , most sunny period , this insuring a good yearly  profitability ; also energy storage in the tank – standard low cost electric water heater – allow to store energy during the night without specific equipment .

Then we can define this installation is a Resistive storage Photovoltaic System.

For the design of such system only Ohm law knowledge is necessary; also installation shall be designed under electrical design and safety rules.

The use of photovoltaic energy during all the year presents such advantages:

-          No fluid used outside then no frost risks

-          Simplicity and reliability of the design

-          Best efficiency in winter ( under low temperature )

Averaged production is then not very different along the year as in winter, efficiency is good but sunny hours are low, and in summer efficiency is lower but sunny hours are higher.

3.                      Definitions


For this document we will use such definitions:

Steatite: electrical resistor of a pressure tank being independent of the tank (not in contact with heated water and resistor replacement requiring not tank draining) 

kWh: energy unit of an 1kW power apparatus in service during 1 hour ; for costs calculations we will assume 15 Eurocent/ kWh (domestic fare, subscription charges excluded).

4.                      Economic equation

The used photovoltaic panel is used as a standard equipment generating electricity with solar ; for the  latitude - 47°Nord- it will produce during 1800 hours per year  ;  with 15.6%  efficiency and  solar radiation  1000 W/m2, we will recover for a 1,60 m2 panel – south oriented (polycrystalline standard 60 cells 1640 x 990 mm) :

Panel power: 1000 W/m2 x 0.156% x 1.60m2 = 250 W then 0.25 kW

Recovered yearly energy: 0.22 kW x 1800 h x 0.70 = 277 kWh (assuming 70% of max power, then 1260 kWh/kWc).

Yearly Production = 277 kWh x 0.15 €/kWh = 42 € (per panel)

Panel cost being 100 € we need then approx. 2 years for amortizing. Profitability is then easy, if only panel cost is considered. Of course if  electronics ( voltage regulator , power supply , … etc. ) are used ( approx. 1000 € ) it is completely different, and in that case no profitability would be possible even at  plant start up ; maintenance of electronics during equipment time life  would also increase  total cost .

It is then required to use such design for minimum profitability for all installation without investment grant.

Such designed installation, fully static type, would guarantee for a 25 year’s life time a good profitability (approx. 10 times panel cost recovered over 25 years operation). It’s then a good bargain, and a friendly environmental equipment producing power without any pollution.

We have to keep a record that electricity is charged with a lot of taxes (approx. 70 %, refer to chapter 9 Taxes sur électricité), but taxes are a help for profitability for a self-production installation. Without taxes, cost of 1 kWh would be 0, 09 €/kWh and then a panel will recover 277x 0.09 = 25€ / year instead of 42 € with all taxes.


1) If we consider water heater cost (200 €  for 50L capacity) for profitability calculations  ,of course the impact is important , but it would be questionable to consider it  , as the heater tank can be considered as part of domestic installation and not part solar installation ( whatever the installation is , heater tank is required ).

2) Current kWh cost is 0, 15€ but we can expect escalation during 25 years period.

3) 1800 h per year of sun, it’s average   4,9 h/ day  or 34,5 h / week.

5.                      Panel installation

For an optimized installation the panel shall be preferably rested as follow:

-          South orientation 

-          Out of  any shadow impact  (all the day )

-          With a slop 15° to 35°  (35° being the yearly optimum ) ; 15° slope is the optimum for winter

No shadow for the entire panel is a mandatory requirement as the panel consisting in cells mounted in series, even if only one is under shadow all the series will be impacted.

Installation at grade is also preferred for an easier electrical connection and also for easier panel cleaning.

6.                      Water heater

The water heater is a standard water heater; only it electrical resistor shall be of steatite type in order to modify it; this is necessary for its voltage adaptation: to be 30V instead of 230 V.

50 L capacity for one  220 W  panel  (220W  at selected operating point) in order to optimize energy storage  ; for a complete sunny day water production – with water from 15°C ( summer conditions) to 45°C -will be then  :

0.220 x 3600 / 4.180 x (45-15) = 6.32 l/h ; then 7,9 hours  as heating time for a tank  50 L is necessary  ; if temperature controller was settled at  65°C it could be possible to store all the energy produced during 13,2 h of sun ,  this duration being approx. the max sun duration of a summer day.

As a average value , sun duration is about  4,9 h / day  (1800 h / 365) involving  an entirely free water  production of 31 l /  day ; for a week , it’s 217 liters.

Note : a water heater with a 50 L storage tank 50 L at  65°C  is equivalent to a 241 Ah electrical battery  12 V (2900 Wh).

The water heater is installed as close as possible of water consumers for minimum heat losses  ( refer to chapitre 3 Chauffe-eau ); it  could be hydraulically independent , or used as a complement of a main water producer  ( 230V  electrical  water heater or boiler ) and connected in series and upstream .

7.                      Electrical installation


The installation is strictly segregated from the domestic 230 V grid and consists mainly in (for one panel 30V- 250W maxi- refers to Annex P1 Pictures):

-          A general switcher 2 poles ( for mini 20 A breaking )

-          A circuit breaker 2 poles ( for mini 20 A breaking )

-          A temperature controller dual type (control and safety functions); the one’s provided with water heater should be acceptable if breaking capacity is sufficient.

A numeric voltmeter – wall mounting type – allowing operating conditions checking   ; an electronic resistor  (1000 Ohm) is provided on power supply for high voltage protection  (as max panel voltage is 36 V)  and , the voltmeter being powered by 4/30 V ; moreover this resistance avoid indication blinking  indication when voltage is lower than mini required  (lower than    14V).

Cross section area of wires shall be 1.5 mm2 mini (copper) for a 250W panel with a max distance panel / heater of and a max distance 5 m.

For any installation it’s required to check applicable rules and  especially for different design - several panels and /or different voltage or power - and to add necessary complementary protection devices ( differential breaker , grounding system , breakers …. etc. ) depending on connection  type ( series , parallel ) ; refer also to link n°5 here bellow .

8.                      30 Volt Resistor

It’s the only specific item of the installation , as it’s necessary to modify the resistance into a low voltage DC as supplied by the panel ; it’s designed with (SS) stainless steel wire (0,5 mm2 c.s.a for main part , 2 mm2 for connections to wiring blocks) and with a length as required to  design value .


Electrical laws as follow to be applied:

-            Ohm law  U = R.I  (U : voltage in  Volt, R : résistance in Ohm, I : intensity in A)

-            P = U. I = R. I^2 (P : power in  W)

-            R = r .L / S   (r : resistivity  in Ohm/mm2/m, L : length  in m, S : cross section area in mm2)

These 3 laws are applied as per following sequence (refer also to annex P2 résistance design):

1.         From the panel characteristic  (annex P3) operating  point to be selected   ( close to  maxi power ) , power and voltage to be then read for characteristic curve  (P = U.I)

2.         Knowing  P, U and  I  then  R  is deducted (R= P / I^2)

3.         Knowing  R wire diameter is selected  

The example as P2 Annex consider the conductivity ( r)  at operating wire temperature , assumed 430°C ( radiating flux calculations out of this document purpose ) ; this have an important impact on resistance design as SS resistivity is highly sensitive with temperature.

You will note that for the resistor - main component - only  3 grams of SS is required ; even at 20€ / kg , cost is very low .

Important note: connections to wiring blocks shall be of higher section - mini 2 mm2 - for avoid any high temperature at wiring points.

9.                      Perspectives


It’s sure that photovoltaic technology will improve performances of the panels for next times ; with a same surface we can expect higher efficiency  and  power  ; then a present installation  1.6 m2 today , could be easily modifiable into a higher power and then more profitable plant   (panel replacement expected within 25 years).

It will be also an important improvement if panels could operates with light  of the day instead of sun radiations , as  obviously period without sun represents 79% of the total time ( 1800 hours  / year with is 8760 hours ) ; electrical production would be then 2.5 time more , we have only to wait and expect ….

Another way of improvement would be to add a sun tracker; it’s envisaged at this time….

Selection of the operating point at max power – by design of resistance value – could be also optimized in order to increase yearly production.

Also it’s not at all expected that taxes on electricity would decrease – due to costs of nuclear wastes management for thousands of millions of years??-  and then this would increase profitability of self-electrical production.

Maintenance costs are most probably higher than supposed at the date and then such free maintenance installation - no electronics - would become then more attractive.

Also this installation is within the “local producing philosophy” which is under large development; vegetables could be locally produced but electricity also, and if moreover as we can produce during the day and store during night, what would be better?

As a conclusion this self- construction installation is also a very good way to manage a simple electricity production; you could organize visit with yours friends and envisage to write a book “the electricity without wastes explained to my children “.

This installation will produce for next 30 years, not only a small amount of money – without any public subsidies- but mainly it will produce power without any wastes bequeath to generations to come.

10.                  Annexes

Annex P1: Picture  

Annex P2: Design of the résistance

Annex P3: Panel curves with operating point

11.                  References


Some complementary links ( for information only) :

1-Production evaluating: http://www.photovoltaique.info/Estimer-la-production.html

2- Production evaluating: http://ines.solaire.free.fr/pvreseau_1.php

3-Solar data: https://www.sunearthtools.com/dp/tools/pos_sun.php?lang=fr (it’s a kind of Google solar maps; enter your address in menu « user »)

4-Electrical safety data (France)   : https://www.ademe.fr/sites/default/files/assets/documents/maitriser-risque-lie-installations-photovoltaiques-2013.pdf


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