Large scale implementation of Solar Home Systems in remote, rural areas

Abstract

Large-scale implementation of Solar Home Systems (SHSs) to provide electricity for people lacking electric power may have several constraints. Some of these are on the input side to realise the potential, and some are on the dismantling side, which are concerned with environmental issues. The questions analysed within this study are: will the industrial production capacity and distributor network grow fast enough to serve market demand and does the flux of lead induced by such a global growth of SHS represent a potential hazard to the environment. Some of the surprising findings are as follows. (i) The photovoltaic (PV) module and other SHS components can be manufactured on time to serve the growing market, even if implementation will take place over 25 years. (ii) The setting up of a distribution network represents a real bottleneck. (iii) Enhancing the average lifetime of SHS batteries from 3 to 5 years, which will result from an improved quality procedure such as implemented by the PV Global Approval Process (PVGAP), has the same effect as improving the recycling rate by 40% and is therefore undoubtedly the most appropriate urgent first step in reducing the impact of lead from SHS on the environment. In addition, recycling rates should be enhanced, and financial agencies and PV distributors may play an important role in stimulating the installation of facilities to undertake the proper recycling of used batteries.

Appendix: mathematical model for the "lead flux system"

Variables according to Fig. 2:

$$ \matrix{ {M^{\left( 1 \right)} ,...,M^{\left( 5 \right)} } & : & {{\rm{lead stocks}}} \cr {A_{12} ,\;A_{23} ,\;A_{32} ,\;A_{24} ,\;A_{42} ,\;A_{35} ,\;A_{45} } & : & {{\rm{lead fluxes}}} \cr } $$

(8)

Balance equations:

$$\dot M^{\left( 1 \right)} = - A_{12} $$

(9)

$$\dot M^{\left( 2 \right)} = A_{12} + A_{32} + A_{42} - A_{23} - A_{24} $$

(10)

$$\dot M^{\left( 3 \right)} = A_{23} - A_{32} - A_{35} $$

(11)

$$\dot M^{\left( 4 \right)} = A_{24} - A_{42} - A_{45} $$

(12)

$$\dot M^{\left( 5 \right)} = A_{35} + A_{45} $$

(13)

Model equations:

Assumed growth functions for the number of car and SHS batteries:

$$ \matrix{ {M^{\left( 3 \right)} = P_3 \left( t \right)} & : & {{\rm{linear growth}}} \cr } $$

(14)

$$ \matrix{ {M^{\left( 4 \right)} = P_4 \left( t \right)} & : & {{\rm{logistic growth}}} \cr } $$

(15)

No average stock change in battery factories:

$$\dot M^{\left( 2 \right)} = 0$$

(16)

Assumed residence time distributions for car and SHS batteries:

$$ {A_{{32}} {\left( t \right)} + A_{{35}} {\left( t \right)} = {\int\limits_0^t {k_{2} {\left( {t,t'} \right)}A_{{23}} {\left( {t'} \right)}{\mathop{\rm d}\nolimits} t'} }} $$

(17)

$$ {A_{{42}} {\left( t \right)} + A_{{45}} {\left( t \right)} = {\int\limits_0^t {k_{3} {\left( {t,t'} \right)}A_{{24}} {\left( {t'} \right)}{\mathop{\rm d}\nolimits} t'} }} $$

(18)

Known recycling rate for car and SHS batteries:

$$ {A_{{32}} {\left( t \right)} = P_{5} {\left( t \right)}{\left[ {A_{{32}} {\left( t \right)} + A_{{35}} {\left( t \right)}} \right]}} $$

(19)

$$ {A_{{42}} {\left( t \right)} = P_{6} {\left( t \right)}{\left[ {A_{{42}} {\left( t \right)} + A_{{45}} {\left( t \right)}} \right]}} $$

(20)

The parameter function P ₄ is similar to P ₁ and k ₂ and k ₃ are similar to k. P ₅ and P ₆ are constant as a function of time, representing a constant recycling rate to a first approximation. For P ₃ a linear growth has been assumed:

$$P_3 = p_{3,1} + p_{3,2} \left( {t - p_{3,3} } \right)$$