4.3 Solar power

In WITCH, both solar PV (Photovoltaic) and CSP (Concentrated Solar Power) are modelled as individual technologies.

The supply curves are provided by the German Aerospace Centre (DLR) and the Potsdam Institute for Climate Impact Research (PIK), see (Pietzcker et al. 2014). They provide the maximum amount of capacity which can be installed in each region as a function of:

  1. capacity factor / full load hours (solar_class in the model) - Twenty-six classes: from 350 to 2450 h/yr for PV, from 700 to 6600 h/yr for CSP (which is modelled in a SM2 configuration, i.e. with a 6h-thermal storage)
  2. distance from load centres (solar_distance in the model) - Two classes: near (1-50 km), far (50-100 km)

The following table summarizes the parameters at the global level:

Parameter PV CSP
Global capacity 3 GW (2005) 0.4 GW (2005)
38 GW (2010) 1 GW (2010)
170 GW (2015) 5 GW (2015)
Base year investment cost 4650 USD/kW 6123 USD/kW
Lifetime 25 years 25 years
O&M cost 43 USD/kW 120 USD/kW
Learning rate 17% 10%
Floor cost 400 USD/kW 1500 USD/kW

The capacity is fixed up to the year 2015 in order to allow the model capturing the tremendous growth which has been taking place in recent years and which otherwise would not be replicated.

Investment costs are the same in all regions and decline over time through a learning-by-doing process. The learning process thus depends on the cumulative capacity installed worldwide and the learning rate.

The relevant variables in this section are investments, energy generation and capacity in PV and CSP. The equations which combine these variables perfectly replicate the scheme described in the “Energy sector” module. However, the variables are now specified per capacity factor class and distance from load centres.

4.3.1 Competition area

Solar PV and CSP partially compete for the same land. Indeed, CSP requires types of ground characterized by a lower slope, so the curves provide information on the “PV-only” area and the “Competition” area, where both PV and CSP can be installed. The module thus reports the total installable PV capacity (PV-only + Competition) and the total installable CSP capacity (Competition), and moreover it adds a constraint on land occupation in the Competition area:

\[ \sum_{solar\_class} (K_{EN\_PV}(solar\_distance,solar\_class,t,n) * 1e6 / dens('elpv',n) + K_{EN\_CSP}(solar\_distance,solar\_class,t,n) * 1e6 / dens('elcsp',n)) \le area(solar\_distance,n) \]


Pietzcker, Robert Carl, Daniel Stetter, Susanne Manger, and Gunnar Luderer. 2014. “Using the Sun to Decarbonize the Power Sector: The Economic Potential of Photovoltaics and Concentrating Solar Power.” Applied Energy 135 (December). Elsevier BV: 704–20.