4.5 System integration

The system integration module of WITCH is dedicated to modelling the integration of variable renewable energies (VRE) - specifically wind and solar PV - into the electrical grid. A detailed description of this modeling is available in (Carrara and Marangoni 2016).

Apart from the implicit constraint represented by the CES structure, the limitation to VRE penetration into the electrical grid is modelled through two explicit constraints, based on (Sullivan, Krey, and Riahi 2013).

  1. A constraint on the flexibility of the power generation fleet

  2. A constraint on the installed capacity of the power generation fleet

4.5.1 Flexibility constraint

The flexibility constraint requires that the annual average energy production be sufficiently flexible to be borne by the grid and to be able to follow the load. All energy technologies are assigned a value from -1 to 1 accounting for their grade of flexibility. Negative values are assigned to inflexible, variable technologies (i.e. VREs). Zero is assigned to those technologies which are not inflexible, but, due to technical constraints, cannot assure flexibility to follow the load (e.g. nuclear and concentrated solar power, CSP, which we assume coupled with a thermal storage which guarantees some dispatchability). Higher and higher positive coefficients are instead assigned to the progressively more flexible technologies, up to 1 which characterises storage, that by definition provides full flexibility. Gas is assigned 0.5 because in WITCH we only model Combined Cycles: Combustion Turbines would be characterised by full flexibility (1). A negative value (-0.1) is also assigned to the overall demand, in order to account for the fact that the grid itself requires some flexibility to meet changes and uncertainty in the load.

Power technology Flexibility coefficient
Load -0.1
Wind -0.08
PV -0.05
Nuclear 0
Coal 0.15
Oil 0.3
Biomass 0.3
Gas 0.5
Hydro 0.5
Storage 1

The constraint is then formulated so that the sum of the energy generated by the different technologies weighted on the corresponding flexibility coefficients, which can be called flexible generation, result higher or equal than zero.

\[ \sum_{jel} Q_{EN}(jel,t,n) \times f(jel) + Q_{EN}('el',t,n) \times f(LOAD) \geq 0 \]

Storage is not supposed to actually generate useful electricity, being essentially adopted for flexibility purposes (indeed, it could be thought as a flexibility measure not only on the generation side, but also for the demand side management). Within this constraint, the equivalent electricity contribution from storage is obtained by multiplying its capacity by a fixed value of 2000 h/yr.

4.5.2 Capacity constraint

The capacity constraint guarantees that sufficient capacity is built to meet the instantaneous peak electricity demand. In particular, the so called firm capacity must be at least 1.5-2 times (depending on the region) as the yearly average load, the latter being simply calculated as the yearly energy demand divided by the yearly hours (8760). The firm capacity represents the capacity that is considered guaranteed. For non-variable technologies it is simply the nameplate capacity. For variable technologies, the firm capacity is calculated multiplying the installed capacity by two parameters: the capacity factor and the capacity value. The capacity factor is the ratio between the actual energy output over a time period and the maximum theoretical output which would be achievable by running the plant at the nameplate capacity over the same time period. It substantially indicates the average capacity in normalised terms. The capacity value is a factor decreasing with increasing penetration in the electricity mix (starting from 0.9 with no penetration) which indicates that for variable technologies not only is the average capacity not always guaranteed (thus the 0.9 even with no penetration), but this fact becomes more and more critical with increasing levels of VRE penetration. Storage capacity is multiplied by a capacity value as well, fixed to 0.85, which takes into account the reduction of its contribution at high shares of VRE penetration.

\[ \sum_{jel(non-VRE)} K_{EN}(jel_{non-VRE},t,n) + \sum_{jel(VRE)}^{ } K_{EN}(jel_{VRE},t,n) \cdot cf(jel,t,n) \cdot cv(SHARE_{EL}) + K_{EN}('elstorage',t,n) \cdot cv_{storage} \geq c(n) \cdot Q_{EN}('el',t,n)/8760 \]


\[ SHARE_{EL}(jel,t,n) = Q_{EN}(jel,t,n) / Q_{EN}('el',t,n) \]

4.5.3 Electrical grid

In order to take into account the investment in the electrical grid needed, we use a stylized model based only on grid capital:

\[ K_{EN\_GRID}(t+1,n) = K_{EN\_GRID}(t,n)\left(1-\delta\_grid(t+1,n)\right)^{\Delta_t} + \Delta_t \cdot \frac{I_{EN\_GRID}(t,n)}{grid\_cost} \]

The grid capital stock is adjusted to power capacity, taking into account a linear relationship between grid capacity and the capacity of traditional power generation technologies (indicated as standard in the formula). Moreover, it includes an additional grid stock requirement for i) connecting wind and solar plants located far from load centres or shore, and ii) building a wider interconnection for the integration of VREs (curtailment reduction, dispatchability increase, etc.), which increases exponentially with VRE penetration.

\[\begin{align*} K_{EN\_GRID}(t,n) &= \sum_{jel(standard)} K_{EN}(jel_{standard},t,n)\\ &+ \sum_{jel} \sum_{distance} K_{EN}(jel,t,n) \cdot \frac{transm\_cost(jel,distance)}{grid\_cost}\\ &+ \sum_{jel(VRE)} K_{EN}(jel_{VRE},t,n) \cdot (1 + SHARE_{EL}(jel_{VRE},t,n)^{k}) \end{align*}\] where the coefficient \(k\) is calibrated to be equal to 1.55.


Carrara, Samuel, and Giacomo Marangoni. 2016. “Including System Integration of Variable Renewable Energies in a Constant Elasticity of Substitution Framework: The Case of the Witch Model.”

Sullivan, Patrick, Volker Krey, and Keywan Riahi. 2013. “Impacts of Considering Electric Sector Variability and Reliability in the MESSAGE Model.” Energy Strategy Reviews 1 (3): 157–63.