*2.1. NEMESYS Model Logic*

Generation plant technologies and associated plant costs are essential inputs to the security-constrained unit commitment model. Two key variables for each generation technology are (unit) marginal running costs *vi* and plant fixed and sunk costs, ϕ*i*. These inputs have been derived from a power plant cost model (PF model—the logic of which appears in Appendix A). The PF model derives generation technology (generalized) long run marginal costs *pi*ε and total revenues including normal profit *Ri* for a given level of output *oi*.

$$\left(\boldsymbol{\sigma}^{i}\cdot\boldsymbol{\sigma}^{i}\right) + \boldsymbol{\varphi}^{i} \equiv \boldsymbol{R}^{i} \left| \boldsymbol{R}^{i} = \boldsymbol{p}^{i\boldsymbol{\epsilon}} \cdot \boldsymbol{\sigma}^{i} \right. \tag{1}$$

NEMESYS orders plant capacity and dispatches the fleet of power generating units to satisfy security constraints and differential equilibrium conditions given specified plant options available.

Let *H* be the ordered set of all half-hourly periods.

$$n \in \{1 \ldots |H|\} \land h\_{\mathcal{U}} \in H \tag{2}$$

Let *E* be the set of all electricity consumers in the model.

$$k \in \{1 \ldots |E|\} \land c\_k \in E \tag{3}$$

Let *Ck*(*q*) be the valuation that consumer segments are willing to pay for quantity *q* MWh of power. The model assumes that demand in each period *n* is independent of other demand periods. Let *qnk* be the metered quantity consumed by customer *en* in each period *hk* expressed in MWh.

Let Ψ be the set of existing installed power plants and available augmentation options for each relevant scenario.

$$i \in \{1 \ldots |\Psi|\} \land \psi^i \in \Psi \tag{4}$$

As outlined in Equation (1), let ϕ*i* be the fixed operating and sunk capacity costs and *vi* be the (unit) marginal running cost of plant ψ*i* respectively. Let *oi* be the maximum continuous rating of power plant ψ*i*. Power plants are subject to scheduled and forced outages. *<sup>F</sup>*(*<sup>n</sup>*, *i*) is the availability of plant ψ*i* in each period *hn*. Annual plant availability is therefore:

$$\sum\_{j=0}^{|P|} F(n, i) \,\,\forall \psi^i \tag{5}$$

Let *oi n* be the quantity of power produced by plant ψ*i* in each period *hn*.
