\frametitle{Linear optimisation of annual system costs}

Find the long-term cost-optimal energy system, including investments and short-term costs:
\begin{equation*}
  \textrm{Minimise} \left(\parbox{6em}{\centering\alert{Yearly\\system costs}}\right) = \sum_i \left(\parbox{6em}{\centering\alert{Annualised capital costs}}\right) + \sum_{i,t} \left(\parbox{5em}{\centering\alert{Marginal costs}}\right)
\end{equation*}
subject to
\begin{itemize}
\item meeting \alert{energy demand} at each node $i$ (e.g. region) and time $t$ (e.g. hour of year)
\item wind, solar, hydro (variable renewables) \alert{availability time series} $\forall\: i,t$
\item \alert{transmission constraints} between nodes, \alert{linearised power flow}
\item (installed capacity) $\leq$ (\alert{geographical potentials} for renewables)
\item \alert{CO${}_2$ constraint} (e.g. 95\% reduction compared to 1990)
\end{itemize}

In short: mostly-greenfield investment optimisation, multi-period with linear power flow.

Optimise transmission, generation and storage \alert{jointly}, since they're strongly interacting.