# Additional Features

## Modeling to Generate Alternatives

`Dolphyn.mga`

— Method`mga(EP::Model, path::AbstractString, setup::Dict, inputs::Dict, outpath::AbstractString)`

We have implemented an updated Modeling to Generate Alternatives (MGA) Algorithm proposed by Berntsen and Trutnevyte (2017) to generate a set of feasible, near cost-optimal technology portfolios. This algorithm was developed by Brill Jr, E. D., 1979 and introduced to energy system planning by DeCarolia, J. F., 2011.

To create the MGA formulation, we replace the cost-minimizing objective function of GenX with a new objective function that creates multiple generation portfolios by zone. We further add a new budget constraint based on the optimal objective function value $f^*$ of the least-cost model and the user-specified value of slack $\delta$. After adding the slack constraint, the resulting MGA formulation is given as:

\[\begin{aligned} \text{max/min} \quad &\sum_{z \in \mathcal{Z}}\sum_{r \in \mathcal{R}} \beta_{z,r}^{k}P_{z,r}\\ \text{s.t.} \quad &P_{zr} = \sum_{y \in \mathcal{G}}\sum_{t \in \mathcal{T}} \omega_{t} \Theta_{y,t,z,r} \\ & f \leq f^* + \delta \\ &Ax = b \end{aligned}\]

where, $\beta_{zr}$ is a random objective fucntion coefficient betwen $[0,100]$ for MGA iteration $k$. $\Theta_{y,t,z,r}$ is a generation of technology $y$ in zone $z$ in time period $t$ that belongs to a resource type $r$. We aggregate $\Theta_{y,t,z,r}$ into a new variable $P_{z,r}$ that represents total generation from technology type $r$ in a zone $z$. In the second constraint above, $\delta$ denote the increase in budget from the least-cost solution and $f$ represents the expression for the total system cost. The constraint $Ax = b$ represents all other constraints in the power system model. We then solve the formulation with minimization and maximization objective function to explore near optimal solution space.

## Method of Morris

`Dolphyn.MatSpread`

— Type`morris(EP::Model, path::AbstractString, setup::Dict, inputs::Dict, outpath::AbstractString, OPTIMIZER)`

We apply the Method of Morris developed by Morris, M., 1991 in order to identify the input parameters that produce the largest change on total system cost. Method of Morris falls under the simplest class of one-factor-at-a-time (OAT) screening techniques. It assumes l levels per input factor and generates a set of trajectories through the input space. As such, the Method of Morris generates a grid of uncertain model input parameters, $x_i, i=1, ..., k$,, where the range $[x_i^{-}, x_i^{+}$ of each uncertain input parameter i is split into l intervals of equal length. Each trajectory starts at different realizations of input parameters chosen at random and are built by successively selecting one of the inputs randomly and moving it to an adjacent level. These trajectories are used to estimate the mean and the standard deviation of each input parameter on total system cost. A high estimated mean indicates that the input parameter is important; a high estimated standard deviation indicates important interactions between that input parameter and other inputs.