Modelling to Generate Continuous Alternatives: Enabling Real-Time Feasible Portfolio Generation in Convex Planning Models

Abstract

Decarbonization provides new opportunities to plan energy systems for improved health, resilience, equity, and environmental outcomes, but challenges in siting and social acceptance of transition goals and targets threaten progress. Modelling to Generate Alternatives (MGA) provides an optimization method for capturing many near-cost-optimal system configurations, and can provide insights into the tradeoffs between objectives and flexibility available in the system. However, MGA is currently limited in interactive applicability to these problems due to a lack of methods for allowing users to explore near-optimal feasible spaces. In this work we describe Modelling to Generate Continuous Alternatives (MGCA), a novel post-processing algorithm for convex planning problems which enables users to rapidly generate new interior solutions, incorporate new constraints, and solve within the space with convex objectives. MGCA begins with a dimensionality reduction to capacity decisions and metric values. We then take advantage of convex combinations to generate interior points by allowing user weight specification and encoding convex combinations in an optimization problem with user-defined additional constraints and objective. Dimensionality reduction enables this problem to solve in tenths of a second, suitable for analysis in interactive settings. We discuss the interpolation of capacity and operational metric values, finding capacity metrics can be perfectly interpolated while operational metrics remain within the feasible range of the points used to create them. We demonstrate interpolated solutions can be exported and re-solved with an economic dispatch model to provide operational metric values consistent with least-cost decision-making and show interpolated metric values are generally within 10% of the optimal value.

Figures (11)

• Figure 1: MGCA dimensional reduction and metric interpolation visualization. A. Dimensional reduction from capacity and operational variables and metrics to capacity variables and metric values. B. Convex combination of affine capacity metrics, which can be precisely calculated. C. Convex combination of operational cost, the actual value of which will always be less than or equal to the interpolated value, as it is an argmin, a convex function. D. Interpolation of other operational metrics, which is guaranteed to produce a feasible value, but not the actual value.
• Figure 2: Aggregate capacities for all MGA solutions found for 3-Zone GenX ISONE Case. Solutions indicated by dots, convex hull indicated by dashed line. Least-cost solution in red.
• Figure 3: Capacities of 50 randomly generated interior MGCA interpolates (orange) and original MGA points (blue)
• Figure 4: Capacities of solution found through exploration problem with objective minimizing natural gas (maroon X) and original MGA points (blue). Least-cost solution in red.
• Figure 5: MGA capacity space with 6% budget (gray) superimposed over 10% budget (blue). Individual solutions are shown by x's (6%) and dots (10%) respectively. Least-cost solution in red.