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Solar hosting capacity analysis (HCA) assesses the ability of a distribution network to host distributed solar generation without seriously violating distribution network constraints. In this paper, we consider risk-sensitive HCA that limits the risk of network constraint violations with a collection of scenarios of solar irradiance and nodal power demands, where risk is modeled via the conditional value at risk (CVaR) measure. First, we consider the question of maximizing aggregate installed solar capacities, subject to risk constraints and solve it as a second-order cone program (SOCP) with a standard conic relaxation of the feasible set of the power flow equations. Second, we design an incremental algorithm to decide whether a configuration of solar installations has acceptable risk of constraint violations, modeled via CVaR. The algorithm circumvents explicit risk computation by incrementally constructing inner and outer polyhedral approximations of the set of acceptable solar installation configurations from prior such tests conducted. Our numerical examples study the impact of risk parameters, the number of scenarios and the scalability of our framework.
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Reliability Assessment of Scenarios for CVaR Minimization in Two-Stage Stochastic Programs
The mass transportation distance rank histogram (MTDRh) was developed to assess the reliability of any given scenario generation process for a two-stage, risk-neutral stochastic program. Reliability is defined loosely as goodness of fit between the generated scenario sets and corresponding observed values over a collection of historical instances. This graphical tool can diagnose over- or under-dispersion and/or bias in the scenario sets and support hypothesis testing of scenario reliability. If the risk-averse objective is instead to minimize CVaR of cost, the only important, or effective, scenarios are those that produce cost in the upper tail of the distribution at the optimal solution. We describe a procedure to adapt the MTDRh for use in assessing the reliability of scenarios relative to the upper tail of the cost distribution. This adaptation relies on a conditional probability distribution derived in the context of assessing the effectiveness of scenarios. For a risk-averse newsvendor formulation, we conduct simulation studies to systematically explore the ability of the CVaR-adapted MTDRh to diagnose different ways that scenario sets may fail to capture the upper tail of the cost distribution near optimality. We conjecture that, as with the MTDRh and its predecessor minimum spanning tree rank histogram, the nature of the mismatch between scenarios and observations can be observed according to the non-flat shape of the rank histogram. On the other hand, scenario generation methods can be calibrated according to uniform distribution goodness of fit to the distribution of ranks.
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- Award ID(s):
- 2132200
- PAR ID:
- 10352209
- Editor(s):
- Ellis, K.; Ferrell, W.; Knapp, J.
- Date Published:
- Journal Name:
- Proceedings of the IISE Annual Conference & Expo 2022
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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