A multi-scenario decision support system for real-time operation of over-year multi-reservoir systems 2. dss simulation

Abstract

A companion paper (Arena et al, 2019) has introduced the architecture of the DSS and has described its governing equations. In a real-time, dynamic decision-making context, it is a tool to support decisions at the current time step concerning water allocations to municipal demand centres and irrigation districts as well as additional intakes from costly water sources in a water resources system featuring reservoirs with over-year behaviour. The DSS is designed as a linearized MIP (mixed integer programming) optimization model and as such, it includes an objective function and constraints on 1) mass balances at system's nodes, 2) systems' topology, 3) component's capacity, 4) spills, as well as non-empty conditions on reservoir storage at the end of the Forecasting Horizon (FH). It is a multi-scenario optimization tool because future, uncertain inflows are modelled, until the end of the current water year, as three different inflow scenarios: Low flows, normal flows and high flows. The optimization model is solved for the three different scenarios and a unique solution that can be turned into one actual, implementable, decision at the present time step is obtained by imposing non-anticipatory (or congruity) constraints according to the principle of scenario aggregation (Rockfellar and Wets, 1987). The objective function is the weighted sum of the scarcity costs at all demand centres and of cost of water supply from additional sources along the multi-year FH, discounted to their present value, being the weights the occurrence probability of each of the three inflow scenarios. Given the over-year nature of the systems of interest for this study, the time unit is one month. This paper first discusses estimation of scenario probabilities and of scenario inflows, then describes the application of the DSS to a real-world, two-reservoir system in Southern Italy. Its performances, in terms of scarcity costs and costs of additional, costly, water resources, are simulated over a forty-year historical period, on a monthly basis. Sensitivity of the DSS to different demand levels is explored considering different drift scenarios. Furthermore, in order to contrast the performances of the multi-scenario DSS presented here (DSS-SC), we introduce a single-scenario DSS, identical to the multi-scenario one, except that decisions are made based on exogenous inflow forecast vectors. We look at two different types of forecast vectors that are meant to provide a lower and upper bound of DSS performances: The first type is a vector containing only the long-term means of monthly inflows and gives rise to DSS-WF (where WF stands for "worst forecast"). The second vector type contains instead real (i.e. actually occurred) inflows in the first six months of the FH and long-term means of monthly inflows for the remaining FH-6 months. It gives rise to a DSS-BF (BF stands for "best forecasts"). Results show that DSS-SC compares quite favourably with DSS-BF: Differences in total costs range from 37% for drift=0.75 to 27% for drift = 0.5. DSS-BF clearly outperforms DSS-WF with improvements ranging from 17% (drift = 0.75) to 62% (drift = 0.90). In one demand condition, described by a drift of 0.9, DSS-SC even outperforms DSS-BF. Investigation of this behaviour led to recognize that, at least for this drift, DSS-SC would manage the system so to keep the largest reservoir of the system full enough to allow issuing less restrictive irrigation supply reductions than its DSS-BF counterpart, and would therefore reduce the associated scarcity costs. This thought-provoking situation, if on the one hand confirms that in these long-memory systems "abrupt" failures can be the consequence of long-term policies and decision styles, on the other hand stimulates the reflection that DSS performances can indeed depend on a number of different factors that need to be investigated in deeper detail. From this standpoint, a single historic time series is probably not enough to explore the different possible behaviours of the DSS. For this reason, a stochastic validation of DSS-SC, by simulating its behaviour through synthetic time series, is in order and is the next research objective.