Using Model Predictive Control in a Water Infrastructure Planning Model for the Zambezi River Basin

Water infrastructure development plans must consider the interdependencies within the water-energy-food nexus. Ecosystem preservation, hydropower and irrigation development will contribute to multiple Sustainable Development Goals (United Nations, 2015). Moreover, evolving socio-economic context, uncertain future climate, and stakeholders with conflicting interests, lead to a highly complex decision problem. Therefore, there is a need for decision support tools to objectively determine the value of investments and the risks linked to uncertainties. Perfect foresight is a common approach to sectorial planning models (e.g. Kahil et al. (2018) and Khan et al. (2018)). This means that optimal management decisions anticipate future conditions such as droughts by cultivating crops with lower water requirements or storing additional water, leading to overestimate infrastructure performance. In reality, water planners and managers will not have perfect foresight, and will be limited by the availability and skill of existing forecasting systems. As droughts have important economic impacts (SADC et al., 2015), a more realistic way of modelling reservoir operations and agriculture decisions could improve the reliability of the results. One way to implement this in perfect foresight modelling frameworks is to use Model Predictive Control (MPC) and iteratively solve the optimal management decisions in each time step with a limited knowledge of the future (Sahu, 2016). We implement the MPC framework in an existing open-source hydroeconomic optimization model, linking in a holistic framework, representations of the water, agriculture, and power systems. The model represents the joint development of nexus related infrastructure and policies and evaluates their economic impact, as well as the risks linked to uncertainties in future climate and socio-economic development. We apply the methodology to evaluate the infrastructure investment plans in the Zambezi river basin (World Bank, 2010). By comparing MPC and perfect foresight, we show how the perfect foresight assumption affects the valuation of the hydropower and irrigation investment plans. We investigate in which cases the perfect foresight assumption might bias the investment decision.