Maximizing power production in path and tree riverine networks

Abstract A majority of electricity generation in the US is produced by thermoelectric power plants which require a constant supply of water for cooling. Many of these plants consequently eject large quantities of hot water into an adjacent river, causing thermal pollution, which harms the local ecosystems and aquatic life. Plants commonly lie within interconnected river networks, whence thermal pollution from plants upstream flows to downstream plants, causing less-effective cooling, and decreases in efficiency. Plants are managed individually, and government regulations combating thermal pollution take the form of local river temperature constraints. We propose analyzing this situation regionally, as an optimization problem, where we seek to balance the trade-off between satisfying power demand and obeying temperature limits. Our primary focus is fractional variants of this problem where we can specify the amount of power a plant will generate, up to its maximum capacity. After providing optimal schedules or algorithms for several special cases of this problem, we provide an optimal polynomial-time algorithm for this problem on river topologies taking the form of (a) a path graph and (b) a “merge-only” tree. We also investigate a 0/1 version of the problem (plants are either fully on or off), which is NP-hard already for path graphs. We provide a dynamic programming FPTAS for this case. Finally, we carry out an extensive performance evaluation comparing our fractional optimal algorithms to baseline heuristics in simulation. These experiments are performed both on synthetically generated problem instances and on problem instances constructed using real-world river network data, in particular the power plant network along the Hudson River in New York State. These experiments provide insight as to when naive greedy algorithms diverge from the optimal and on which problem instance parameters optimal performance is more sensitive too.