Optimal Unit Commitment and Economic Dispatch of Cogeneration Systems with a Storage

Due to its relatively high total energy eeciency, the application of cogeneration is attracting increased attention. Today cogeneration is an essential element in the energy supply system in many countries, and when environmental and economic aspects are considered too, it seems to be a relevant option in expansion planning in many situations. The present paper presents a quite general and yet detailed modeling of a cogeneration plant which feeds its output water into a district heating network, and which includes several possible types of energy transformation units, the central one being the cogeneration unit. The modeling also includes a heat water storage. The model cost function is nonlinear and has linear constraints. Storage losses, minimalup and down times and time depending start-up costs are considered. The time horizon is partitioned into a nite number of discrete intervals. In this paper, the unit commitment problem in combination with the economic dispatch problem is solved using an algorithm based on Lagrangian relaxation. If all unit-coupling constraints are relaxed, the problem decomposes into one separate problem for each unit. The individual problem is essentially a simple unit commitment problem that is easily solved by dynamic programming. Using Lagrangian relaxation to solve the problem will generate a set of dual costs in each time interval. The updating of the Lagrangian multipliers may be done in various ways. Here, two methods are compared. One is the relatively popular so-called Polyak rule II, which is easily applied and gives robust results. The other method exploits the interdependencies between the individual multipliers that are introduced due to the time coupling in the heat storage. This is implemented in a special forwards-backwards projection algorithm. The paper describes a number of detailed computational results of a Swedish case study. The two updating methods for the Lagrangian multipliers are compared, and it is shown how the mechanisms of the forwards-backwards projection algorithm may be interpreted in economic terms.