An Efficient Envelope-Based Branch and Bound Algorithm for Combined Heat and Power Production planning Under the Deregulated Power Market

Combined heat and power (CHP) production is universally accepted as one of the most energy-efficient technology to produce energy with lower fuel consumption and fewer emissions. In CHP production, heat and power generation follows a joint characteristic. Traditional CHP production is usually applied in backpressure plants, where the joint characteristic can often be represented by convex (linear programming, LP) model. Advanced CHP production technologies such as backpressure plants with condensing and auxiliary cooling options, gas turbines, and combined gas and steam cycles may require non-convex models. Cost-efficient operation of a CHP system can be planned using an optimization model based on hourly load forecasts. A long-term planning model decomposes into thousands of hourly model, which can be formulated as mixed integer programming (MIP) problems. In this paper, we introduce the EBB algorithm, for solving the hourly non-convex CHP models of a long-term planning problem under the deregulated power market. EBB is based on a double bounding Branch and Bound (B&B) algorithm where linear subproblems are solved through an efficient envelope-based dual algorithm. We compare the performance of EBB with realistic models against the ILOG CPLEX 9.0 MIP solver and the Power Simplex (PS) based B&B algorithm (PBB). PS is an extremely efficient specialized Simplex algorithm developed for convex CHP planning problems. For reusing the previous solutions, EBB is from 664 to 947 times (average 794) faster than CPLEX and from 11 to 31 times (average 24) faster than PBB.