A new gradient projection active set approach for reliable and economic operation of combined energy systems

• Novel Active Set algorithm with Gradient Projection for complex CHPED problems. • Efficiently handles inequality constraints by partitioning into active/inactive sets. • Decomposes non-convex CHP operating regions into convex sub-regions for solution. • Achieves superior, robust optimal solutions across diverse CHPED test systems. • Outperforms existing methods, providing feasible solutions for challenging CHPED. The challenge of combined heat and power economic dispatch (CHPED) lies in its complex nature as a multi-constrained and nonlinear optimization task. Its difficulty arises from the strong interdependence between electricity and thermal production in cogeneration systems, and from the existence of non-convex feasible domains, particularly when valve-point characteristics are considered. To address these issues, this work proposes an innovative active set approach based on the Gradient Projection method, aiming to provide an effective solution to the CHPED task. The method classifies inequality constraints into active and inactive groups, where active ones are treated as equalities, thereby improving the efficiency of the computational process. By projecting the negative gradient of the objective function into the feasible region, the gradient projection strategy ensures effective progress within the search space, while also decomposing complex regions into smaller convex subsets. The central aim is to reduce overall generation costs while fulfilling all electricity and heat demands under operational restrictions. The effectiveness of the algorithm is evaluated across four benchmark systems of different scales, covering scenarios with valve-point characteristics and power transmission losses. Comparative experiments against a wide range of advanced techniques highlight the superior robustness, accuracy, and ability of the proposed method to consistently deliver practical and cost-effective solutions.