Real-time economic dispatch with line flow and emission constraints using quadratic programming

The presence of multiple constraints due to network line flow limits and emission allowances in the economic dispatch of modern power systems makes the conventional Lambda-Delta iterative approach no longer effective. This paper proposes a practical strategy based on quadratic programming (QP) techniques to solve the real-time economic dispatch problem. It formulates the problem with a quadratic objective function based on the unit's cost curves in quadratic or piecewise-quadratic forms. The operation constraints are modeled as linear equality/inequality equations, resulting in a typical QP problem. Goal programming techniques are also incorporated in the formulation which guarantees the best available solution even under infeasible conditions. In addition, the proposed strategy formulates the problem in the second phase dispatch in real-time by including a set of emergency control variables to provide effective control strategies for properly relieving constraint violations if they exist. The effectiveness of the proposed strategy is demonstrated by an example power dispatch problem.