  This paper presents a tractable algorithm to procure the strategic bidding of
generation units in an electricity market with AC power flow constraints. The
strategic bidding problem is formulated as a profit maximization problem
constrained by the market-clearing problem. The market-clearing problem which
is solved by the independent system operator (ISO) is formulated as a cost
minimization problem with a non-linear and non-convex AC power flow model. The
problem is formulated as a bi-level optimization problem, where the upper-level
problem is the profit maximization problem and the lower-level problem is the
market-clearing problem. To solve the bi-level problem, the lower-level problem
is reformulated into second-order conic programming (SOCP) relaxation form. The
convexified lower-level problem is then presented in a closed-form by the set
of primal-dual constraints. However, the strategic bidding encounters nonlinear
terms in the lower-level problem. The dual form of the lower-level problem and
complementary slackness conditions are leveraged to replace a set of nonlinear
terms with equivalent mixed-integer terms. The merit of the procured strategic
bidding is illustrated in the case study by comparison with a market-clearing
problem with DC power flow constraints and the original non-convex power flow
formulation.
