  Optimal power flow (OPF) is the fundamental mathematical model in power
system operations. Improving the solution quality of OPF provide huge economic
and engineering benefits. The convex reformulation of the original nonconvex
alternating current OPF (ACOPF) model gives an efficient way to find the global
optimal solution of ACOPF but suffers from the relaxation gaps. The existence
of relaxation gaps hinders the practical application of convex OPF due to the
AC-infeasibility problem. We evaluate and improve the tightness of the convex
ACOPF model in this paper. Various power networks and nodal loads are
considered in the evaluation. A unified evaluation framework is implemented in
Julia programming language. This evaluation shows the sensitivity of the
relaxation gap and helps to benchmark the proposed tightness reinforcement
approach (TRA). The proposed TRA is based on the penalty function method which
penalizes the power loss relaxation in the objective function of the convex
ACOPF model. A heuristic penalty algorithm is proposed to find the proper
penalty parameter of the TRA. Numerical results show relaxation gaps exist in
test cases especially for large-scale power networks under low nodal power
loads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.
