It has been known that the second-order conic programming (SOCP) relaxation of an alternating current optimal power flow (ac OPF) problem is a computationally friendly formulation, whereas the semidefinite programming (SDP) relaxation is a theoretically stronger one. This paper presents a method to strengthen the (SOCP) relaxation by generating new cutting planes, i.e., valid inequalities, using SDP relaxation, which remove SOCP solutions that are infeasible to SDP formulation. This new method relies on solving a least square estimation (LSE) problem for every cycle in a cycle basis. General feasibility cutting plane method is also employed for cuts generation. We show that the SDP cuts generated by the LSE method are indeed feasibility cuts. Numerical results show that those new cuts can effectively reduce the search space and lead to a tighter relaxation. The new cuts are comparable to the SDP cuts in <xref ref-type="bibr" rid="ref1">[1]</xref>. Case studies on systems with several buses to thousands buses have demonstrated the method is also scalable.