  Traditional largest normalize residual (LNR) test for bad data identification
relies on state estimation residuals and thus can only be implemented after
running Power System State Estimation (PSSE). LNR may fail to detect bad data
in leverage point measurements and multiple interacting and conforming bad
data. This paper proposes an optimization problem formulation for joint state
estimation and bad data identification based on second-order cone programming
(SOCP) convex relaxation. L1 -norm of the sparse residuals is added in the
objective function of the state estimation problem in order to recover both bad
data and states simultaneously. To solve the optimization problem in polynomial
time, first, SOCP convex relaxation is applied to make the problem convex.
Second, least squares error (LSE)-based semidefinite programming (SDP) cutting
plane method is implemented to strengthen the SOCP relaxation of PSSE.
Numerical results for the proposed algorithm demonstrate simultaneous state
estimation and bad data identification for networks with small sizes and
thousand buses. Compared to the LNR method, the proposed method can detect bad
data in leverage point measurements and multiple conforming bad data.
