As there may be errors and incompleteness in electric parameters mastered by attackers

and bad data may also exist in measurements

an injected attack strategy for false data based on Lagrange multipliers method is proposed. First

bad data is identified and unknown branch impedance is estimated by the Lagrange multipliers method and augmented state estimation method

respectively. Then

in the convex relaxation framework

the classic false data injected attack model aimed at attacking an arbitrary specific measurement is transformed into a basis-pursuit(BP)model. Finally

the suboptimum attack vector is quickly solved by alternating the direction method of multipliers(ADMM). In order to evaluate the strategy

simulations are tested in typical IEEE bus test systems. The results show that ADMM is more efficient than classic linear programming(LP)based on the BP model when the classic false data injected attack model is transformed into a BP model. It is also found that when the number of impedance unknown branches is small

the success rate is relatively high. But when the standard deviation of error vector for state variables decreases

the effect of the quantity of impedance unknown branches on the success rate will be weak. Moreover

this strategy does not significantly increase the attack cost.