Abstract— This paper presents a method based on Lagrange multipliers for capacitor banks allocation at industrial plant networks. The aim of compensation is to avoid penalties in (JD/$) enforced on electricity bills due to low power factor, and to minimize the power losses at the plant’s network. Capacitor banks will be allocated at the main board (MB) as a fixed type and at secondary distribution boards (SDB) as a regulated type. For this purpose, a mathematical formulation of the problems has been established and solved. The “equivalent consumed active energy” amount is calculated based on a newly devolved equation for finding the “equivalent working time” which is used to calculate the total amount of reactive power compensation. The proposed method is applied to the data extracted from the monthly electricity bill of an industrial plant network. A numerical example and discussion have been introduced to illustrate the effectiveness of the proposed method.