• Transmission loss equation

    Generally, in a power system, several plants are situated at different places. They are interconnected by long transmission lines. The entire system load along with transmission loss shall be met by the power plants in the system. Transmission loss depends on i) line parameters ii) bus voltages and iii) power flow. Determination of transmission loss requires complex computations. However, with reasonable approximations, for a power system with N number of power plants, transmission loss can be represented as

    PL = PTBP

    Thus PL can be written as

    When the powers are in MW, the Bmn coefficients are of dimension 1/ MW. If powers are in per-unit, then Bmn coefficients are also in per-unit. Loss coefficient matrix of a power system shall be determined before hand and made available for economic dispatch.

    For a two plant system, the expression for the transmission loss is

    Since Bmn coefficient matrix is symmetric, for two plant system

    Consider the simple case of two generating plants connected to an arbitrary number of loads through a transmission network as shown in figure.



    Let,  I1 = Current through line AC

    I2 = Current through line BC

    I1 + I2 = Current through line CD

    RAC = Resistance of line AC

    RBC = Resistance of line BC

    RCD = Resistance of line CD

    IV1I= Voltage magnitude at bus A

    IV2I= Voltage magnitude at bus B

    P1 = Power generated by plant - 1

    P2 = Power generated by plant - 2

    cosØ1 = power factor at bus A

    cosØ2 = power factor at bus B


    Transmission loss for the given system is

    PL = 3*II1I2*RAC  + 3*II2I2*RBC + 3*II1 + I2I2*RCD


    II1I = P1/(1.732 *IV1I* cosØ1)

    II2I = P2/(1.732 *IV2I* cosØ2) and assume that I1 & I2 are in phase.


    PL = (P1)2B11 + 2(P1)(P2)B12 + (P2)2B22


    The term Bmn are called loss coefficient or B-coefficient.

    cosØ1 = power factor at bus AcosØ1 = power factor at bus A