• 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

Since

II1I = P1/(1.732 *IV1I* cosØ1)

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

So,

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

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

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