Calculating Wattage with Three Phase Devices

Have you ever wondered why the wattage of a three phase device is calculated using the formula: volts x amps x 1.73? I have. I am going to try to explain this without using too many mind bending formulas. First, there is the matter of not being able to read the total line current at one time. There are essentially three circuits in a three phase device – from L1 to L2, from L2 to L3, and from L1 to L3. Each leg carries only two of the three circuits, so measuring amps on any one leg checks the current of only two of the three circuits. The 1.73 factor is added to account for the effect of the current in the circuit that is not being measured. But why 1.73? 1.73 is actually an approximation of the square root of 3. We arrive at this factor by using trigonometry to calculate the combined effect of all the phases. Trigonometry is needed because the three phases are out of phase with each other, so simple addition and subtraction won’t work. The effect of the phases is described by a mathematical concept called a vector. A vector has both a direction and strength. An easy way to understand vectors is to imagine a wagon with a rope pulling it. With one rope, the wagon will go at the same speed and direction as the person pulling the rope. Tie a second rope to the wagon and have two people pulling in different directions, and now the wagon will travel a path somewhere between the two people. Now have one person pull faster than the other, and the wagon will travel a little more in that direction. Adding different AC voltages and currents is done with vectors because vectors can account for differences in strength and direction. Vectors involve angles and one of the best ways to calculate the effect of angles is with trigonometry, which simply means the study of triangles; specifically, right triangles. If you draw a line right down the middle of the 120° angle formed by two phases of a wye wound three phase device, you form two right triangles with 60° angles at their tips (120°/2). The remaining angle in each triangle is 30° because all the angles must add up to 180° (90°+60°+30°). The length of the line next to the 30° angle is found using the Trig function cosine of 30°, which happens to be the square root of 3 divided by 2. Since we have two of these triangles, the total difference simply the square root of three, which we approximate as 1.73.

Wattage of a three phase load is then calculated as watts = volts x amps x 1.73. Some refinements are necessary for accuracy. If the voltage and current are not identical in all three phases, you must average the volts and amps of the three phases, so the formula becomes watts  = average volts x average amps x 1.73. If you are checking an inductive load, such as a motor, you also need to include the power factor to compensate for the fact that the voltage and current in an inductive device are out of phase with each other. The formula becomes watts = average volts x average amps x 1.73 x power factor.