Learn From Your Electric Bills, Part 2

Figure 1. Simple trigonometry can be used to determine power factor.

The beauty of using the PF triangle is that the standard trigonometric relations (sine, cosine, etc.) enable you to solve the elements of the triangle given the minimal information of any right triangle. The PF is equal to the cosine of the phase angle.

As discussed in my previous column (see, “Learn from Your Electric Bills, Part 1”), most electric companies bill industrial customers both for energy used (kWh), and for demand (rate of energy used, kW). PF can affect the billed demand, although the energy delivery companies in Texas have several different ways of handling this. Some bill on total apparent power (kVA), so any increase in PF reduces the bill. Others specify a minimum PF (PF_min) in their rate tariffs. If the actual power factor (PF_actual) exceeds the minimum, billed demand will equal actual demand — i.e., the real power (kW). If PF is less, the formula used to set the billed demand is

Billed demand = actual demand × (PF_min ÷ PF_actual)

With a PF_min of 0.95 and a PF_actual of 0.75, this calculation gives a ratio of 1.267. This means your billed demand is 26.7% more than your actual demand.

Installing a capacitor bank will increase the PF. The capacitors function exactly opposite to the reactive power vector, reducing the total reactive power and the phase angle, and shortening the apparent power vector as seen in Figure 1.

Using the geometry of the PF triangle, we can readily calculate the impact of a capacitor bank, and the resulting demand savings in an electric bill. This is how the IAC determined the savings for the plant mentioned in the first paragraph. Appendix 1 (see below) contains a detailed calculation of a similar example.

Now, find 12 months of your electric bills and discover the savings for PF correction at your site!

JIM EGGEBRECHT, PE, is a guest contributor. You can email him at [email protected]

Editor’s note: This article was written by a colleague of our regular columnist, Alan Rossiter. Jim Eggebrecht, PE has worked at the Industrial Assessment Center (IAC) at Texas A&M University in College Station, Texas for over 27 years as the assistant director. The IAC is a national program of the U. S. Department of Energy’s Advanced Manufacturing Office. Eggebrecht has completed over 450 energy assessments for a range of manufacturing facilities. He is also the executive director of the Industrial Energy Technology Conference, hosted by the Texas A&M Engineering Experiment Station, the Texas State Energy Conservation Office, and the Louisiana Department of Natural Resources.