An AC/C Network Primer for Energy Economists: Part 1: Basic EE and PTDFS

49 Pages Posted: 8 May 2012

Date Written: May 7, 2012


This is the first of a two-part series (given sufficient interest) of papers providing a technical primer for the energy economist wishing to study the optimal power flow problem, but, who like this paper’s author, find it difficult to simply plow through Schweppe et al. (1988). This paper’s aim is to provide the reader with sufficient technical background sufficient to calculate power transfer distribution factors (PTDF’s, or network shift factors) for a more complicated model than the simple 3-node model common to energy economics studies. The point of departure for this work is basic electrical engineering fundamentals. We start off Section 2 with a simple direct current (DC) circuit analysis, demonstrating Ohm’s law, and Kirchhoff’s laws. As these are captured by very basic equations, we quickly move on to alternating current (AC) analysis. Here, we spend quite a bit of effort manipulating fairly straightforward (i.e. sinusoidal) AC voltage equations to derive equations for average voltage, current, and power in an AC circuit. From there, we delve into the concept of “phase angles,” showing how electrical components such as inductors and capacitors bring voltage and current “out of phase.” We then demonstrate both graphically and algebraically the effect of non-zero phase angles on resistance and power relations in an AC circuit. The goal of section 2 is to familiarize the reader with concepts that economists and operations researchers generally take for granted, but are quite foreign to those of us who are self-taught.

Suggested Citation

Benjamin, Richard M., An AC/C Network Primer for Energy Economists: Part 1: Basic EE and PTDFS (May 7, 2012). USAEE Working Paper No. 2054116. Available at SSRN: or

Richard M. Benjamin (Contact Author)

Round Table Group ( email )

United States
410-672-5319 (Phone)

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