# Optimal power flow vs. economic dispatch

What is the difference between the two common optimization models for electricity systems, optimal power flow (OPF) and economic dispatch (ED)?

I've heard people say that ED is just a multi-period version of OPF. I've also heard people say that OPF includes power flow constraints while ED only includes constraints on the total generation.

Can anyone clarify?

The basic power flow (PF) problem calculates how much power should be sent around a transmission or distribution network in one time period (at one snapshot in time). It ignores how that power is produced.

Economic dispatch calculates how much power is produced at each power generator, ignoring the transmission network. Economic dispatch is a very simple but fast model. More accurate models use unit commitment in place of economic dispatch.

Optimal power flow (OPF) combines the power flow and economic dispatch problems. More advanced versions cover multiple time periods and replace economic dispatch with unit commitment.

The book "Power Generation, Operation, and Control" by Wood, Allen J. and Wollenberg, Bruce F. and Sheblé, Gerald B. is a reasonably good but not too formal reference.

• When you say "ignores how power is produced", what do you mean? My understanding is that OPF does decide how much to produce at each generator, right? Commented Jun 2, 2019 at 1:39
• Sorry. Somehow I had the PF problem in my mind. Corrected my answer. Commented Jun 2, 2019 at 7:10
• Aha! That clears it up. Thanks! Commented Jun 2, 2019 at 11:10

[taylor2015convex] provides a holistic view on economic dispatch, unit commitment, and optimal power flow. The continuous operation of power systems requires multi-period optimal power flow, which is discussed in chapter 4.

The decision concerning long-term investments is the most complicated programming problems in power systems, which is discussed in chapter 5, based on multi-period OPF.

There are mature algorithms to handle power flow (or load flow) problems, but they are fundamentally different from the lift-and-project relaxation for OPF used in the book.

• Taylor, J. A. (2015). Convex optimization of power systems. Cambridge University Press.