APT

Power Flow

Part 1 - Some background information

Purpose: This page is not intended to teach the topic of power flow, but rather to introduce the topic. After reading the information on this page, the reader should have a intuitive understanding of why calculating power flow in a networked transmission system can be challenging. EE454 is an excellent course for students who would like to learn more about power flow analysis. It is assumed that the reader has an understanding of basic circuit analysis.

1 - a simple DC circuit analogy

There exist some well developed, but complicated methods for solving the power flow problem. Two methods that are part of the EE454 curriculum are the Newton-Raphson method and the Fast Decoupled method of power flow analysis. Both of these methods are equally accurate. It might be helpful to understand, on a more intuitive level, what makes the power flow problem a challenge.

Example 1-1

- Start - a simple series resistive DC circuit:
Suppose RS is the resistance of the wire, rather than being an actual circuit element, while RL is the load attached to the source. Clearly some voltage drop occurs and some power is dissipated along the length of the wire. Of course most of the power is sent to the load.

Example 1-2

A simple parallel resistive DC circuit

PRS Is the power dissipated across the parallel equivalent circuit (Rs||Rs||Rs).

Example 1-3

Now - See what happens if one of the Parallel elements becomes an open Circuit

As in the previous example, suppose the parallel resistances (RS) represent the resistance of the wires that connect the load (RL) to the source. Not surprisingly, when one of the parallel branches is open circuited, the parallel equivalent resistance increases causing the voltage drop across the parallel network to increase. The power dissipation across the remaining parallel lines increases and the power delivered to the load (PL) decreases as a result.

How does this relate to The Power Flow problem?

In a power transmission system, a power line might be open circuited either intentionally or unintentionally. Suppose in the last example, the load (RL) represented the load a city places on a power system and the three parallel branches represent the transmission lines that deliver power from some distant generating station(s). From time to time it might be necessary to take one of the transmission lines out of service for maintenance. The question that operators must ask is: How will this change the system operating parameters?

Suppose that we desire the voltage at the load to remain above 0.95 per unit (pu). Our small system has a 1V base so we need not do much math to determine if we have violated the requirement. In the last example, when one of the lines was open circuited, the load voltage decreased to .983pu. It looks like everything is fine. What happens if a problem occurs? Suppose something happens to one of the two lines remaining in service. Will the voltage criteria still be met? Is the system secure in its current operating state? What is the next possible contingency that may affect system operation?

Example 1-4

-Suppose one more line removed from service

Apparently the system's voltage criteria has not been violated given the current load. The one remaining line can carry all of the current without causing excessive voltage drop. Note that in each of examples 2, 3 and 4 the power delivered to the load has decreased. The voltage across the load in each case has decreased as well. What would happen if the load were variable - suppose the load resistance decreased? If the load resistance went down to 75 ohms would the systems voltage criteria still be met? What if the load resistance drops to 50 ohms? Clearly the voltage across the load will drop if the load demands more power while the line impedance remains constant. Could this cause a violation of the stated voltage criteria?

In the examples shown it is not too difficult to predict what might happen. The next contingency is fairly simple to recognize. In a more complex system things are not so straightforward. In a large, complex system, there may be hundreds or even thousand of possible "next contingencies". Each possible failure takes time to evaluate. See section 2 for more details.

Links

Power section Flow 2

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