ECE 476 POWER SYSTEM ANALYSIS Lecture 19 Fault Analysis, Grounding, Symmetrical Components Professor Tom Overbye Department of Electrical and Computer Engineering

Announcements Homework 8 is 7.1, 7.17, 7.20, 7.24, 7.27 Should be done before second exam; not turned in Be reading Chapter 7 Design Project has firm due date of Dec 4. Exam 2 is Thursday Nov 13 in class. Closed book, closed notes, except you can bring one new note sheet as well as your first exam note sheet.

Network Fault Example For the following network assume a fault on the terminal of the generator; all data is per unit except for the transmission line reactance generator has 1.05 terminal voltage & supplies 100 MVA with 0.95 lag pf

Network Fault Example, cont'd Faulted network per unit diagram

Network Fault Example, cont'd

Fault Analysis Solution Techniques Circuit models used during the fault allow the network to be represented as a linear circuit There are two main methods for solving for fault currents: Direct method: Use prefault conditions to solve for the internal machine voltages; then apply fault and solve directly Superposition: Fault is represented by two opposing voltage sources; solve system by superposition first voltage just represents the prefault operating point second system only has a single voltage source

Superposition Approach Faulted Condition Exact Equivalent to Faulted Condition Fault is represented by two equal and opposite voltage sources, each with a magnitude equal to the pre-fault voltage

Superposition Approach, cont’d Since this is now a linear network, the faulted voltages and currents are just the sum of the pre-fault conditions [the (1) component] and the conditions with just a single voltage source at the fault location [the (2) component] Pre-fault (1) component equal to the pre-fault power flow solution Obvious the pre-fault “fault current” is zero!

Superposition Approach, cont’d Fault (1) component due to a single voltage source at the fault location, with a magnitude equal to the negative of the pre-fault voltage at the fault location.

Two Bus Superposition Solution This matches what we calculated earlier

Determination of Fault Current

Determination of Fault Current

Three Gen System Fault Example

Three Gen Example, cont’d

Three Gen Example, cont’d

Three Gen Example, cont’d

PowerWorld Example 7.5: Bus 2 Fault

Problem 7.28

Grounding When studying unbalanced system operation how a system is grounded can have a major impact on the fault flows Ground current only impacts zero sequence system In previous example if load was ungrounded the zero sequence network is (with Zn equal infinity):

Grounding, cont’d Voltages are always defined as a voltage difference. The ground is used to establish the zero voltage reference point ground need not be the actual ground (e.g., an airplane) During balanced system operation we can ignore the ground since there is no neutral current There are two primary reasons for grounding electrical systems safety protect equipment

How good a conductor is dirt? There is nothing magical about an earth ground. All the electrical laws, such as Ohm’s law, still apply. Therefore to determine the resistance of the ground we can treat it like any other resistive material:

How good a conductor is dirt?

How good a conductor is dirt?

Calculation of grounding resistance Because of its large cross sectional area the earth is actually a pretty good conductor. Devices are physically grounded by having a conductor in physical contact with the ground; having a fairly large area of contact is important. Most of the resistance associated with establishing an earth ground comes within a short distance of the grounding point.

Calculation of grounding R, cont’d Example: Calculate the resistance from a grounding rod out to a radial distance x from the rod, assuming the rod has a radius of r:

Calculation of grounding R, cont’d The actual values will be substantially less since we’ve assumed no current flowing downward into the ground

Analysis of Unsymmetric Systems Except for the balanced three-phase fault, faults result in an unbalanced system. The most common types of faults are single line-ground (SLG) and line-line (LL). Other types are double line-ground (DLG), open conductor, and balanced three phase. System is only unbalanced at point of fault! The easiest method to analyze unbalanced system operation due to faults is through the use of symmetrical components

Symmetric Components The key idea of symmetrical component analysis is to decompose the system into three sequence networks. The networks are then coupled only at the point of the unbalance (i.e., the fault) The three sequence networks are known as the positive sequence (this is the one we’ve been using) negative sequence zero sequence

Positive Sequence Sets The positive sequence sets have three phase currents/voltages with equal magnitude, with phase b lagging phase a by 120°, and phase c lagging phase b by 120°. We’ve been studying positive sequence sets Positive sequence sets have zero neutral current

Negative Sequence Sets The negative sequence sets have three phase currents/voltages with equal magnitude, with phase b leading phase a by 120°, and phase c leading phase b by 120°. Negative sequence sets are similar to positive sequence, except the phase order is reversed Negative sequence sets have zero neutral current

Zero Sequence Sets Zero sequence sets have three values with equal magnitude and angle. Zero sequence sets have neutral current

Sequence Set Representation Any arbitrary set of three phasors, say Ia, Ib, Ic can be represented as a sum of the three sequence sets

Conversion from Sequence to Phase

Conversion Sequence to Phase

Conversion Phase to Sequence

Symmetrical Component Example 1

Symmetrical Component Example 2

Symmetrical Component Example 3

Use of Symmetrical Components Consider the following wye-connected load:

Use of Symmetrical Components

Networks are Now Decoupled