ECE 530 – Analysis Techniques for Large-Scale Electrical Systems

ECE 530 – Analysis Techniques for Large-Scale Electrical Systems Lecture 7: Advanced Power Flow Topics Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign overbye@illinois.edu

Announcements • No class Sept 24 because of NAPS • HW 2 is due Sept 19

Power Down a Line • The power flowing into transmission line k, going between buses i and j, with impedance Rk + jXk and charging of Yc,k at bus iis

37 Bus Example Design Case This is Design Case 2 From Chapter 6 of Power System Analysis andDesign by Glover, Sarma, and Overbye, 4th Edition, 2008 PowerWorld Case: TD_2012_Design2

Good Power System Operation • Good power system operation requires that there be no reliability violations for either the current condition or in the event of statistically likely contingencies • Reliability requires as a minimum that there be no transmission line/transformer limit violations and that bus voltages be within acceptable limits (perhaps 0.95 to 1.08) • Example contingencies are the loss of any single device. This is known as n-1 reliability.

Looking at the Impact of Line Outages Opening one line (Tim69-Hannah69) causes an overload. This would not be allowed

Contingency Analysis Contingencyanalysis providesan automaticway of lookingat all the statisticallylikely contingencies. Inthis example thecontingency set Is all the single line/transformeroutages

Power Flow And Design • One common usage of the power flow is to determine how the system should be modified to remove contingencies problems or serve new load • In an operational context this requires working with the existing electric grid • In a planning context additions to the grid can be considered • In the next example we look at how to remove the existing contingency violations while serving new load.

An Unreliable Solution Case now has nine separate contingencies with reliability violations

A Reliable Solution Previous case was augmented with the addition of a 138 kV Transmission Line PowerWorld Case: TD_2012_Design2_ReliableDesign

Generation Changes and The Slack Bus • The power flow is a steady-state analysis tool, so the assumption is total load plus losses is always equal to total generation • Generation mismatch is made up at the slack bus • When doing generation change power flow studies one always needs to be cognizant of where the generation is being made up • Common options include system slack, distributed across multiple generators by participation factors or by economics

Generation Change Example 1 PowerWorld Case: TD_2012_37Bus_GenChange

Generation Change Example 1 Display shows “Difference Flows” between original 37 bus case, and case with a BLT138 generation outage; note all the power change is picked up at the slack

Generation Change Example 2 Display repeats previous case except now the change in generation is picked up by other generators using a participation factor approach

Generator Reactive Limits • Generators are P-V buses (P and V are specified). • QGiof generator i must be within specified limits • During the PF solution process • the bus is now a P-Q bus and the originally specified V at this bus is relaxed and calculated.

Voltage Regulation Example: 37 Buses Display shows voltage contour of the power system, demo will show the impactof generator voltage set point, reactive power limits, and switched capacitors PowerWorld Case: TD_2012_37Bus_Voltage

Remote Regulation and Reactive Power Sharing • It is quite common for a generator to control the voltage for a location that is not its terminal • Sometimes this is on the high side of the generator step-up transformer (GSU), sometimes it is partway through the GSU • It is also quite common for multiple generators to regulate the same bus voltage • In this case only one of the generators can be set as a PV bus; the others must be set as PQ, with the total reactive power output allocated among them • Different methods can be used for allocating reactive power among multiple generators

Multiple PV Generator Regulation In this caseboth theBus 2 andBus 4 gensare set to regulatethe Bus 5voltage. Note, theymust regulate itto the samevalue!! PowerWorld Case: B7Flat_MultipleGenReg

NR Initialization • A textbook starting solution for the NR is to use “flat start” values in which all the angles are set to the slack bus angle, all the PQ bus voltages are set to 1.0, and all the PV bus voltages are set to their PV setpoint values • This approach usually works for small systems • It seldom works for large systems. The usual approach for solving large systems is to start with an existing solution, modify it, then hope it converges • If not make the modification smaller • More robust methods are possible, but convergence is certainly not guaranteed!!

Modeling Transformers with Off-Nominal Taps and Phase Shifts • If they have a turns ratio that matches the ratio of the per unit voltages than transformers are modeled in a manner similar to transmission lines. • However it is common for transformers to have a variable tap ratio; this is known as an “off-nominal” tap • Phase shifting transformers are also used sometimes, in which there is a phase shift across the transformer

m k Transformer Representation • The one–line diagram of a branch with a variable tap transformer • The network representation of a branch with off–nominal turns ratio transformer is

t :1 k the tap is on the side of bus k Transformer Representation where t denotes the tap setting value • We first recall that for an ideal transformer

Transformer Representation • In the p.u. system, the transformer ratio is 1:1 if and only if this ratio equals the system nominal voltage ratio • For off-nominal conditions, the turns ratio is obtained as a ratio of two p.u.quantities

Ideal Transformer Representation secondary side of transformer primary side of transformer t : 1 + + – –

Transformer Nodal Equations • From the network representation • Also,

Transformer Nodal Equations • We may rewrite these two equations asThis approach is presented in F.L. Alvarado, “Formation of Y-Node using the Primitive Y-Node Concept,” IEEE Trans. Power App. and Syst., December 1982

k m THE  – EQUIVALENT CIRCUIT FOR A TRANSFORMER BRANCH

Variable Tap Voltage Control • A transformer with a variable tap, i.e., the variable t is not constant, may be used to control the voltage at either the bus on the side of the tap or at the bus on the side away from the tap • This constitutes an example of single criterion control since we adjust a single control variable– the transformer tap t – to achieve a specified criterion: the maintenance of a constant voltage at a designated bus

Variable Tap Voltage Control • A typical power transformer may be equipped with both fixed taps, on which the turns ratio is varied manually at no load, and automatic tap changing under load (TCUL) or variable taps ratio transformers • For example, the high-voltage winding might be equipped with a nominal voltage turns ratio plus four 2.5% fixed tap settings to yield  5% buck or boost voltage capability

Variable Tap Voltage Control • In addition to this, there may be on the low-voltage winding, 32 incremental steps of 0.625% each, giving an automatic range of 10% • It follows from the –equivalent model for the transformer that the transfer admittance between the buses of the transformer branch and the contribution to the self admittance at the bus away from the tap explicitly depend on t • However, the tap changes in discrete steps; there is also a built in time delay in how fast they respond • Voltage regulators are devices with a unity nominal ratio, and then a similar tap range

Ameren Champaign Test Facility Voltage Regulators These are connectedon the low side of a 69/12.4 kV transformer; eachphase can beregulated separately

LTCs in the Power Flow • LTCs (or voltage regulators) can be directly included in the power flow equations by modifying the Ybus entries; that is by scaling the terms by 1, 1/t or 1/t^2 as appropriate • If t is fixed then there is no change in the number of equations • If t is variable, such as to enforce a voltage equality, then it can be included either by adding an additional equation and variable (t) directly, or by doing an “outer loop” calculation in which t is varied outside of the NR solution

Five Bus PowerWorld Example With an impedanceof j0.1 pu betweenbuses 4 and 5, the y node primitive with t=1.0 is If t=1.1 then it is PowerWorld Case: B5_Voltage

Outer Loop Tap Control • The challenge with implementing tap control in the power flow is it is quite common for at least some of the taps to reach their limits • Keeping in mind a large case may have thousands of LTCs! • If this control was directly included in the power flow equations then every time a limit was encountered the Jacobian would change • Also taps are discrete variables, so voltages must be a range • Doing an outer loop control can more directly include the limit impacts; often time sensitivity values are used in the calculation

ECE 530 – Analysis Techniques for Large-Scale Electrical Systems