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ECE 530 – Analysis Techniques for Large-Scale Electrical Systems Prof. Hao Zhu Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign 9/16/ Lecture 7: Advanced Power Flow Topics

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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. 2

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37 Bus Example Design Case This is Design Case 2 From Chapter 6 of Power System Analysis and Design by Glover, Sarma, and Overbye, 4 th Edition, 2008 PowerWorld Case: TD_2012_Design2 3

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Looking at the Impact of Line Outages Opening one line (Tim69-Hannah69) causes an overload. This would not be allowed 4

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Contingency Analysis Contingency analysis provides an automatic way of looking at all the statistically likely contingencies. In this example the contingency set is all the single line/ transformer outages (N-1 rule) 5

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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. 6

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An Unreliable Solution Case now has nine separate contingencies with reliability violations 7

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A Reliable Solution Previous case was augmented with the addition of a 138 kV Transmission Line 8 PowerWorld Case: TD_2012_Design2_ReliableDesign

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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 9

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Generation Change Example 1 10 PowerWorld Case: TD_2012_37Bus_GenChange

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Generation Change Example 1 Display shows “Difference Flows” between original 37 bus case, and case with a BLT138 generation outage; note without AGC all the power change is picked up at the slack 11

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Generation Change Example 2 Display repeats previous case except now the change in generation is picked up by other generators using a participation factor AGC approach 12

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Generator Reactive Limits Generators are P-V buses (P and V are specified). Q Gi of 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. 13

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Voltage Regulation Example: 37 Buses Display shows voltage contour of the power system, demo will show the impact of generator voltage set point, reactive power limits, and switched capacitors 14 PowerWorld Case: TD_2012_37Bus_Voltage

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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 15

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Multiple PV Generator Regulation 16 PowerWorld Case: B7Flat_MultipleGenReg In this case both the Bus 2 and Bus 4 gens are set to regulate the Bus 5 voltage. Note, they must regulate it to the same value!!

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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 17

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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 Transformer Representation k m the tap is on the side of bus k k t :1

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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

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Recall an ideal transformer with t as the tap setting value Ideal Transformer

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Transformer Nodal Equations From the network representation Also,

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Transformer Nodal Equations We may rewrite these two equations as This 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

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–equivalent Circuit for Transformer Branch k m

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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

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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

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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

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Ameren Champaign Test Facility Voltage Regulators 27 These are connected on the low side of a 69/12.4 kV transformer; each phase can be regulated separately

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Variable Tap Voltage Control LTCs (or voltage regulators) can be directly included in the power flow equations by modifying the Y bus 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

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Five Bus PowerWorld Example 29 PowerWorld Case: B5_Voltage With an impedance of j0.1 pu between buses 4 and 5, the y node primitive with t=1.0 is If t=1.1 then it is

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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; usually sensitivity values are used in the calculation 30

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Phase-Shifting Transformers Phase shifters are transformers in which the phase angle across the transformer can be varied in order to control real power flow – Sometimes they are called phase angle regulars (PAR) – Quadrature booster (British usage) They are constructed by include a delta- connected winding that introduces a 90º phase shift that is added to the output voltage Image:

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Phase-Shifter Model We develop the mathematical model of a phase shifting transformer as a first step toward our study of its simulation Let buses k and m be the terminals of the phase–shifting transformer The latter differs from an off–nominal turns ratio transformer in that its tap ratio is a complex quantity, i.e., a complex number 32

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Phase-Shifter Model For a phase shifter located on the branch (k, m), the admittance matrix representation is obtained analogously to that for the LTC Note, if there is a phase shift then the Ybus is no longer symmetric!! In a large case there are almost always some phase shifters

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Phase-Shifter Representation one-line diagram of a branch with a variable phase shifting transformer network representation of a branch with a variable phase shifting transformer k : 1 m k m tap is on the side of bus k

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Integrated Phase-Shifter Control Phase shifters are usually used to control the real power flow on a device Similar to LTCs, phase-shifter control can either be directly integrated into the power flow equations (adding an equation for the real power flow equality constraint, and a variable for the phase shifter value), or they can be handled in with an outer loop approach As was the case with LTCs, limit enforcement often makes the outer loop approach preferred 35

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Two Bus Phase Shifter Example 36 PowerWorld Case: B2PhaseShifter Top line has x=0.2 pu, while the phase shifter has x=0.25 pu.

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