Ece 476 power system analysis
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ECE 476 POWER SYSTEM ANALYSIS. Lecture 13 Power Flow Professor Tom Overbye Department of Electrical and Computer Engineering. Announcements. Be reading Chapter 6, also Chapter 2.4 (Network Equations).

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ECE 476 POWER SYSTEM ANALYSIS

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Ece 476 power system analysis

ECE 476POWER SYSTEM ANALYSIS

Lecture 13

Power Flow

Professor Tom Overbye

Department of Electrical andComputer Engineering


Announcements

Announcements

  • Be reading Chapter 6, also Chapter 2.4 (Network Equations).

  • HW 5 is 2.38, 6.9, 6.18, 6.30, 6.34, 6.38; do by October 6 but does not need to be turned in.

  • First exam is October 11 during class. Closed book, closed notes, one note sheet and calculators allowed. Exam covers thru the end of lecture 13 (today)

  • An example previous exam (2008) is posted. Note this is exam was given earlier in the semester in 2008 so it did not include power flow, but the 2011 exam will (at least partially)


Multi variable example

Multi-Variable Example


Multi variable example cont d

Multi-variable Example, cont’d


Multi variable example cont d1

Multi-variable Example, cont’d


Possible ehv overlays for wind

Possible EHV Overlays for Wind

AEP 2007 Proposed Overlay


Nr application to power flow

NR Application to Power Flow


Real power balance equations

Real Power Balance Equations


Newton raphson power flow

Newton-Raphson Power Flow


Power flow variables

Power Flow Variables


N r power flow solution

N-R Power Flow Solution


Power flow jacobian matrix

Power Flow Jacobian Matrix


Power flow jacobian matrix cont d

Power Flow Jacobian Matrix, cont’d


Two bus newton raphson example

Two Bus Newton-Raphson Example

For the two bus power system shown below, use the

Newton-Raphson power flow to determine the

voltage magnitude and angle at bus two. Assume

that bus one is the slack and SBase = 100 MVA.


Two bus example cont d

Two Bus Example, cont’d


Two bus example cont d1

Two Bus Example, cont’d


Two bus example first iteration

Two Bus Example, First Iteration


Two bus example next iterations

Two Bus Example, Next Iterations


Two bus solved values

Two Bus Solved Values

Once the voltage angle and magnitude at bus 2 are

known we can calculate all the other system values,

such as the line flows and the generator reactive

power output


Two bus case low voltage solution

Two Bus Case Low Voltage Solution


Low voltage solution cont d

Low Voltage Solution, cont'd

Low voltage solution


Two bus region of convergence

Two Bus Region of Convergence

Slide shows the region of convergence for different initial

guesses of bus 2 angle (x-axis) and magnitude (y-axis)

Red region

converges

to the high

voltage

solution,

while the

yellow region

converges

to the low

voltage

solution


Pv buses

PV Buses

  • Since the voltage magnitude at PV buses is fixed there is no need to explicitly include these voltages in x or write the reactive power balance equations

    • the reactive power output of the generator varies to maintain the fixed terminal voltage (within limits)

    • optionally these variations/equations can be included by just writing the explicit voltage constraint for the generator bus |Vi| – Vi setpoint = 0


Three bus pv case example

Three Bus PV Case Example


Ece 476 power system analysis

The N-R Power Flow: 5-bus Example

T2

800 MVA

345/15 kV

T1

1

5

4

3

520 MVA

Line 3 345 kV

50 mi

400 MVA

15 kV

800 MVA

15 kV

400 MVA

15/345 kV

345 kV 100 mi

40 Mvar

80 MW

345 kV 200 mi

Line 2

Line 1

2

280 Mvar

800 MW

Single-line diagram


Ece 476 power system analysis

The N-R Power Flow: 5-bus Example

Table 1.

Bus input

data

Table 2.

Line input data


Ece 476 power system analysis

The N-R Power Flow: 5-bus Example

Table 3.

Transformer

input data

Table 4. Input data

and unknowns


Ece 476 power system analysis

Time to Close the Hood: Let the Computer Do the Math! (Ybus Shown)


Ybus details

Ybus Details

Elements of Ybus connected to bus 2


Here are the initial bus mismatches

Here are the Initial Bus Mismatches


And the initial power flow jacobian

And the Initial Power Flow Jacobian


Ece 476 power system analysis

And the Hand Calculation Details!


Five bus power system solved

Five Bus Power System Solved


37 bus example design case

37 Bus Example Design Case


Good power system operation

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.

North American Electric Reliability Corporation now has legal authority to enforce reliability standards (and there are now lots of them). See http://www.nerc.com for details (click on Standards)


Looking at the impact of line outages

Looking at the Impact of Line Outages

Opening one line (Tim69-Hannah69) causes an overload. This would not be allowed


Contingency analysis

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

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

An Unreliable Solution

Case now has nine separate contingencies with reliability violations


A reliable solution

A Reliable Solution

Previous case was augmented with the addition of a 138 kV Transmission Line


Generation changes and the slack bus

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

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

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


Voltage regulation example 37 buses

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


Solving large power systems

Solving Large Power Systems

  • The most difficult computational task is inverting the Jacobian matrix

    • inverting a full matrix is an order n3 operation, meaning the amount of computation increases with the cube of the size size

    • this amount of computation can be decreased substantially by recognizing that since the Ybus is a sparse matrix, the Jacobian is also a sparse matrix

    • using sparse matrix methods results in a computational order of about n1.5.

    • this is a substantial savings when solving systems with tens of thousands of buses


Newton raphson power flow1

Newton-Raphson Power Flow

  • Advantages

    • fast convergence as long as initial guess is close to solution

    • large region of convergence

  • Disadvantages

    • each iteration takes much longer than a Gauss-Seidel iteration

    • more complicated to code, particularly when implementing sparse matrix algorithms

  • Newton-Raphson algorithm is very common in power flow analysis


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