a power flow method using a new bus type for computing ... · • if the load bus voltage angle is...

Rensselaer Polytechnic Institute Electrical, Computer, and Systems Engineering

EPCC Workshop – 06/03/2013 J. H. Chow 1

12th International Workshop on Electric Power Control Centers

A Power Flow Method using a New Bus Type for

Computing Steady-State Voltage Stability Margins

Scott G. Ghiocel and Joe H. Chow

Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute

June 3, 2013



• NSF/DOE CURENT ERC: Center for Ultra-wide Resilient Electric Energy Transmission Networks

• DOE CERTS: Voltage stability applications using synchrophasor data, in collaboration with BPA and SCE

Voltage Stability Projects at Rensselaer



CERTS Project Overview

• Traditional voltage stability analysis approaches

• Full-order detailed model – off-line analysis ; real-time analysis with SCADA measurements or SE solutions; an example is the VSTAB program; high computation burden and dependent on the load model

• Single-load stiff-bus model, such as the voltage instability predictor (VIP) approach; applicable to radial systems, and also dependent on load models

• This project aims at developing an alternative (hybrid) approach with less computation than VSTAB type programs, but capable of handling more complex power transfer paths

Increasing level of complexity

Single load center, VIP model

Full detailed model, SCADA based

Hybrid model, PMU based, high-voltage

transmission grid



Project Overview

• Consider the voltage stability analysis of a more complex power transfer path like the Pacific AC Intertie:

• Network characteristics

• Large number of injection and out flow points

• Loads with multiple infeeds

• Important to know

• PMU data – as a means of obtaining actual voltage sensitivity and measuring injections and outflows

• Network parameters

• Flow sensitivities at injection and outflow points

• Multiple vulnerabilities and reactive power supply at each location

The Dalles

(3)Inflow

Grizzly

(3)

Malin

(2) (2) (2)R. Mtn T. Mtn

(1) Tracy/ Tesla

Moss Landing

Inflow

(3)

Diablo Canyon

Inflow

(2)

Midway

(3)

Vincent

Victorville/ Adelanto

To other load buses

Inflow from East



PMU-Based Voltage Stability Analysis for New York

• Use PMU data from loss-of-generation disturbance events to construct external system equivalents (at Buses 1, 2, 3, 7, and 8)

• Compute PV-curves using PMU data-based model

7

3

2

5 9

4

6

1

SVC

8External

system



PV Curves for a Stability Interface in Central NY

0 2 4 6 8 10 12 14

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

Change in Power Transfer (p.u.)

Vo

ltag

e M

ag

nit

ud

e (

p.u

.)

Bus 1 Data

Bus 1 Model

Bus 8 Data

Bus 8 Model

SVC Saturation Limit



Steady-State Voltage Stability Margin Calculation

• Difficulty – the power flow Jacobian J becomes singular at the voltage collapse point. The Newton-Raphson method does not converge, sometimes far from the voltage collapse point (the Gauss-Seydel method will have same problem).

• Method of homotopy (continuation power flow method) – introduces a load parameter so that the dimension of Jacobian matrix J increases by 1 to make J nonsingular. Special software packages using such methods to compute voltage stability (VS) margin have been developed, such as CPFLOW.

• Our approach – define a new bus type and take the singularity directly out of J



Single-Load Stiff-Bus System

• Treating the load bus as a PQ bus, the Jacobian is

• The Jacobian is singular when



Single-Load Stiff-Bus System

• Voltage stability analysis with constant power factor loads



Load Bus Angle Variations

• Load bus voltage angle is seldom analyzed in this context



New Idea of Specifying Load Bus Voltage Angle

• If the load bus voltage angle is specified, the power flow analysis reduces to 1 nonlinear equation of solving for the reactive power balance at the load bus.

• For a constant power factor load, the reduced Jacobian is

• This value becomes 0 not at the critical voltage collapse point, but at VL = 0 (see right figure on p. 9)



Generalization to Large Power Systems

• Power flow bus types

Bus types Bus representation Fixed values

PV Generator buses Active power generation and bus voltage

PQ Load buses Active and reactive power consumption

AV Swing bus (generator)

Voltage magnitude and angle (A)

AQ Load bus Voltage angle and reactive power consumption



Advantages of using an AQ Bus

• With the angle of the AQ load bus specified, only the reactive power balance equation is included in the load flow solution. Thus the dimension of the reduced Jacobian JR is lowered by 1, eliminating the singularity.

• The active power consumption P at the AQ bus is determined from the converged power flow solution – it cannot be specified ahead of time.

• For voltage stability margin calculation, the AQ bus is designated as one of the buses with large load increases. The separation angle between the swing bus and the AQ bus is progressively increased to generate the PV curve and thus the VS margin.



Advantages of using an AQ Bus

• The AQ-bus method can accommodate constant power factor loads by adjusting the rows of the reduced Jacobian JR

• The method also allows load increases at multiple load buses with supply coming from multiple generators, using only 1 AQ bus

• All features in a regular power flow program can be used, such as sparse factorization, tap changing transformers, reactive power generation limits, and decoupled power flow, because this new method conforms to the power flow program structure



2-Area, 4-machine System Example

• Constant power factor load increase on Bus 14, with supply from Generator 1

• Base case: no var limit on generators; Case 1: var limit on Generator 2



NPCC 48-machine System Example



NPCC 48-machine Gen/Load Schedule

50 36

30

16 15 4



NPCC 48-machine Contingency List

1 2

3 4 5



NPCC 48-machine PV-curve Contingency Analysis

0 2 4 6 8 10 12 14

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Active power loading margin at AQ-bus (Bus 16) (pu)

AQ

-bus (

Bus 1

6)

voltage m

agnitude (

pu)

Line Trip Contingency Analysis based on PV Curves

Base Case

Line 73--74 (72 MW)

Line 8-73 (97 MW)

Line 2--37 (53 MW)

Line 3--2 (295 MW)

Line 3--18 (50 MW)

AQ

Bus

vol

tage

mag

nitu

de (p

u)

Active power margin (ΔP) at AQ Bus (pu)

22

Acknowledgements

This work was supported primarily by the ERC Program of

the National Science Foundation and Department of Energy

under NSF Award Number EEC-1041877.

Other US government and industrial sponsors of CURENT

research are also gratefully acknowledged.

a power flow method using a new bus type for computing ... · • if the load bus voltage angle is...

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