Electric Power System Modeling & Simulation

Michael Smith

02/15/2010

Outline• Introduction

• Power System Introduction/Background

• Data Requirements

• Model/Simulation Development

• Analysis

• Conclusion

IntroductionObjective:

• Understand the behavior of Electric Power (EP) systems

Properties of EP systems:

• Large scale, complicated, dynamic and nonlinear

• Composed of interdependent, heterogeneous components

• Result from incremental evolution in system configuration driven by response to failures and adoption of innovation

• Possess considerable system structure (e.g., power law statistics, HDS configuration)

100

101

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10-3

10-2

10-1

100

North American Power System Outages (NERC Data 1984-2002)

Fre

quency o

f outa

ge

Number of customers affected by outage

2003 NE Outage

1965 NE Outage

1977 NY Outage

1996 Western Outage

Introduction/Motivation

The Cost of “Unreliability”

• Since 9/11, [reported] attacks on industrial process control systems have increased 10 fold

• 10 second electric power outage at LAX– Tower-to-tower communication

lost for three hours– Approximately 80 – 100 flights

delayed

• Ohio nuclear power plant disrupted by SQL Slammer worm

• Stock market crashes

August 14th Blackout1

2 Canadian Provinces

8 U.S. states

3 deaths

12 airports closed

23 cases of looting in Ottawa

100 power plants

9,266 square miles

61,800 MW of power lost

1.5 million Cleveland residents

without water

50 million people

$4-6 billion in economic activity lost

1. US DOE, Office of Electric Transmission and Distribution, December 1, 2003, Bill Parks

Power System Background

Pictorial View

• Components

• Generation Station, Transmission network, Substation, Loads

• Key Terms

• Voltage, Power, Load flow, Steady State, Transient, Dynamic

jX1

jX2

V0 0 V

generation station transmission lines substation load

Power Systems Background

Model view

Data Required for ModelingData for Load-Flow/Power-Flow Model

The first type of data requested is that needed to develop a load-flow/power-flow model of a power system area:– topology of the area with connection points (busses) as nodes and transmission lines and transformers

as edges, – transmission line parameters such as pi-model parameters, compensation and ratings/limits, – transformer parameters such as pi-model, turns ratio and ratings/limits, – tie-line locations and ratings, – generation location and ratings/limits, – load locations and load compensation, and – any complete load-flow/power-flow solutions for area (from model or instrumentation) with data

mentioned above, generator powers, load powers, line powers, and bus voltages and phase angles. Data for Dynamic Model

In order to perform transient analysis and stability studies additional power system data is required to supplement that identified above for load-flow/power-flow models. Example data that would assist with construction of a dynamic model include: – number, size and type of generators with any available mechanical, electrical, and control (governor,

voltage regulation, etc.) parameters, – mix of residential, commercial and industrial load at each bus,– location and specifications for distributed control devices such as tap-changing transformers, switched

shunt compensation, static Var compensators, flexible AC transmission systems, etc., – location and specifications for protection devices such as relays and load shedding, and– location and specifications of any other relevant control and/or protection devices.

Data for Model ValidationTime-series data (generator powers, load powers, line powers, voltages, voltage phase angles, frequency, currents, etc.) recorded from the power system in response to short-term load fluctuation, 24-hour load variation or known disturbance is requested to support model validation studies and dynamic grid analysis. Data captured over the short term would be sampled at sub-second or faster while long-term would be sampled on intervals of 15 minutes.

Sinusoidal Steady-State Analysis

Detailed Model View• Equivalent π transmission line models• Single phase assuming 3 phases are symmetrical• p.u. (per unit system) ease of power system analysis

Complex Current Injections & Network Line Powers

Real/Imaginary Network & Power Balance Equations

Simplified Generator/Load Equations

• Internal generator dynamics

• Fixed load model

– Power (fixed)

– Internal dynamics (none)

Model

disturbances

set points

mode

changesgrid

outputs

discrete system:

switching and saturation

qi+1 = h(qi, k(x,y), r)

q1

q0

q2

continuous system:

generators, loads and network

dx/dt = fq(x, y, u)

0 = gq(x, y)

G

GL

L

Hybrid Dynamical System (HDS)

ModelKey features:

• physics-based models of network, generators (electromechanical), and loads (aggregate)

• emphasis placed upon– capturing saturation and switching behavior

– drawing conclusions about system behavior (time evolution governed by dynamics) with limited data and uncertainty

– keeping an eye towards analysis

• Both dynamic and steady-state representations for the model

Model: dynamic vs. static modelHDS Model

qi+1 = h(qi, k(x,y), r)

dx/dt = fq(x, y, u)

0 = gq(x, y)

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0.2

0.4

0.6

0.8

1

Area C Load Busses

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Static (load flow) Model

0 = f(x, y, u)

0 = g(x, y)

(switching is exogenous)

0 50 100 150 200 250 300 350 400 450 5000.9

0.95

1

1.05Area C Load Busses

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static (equilibrium)

solutions

trajectory

Questions