ANN-Based Operational Planning of Power Systems

M. E. El-Hawary

Dalhousie University

Halifax, Nova Scotia, Canada

7th Annual IEEE Technical Exchange Meeting, April 18-19, 2000

Saudi Arabia Section, and KFUPM

What am I to do?• I suspect that the

audience includes people who are not power-oriented.

• Offer a generic presentation.

• Power examples are easily related to other areas.

ANN Basics

Emulate behavior of systems of neurons.

A neuron nudges its neighbor in proportion to its stimulus.

The strength of the nudge is a weight.

Sum the weighted stimuli.

Scale using sigmoidal function

Basic Neuron Model

)( ii

j

m

iji

ufv

xWu

1

W1j

W2j

W3i

Neuron ix1

x2

x3

vi

Sigmoid Function

• Use plain sigmoid formula

01

1)(

u

uii i

e

ug

V f uu

ui i ii

( ) . tanh05 10

Alternatively

x1 xj

xm

y1 ynyi

W1q

v1q

q

Three Layer Back Propagation Network

The Process• Learning based on training patterns.• Initialize weights.• Present training patterns and successively update

weights.• Updates initially based on steepest decscent.• Current trend is to use an appropriate NL descent

method.• Iterate on weights until no further improvements.

Hopfield Network•Each neuron contains two op amps.

•The output of neuron j is connected to input of neuron i through a conductance Wij

HNN Formulae

ii

iii

i

jiji

ij

VVI

VVTE

5.0

Energy Function Neuron Dynamics

dU

dtT V Iiij

jj i

U TV Ii iji j

j i

General Idea• Take NLP problem

Minimize f x

Subject to g x

h(x) > 0

( )

( ) 0

MappingIgnore inequality constraintsRelate variable X to neuron output V E F V G Vi

ii ( ) [ ( )]2

The energy function will contain the m equality constraint terms in addition to the objective.

Sample Operational Planning Problems• Unit Commitment

• Economic Dispatch

• Environmental Dispatch

• Dynamic Dispatch

• Maintenance Scheduling

• Expansion Planning

Unit Commitment• Given a set of available generating units

and a load profile over an optimization horizon.

• Find the on/off sequence for all units for optimal economy.

• Recognize start up and running costs.

Constraints• Minimum up and down times

• Ramping limits.

• Power balance

Economic Dispatch

• Find optimal combination of power generation to minimize total fuel cost.

• We know the cost model parameters:

C a b P c Pi i i i ii

2

Constraints• Meet power balance equation including

losses.

• L represents the losses and D is the demand

• Losses are assumed constant

D L Pii

L B PPijji

i j

• Satisfy upper and lower limits on power generations

P P Pi i i

NN Aided Unit Commitment

B ack P rop ag a tion Typ e H op fie ld Typ e

A p p roach es

Back Propagation Assisted Unit Commitment

Multi-stage ApproachAN N -Priority L ist-AN N R efined

H ybrid AN N / R efinedD ynam ic P rogram m ing

Pattern Matching AN NBack P ropagation Type

Approach A-1Multi-stage Approach

ANN-Priority List-ANN Refined

• Ouyang and Shahidehpour (May 1992)

• Three stage process

• Stage 1: ANN Prescheduling

• Stage 2: Priority based heuristics.

• Stage 3: ANN Refinement

• Obtain a set of load profiles & corresponding commitment schedules.

• Cover basic categories of days.

• Train ANN.

• Feed forecast load to trained ANN.

• Output of ANN is a preschedule.

Stage 1:ANN Prescheduler

Pre-scheduling (cont.)• Input is 24 x N matrix.

• N is load demand segments.

• Each matrix element is related to a neuron in the input layer.

• Each training load pattern corresponds to an index number in the output layer

Pre-scheduling (cont.)• Recommends 50 to 100 training patterns.

• NN prescheduling saves time and offers better matching.

Stage 2:Sub-optimal Schedule

• Consider outcome of prescheduling.

• Use priority list.

• Check minimum up and down times.

• Examine on/off status of units and modify.

Stage 3:ANN Schedule Refiner

• Trained using pairs of sub-optimal solutions as input and optimal solution as output.

• NN generalizes the refinement rule.

• Used three different techniques.

Training Pattern Generation(Cont.)

• Operator generated better unit commitment solutions.

• Base units are not involved in the refinement process.

Hopfield Implementaions• Usually BP Nets are good at pattern

recognition.

• For optimization problems, the Hopfield network has been shown to be more effective.

• By way of example, we show the application to economic dispatch.

Mapping ED to HNN• Write the energy function as:

E A D L P

Ba b P c P

ii

i i i i ii

2

2

2

• Finds mappings as:

T A Bc

T A

I A D L Bb

ii i

ij

i i

( ) .05

Improvements

Choose large AUse momentum term

u t u t u t

u ti i i

i

( ) ( ) ( )

( )

1

1

What Else?• Virtually every area involving prediction or

optimization has been treated using ANN.

• Examples include hand movement animation.

• Computer communication network congestion management.

• Computer communication network routing

Thanks• I hope that we

learned something together.

• Thanks to all of you, and specially Dr. Samir Al-Baiyat and the Organizing Committee