Lecture 2 Intelligent Energy Systems: Monitoring Basics · Lecture 2 Intelligent Energy Systems: Monitoring Basics Dimitry Gorinevsky Seminar Course 392N Spring2012 . Traditional

ee392N - Spring 2012 Stanford University

Intelligent Energy Systems © Dimitry Gorinevsky

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Lecture 2 Intelligent Energy Systems:

Monitoring Basics

Dimitry Gorinevsky

Seminar Course 392N ● Spring2012

Traditional Grid

• Worlds Largest Machine! – 3300 utilities – 15,000 generators, 14,000

TX substations – 211,000 mi of HV lines

(>230kV)

• A variety of interacting information decision and control systems


2 Intelligent Energy Systems © Dimitry Gorinevsky

Smart Energy Grid

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Conventional Electric Grid

Generation Transmission

Distribution Load

Intelligent Energy Network

Load IPS

Source IPS

energy subnet

Intelligent Power Switch

Conventional Internet ee392N - Spring 2012 Stanford University


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Outline

1. Monitoring Applications 2. Statistical Process Control - SPC 3. Multivariate SPC – MSPC 4. Principal Component Analysis - PCA



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Business Logic

Internet Applications



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Database

Presentation Layer

Backend

Computer

Tablet Smart phone

Internet

CRM and ad analytics Portfolio optimization Decision support Fraud detection

Business Logic

Intelligent Energy Applications



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Database

Presentation Layer

Computer

Tablet Smart phone

Internet Communications

Energy Application

Application Logic (Intelligent Functions)



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Control Functions

• Control function in a systems perspective – Closed loop



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Monitoring & Decision Support

• Monitoring functions are open-loop - Data presentation to a user

Power Generation Time Scales



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Power Supply Scheduling

• Power generation and distribution • Energy supply side

Time (s) 1/10 10 1000 1 100 http://www.eeh.ee.ethz.ch/en/eeh/education/courses/viewcourse/227-0528-00l.html

Anomalies & Sustainment

Power Demand Time Scales • Power consumption

– DR, Homes, Buildings, Plants

• Demand side



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Demand Response

Home Thermostat

Building HVAC

Enterprise Demand Scheduling

Time (s) 100 1,000 10,000

Anomalies & Sustainment



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Monitoring Goals

• Situational awareness – Anomaly detection – State estimation

• System health management – Fault isolation – Condition based maintenances



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Condition Based Maintenance

• DOD CBM+ Initiative

Outline

1. Monitoring Applications 2. Statistical Process Control - SPC 3. Multivariate SPC – MSPC 4. Principal Component Analysis - PCA



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Anomaly Detection - SPC

• SPC - Statistical Process Control – Introduced for monitoring of manufacturing processes – Warning for off-target quality

• SPC vs. EPC – Engineering Process Control = feedback control

• Main SPC method – Shewhart Chart (Control Chart)

• Other SPC methods – EWMA, CuSum, Western Electric Rules

Plant/System Data

Exceedance Monitoring

• Currently used in most monitoring systems • Example: grid frequency deviation from 60Hz

– Empirical exceedance threshold



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Monitoring Function: Exceedance

Detected Anomalies



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SPC: Shewhart Control Chart • W.Shewhart, Bell Labs, 1924 • Statistical Process Control (SPC) • UCL = µ + 3·σ • LCL = µ - 3·σ

Walter Shewhart (1891-1967)

sample 3 6 9 12 12 15

mean µ

qual

ity v

aria

ble

Lower Control Limit

Upper Control Limit

Exceedance / Out of control



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Shewhart Chart, cont’d • Quality variable assumed randomly

changing around a steady state • Detection: y(t) > UCL = µ + 3·σ • For a normal distribution, false alarm

probability is 0.27%

P(z > 3) = 1-Φ(3) = 0.1350·10-2 P(z < 3) = Φ(-3) = 0.1350·10-2

σµ−

=)()( tytz

UCL LCL



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SPC: Use Examples

• SPC in manufacturing • Fault monitoring for PHM/CBM • Sensor integrity monitoring

– Fault tolerance and redundancy management

Sensor

Reference - +

Fault

|v| < 3σ Normal yes

no

Outline

1. Monitoring Applications 2. Statistical Process Control - SPC 3. Multivariate SPC – MSPC 4. Principal Component Analysis – PCA



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Multivariate SPC • Univariate process: y(t)

• Two univariate processes

( ))(1)(

)1,(1 222

cccFczP

Φ−+−Φ=−=>2

202 ~ χ

σµ

−

=yz

Chi-squared CDF



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MSPC Explanation

• MSPC=Multivariate Statistical Process Control • Scatter plot for correlated channels

Time series data Keep the data values, ignore the time stamp

y1(t)

y2(t)

y1

y2



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Multivariate SPC

• Two correlated univariate processes y1(t), y2(t)

=

2

1

yy

y

=

2

1

µµ

µ

cov(y) = P

multivariate outlier: out of control



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Whitened Variables

• Uncorrelated linear combinations z(t) = L·[y(t)-µ]

LTL= P-1 cov(z) = I

• Declare fault (anomaly) if

( ) ( ) 22

12 ~ χµµ −−= − yPyz T

( ) )2;(1 222 cFczP −=>

( ) ( ) 21 cyPy T >−− − µµ

CDF for Chi-squared with 2 DOF

Plant / System Data

Multivariate Monitoring



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Monitoring data processing:

Advisory Info: • Anomaly

Historical Data Set

Models: Performance, Noise

xPxT

yxT 12 ˆ

ˆ−=

−= µ)(ty

P̂,µ̂

22 cT >



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Hotelling's T2

• Empirical parameter estimates

( )

( )µµµ

µ

−≈−−=

≈=

∑

∑

=

=

ytytyN

P

yEtyN

TN

t

N

t

cov)ˆ)()(ˆ)((1ˆ

)(1ˆ

1

1

• Hotelling's T 2 two-sample statistics is

• T 2 distribution differs from since are

considered as random variables, y(t) ~ N(µ,P)

Harold Hotelling (1895-1973)

2χ µ̂,P̂

( ) ( )µµ ˆ)1(ˆˆ)1( 11

2 −+−+⋅= −+ NyPNyT T

NN

Multivariate SPC with T2

• The anomaly detection decision is • Threshold c is defined by the false positive/false

negative tradeoff based on the distribution

where F is the Fisher-Snedecor’s F-distribution p is the dimension of the data vector y N is the size of the training data set ee392N - Spring 2012 Stanford University


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22 cT >

pNpFpN

pNT −−−

,2

)()1(~

Outline

1. Monitoring Applications 2. Statistical Process Control - SPC 3. Multivariate SPC – MSPC 4. Principal Component Analysis – PCA



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PCA

• PCA = Principal Component Analysis

• What if empirical covariance P=XXT/N is not invertible? Cannot compute xTP-1x – This happens in most real cases

• SVD of the data and covariance matrix X = U⋅ S⋅ VT = ∑k uk skvk

T

XXT= U⋅ S2⋅ UT = ∑k uk sk2uk

T

VTV = I ee392N - Spring 2012

Stanford University Intelligent Energy Systems

© Dimitry Gorinevsky 29

Scores

Loadings

[ ]µµµ ˆ)(ˆ)2(ˆ)1( −−−= NyyyX

PCA Structure

• Singular vectors (principal components) U = [UR U0]

UR - Range Space; nonzero singular values, sk > 0 U0 - Null Space; zero singular values, sk=0

>>[U,S,W]=svd(X*X’) % 2ms for 100x100



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• Singular values sk

nonzero

‘zero’

k

PCA, T2, and Q statistics

• T2 statistics is used in Range Space of P is Range Space projection of x

• Range Space: covariance is invertible

• Must also monitor Null Space projection • Q statistics: Q = xTU0U0 x

– a.k.a. SPE (squared prediction error)



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2RxxQ −=

xUUx RTRR =

RRTR xPxT 12 −=

PCA, T2, and Q Summary



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Q T2

principal component #2

principal component #1

PCA Prediction Model

• Null space defines linear dependency between monitored variables

U0x = v ≈ 0 m linear equations • Can be interpreted as a dependence between two

subsets of variables

• SPE yields model prediction error:



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=

zy

x vbzy +=m

k

2bzy −

End of Lecture 2



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Documents

Lecture 2 Intelligent Energy Systems: Monitoring Basics · Lecture 2 Intelligent Energy Systems: Monitoring Basics Dimitry Gorinevsky Seminar Course 392N Spring2012 . Traditional