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    Load Forecasting

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    yogi_maha
    The document discusses load forecasting techniques. It covers classification of loads, approaches to load forecasting including extrapolation and correlation methods. It describes requirements for load forecasting such as data collection and validation. Key factors influencing electricity demand are identified such as demographic growth, policies, and economic growth. Load forecasting is described as necessary for electricity sector planning, development projects, and supply reviews. Forecasting methodologies including short, medium, and long term are covered. Extrapolation and correlation forecasting techniques are summarized.

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    Load Forecasting

    Uploaded by

    yogi_maha
    877 views30 pages
    The document discusses load forecasting techniques. It covers classification of loads, approaches to load forecasting including extrapolation and correlation methods. It describes requirements for load forecasting such as data collection and validation. Key factors influencing electricity demand are identified such as demographic growth, policies, and economic growth. Load forecasting is described as necessary for electricity sector planning, development projects, and supply reviews. Forecasting methodologies including short, medium, and long term are covered. Extrapolation and correlation forecasting techniques are summarized.

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    electrical load forecasting

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    The document discusses load forecasting techniques. It covers classification of loads, approaches to load forecasting including extrapolation and correlation methods. It describes requirements for load forecasting such as data collection and validation. Key factors influencing electricity demand are identified such as demographic growth, policies, and economic growth. Load forecasting is described as necessary for electricity sector planning, development projects, and supply reviews. Forecasting methodologies including short, medium, and long term are covered. Extrapolation and correlation forecasting techniques are summarized.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    877 views30 pages

    Load Forecasting

    Uploaded by

    yogi_maha
    The document discusses load forecasting techniques. It covers classification of loads, approaches to load forecasting including extrapolation and correlation methods. It describes requirements for load forecasting such as data collection and validation. Key factors influencing electricity demand are identified such as demographic growth, policies, and economic growth. Load forecasting is described as necessary for electricity sector planning, development projects, and supply reviews. Forecasting methodologies including short, medium, and long term are covered. Extrapolation and correlation forecasting techniques are summarized.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 30

    LOAD FORECASTING

    LOAD FORECASTING
    ØCLASSIFICATION OF LOAD.
    ØCHARACTERISTIC OF LOAD.
    ØAPPROACHES TO LOAD FORECASTING.
    ØFORECASTING METHODOLOGY.
    1.EXTRAPOLATION .
    2.CORRELATION.
    REQUIREMENTS FOR FORECAST
    ØCATEGORIZATION OF CONSUMPTION SECTORS.
    ØCOLLECTION & COMPILATION OF PAST DATA.
    ØDECOMPOSITION OF DATA.
    ØVALIDATION OF PAST DATA & ANALYSIS.
    ØSELECTION OF SUITABLE FORECAST
    TECHNIQUE.
    ØCOLLECTION OF DATA OF ECONOMIC VARIABLES
    FOR ECONOMETRIC MODELLING.
    KEY ISSUES
    ØENERGY SHORTAGE DUE TO RESTRICTIONS &
    UNSCHEDULED CUTS.
    ØENERGY EFFICIENCY & CONSERVATION
    MEASURES.
    ØSPECIAL IMPETUS ON RURAL ELECTRIFICATION &
    IRRIGATION.
    ØTHRUST TO ECONOMICALLY WEAKER STATES &
    REGIONS
    Ø
    FACTORS
    INFLUENCING ELECTRICITY DEMAND
    ØDEMOGRAPHIC GROWTH.
    ØGEOGRAPHIC VARIATIONS.
    ØMETEOROLOGICAL VARIATIONS.
    ØNATIONAL POLICIES FOR SECTORAL GROWTH
    §NATIONAL ELECTRICITY POLICY
    §INFRASTRUCTURE DEVELOPMENT PLANS.
    ØECONOMIC GROWTH.
    ØDIVERSITY FACTORS-INTER STATE, INTER
    REGIONAL.
    ØINTERNATIONAL ECONOMY LIKE FUEL /OIL PRICE,
    ETC.
    ELECTRICITY DEMAND FORECASTING:
    A NECESSITY

    a)ELECTRICITY SECTOR PLANNING: NATIONAL LEVEL


    STATE LEVEL
    •GENERATION
    •TRANSMISSION
    •DISTRIBUTION
    b)DEVELOPMENT PLANS OF ‘ELECTRICITY-
    CONSUMPTION SECTORS’
    - STAKE- HOLDERS
    - INFRASTRUCTURE SECTORS
    c)REVIEW OF ELECTRICITY SUPPLY POSITION:
    NATIONAL AND STATE LEVEL
    FORECASTING
    METHODOLOGY


     Short term forecasting

     Medium Term forecasting

     Long term forecasting
    FORECASTING
    TECHNIQUES

    Mainly Classified in
     Extrapolation
     Correlation
     Combination of both
    Further Classified in

     Deterministic
     Probabilistic
     Stochastic


    EXTRAPOLATION
     Extrapolation techniques involve fitting trend
    curves to basic historical data adjusted to
    reflect the growth trend .
     Forecast obtain by trend curve
    Deterministic extrapolation

     Random errors not accounted


     Standard analytical functions
     1.Straight line: Y=a+bx

    2.Parabola: Y=a+bx+cx2

    3.S curve: Y=a+bx+cx2+dx3

    4.Exponantial: Y=cedx

    5.Gompertz: Y=In-1 (a+cedx )


     Probabilistic Extrapolation
     Uncertainty of extrapolated results is quantified using
    statistical mean & variance.
     Uncertainty arises in historical data & analytical
    model.
    Stochatic Extrapolation Model

     Generate forecast from random inputs derived from


    historical data investigated in 1975
     Not wide spread
     Based on
     - Random change in the trend component, -
    Random slope in seasonal component, -
    Associated weighting factor,
     - A general noise component.
     Perform by transformation of basic model
     Because basic model & data nonstationary
     Obtain by exciting the transformed model by random
    inputs with known statistics


    CORRELATION
     Relate system loads to various
    demographic and economic factor
     Advantageous for understanding
    interrelationship between load growth &
    other measurable factors
     Disadvantage- results from the need to
    forecast demographic & economic
    factors, which can be more difficult than
    forecasting system load.
     Typically used factors
     Population employment
    building permits appliance saturation
     business indicators weather data

     No one forecasting method, it must be
    emphasized is effective in all
    situations.
     Curve fitting method is adequate for
    some utilities & completely worthless
    for others.
     Forecasting – As tools to aid the planner
     Gives good judgment & experience.
     Never be completely replaced.

    ENERGY FORECASTING

     Energy forecast classified in


    ○ Residential
    ○ Commercial
    ○ Industrial
     Each class separately forecast because
    of different characteristics


    Residential Sales
    Forecasts
    Population Method

     Residential energy requirements are dependent on


    for

     1. Residential Consumers week


     2. Population per consumer month
     3. Per capita energy consumption etc.

     Forecast could be obtain by multiply three


    factors
     Simple curve fitting or Regression analysis is
    used
    Synthetic method
    - Requires detail look at each consumer

    - Major factors

     1. Saturation level of major appliances


     2. Average energy consumption per appliance
     3. Residential consumers
    - These factors extrapolated and multiplied.
    - Projection phase involves data gather from

    customers, Builders.
    - Rapid growth is an extremely important step
    Commercial Sales
    Forecast
     Commercial establishments are usually
    service oriented
     Hence growth patterns are close to
    residential sales
     By using method of extrapolation ratios of
    commercial to residential sales in to
    the future & then multiply by residential
    sales forecast
     Another approach to extrapolate
    historical commercial sales.
    Industrial sales forecast
     Industrial sales are tied very closely to the overall economy
    & overall economy not stable over selected periods.

     Approaches in view
     1. Multiply forecasted production levels by forecasted
    energy consumption per unit of production
     2. Multiply forecasted number of industrial workers by
    forecasted energy consumption per worker.

     Approaches depends upon type &location of industry


     For Accurate forecasting – Historical data is decompose


    into subclasses for broad spectrum of industries

     Final step is tuning the forecast


    PEAK DEMAND
     FORECASTING
    Extrapolating historical demand data over the last 5 years for accurate
    peak demand forecast.
     Can get weekly, monthly, yearly peak demand forecast by changing
    data sampling rate
     The basic approach
    Ø Determine seasonal weather load model
    Ø Separate weather sensitive or non weather sensitive component of
    demand
    Ø Forecast mean, variance of NWS component of demand
    Ø Extrapolate weather load model & forecast mean, variance of NWS
    component
    Ø Determine mean, variance, and density function of total weekly forecast
    Ø Calculate density function of monthly or annual forecast.
    o Seasonal variation in peak demand due to weather conditions
    o For elimination of seasonal variation method proposed by Shiskin,
    database of at least 12 yrs is required

    Weather Load Model

    W= Ks(T-Ts) if T > Ts Ts, Tw-Threshold Temp.


    W= -Kw(T-Tw) if T<Tw Ks, Kw- slopes
     =0 if Tw < T < Ts
    Ø Drawing of scatter diagram is Req.- Daily peaks verses
    weather variables
    e. g. Dry bulb Temp., Humidity etc
    linier reggration is used

    Three Bus Layout



    Separating weather sensitive &
    weather non-sensitive
    Components
    NON WEATHER SENSITIVE
    FORECAST (NWSF)
     Discounted multiple regression(DMR) to fit a time
    polynomial to the NWS component of historical weekly
    peak demand
     NWS weekly peak demands described by deterministic
    time polynomial + random variable
     Variations described by
     ξ(t)=a1+a2 = a1f1(t) +a2f2(t)
     f1(t) =1.0 Fitting functions
     f2(t)= t
     a1, a2 – DMR Coefficients
     From a1, a2 we can calculate NWS component of peak
    demand at some future week.

    Discounted Multiple
    Regression
     Historical weekly peak demand data as
    l(t)= ξ(t)+η(t) where, a’=1.n coefficient =a’f(t)
    +η(t) f(t)=n.1 fitting function
    vector
     η(t)=random variable
     l(t)&ξ(t) - variations
    Assume, η(t)=0
    ε(η(t))=ň(t)=0 property 1
    Indicates sum of η(t) over all time, average=0

    Addition of gaussian noise component


     f(η(t))=(1/ση√2pi)exp(-1/2*(η(t)/ ση)2) Property 2
     It says noise component is Gaussian distributed about
    its mean in bell shape.
     Probability density range:- η(t) to dη(t)
     e.g. F(∞)=-∞ ∫∞ f(η(t))dη(t)=1.0
     Based on property 1 average value 0


     ε(η(t) η(t+Ɣ))=0 Ɣ≠0 property 3
     = ση Ɣ=0
    σ 2 = Variance large σ 2indicates noise vary about its
    η η
    mean
    σ 2 =0 means η=ň
    η
    Σ defines 99% confidence interval
    η
     Random weekly peak historical data gives values of
    coefficients on the fitting functions.
     That is done by minimizes squared difference
    between weekly peak demand l (t) & true peak
    demand ξ(t)

    n

    function J= ∑1/2W2(t)[l(t)-ξ(t)]2
     t=1

     W(t) = √ᵦN-t where, t is discrete variable



    ᵦ is discount factor

     ξ(t)=(a1 a2) f1(t) matrix form


     f2(t)
     l(t)= l(t) W(t)=W(t)

    J=1/2W2(1)[l(1)-a’f(1)]2+1/2W2(2)[l(2)-a’f(2)]2 +…

     J=1/2[L(N)-a’R(N)]W(N)W’(N)[L(N)-a’R(N)]’

    Where, L(N)=1*N Vector whose elements are l(t)
     a’= 1*n Fitting function coefficient vector
     R(N)=n*N fitting function matrix whose columns
    are f(t)
    By taking partial derivative


    â= [L(N)W(N)W’(N)R’(N)][R(N)W(N)W’(N)R’(N)]-1

     Letting, F(N)=[L(N)W(N)W’(N)R’(N)]

    G(N)=)[R(N)W(N)W’(N)R’(N)]

    â= F(N) G(N)-1


    Recursive formula F(N)

    Fik =∑N fi(t)ᵦN-t fk(t)
     t=0


    = fi(N)fk(N)+ ∑N-1 fi(t)ᵦN-1-t fk(t)
     But ∑N-1 fi(t)ᵦN-1-t fk(t) = Fik (N-1)
     t=1

    Thus recursive relationship for the ikth element of F
     Fik = fi(1) fk(1)
     Initial values of Fik for fitting function describing 3 bus
    system
     F11 = f12(1) =0.1
     F12 = f1(1) f2(1)= 0.1
     F21 = f2(1) f1(1)=0.1
     F22 = f22(1) =0.1
     Recursive formula G(N)

    Gn =∑N l(t)ᵦN-t fn(t)
     t=1


    = l n(N)fn(N)+ ᵦ ∑N-1 l (t)ᵦN-1-t fn(t)
     t=1

     = l n(N)fn(N)+ ᵦ Gn(N-1)

     ξ(t) = â(n)f(t)………equation for NWS peak demand



    Mean & Variance

    Coefficients
    The Variance of a (N) qualifies the range over
    1
    which the elements of a(N) varies as data are
    simultaneously processed.
     Determination of coefficient variance

    con(â(N))= ε([(â(N)-ẫ(N)] [â(N)-ẫ(N)]’)
     ẫ(N) mean value of (â(N)

    â(N) = [εL(N)] [L(N)W(N)W’(N)R’(N)F(N)-1 ]
     since [εŋ(N)] =0

    ẫ(N) = F(N)-1 R(N)W(N)W’(N)ξ’(N)
     con(â(N))= ε(â(N)â’(N)-ẫ(N)â’(N)+ẫ(N)ẫ’(N))
     = ση2 F(N)-1 R(N)W(N)W’(N)W(N)W’(N)R(N)F(N)-1

     ση2 = (N-n)-1 ∑nt-1 r2(t)


     ξ(t) used for finding NWS component when
    t=104

    FORECAST VARIANCE
     variance qualifies uncertainty of forecast

     ε(ξ(t))= â’(N)f(t)
     var(ξ(t))= ε[ξ(t)ξ’(t)][ξ(t) ξ’(t)]

    = f’(t)con[â’(N)f(t)]
     = σξ2

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