Wide-area Phasor Measurements

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Monitoring and Control of Power System Oscillations using Wide-area Phasor Measurements

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  • SYNCHRONIZED PHASOR MEASUREMENTTECHNIQUES

    A.G. Phadke

  • Lecture outline:

    Development of Phasor Measurement Units

    Power system state estimation

    Control with feed-back

    Adaptive relaying

    Remedial Action Schemes

    Phasor Estimation

    Off-nominal frequency phasors

    Evolution of PMUs

    Standards

    Applications of PMUs

    Comtrade Synchrophasor

  • History of Wide-Area Measurements

    Wide-area measurements in power systems have been used in EMS functions for a long time. Economic Dispatch, tie line bias control etc. all require wide area measurements.

    EMC

    However, the birth of modern wide-area measurement systemscan be traced back to a very significant event which took placein 1965.

    The state estimators as we know them today were developedfollowing the technical assessments of the causes of the failuresin 1965.

  • The Birth of the PMUs

    Computer Relaying developments in 1960-70s.

    Symmetrical Component Distance Relay Development.

    Significance of positive sequence measurements.

    Importance of synchronized measurements.

    Development of first PMUs at Virginia Tech ~ 1982-1992

    Development funded by AEP, DOE, BPA, and later NYPA

    First prototype units assembled at Va Tech and installedon the BPA, AEP, NYPA systems.

  • (b)

    GPSreceiver

    PMU

    Signalconditioning

    unit

    UserInterface

  • PHASOR ESTIMATION

  • Introduction to phasors

    Real

    Imag

    inar

    y

    The starting time defines the phase angle of the phasor.

    This is arbitrary. However, differences between phase angles are

    independent of the starting time.

    t=0

  • Sampling process, Fourier filter for phasors

    sin and cosfunctions

    t

    Input signal

    xnxn-1.

    .x1

    Dat

    asa

    mpl

    es

    cosi

    nes

    sine

    s

    Phasor X = -- xk(cosk - j sink)2N

  • Sampling process, Fourier filter for phasors

    Fourier filters can also be described as:

    Least-squares on a period Cross-correlation with sine and cosine Kalman filters (under many circumstances)

    t

    Xc - jXs = -- xk(cosk - j sink)Phasor X = (AXc+BXs)+j(CXc+DXs)

    2N

    Phasors from fractional cycle:

    High speed relaying

  • Non-recursive phasor calculations

    t

    1

    1

    2

    2 = 1 + k

    The non-recursive phasor rotates in the forwarddirection, one sample angle per sample.

  • Recursive phasor calculations

    t

    1

    1The recursive phasor remains fixed if the inputwaveform is constant.

    2= 1

    2 = 1

  • Effect of noise on phasor calculations

    Harmonics eliminated correctly if Nyquistcriterion is satisfied.

    Non-harmonic components

    Random Noise

    True Phasor

    Circle ofuncertainty

    Size

    of c

    ircle

    of

    unce

    rtai

    nty

    Measurement data window

  • Motivation for synchronization

    By synchronizing the sampling processes fordifferent signals - which may be hundreds of milesapart, it is possible to put their phasors on the samephasor diagram.

    Substation A Substation B

    At different locations

  • Sources for Synchronization

    Pulses Radio GOES GPS

  • Anti-aliasingfilters

    16-bitA/D conv

    GPSreceiver

    Phase-lockedoscillator

    AnalogInputs

    Phasormicro-processor

    Modems

    A phasor measurement unit

    Except for synchronization, the hardware is the sameas that of a digital fault recorder or a digital relay.

  • Sampling process, Fourier filter for phasors

    sin and cosfunctions

    t

    Input signal

    xnxn-1.

    .x1

    Dat

    asa

    mpl

    es

    cosi

    nes

    sine

    s

    Phasor X = -- xk(cosk - j sink)2N

    Sampling clock based on nominal frequency

  • Fixed clocks, DFT at off-nominal frequency

    Consider frequency excursions of 5 Hz The definition of phasor is independent of frequency

    t=0

    off-nominal sineoff-nominal cosine

    nominal sine nominal cosine

    x

    off-nominal signal

    Phasor:

    X = (Xm /2) jXm

  • tDat

    asa

    mpl

    es

    cosi

    nes

    sine

    s

    X = -- xk(cosk - j sink)2N

    Sampling clock based on nominal frequency

    Input signal at off-nominal frequency:

    ^

  • Fixed clocks, DFT at off-nominal frequency Using the normal phasor estimation formula withxr being the first sample, the estimated phasor is:

    Xr = PX jr()t + QX* jr(+)t^where t is the sampling interval, is the actualsignal frequency, and 0 is the nominal frequency.P and Q are independent of r, and are given below:

    N(0)t2P =

    sin

    (0)tN sin2

    N(0)t2 j(N-1)

    N(+0)t2Q =

    sin

    (+0)tN sin2

    N(0)t2 -j(N-1)

  • Fixed clocks, DFT at off-nominal frequency

    At off-nominal frequency constant input, the phasor estimate is no longer constant, butdepends upon sample number r.

    The principal effect is summarized in the Pterm. It shows that the estimated phasorturns at the difference frequency.

    The Q term is a minor effect, and has arotation at the sum frequency.

    For normal frequency excursions, P is almostequal to 1, and Q is almost equal to 0.

  • Fixed clocks, DFT at off-nominal frequency

    For small deviations in frequency, P is almost 1 and Q is almost 0.

    -5 -4 -2 0 2 4 50.988

    0.992

    0.996

    1

    Frequency deviation

    Mag

    nitu

    de

    0

    5

    10

    15

    Phas

    e Sh

    ift

    degr

    ees

    (dot

    ted)

    -5

    -10

    -15

    The function P

  • Fixed clocks, DFT at off-nominal frequency

    For small deviations in frequency, P is almost 1 and Q is almost 0.

    -0.05-0.04

    -0.02

    0.02

    0.040.05

    Frequency deviation

    Mag

    nitu

    de

    Phas

    e Sh

    ift

    degr

    ees

    (dot

    ted)

    -5 -4 -2 0 2 4 50

    5

    10

    15

    20

    25

    30

    0.00

    The function Q

  • Fixed clocks, DFT at off-nominal frequency

    A graphical representation of Xr:^

    (0)

    (+0)

    PX

    Xr^

    QX*

    Errors havebeen exaggeratedfor illustration.

    In reality, Q is verysmall.

  • Fixed clocks, DFT at off-nominal frequency

    If a cycle by cycle phasor is estimated at off-nominalfrequency, the magnitude and angle will show a ripple at (+0), and the average angle will show a constant slope corresponding to (0)

    Phasor index r

    Mag

    nitu

    de

    Ang

    le

    Ripples are at (+0)

    Slope of angle is (0)

  • Fixed clocks, Symmetrical Components atoff-nominal frequency

    If the off-nominal frequency input is unbalanced, andhas symmetrical components of X0, X1, and X2, theestimated symmetrical components are given by

    = P jr()t + Q jr(+)tXr0

    Xr1

    Xr2

    ^

    ^

    ^

    X0

    X1

    X2

    X0

    X2

    X1

    *

    *

    *

    Note that positive sequence creates a ripple in thenegative sequence estimate, and vice versa. The zerosequence is not affected by the other components.

    Also, more importantly, if the input has no negativesequence then the positive sequence estimate iswithout the corrupting ripple.

  • Balanced 3-phase voltages at

    Positive sequencevoltage at

    Fixed clocks, Symmetrical Components atoff-nominal frequency

    The ripple components of the three phase voltagesare equal and 120 apart, and thus cancel in the positive sequence estimate.

  • Frequency De

    viation Df

    Per unit negative sequence

    Com

    pone

    nt a

    t (w

    +w0)

    Error in positive sequence estimate as a function of per unit negative sequence and frequency deviation.

  • Summary of fixed clock DFT estimation of phasors:

    For small frequency deviations, a single phaseinput with constant magnitude and phase will lead to an estimate having minor error terms.

    The principal effect is the rotation of the phasorestimate at difference frequency (0), and a small ripple component at the sum frequency (+0).

    A pure positive sequence input at off-nominalfrequency produces a pure positive sequenceestimate without the ripple. The positive sequenceestimate rotates at the difference frequency.

  • APPLICATIONS FOR MONITORING, PROTECTIONAND CONTROL

  • Frequency measurement with phasors

    3-phase voltagesat

    d/dt

    Positive sequencevoltage at

    0

    timefreq

    uenc

    y

  • Present practice

    ControlCenter

    Measurementsare primarilyP, Q, |E| = [z]

    State is the vectorof positive sequencevoltages at all network buses [E]

    Measurementsare scannedand are NOTsimultaneous

    Phasor measurement based state estimation offersmany advantages as will be seen later.

    Power system state estimation

  • ControlCenter

    Estimation with phasors Since the currents andvoltages arelinearly relatedto the state vector,The estimatorequations arelinear, and noiterations arerequired.

    [Z] = [A] [E] , and once again the weighted leastsquare solution is obtained with a constantgain matrix.

    Power system state estimation

  • Incomplete observability estimators:

    One of the disadvantages of traditional state estimatorsis that at the very minimum complete tree of the network must be monitored in order to obtain a state estimate.The phasor based estimators have the advantage thateach measurement can stand on its own, and a relativelysmall number of measurements can be used directlyif the application requirements could be met.

    Monitoringor controlsite

    For example considerthe problem of controllingoscillations between twosystems separated bygreat distance.

    In this case, only twomeasurements would be sufficient to provide a usefulfeed-back signal.

  • Incomplete observability estimators:

    How many PMUs must be installed?

    For complete observability, about 1/3 the numberof buses (along with the currents in all the connectedlines) in the system need to be monitored.

    PMU Indirect

  • Incomplete observability estimators:

    PMU placement for incomplete observability andinterpolation of unobserved states:

    PMU

    Indirectlyobserved

    Unobserved

    The unobserved set can be approximated by interpolation from the observed set

    [Eun-observed ] = [B][Eneighbors]

  • State estimation with phasor measurements:

    Summary:

    Linear estimator True simultaneous measurements Dynamic monitoring possible

    Complete observability requires PMUs at 1/3buses

    Incomplete observability possible Few measurements become useful for control

  • ADVANCED CONTROL FUNCTIONSPresent system: model based controls

    Controller

    Measurements ControlledDevice

    Control with feed-back

  • Phasor based: Feedback based controlADVANCED CONTROL FUNCTIONS

    ControlledDevice

    ControllerMeasurements

    Control with feed-back

  • Example of control with phasor feed-back

    System A System B

    Power demand Controller

    A- B

    time

    Performance withconstant power control law

    Desired performance

  • Example 1: HVDC Controller

    1640 MW

    820 MW

    (200+j20) MVA

    590 MVAR

    680 MVAR3 phase faultcleared in 3 cycles

    G1

    G2

  • Example 1: HVDC Controller

    Control law 1: Constant current, constant voltage on HVDCControl law 2: Optimal controller

    1

    2

    t (seconds) 5

  • DefinitionAdaptive protection is a protectionphilosophy which permits and seeksto make adjustments in various protection functions automatically in order to make them moreattuned to prevailing power systemconditions.

    Adaptive Relaying

  • Adaptive out-of-step relaying

    Conventionalout-of-steprelaying

    stable

    unstable

  • Adaptive out-of-step relaying

    pmupmu

    P

    tob

    serv

    e

    predict

  • Controlled Security & Dependability

    A

    r

    b

    i

    t

    r

    a

    t

    i

    o

    n

    L

    o

    g

    i

    c

    System State

    And

    Vote

    ProtectionNo

    ProtectionNo

    ProtectionNo

    1

    2

    3

    Or

    T

    o

    C

    i

    r

    c

    u

    i

    t

    B

    r

    e

    a

    k

    e

    r

    s

    Adaptive Relaying

  • FUTURE PROSPECTS

    Applications a very active area of investigation

    Intense industry interest in installations of PMUs New revised standard a step forward System post-mortem analysis the first application State estimation is an ideal application Control and adaptive relaying applications will follow