Fundamentals of power and energy measurement

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Fundamentals of power and energy measurement

• 30 noiembrie 2010
• Mihaela Albu

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Definitions
According to the IEC (Electropedia) The energy
associated with an electromagnetic field
where E, D, H and B are the vectors determining
the electromagnetic field in a linear medium of
volume V.
The flux of the Poynting vector through a closed
surface is the electromagnetic power passing
through this surface. For a periodic
electromagnetic field, the time average of the
Poynting vector is a vector of which, with
certain reservations, the direction may be
considered as being the direction of propagation
of electromagnetic energy and the magnitude
considered as being the average electromagnetic
power flux density.
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Definitions. n-terminal circuits
The instantaneous power for a two - terminal
circuit
The instantaneous power for a n-terminal circuit
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Definitions. Constant waveforms
Simplest circuit two-terminals (A,B) Simplest
waveforms constant current and voltage
For such two terminal circuits, the active power
is defined as
For dc power transfer the active power is
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Power Measurement in d.c. circuits

• Direct measurement
• dynamometer (electrodynamic force between two
  coils, one fixed each current is made
  proportional to I, and U respectively
• Hall Effect-based wattmeter
• electronic wattmeter (based on multipliers)

Indirect measurement analog multipliers U is
measured with a voltmeter I is measured with an
ampermeter compute PUI double pulse
modulation in which the voltage signal is pulse
width modulated and the current signal is pulse
amplitude modulated The signals are multiplied
to obtain the area of the pulse which is
proportional to the instantaneous power it can
be integrated over several cycles and then
displayed as average active power digital from
available 2N (synchronous) samples Uk,Ik,
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Definitions. A historical approach
Power and energy measurement became necessary in
power systems for billing purposes and for state
estimation (stability studies, power flow,
generators dispatch optimization). The available
measurement systems analog (wattmeter), where
reading is a function of the average (rms) values
of current and voltage The information was
obtained at the output of instrument transformers
with limited bandwidth (no available methods to
directly investigate the voltage and current
waveforms) The available systems linear, with
sinusoidal waveforms for both currents and
voltages Three-phase systems symmetrical, with
3 or 4 wires. ? The definitions were good enough
for coping with the available devices and
knowledge on signals
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Definitions . Sinusoidal waveforms
Application to power systems - single phase
circuits for more than one century linear
systems with power transfer described by
periodic, sinusoidal signals u(t) and i(t)
For such two terminal circuits, the active power
is defined as
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Definitions. Sinusoidal waveforms
Application to power systems single phase
circuits Linear ac systems are conveniently
described in frequency domain by using phasors,
as complex quantities uniquely associated with
periodic waveforms of frequency f1/T Ferraris
1890
For any periodic waveforms of period T(not
necessarily sinusoidal) one defines the rms value
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Definitions. Sinusoidal waveforms
Power transfer in linear systems with sinusoidal
voltage
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Definitions. Sinusoidal waveforms
Application to power systems definitions
conveniently derived in frequency domain
P active power W Q reactive power
var S complex power S apparent power VA
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Definitions. Sinusoidal waveforms
For single phase system energized with sinusoidal
voltage (frequency f), the definition of active
power holds
The power transfer is described by the complex
power S - as real and imaginary components P
and Q or - as apparent power S and the power
factor
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Definitions. Sinusoidal waveforms
For single phase system energized with sinusoidal
voltage (frequency f), where the load is linear,
described by a resistance in series with an
inductance (as in figure below) there is a
perfect mapping of vectorial representations of
physical elements (ZRjX), current and voltage
waveforms (described by the rms values I, U and
phase j) and the power transfer as described by
either (active power P, reactive power Q) or the
complex power S or (the apparent power S, phase
j).
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Typical measurement device electrodynamic
instrument - Wattmeter

• It has two circuits the current sensing
  circuit (1) and the voltage circuit (2).
• The frequency response of the coils is however
  limited.
• The average deflection of the pointer is
  proportional to the product of the rms value of
  the current (1), the rms value of the current in
  (2), and the cosine of the phase angle between
  the two current waveforms assumed sinusoidal in
  (1) and (2) . When one of the to currents is
  proportional to the voltage at any moment t, then
  the pointer deflection is proportional to the
  active power P.

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Definitions . Nonsinusoidal conditions
Linear systems with where at least one of the
signals are periodic, but non-sinusoidal various
definitions evolve from the sinusoidal case. u(t)
and i(t) are periodic of T ? Both signals admit a
Fourier series expansion
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Definitions . Nonsinusoidal conditions
Linear systems with periodic, nonsinusoidal
waveforms Budeanu theory (1927) u(t) and i(t)
are periodic of T ? Apparent power
Active power P Reactive power
Q Distortion power D
Power factor
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Definitions . Nonsinusoidal conditions
Linear systems with periodic, nonsinusoidal
waveforms Fryze theory (1932) u(t) and i(t) are
periodic of T ?
Active power P Apparent power S Reactive
power Pb ? Active power P
Active power factor Active voltage and
current Reactive power factor Reactive
voltage and current
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Definitions . Three phase systems.Sinusoidal
waveforms in linear, balanced and symmetrical
systems
Linear systems energized with periodic (T),
sinusoidal waveforms Three phase systems 4 wire
or 3 wire symmetry describes the voltages
derived from energizing the system balance
describes the physical symmetry, as derived from
the rest of the system (loads, conductors,
transformers etc) Distortion describes the
currents and/or voltages across loads, when
non-sinusoidal (however periodic with T)
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Definitions . Three phase systems.IEC approach
(62053)
The physical layer is considered linear and
superposition of the energy transfer on each
phase will result in the total apparent power and
its components (active and reactive powers) They
represent the result of time averaging (rms
values). for a two-terminal element or a
two-terminal circuit under periodic conditions,
one defines the non-active power The
non-active power factor Displacement angle ?
where
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Definitions . Three phase systems.IEC approach
(62053)
symmetric three phase system system in which
the m3 quantities (voltages currents) have the
same amplitude and initial phases given
by instantaneous power sum of the
instantaneous powers in all phase elements of a
polyphase element. For a symmetric polyphase
element, under symmetric conditions, the average
of the instantaneous power is time independent
and equal to the active power. active power sum
of the active powers in all phase elements of a
polyphase element. For a symmetric polyphase
element, under symmetric conditions, the active
power is equal to the active power for any phase
element multiplied by the number of phases.
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Definitions . Three phase systems.IEC approach
(62053)
active power for a three phase line average
value, taken over one period, of the
instantaneous power. For a three-phase line under
symmetric and sinusoidal conditions, the active
power is where U is the rms value of any
line-to-line voltage, I is the rms value of any
line current and f is the displacement angle
between any line-to-neutral voltage and the
corresponding line current. for billing
purposes active energy the electrical energy
transformable into some other form of energy
(601-01-19) reactive energy in an a.c. system,
the captive electrical energy exchanged
continuously between the different electric and
magnetic fields associated with the operation of
the electrical system and of all the connected
apparatus (601-01-20).
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Analog power measurement in three phase systems
(n-wire)

• The basic instrument to measure power is the
  analog single-phase wattmeter
• It is assumed sinusoidal waveforms physical
  symmetry
• Physical or electrical asymmetries are first
  treated by decomposing the circuit in three
  linear, symmetrical circuits (direct, inverse,
  and zero sequences) this is possible only in
  case of physical symmetry otherwise the modal
  theory is applied (and all signals are analyzed
  in terms of their modal components)
• The total power is decomposed in active and
  reactive components
• The total active power is measured using (n-1)
  wattmeters
• Each wattmeter indicates a value with no
  associated electrical meaning

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Active power - Three phase systems 3 wires, 2
wattmeter method
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Active power - Three phase systems 4 wires, 3
wattmeter method
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Measurement of reactive power

• Accomplished using phase shifted signals.
• It is only valid for signals with same frequency
  (50 Hz/60 Hz)
• Can be done digitally by first finding the DFT of
  the voltage and current (phasors associated with
  the fundamental frequency). Then shift U or I by
  ?/2 and obtain the (scalar) product.
• Both digital and analog instruments are available

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reactive power - Three phase systems 3 wires,
2 wattmeter method
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reactive power - Three phase systems 4 wires, 3
wattmeter method
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Definitions . Three phase systems.IEEE 1459-2000
Information on the physical system and signal
waveforms is concentrated into equivalent rms
quantities for currents and voltages. They
represent the result of time averaging (rms
value), and spatial averaging and results in the
effective apparent power Se
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Definitions. Three phase systems.Instantaneous
powers (time approach) in the p-q Theory
For a real time control of the energy transfer in
a multi-port (three phase system, with 3 or 4
wires), one defines three phase instantaneous
active power p3F and the associated currents and
voltages in different reference frames as to
allow specific control strategies (series voltage
or shunt current compensation)
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Definitions. Three phase systems.Instantaneous
powers (time approach) in the p-q Theory
One measures the phase currents ia, ib, and ic
and the phase voltages as choosing a reference
potential (for example applied to instantaneous
values of the currents an voltages ? quantities
in the reference frame (0, a, b)
The three-phase instantaneous active power p3F
(t) describes the total instantaneous energy flow
per second between two sections (generator and
load) of the grid.
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Definitions. Three phase systems.Instantaneous
powers (time approach) in the p-q Theory
One can re-write the above definition of the
three-phase instantaneous active power p3F (t) as
to highlight its two components p0 and p
together with a new quantity q
p0 zero-sequence power in 3-wire systems always
p0 0. p real instantaneous power q real
instantaneous imaginary power
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Definitions. Three phase systems.Instantaneous
powers (time approach) in the p-q Theory
Modified p-q theory highlights the components of
q, as based on the instantaneous voltage and
current vectors in the (a, b, 0) frame
p3F instantaneous active power denoted usually
with p q instantaneous imaginary power
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Definitions. Three phase systems.Instantaneous
powers (time approach) in the p-q Theory
The instantaneous power can be then directly
derived as a vector with four real values
components
and the total instantaneous imaginary power will
be the scalar
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The measurement chain. Input converters

• Measurement of electric quantities (voltage,
  current, power, energy) in the power systems
  include signal conditioning units, typically
  transformers, for providing both isolation of
  measurement equipment from the high voltage and
  for resulting in a standardization at low voltage
  level.
• Technologies
• Current and voltage transformers metering grade
  (intended for revenue metering, low bandwidth,
  high accuracy, calibrated, some intended for use
  with digital transducers) laboratory grade (wide
  bandwidth, usually high accuracy, calibrated)
• Shunts voltage dividers
• Optical devices
• Transformers with optical signal transmission

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Energy measurement

• Wattmeters
• Analog
• Digital
• Related energy measurement instruments
• Induction disk watt-hour meter
• Digital energy meters ( with additional time of
  energy use signals some with bidirectional
  communication for updating the energy price and
  DSM control signals)

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The IEC approach(meters for active and reactive
energy measurements)
CEI 60687 - Alternating current static watt-hour
meters for active energy classes 0.2S and
0.5S. CEI 61036 - Alternating current static
watt-hour meters for active energy classes 1 and
2 CEI 61268 - Alternative current static
var-hour meters for reactive energy classes 2 and
3 CEI 60521 - Class 0.5, 1 and 2
alternating-current watt-hour meters
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IEEE 1459-2010IEEE Standard Definitions for
the Measurement of Electric Power Quantities
Under Sinusoidal, Nonsinusoidal, Balanced, or
Unbalanced Conditions.
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Definitions . Three phase systems.IEEE 1459-2010

• Defines following quantities
• The power frequency (60/50 Hz or fundamental) of
  apparent, active, and reactive powers.
• The effective apparent power in three-phase
  systems,
• the nonfundamental apparent power SN
• Current distortion power DI identifies the
  segment of nonfundamental nonactive power due to
  current distortion.
• Voltage distortion power DV separates the
  nonfundamental nonactive power component due to
  voltage distortion.
• Apparent harmonic power SH indicates the level of
  apparent power due to harmonic voltages and
  currents alone. (the smallest component of SN and
  includes the harmonic active power PH).

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Definitions . Three phase systems.IEEE 1459-2010
This standard is meant to serve the user who
wants to measure and design instrumentation for
energy and power quantification. Structure Singl
e phase, sinusoidal quantities Single phase,
nonsinusoidal quantities Three phase,
nonsinusoidal and non balanced quantities
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Definitions . Three phase systems.IEEE 1459-2010
Single phase, sinusoidal quantities Active
power P Reactive power Q Apparent power S Power
factor ? Complex power S
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Definitions . Three phase systems.IEEE 1459-2010
Single phase, nonsinusoidal quantities steady-sta
te conditions, nonsinusoidal periodical
instantaneous signal x(t) has one fundamental
component and a harmonic component (which
includes dc component) ? Intsantaneous power p
has two components pa and pq ? Active power P is
the average of pa and has two components PP1
PH P1 fundamental active power PH harmonic
active power (nonfundamental active power)
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Definitions . Three phase systems.IEEE 1459-2010
Single phase, nonsinusoidal quantities Q1
fundamental reactive power S apparent power
SUI S1 fundamental apparent power SN
nonfundamental apparent power DI current
distortion power DU voltage distortion power SH
harmonic apparent power DH harmonic distortion
power N nonactive power Fundamental power factor
(displacement power factor) Power factor
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Definitions . Three phase systems.IEEE 1459-2010
three phase, sinusoidal quantities and balanced
system Instantaneous power p, active power P ,
reactive power Q, apparent power S, power
factor. three phase, sinusoidal quantities and
unbalanced system Instantaneous power in 3 wire
systems Instantaneous power in 4 wire
systems Active power P is the sum of phase
active powers
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Definitions . Three phase systems.IEEE 1459-2010

• three phase, sinusoidal quantities and unbalanced
  system (cont.)
• symmetrical components ?
• positive-sequence active power
• negative-sequence active power
• zero-sequence active power
• the total active power P
• Analog expressions for reactive power Q
• positive-sequence reactive power
• negative-sequence reactive power
• zero-sequence reactive power
• the total reactive power P

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Definitions . Three phase systems.IEEE 1459-2010

• three phase, sinusoidal quantities and unbalanced
  system (cont.)
• Phase apparent powers
• Arithmetic apparent power
• Vector apparent power
• positive, negative an zero- sequence apparent
  powers

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Definitions . Three phase systems.IEEE 1459-2010
three phase, sinusoidal quantities and unbalanced
system (cont.) effective quantities (a
virtual balanced circuit that has exactly the
same line power losses as the actual unbalanced
circuit) Effective apparent power Unbalanced
power ? Effective power factor (vector
power factor arithmetic power factor positive
sequence power factor etc.)
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Definitions . Three phase systems.IEEE 1459-2010
three phase, sinusoidal quantities and unbalanced
system fundamental effective apparent power
non-fundamental effective apparent power SeN
current distortion power DeI voltage distortion
power, DeU harmonic apparent power, SeH
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Active energy measurements

• Energy measurement instruments requirements as a
  function of the applicability
• Class A in circuits with Sgt100 MVA or annual
  energy gt10 GWh
• only electronic meters are allowed
• special requirements for the instrument
  transformers on the measurement chain
• Class B in circuits with Slt100 MVA or 200 MWhlt
  annual energy lt10 GWh
• only electronic meters are allowed
• Class C 50 MWhltannual energy lt200 MWh static
  meters
• where annual energy lt50 MWh it is allowed to
  use induction- based energy meters
• residential loads no mandatory reactive energy
  metering

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Example of energy measurement results using
various meters 09.08.2002 02.10.2002 )
ACTIVE (REAL) ENERGY ACTIVE (REAL) ENERGY ACTIVE (REAL) ENERGY REACTIVE ENERGY REACTIVE ENERGY REACTIVE ENERGY
Initial Index Final Index Energy kWh Initial Index Final Index Energy kVArh
ALPHA A1-R (P-Q-S) 13488.2 13884.4 7924 8394.1 8696.2 6042
ALPHA POWERPLUS (P-Q-S) 68.4 464.53 7922.7 57.3 359.2 6038
CEET-15 (Hilbert Transform) 19.62 416.27 7933 8.67 112.17 2070
CR 43 (inductive) 31.3 137.3 2120
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News from power systems
Changes in the elements functionality -gt requires
changes in the electrical model State estimation
until now required measurements on P, Q, S in
order to provide information on voltage and
current waveforms in each node and branch (Uk,
Iml) ? synchronized measurement units (PMUs)
provide directly this information Generation is
not mainly provided by synchronous machines ? the
extended use of power electronics interfaces ?
Frequency is not anymore a system variable ?
phasor representation is not suitable
anymore New software models take into account
the actual network for operational studies while
planning uses generic models ? inadequacies in
the power flow results(missing 1000 MW
problem). Smart metering enables identification
of both technical and non-technical losses. It
provides however information only on the
classical definitions of active and reactive
power.
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Smart meters
Energy meters
Advanced Metering Infrastructure (AMI)
Automated Meter Reading (AMR)
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Smart meters
PRI Home Energy Controller
PowerPlayer
EcoMeter
EWE-Box
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Smart meters
www.esma-home.eu European Smart Metering
Alliance www.esmig.eu The European Smart
Metering Industry Group
Sentec Coracle
Home Energy Hub
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Synchronous measurements
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Synchronous measurements
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Questions? albu_at_ieee.org