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Fundamentals of power and energy measurement

- 30 noiembrie 2010
- Mihaela Albu

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.

Definitions. n-terminal circuits

The instantaneous power for a two - terminal

circuit

The instantaneous power for a n-terminal circuit

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

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,

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

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

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

Definitions. Sinusoidal waveforms

Power transfer in linear systems with sinusoidal

voltage

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

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

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).

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.

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

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

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

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)

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

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.

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).

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

Active power - Three phase systems 3 wires, 2

wattmeter method

Active power - Three phase systems 4 wires, 3

wattmeter method

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

reactive power - Three phase systems 3 wires,

2 wattmeter method

reactive power - Three phase systems 4 wires, 3

wattmeter method

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

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)

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.

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

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

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

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

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)

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

IEEE 1459-2010 IEEE Standard Definitions for

the Measurement of Electric Power Quantities

Under Sinusoidal, Nonsinusoidal, Balanced, or

Unbalanced Conditions.

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).

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

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

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)

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

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

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

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

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.)

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

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

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.

Smart meters

Energy meters

Advanced Metering Infrastructure (AMI)

Automated Meter Reading (AMR)

Smart meters

PRI Home Energy Controller

PowerPlayer

EcoMeter

EWE-Box

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

Synchronous measurements

Questions? albu_at_ieee.org