standard methods pq calculation.pdf

Signal Processing and PQ

Z.Leonowicz, PhD

Stationarity

• Normal operation• Steady-state operation• Stationary signal• Statistical properties

Parameters

• Magnitude – rms value• Frequency – counting of zero-crossings• Distortion – spectrum estimation• Unbalance – 3phase• Flicker severity – fast changes in

magnitude < 1s• Very Short Variations (3 s – 10 min)

Voltage Magnitude

• IEC 61000-4-30 – 10 (12) cycles

• RMS

• Max. Amplitudes

RMS

• Noise , Frequency Errors

Three-phase measurements

• Mean

• RMS

• Instantaneous RMS

Frequency

• Counting of zero-crossings• PLL• Advanced methods

Waveform Distortion

• IEC 61000-4-7 IEC 61000-4-30• Measurement setup

61000-4-30

• Harmonic current when emission compared to limits

• Fourier series 10 (12) cycles, rectangular window, synchronized with frequency

• 5 Hz spacing between components

Example, arc furnace current

T1

T2HV

L

-ia

ia,ref+regulator

firingcircuit

MV

-2000

0

2000

0 0.01 0.02 0.03 0.04 0.05

Cur

rent

[A]

Time [s]

200 400 6000

0.01

0.02

0.03

Frequency [Hz]

Am

plitu

de [-

]

Example

Example

Inter/Harmonic & sub/groups

200 ms window

Harmonic Group

• 9 frequency components between n and n+1 harmonic (11 for 60 Hz systems)

• Lowest four -> Group n• Highest four -> Group n+1• Middle one divided into two groups

Harmonic Subgroup

• Harmonic plus adjacent components

Interharmonic group

• All harmonic components between harmonic of order n

Interharmonic subgroup

• Frequency components between the harmonic groups

Example (arc furnace)

Example (normal)

Disturbances in range 2-9 kHz

• IEC 61000-4-7 annex• 100 ms window not synchronized to 50 Hz• Sampling frequency 30-50 kHz• Band pass filter• 10 Hz separation grouped into 200 Hz

bands• 2100, 2300,…,8700,8900 Hz

Three-phase Unbalance

• Negative-sequence voltage

• IEC 61000-4-30

+

−

=UUUunbalance

Problems with Unbalance

1. Maximum deviation from average phase voltage – IEEE 1159

2. Difference between highest and lowest rms voltage (ref. to averaged 3 voltages) – IEEE 936

3. Ratio of negative to positive sequence –IEEE 1159

4. Maximum deviation from average line voltage , ref. to average of line voltages

Example 2% neg-seq. voltage

2

1,3,4

Example 2% neg-seq.+1,5% zero-seq.

2

1

4

Calculation of Unbalance

Unbalance

Unbalance

Positive and negative seq. voltages

Unbalance

Power Quality Indices

• THD Total Harmonic Distortion• TWD Total Waveform Distrotion• TnHD Total Non-Harmonic Distortion

• THDe – Total Even Harmonic Distortion• THDo - ?• THDv THDI

• THDnom, THDrms

Formulas

Formulas

Other indices

• Crest factor• Transformers K-factor• THD cap – Capacitor banks• THD mach – Rotating machines• Telephone Interference

factor

3-phase aggregation

• Balanced THD

• Unbalanced THD

Example

Power and PF

• IEEE 1459• Uses 3 line voltages• Instantaneous power

p(t)=vaia+vbib+vcic• Arithmetic apparent power-sum of S• Vector apparent power – Budeanu def.• PF ratio of active power to apparent

power

Budeanu powers

• Budeanu Powers-1927• Reactive

• Distortion

222BBV DQPS ++=

Problems

• No PF is correct !• Effective voltage & current

PF

Frequency Domain Analysis

• Signal is decomposed into harmonics• Discrete Fourier Transform• Window Functions

Window Size

Interpolation

• Zero-padding• Does not increase frequency resolution• Generates interpolated spectrum• Frequency resolution

tNΔ≈Δ

πω 289.0

Synchronization

Examples

Examples

Examples

Examples