Download understanding vector diagrams

White Paper:
UNDERSTANDING VECTOR DIAGRAMS
Contributed by David Horning July 2013
Abstract
This white paper will discuss what vector diagrams are,
what they display, and how PMI’s power quality recorders
and ProVision can provide the user with this information.
Vector Diagram
The Vector Diagram, as shown in Figure 1 allows a user
to graphically represent the magnitudes of current and
voltage along with their phase angles. The main use of
the Vector Diagram is to show the phase shift between
the current and the voltage. In an AC circuit, the voltage
and current do not peak at the same time if the load is not
purely resistive but has a capacitor or inductor involved.
A sine wave as a function of time t can be described by
three variables: frequency F, amplitude A, and phase q:
x(t) = A SIN(2πFt + q)
For a fixed frequency (normally 60Hz), the only two
free variables are the amplitude and phase. For a pure
sine wave, the amplitude is related to the RMS value by
the familiar sqrt(2) factor: RMS x 1.41 = A. The phase
represents the shift in time referenced to some absolute
time, or relative to another sine wave. Generally voltage
phase A (or the channel 1 voltage input of a PMI recorder)
is considered the reference, and all other channels are
with respect to it. Consequently, the voltage channel 1
phase angle should normally be zero. A vector on the
vector diagram represents a sine wave, and serves as an
easy way to visualize the amplitude and phase of several
sine waves, compared with looking at the raw sinusoids.
phase difference (which becomes a negative phase for a Figure 1. Vector diagram
capacitive circuit since the current leads the voltage and in ProVision
becomes a positive phase for an inductive circuit since
the current lags behind the voltage).
The length of the vector is proportional to the RMS value
Figure 2 shows the voltage ‘V’ leading the current ‘I’ of the sine wave, while the vector’s angle represents the Figure 2. Here voltage
in phase by angle q. The difference between the two phase of the sine wave (with respect to voltage channel is leading the current as
peaks, which is a fraction of a period, is called the 1)” Since a sine wave repeats every cycle, and 360 indicated by q.
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071613 WP127
© Power Monitors, Inc. 2013 • 800.296.4120 • www.powermonitors.com
White Paper:
UNDERSTANDING VECTOR DIAGRAMS
+
I
V
0
-
Time
Figure 3. Voltage and degrees spans a full period of a sine wave, a circular
current in phase vector graph is sufficient to view all the voltage and
Figure 5. Graph menu selection
current vectors.
Typically the voltage vectors for each phase of a 3 phase
wye circuit will be located at 0, 120, and 240 degrees as
in vector diagram in Figure 1. Ideally the current vectors
are very close to the voltage ones (if they’re not, that
implies a worse power factor - PF=1.00 = no phase shift).
In a 3 phase delta, the currents are shifted 30 degrees.
In a single phase system, the two voltage channels are
180 degrees out of phase. The phase current vectors will
be leading, in-phase with (FIgure 3), or lagging (Figure
4) the corresponding voltage vectors depending on the
impedance in each phase.
1. Choose the recording.
2.From the menu click on Graph
3.Click on Harmonic Analysis
4.Click on Vector Diagram as shown in Figure 5.
5.Choose the waveform to graph from the displayed list.
NOTE: If no recording is selected and a recorder is
connected, then the real time graph is displayed.
Vector Diagrams
To create a real time vector diagram follow these steps:
Vector Diagrams in Provision
1. Right-click on the desired recorder in the Devices view.
Provision can be used to view Vector Diagrams real time 2.Click on Waveform Graph.
and in captured waveform data. All angles are taken with 3.Click on Vector Graph as shown in Figure 7.
Figure 4. Voltage and reference to channel 1 voltage input. To create a Vector
current out of phase Diagram from captured waveform data, use these steps:
+
I
V
0
-
Time
Figure 7. Vector graph selection
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© Power Monitors, Inc. 2013 • 800.296.4120 • www.powermonitors.com
White Paper:
UNDERSTANDING VECTOR DIAGRAMS
To the top left of the circle are the values of each of the
Voltage and Current magnitude and phase readings. You
can get a vector diagram breakdown for each harmonic
by clicking the up/down arrows in the upper right side.
There is a separate set of vectors for each harmonic;
ProVision by default shows you the fundamental (1st)
harmonic.
When used with recordings, vector diagrams are
available for the waveform captures. Often, waveform
capture is triggered based on an event like a voltage
sag, etc., and the waveform capture includes non-normal
cycles. Periodic waveform capture can be enabled, and
this allows the capture of “normal” waveforms. To learn
more about waveform capture read the white paper on
using waveform capture for harmonic analysis available
for download by clicking HERE.
NOTE: The Harmonic Analysis report is not available for
real time readings.
The recorder measures voltage line-to-neutral and
these values are the ones shown in the Vector Diagram
by default. Pressing the “I” key while viewing the graph
causes Provision to calculate and display line-to-line
voltage.
CONCLUSION
The Vector Diagram allows a user to graphically
represent the magnitudes of current and voltage along
with their phase angles. Vector diagrams are available for
waveforms in a recording or can be display for real time
data. The “I” keyboard shortcut can be used to toggle the
Vector Diagram from the default line-to-neutral to line-toline display. The Harmonic Analysis Report shows is a
For vectors from waveform capture data, you can slide text report of the phase angles. Analyzing phase angles
the gray rectangle around in the top window to find a is easy using Provision and one of PMI’s many waveform
normal-looking cycle. The vector diagram is computed capturing recorders.
by ProVision from the cycle inside the gray rectangle.
This is not available for the real time vector diagram.
David Horning
Software Developer
To see a text report of recorded waveform phase angles [email protected]
use the Harmonic Analysis Report. The phase angles www.powermonitors.com
for the 1st harmonic should correspond to the vector 800.296.4120
diagram.
To get this report:
1. Choose the recording.
2. From the menu click on Graph
3. Click on Harmonic Analysis
4. Click on Magnitudes.
5. Choose the waveform to graph.
6. Right-click on the graph and choose Launch Report.
Tools you need. People you trust.
071613 WP127
© Power Monitors, Inc. 2013 • 800.296.4120 • www.powermonitors.com