Suppose you have a Y-connected balanced three-phase load which consumes 200 kW with pf of 0.707 lagging. The line-to-line voltag
e of the load is 440 V. Use the line-to-line load voltage as your angle reference. (a) Draw the per-phase equivalent and label all the components. (b) Calculate the a-phase load current. (c) Calculate the capacitive reactive power per phase needed to correct the power factor to 0.8 lagging (d) Draw two power triangles - before and after the power factor correction in (c).
1 answer:
Given Information:
three-phase Y-connected load = P = 200 kW
PF = 0.707 lagging
line-to-line load voltage = VL-L = 440 V
Required Information:
(a) Draw the per-phase equivalent circuit ?
(b) Calculate the a-phase load current = ?
(c) Calculate the capacitive reactive power = ?
(d) Power triangles - before and after the power factor correction = ?
Answer:
a) See attached drawing
b) I = 123.72<-45°
c) Qc = 16.66 kVAR
d) See attached drawing
Explanation:
b) Calculate the a-phase load current
VL-N = VL-L/ = 440/
= 254 V
Three phase load current can be found by
P = 3*VL-N*I*cos(θ)
θ = cos⁻¹(PF) = cos⁻¹(0.707) = 45°
I = P/3*VL-N*cos(45°)
I = 200,000/3*254*cos(45°)
I = 371.18 A
single phase current is
I = 371.18/3 = 123.72 A
In polar form,
I = 123.72<-45° A ( minus sign due to lagging PF)
Since the load is balanced, the current in other phases is same with 120° phase shift
(c) Calculate the capacitive reactive power
Three phase reactive compensation power is
Qc = P (tan(θold) - tan(θnew))
θnew = cos⁻¹(PF) = cos⁻¹(0.8) = 36.86°
Qc = 200 (tan(45°) - tan(36.86°))
Qc = 200 (0.250)
Qc = 50 kVAR
Per phase reactive compensation power is
Qc = 50/3 = 16.66 kVAR
(d) Power triangles - before and after the power factor correction
Before
P = 200 kW
Q = 3*VL-N*I*sin(45° ) = 3*254*123.72*sin(45° ) = 66.66 kVAR
S = P + jQ = 200 + j66.66 kVA = 210.81 kVA
After
I = P/3*VL-N*cos(36.86°) = 200,000/3*254*cos(36.86°) = 328 < -36.86 A
single phase current
I = 328/3 = 109.33 < -36.86 A
Q = 3*VL-N*I*sin(36.86° ) = 3*254*109.33*sin(36.86° ) = 50 kVAR
S = P + jQ = 200 + j50 kVA = 206 kVA
As you can see the current and reactive power are reduced after power factor correction.
The power triangle before and after power factor correction is attached.
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Power supply produces high and low voltages. The high negative voltage and the low positive voltage apply to CRT and other circuits respectively.
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it is the main important block of CRO and consists mainly of four parts. Those are electronic guns, vertical deflection plates, horizontal deflection plates and fluorescent display.
The electron beam, which is produced by an electron gun, is deflected both vertically and horizontally by a pair of vertical deflection plates and a pair of horizontal deflection plates, respectively. Finally, the deflected beam will appear as a point on the fluorescent screen.
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Explanation:
The oscilloscopes which is widely used for analysis purpose of circuits is divided into four main groups: the horizontal and vertical controls, the input controls and the activation controls.
Found in the front panel section marked Horizontal, the oscilloscope's horizontal controls allow users to adjust the horizontal scale of the screen. This section includes the control of the horizontal delay (displacement), as well as the control that indicates the time per division on the x-axis. The first control allows users to scan through a time range, while the latter allows users to approach a particular time range by decreasing the time per division.
Meanwhile, the oscilloscope's vertical controls are usually found in a section specifically marked as Vertical. The controls found in this section allow users to adjust the vertical appearance of the screen and include the control that indicates the number of volts per division on the axis and the grid of the screen. Also in this section is the control of the vertical displacement of the waveform, which translates the waveform up or down on the screen.
Signal activation helps provide a usable and stable display and allows users to synchronize the oscilloscope acquisition in the waveform of interest. The oscilloscope trigger controls allow users to choose the vertical trigger level, as well as the desired trigger capability. Common types of activation include fault activation, edge activation and pulse width activation.
Useful for identifying random errors or failures, the activation of faults allows users to fire at a pulse or event whose width is less than or greater than a specific period of time. This activation mode allows users to capture errors or technical problems that do not occur very frequently, which makes them very difficult to see.
The most famous trigger mode, edge tripping occurs when the voltage exceeds a set threshold value. This mode allows users to choose between shooting on a falling or rising edge.
Although pulse width activation is comparable to fault activation when users search for pulse width, it is, however, more general since it allows users to fire pulses of specified width. Users can also select the polarity of the pulses to be activated and set the horizontal position of the trigger. This allows users to see what happened during pre-shot or post-shot.
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