A.C. Voltage waveforms and harmonics?

In summary: The voltage waveform consists of a fundamental voltage of 100V rms at a frequency of 120Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging.
  • #1
alex.daciz
9
0
Hi, I have the following question:

An A.C. voltage, V comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging.

(1) Write down an expression for the voltage waveform

(2) The voltage at 20ms (milliseconds)

(3) Given an ideal V = 100V rms, what is the percentage error at 20ms

I have an idea for the first and second parts but I get a huge percentage error in (3) which makes me doubt whether the first 2 parts were correct, can anyone help please?

(1) Since V = Vrms x sqrt2 = 141.4V at 120Hz

3rd harmonic = 20% of 141.4 = 28.3V at 360Hz

5th harmonic = 10% of 141.4 = 14.1V at 600Hz

v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)] π=pi


(2) V at 20ms = 36.8 + 20.1 + 13.7 = 70.6V


(3) Error is [(100-70.6)/100]X100 = 29.4% !? That seems like a massive error, where has my equation gone wrong?

Help anyone!?
 
Physics news on Phys.org
  • #2
v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)]

That 5th harmonic is 1.2 radians leading, not lagging.
 
  • #3
BTW. You calculated the error incorrectly, however there is no reason why the percentage error could not be huge when calculated at a single point.

For example, what would the percentage error by at t=0?
 
  • #4
Well spotted, it should be -1.2 but re-calculating V at 20ms it's still 70.5V. How have I calculated the error incorrectly?
 
  • #5
alex.daciz said:
Well spotted, it should be -1.2 but re-calculating V at 20ms it's still 70.5V. How have I calculated the error incorrectly?

Using your equations I get (2) V at 20ms = 82.9 + 26.9 - 13.1.
 
Last edited:
  • #6
Sorry my calculator wasn't in radians! Would that then make the error 3.3%?
 
  • #7
Hi
Im stuck on the same question. I've been using 141.4sin(2pi x f(120) x 0.02), which gives me 9.41v
28.3Sin(2pi x 360 x 0.02) = 21.45v
14.1sin(2pi x 600 x .02 - 1.2) = 18.08v

Then added these up to give combined voltage at 20ms of 48.93v
This is obviously a diffenrent answer to answers above, could someone please point out if I am doing something wrong.
Many thanks
 

1. What is an A.C. voltage waveform?

An A.C. (alternating current) voltage waveform is a graphical representation of the voltage changes over time in an electrical circuit that uses alternating current. It shows the amplitude and frequency of the voltage, as well as the shape of the waveform which can vary depending on the type of circuit and load.

2. What are harmonics in A.C. voltage waveforms?

Harmonics are additional frequency components that are present in an A.C. voltage waveform besides the fundamental frequency. They are caused by non-linear loads in the circuit, such as electronic devices, and can distort the shape of the waveform. Harmonics can cause issues with the performance of the circuit and equipment, and need to be properly managed.

3. How are harmonics measured in A.C. voltage waveforms?

Harmonics can be measured using a power quality analyzer, which is a device that captures and analyzes the electrical signals in the circuit. The analyzer will display the harmonic levels as a percentage of the fundamental frequency, and can also provide information on the specific harmonic orders present in the waveform.

4. Can harmonics cause problems in electrical systems?

Yes, harmonics can cause a range of problems in electrical systems, including overheating of equipment, voltage and current distortions, and interference with other electrical devices. They can also affect the efficiency and reliability of the system, leading to increased energy costs and potential equipment failures.

5. How can harmonics be mitigated in A.C. voltage waveforms?

Harmonics can be mitigated through various methods such as using harmonic filters, adding capacitors or inductors to the circuit, and using power factor correction. It is also important to properly select and install electrical equipment that can handle harmonics, and regularly monitor and maintain the system to prevent issues caused by harmonics.

Similar threads

Harmonic waves - Fundamental voltages
    • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
Engineering AC Circuit Voltage Waveform Analysis
    • Engineering and Comp Sci Homework Help
Replies
7
Views
2K
How Do You Calculate AC Waveform Components and Errors?
    • Engineering and Comp Sci Homework Help
3
Replies
74
Views
36K
Voltage Waveform for 3rd and 5th Harmonics with 120Hz Fundamental at 20ms
    • Engineering and Comp Sci Homework Help
Replies
4
Views
7K
How to sketch harmonic component graph?
    • Introductory Physics Homework Help
Replies
1
Views
5K

Hot Threads

Recent Insights

Back
Top