11th Week: "Three-Phase Circuits"

"Balanced Three-Phase Voltages"


Three-phase voltages are often produced with a three-phase ac generator or alternator whose cross-sectional view is shown below,

The voltage sources can be either wye-connected as shown in Fig.(a) or delta-connected as in Fig (b).

Balanced phase voltages are equal in magnitude and are out

of phase with each other by 120◦.

The phase sequence is the time order in which the voltages pass through their respective maximum values.

A balanced load is one in which the phase impedances

are equal in magnitude and in phase.

Types of Connections:

• Balanced Wye-Wye Connection

• Balanced Wye-Delta Connection

• Balanced Delta-Delta Connection

• Balanced Delta-Wye Connection

Table below presents a summary of the formulas for phase currents and voltages and line currents and voltages for the four connections. Students are advised not to memorize the formulas but to understand how they are derived. The formulas can always be obtained by directly applying KCL and KVL to the appropriate three-phase circuits.

Learning:

• I learned that the generator is consists of rotating magnet.
• For Wye connection IL=Ip and VL=(square root of 3)Vp.
• For Delta connection VL=Vp and IL=(square root of 3)Ip.
• Balanced phase voltages are equal in magnitude and are out of phase with each other by 120◦
• Abc sequence is known as positive sequence.
• Acb sequence is known as negative sequence.

Videos:

For more information, watch the video below:

That's all. Thank You for visiting my blog.

GOD Bless! :)

By:

AYALA, ARNY  S.   BSECE -3

ECE 321

Professor:

ENGR. JAY S. VILLAN, MEP - EE

10th Week: "Power Factor & Complex power"

"Power Factor"


We see that if the voltage and current at the terminals of
a circuit are,

v(t) = Vm cos(ωt + θv)

and

i(t) = Im cos(ωt + θi)

The average power is a product of two terms. The product Vrms Irms is known as the apparent power S. The factor cos(θv − θi) is called the power factor (pf).

S = Vrms Irms

The apparent power (in VA) is the product ofthe rms values ofvoltage and current.

The power factor is dimensionless, since it is the ratio of the average power to the apparent power,

pf =P/S= cos(θv − θi)

The angle θv − θi is called the power factor angle, since it is the angle whose cosine is the power factor.

The power factor is the cosine ofthe phase difference between voltage and current. It is also the cosine ofthe angle ofthe load impedance.

"Complex Power"

Power engineers have coined the term complex power, which they use to find the total effect of parallel loads. Complex power is important in power analysis because it contains all the information pertaining to the power absorbed by a given load.


Complex power (in VA) is the product ofthe rms voltage phasor and the complex conjugate ofthe rms current phasor. As a complex quantity, its real part is real power P and its imaginary part is reactive power Q.


Introducing the complex power enables us to obtain the real and reactive powers directly from voltage and current phasors.

It is a standard practice to represent S, P, and Q in the formof

a triangle, known as the power triangle, shown below,

Learning:

• Real Power (P) in measured in W, Reactive Power (Q) in VAR, and Apparent Power (S) in VA.
• For Power Factor (PF), when theta increases PF decreases, and when theta decreases PF increases.
  
  Reactive Power:
• Q = 0 for resistive loads (unity pf).
• Q < 0 for capacitive loads (leading pf).
• Q > 0 for inductive loads (lagging pf).

Videos:

For more information, watch the video below:

That's all. Thank You for visiting my blog.

GOD Bless! :)

By:

AYALA, ARNY  S.   BSECE -3

ECE 321

Professor:

ENGR. JAY S. VILLAN, MEP - EE

9th Week: "AC Power Analysis"

"AC Power Analysis"

Our study in ac circuit analysis so far has been focused mainly on calculating voltage and current. Our major concern in here is power analysis.

Instantaneous and Average Power

The instantaneous power p(t) absorbed by an
element is the product of the instantaneous voltage v(t) across the element and the instantaneous current i(t) through it. Assuming the passive sign convention,

p(t) = v(t) i(t)

Where,

v(t) = Vm cos(ωt + θv)
i(t) = Im cos(ωt + θi)

Average Power

The average power is the average of the instantaneous power over one period.

Maximum Average Power Transfer 

We solved the problem of maximizing the power delivered by a power-supplying resistive network to a load RL. Representing the circuit by its Thevenin equivalent, we proved that the maximum load if the load resistance is equal to the Thevenin resistance RL = RTh. We now extend that result to ac circuits.


In rectangular form, the Thevenin impedance ZTh and the load impedance ZL are,

ZTh = RTh + jXTh

ZL = RL + jXL

For maximum average power transfer, the load impedance ZL must be equal to the complex conjugate ofthe Thevenin impedance ZTh.

Effective or RMS Value

The effective value of a periodic current is the dc current that delivers the same average power to a resistor as the periodic current.

The effective value of a periodic signal is its root mean square (rms) value.

Learning:

• Power analysis is another chapter and view of understanding in our class since it has lesser circuit analysis. Power is the most important quantity in electric utilities, electronic, and communication systems, because such systems involve transmission of power from one point to another.

Videos:

For more information, watch the video below:

That's all. Thank You for visiting my blog.

GOD Bless! :)

By:

AYALA, ARNY  S.   BSECE -3

ECE 321

Professor:

ENGR. JAY S. VILLAN, MEP - EE