AC circuit

We know that in DC circuit, power can be simply expressed as the product of voltage and current: P=U*I.

Nevertheless, in AC circuit, this expression becomes a little more complicated. The power now is rephrased as "Complex Power", S=U*conjugate (I)=P+jQ.

Facts:
(1) Power factor: inductive loads have lagging power factor, capacitive loads have leading power factor.

The power factor is a ratio of real power to the apparent power, it's value is cos(theta), where theta is the angle between the current and the voltage of loads. If the current is lagging the voltage, we call it has a lagging power factor and vice versa.
Let's consider the inductive loads first (r+jwL). I=U/(r+jx). We will see that I=U/Z^2*(r-jx). If we assume the angle is 0 for U, then the angel of I is -90 degrees (if r is 0). Obviously it is lagging!
Now we consider the capacitive loads (r+1/jwC) . I=U/(r+1/jwC), then it is positive (leading) compared to voltage angle.

(2) Inductive loads absorb reactive power while capacitive loads produce reactive power.

Now that we know complex power S=P+jQ=U*conjugate(I). For inductive loads, S=U*conjugate(I)=U^2/Z^2 (r+jx) (note the sign is changed to + because it is conjugate). OK! Now we see that P is positive, Q is positive, which represent that the inductive loads absorb real power and reactive power. Similar for capacitive loads. The sign for the Q will be negative, indicating that they produce reactive power.
Another way to think about this:
I=Icos(theta)+jIsin(theta), S=U*conjugate(I)=U*(Icos(theta)-jIsin(theta)). Notice that if it is an inductive load, then theta<0, Q=-Isin(theta)>0, meaning that it absorbs reactive power. The derivation also applied to conductive loads.

Transmission

Some knowledge about Electric Power Transmission:

(1) Transmission conductor size ranges from 12mm2 to 750mm2, thicker wires lead to small increase in the capacity limit (or current-carrying capacity)of transmission lines, due to skin effect.

(2) Transmission voltage levels:
EHV: >230KV
Transmission: >110KV
Subtransmission: 33-66KV
Distribution: <33KV
Comparing with the voltage of power generating plants: 2.3KV-30KV

(3) Long distance transmission cost is around $0.005-$0.02/KWh in US. Compare to the production cost of generating units: $0.01-$0.025/KWh, and retail rate: $0.1/KWh (from wikipedia)

(4) Which factor sets the thermal limit for a transmission line:
 short line: The thermal limit is set by the resistance or heating limit of conductors;
 intermediate line:  voltage drop is the one that determines the power limit. P=v1*v2*sin(delta)/x. You don't want the voltage drop too much (v2 small), or it is not suitable for load (usually no more than 5% voltage drop). The voltage drop is defined as the magnitude of the difference of two phasors (|v1-v2|). 
long line: it is the angle delta or system stability that determines the power limit. When the angle approaches 90 degrees, the system approaches its stability margin, which is undesirable for the operation.

HVDC- high voltage direct current

Two years ago, when a person whose major is medicine asked me about the reason to use HVDC(high-voltage direct current) lines to transmit long-distance power from West China to East China, I could not give a very clear explanation, which quite embarrassed me since no excuse could be found for my own limited and obscure understanding of the concept.(It is funny that actually today when I have not finished this article, there is another guy who asked exactly the same question, and I think this time my answer made him satisfied.)

At the time, I was already a second-year PhD student in power engineering, but I still had some trouble in basic knowledge and concepts of power systems (even now I am still learning them). The phenomenon is not rare among PhD students, I believe, at least at some informal discussions with my fellow colleagues.

Therefore, I decide to write down some basic knowledge that a power engineering student should have, and hopefully I can accumulate and update them in this blog regularly as I learn. It may not  be very scientific, but it conveys the basic principle of the concepts and issues.

Well, go back to the question about HVDC, I had known that high voltage line has the capability of reducing the power loss, but why direct current?
Actually several reasons can justify the use of DC lines:
(1) The materials required in DC lines are about 1/3 less than AC lines (Two lines one phase vs Three lines three phases). Look at these two pictures from Chinese state grid website (a is AC lines, b is DC lines):

However, we should also realize the required AC/DC/AC converter station is quite expensive. Due to the trade off between the materials saving (and also the saving from less power loss in DC lines) and the additional cost of converters, a cost-benefit analysis is usually conducted for determining the equivalent distance for both AC and DC lines.  If a transmission needs to be built within the determined equivalent distance (short lines), then AC is more beneficial; DC is more attractive in long distance power delivery. HVDC lines are usually used for long distance, great than 400 miles or 600km.

(2) Additional losses exist in AC lines because of inductance and capacitance, compared to DC lines. The electricity current that is used to charge capacitance in AC lines, can instead be used for customers' power usage in DC lines. In other words, DC lines are more efficient.

(3) DC lines can connect two unsynchronized AC systems, which may not be achievable by AC lines. It thanks to the AC/DC/AC converters that separate the operation of two connected AC systems.

There may be more advantages of DC lines than articulated here, like the capability to survive in fault conditions and so forth. Certainly DC lines have disadvantages, but the technology is still promising in long-distance power delivery (especially for renewable energy integration)!

Wide bandgap semiconductors

Recently I saw the concept of "wide bandgap". To check it out, I found the following paper that describes the characteristics of wide bandgap semiconductors:

Enhance power electronic devices with wind bandgap semiconductors

It states that currently silicon (Si) is used in most power electronic devices(diodes, MOSFET, IGBT). As the high voltage transmission lines (HVDC, EHV line) are obtaining popularity and more widely accepted in many countries, the power electronic devices are in need of much higher break down voltage. Si has its limitation in meeting this requirement. Instead, silicon carbide (SiC, 碳化硅，金刚砂), and gallium nitride (GaN, 氮化镓), and diamond can be considered because of the ten times greater electric field strength.

The appeal of national physicists on integrating renewable energy

See the news: 
New APS Report: Developing Energy Storage Technologies Among Crucial Steps Toward Increasing Renewable Electricity on Nation’s Grid

Integrate Renewable Energy On the Grid



APS (American Physical Society) developed a new report on integrating renewable energy. From the news, there are several recommendations made by the study for policy makers, regulatory agencies(DOE, FERC), forecasts providers, wind plant operators. The focus is mainly on energy storage, long-term transmission, business case and forecasting.

In addition to the perspectives in the report, I would like to make the following comments:
(1) The energy storage: besides searching for battery chemistries, it should be emphasized (worth exploring) that PHEVs could possibly act as economically viable storage devices after their usage is substantially increased (probably in need of government's promotions and subsidies).
(2) I highly agree with the viewpoint that regulatory agencies should develop response other than maintaining conventional reserve (the last point),but one aspect that should be included, besides energy storage and long-distance transmission,  is the demand response. Energy conservation or consumption shifting from peak hours to off-peak hours should be considered as a new type of reserve with great value to reduce the conventional reserve.

Integrate more renewable energy! Let's make effort together.

Learning and creating

I am working everyday, now as a phd student in electric power engineering, but soon will be an employee somewhere.
During my years as students, I can feel every little progress that I have made, and every new thing that I have learned. I enjoy them, and at the same time I feel I teach myself in this way, and most importantly, I can make full use of what I have learned to create useful things.
Now I start writing them down, and sharing with whoever have visited this blog and also got to know something that they did not know before.

By the way, this blog will be bilingual: English and Chinese.