Electrial Power System

Different Between Solid Conductor and Stranded Conductors

Solid Conductor : 

It consists of single piece of metal wire. It is cheap for manufacturing.Skin effect is higher in solid conductors as at higher frequencies current flow on the surface of the conductors results in the increase in the effective resistance. The main disadvantage of the solid wire is its more rigid property. It cannot be bent easily.

Stranded Conductors :

Stranded wire consists of sub conductors touch each other. It is costlier to manufacture compared to solid wire. For the given current carrying capacity the size of the stranded conductor is large compared to solid wire. Different elements of strands can be wound together to get the transmission line of desired property (eg: ACSR conductor contains Aluminum and Steel stands wound together). Proximity and skin effect is reduced using stranded conductors.

Different terms in Power System

Skin Effect :

"The tendency of alternating current to concentrate near the surface of a conductor is known as skin effect."

Due to skin effect, the effective area of cross-section of the con- ductor through which current flows is reduced. Consequently, the re- sistance of the conductor is slightly increased when carrying an alter- nating current. The cause of skin effect can be easily explained. A solid  conductor may be thought to be consisting of a large number of strands, each carrying a small part of the current. The *inductance of each strand will vary according to its position. Thus, the strands near the centre are surrounded by a greater magnetic flux and hence have larger induc-tance than that near the surface. The high reactance of inner strands causes the alternating current to flow near the surface of conductor. This crowding of current near the conductor surface is the skin effect.

The skin effect depends upon the following factors :

1. Nature of material
2. Diameter of wire − increases with the diameter of wire.
   Frequency
3. increases with the increase in frequency.
4. Shape of wire − less for stranded conductor than the solid conductor.

Positive , Negative, Zero sequences in Power System

Considering a three-phase system, symmetrical components (positive sequence, negative sequence, and zero sequence) allow one to analyze power system operation during unbalanced conditions such as those caused by faults between phases and/or ground, open phases, unbalanced impedances, and so on. 

Positive sequences :

The positive sequence set consists of the balanced three-phase currents and line-to-neutral voltages supplied by the system generator. They are always equal in magnitude and phase displaced by 120 degrees rotating at the system frequency with a phase sequence of normally a, b, c. The sequence currents or sequence voltages always exist in three's, never alone or in pairs.

Negative sequences :

The negative sequence set is also balanced with three equal magnitude quantities at 120 degrees apart but with the phase rotation or sequence reversed, or a, c, b. (If the positive sequence is a, c, b as in some power systems, then negative sequence will be a, b, c.) For the negative sequence set, again the sequence currents or sequence voltages always exist in three's, never alone or in pairs.

Zero sequences :

The members of the zero-sequence set of rotating phasors are always equal in magnitude and always in phase. Once again, if zero sequence currents or zero sequence voltages exist, they must exist in all three phases, never alone or in one phase.

In transformers, lines, etc., the phase sequence of the current does not change the impedance encountered, so positive sequence impedance equals negative sequence impedance; X1 = X2.

Surge Impendence Loading (SIL)

The surge impedance loading or SIL of a transmission line is the MW loading of a transmission line at which a natural reactive power balance occurs.  The following brief article will explain the conceptof SIL.

Transmission lines produce reactive power (Mvar) due to their natural capacitance. The amount of Mvar produced is dependent on the transmission line's capacitive reactance (XC) and the voltage (kV) at which the line is energized.  In equation form the Mvar produced is:  

Transmission lines also utilize reactive power to support their magnetic fields.  The magnetic field strength is dependent on the magnitude of the current flow in the line and the line's natural inductive reactance (XL).  It follows then that the amount of Mvar used by a transmission line is a function of the current flow and inductive reactance.  In equation form the Mvar used by a transmission line is:

  

A transmission line's surge impedance loading or SIL is simply the MW loading (at a unity power factor) at which the line's Mvar usage is equal to the line's Mvar production.  In equation form we can state that the SIL occurs when: 

 

If we take the square root of both sides of the above equation and then substitute in the formulas for XL (=2pfL) and XC (=1/2pfC) we arrive at:  

The term  in the above equation is by definition the "surge impedance.  The theoretical significance of the surge impedance is that if a purely resistive load that is equal to the surge impedance were connected to the end of a transmission line with no resistance, a voltage surge introduced to the sending end of the line would be absorbed completely at the receiving end.  The voltage at the receiving end would have the same magnitude as the sending end voltage and would have a phase angle that is lagging with respect to the sending end by an amount equal to the time required to travel across the line from sending to receiving end.

 The concept of a surge impedance is more readily applied to telecommunication systems than to power systems.  However, we can extend the concept to the power transferred across a transmission line.  The surge impedance loading or SIL (in MW) is equal to the voltage squared (in kV) divided by the surge impedance (in ohms).  In equation form:  

.

Note in this formula that the SIL is dependent only on the kV the line is energized at and the line's surge impedance.  The line length is not a factor in the SIL or surge impedance calculations.  Therefore the SIL is not a measure of a transmission line's power transfer capability as it does not take into account the line's length nor does it consider the strength of the local power system.

The value of the SIL to a system operator is realizing that when a line is loaded above its SIL it acts like a shunt reactor - absorbing Mvar from the system - and when a line is loaded below its SIL it acts like a shunt capacitor - supplying Mvar to the system.

Lossless line

For a lossless line, R and G are both zero, so the equation for characteristic impedance reduces to:

The imaginary term j has also canceled out, making Z₀ a real expression, and so is purely resistive.

In electric power transmission, the characteristic impedance of a transmission line is expressed in terms of the surge impedance loading (SIL), or natural loading, being the power loading at which reactive power is neither produced nor absorbed:

in which  is the line-to-line voltage in volts.

Loaded below its SIL, a line supplies reactive power to the system, tending to raise system voltages. Above it, the line absorbs reactive power, tending to depress the voltage. The Ferranti effect describes the voltage gain towards the remote end of a very lightly loaded (or open ended) transmission line. Underground cables normally have a very low characteristic impedance, resulting in an SIL that is typically in excess of the thermal limit of the cable. Hence a cable is almost always a source of reactive power.

 Importance of the X/R Ratio

Purpose of a Short Circuit Study

In some short circuit studies, the X/R ratio is ignored when comparing the short circuit rating of the equipment to the available fault current at the equipment. What is not always realized is that when lowvoltage gear is tested, it is tested at a certain X/R ratio. The X/R ratio is important because it determines the peak asymmetrical fault current. The asymmetrical fault current can be much larger than the symmetrical fault current. The purpose of this article is to introduce such terms as the X/R ratio and asymmetrical fault current and to relate the importance of the X/R ratio to the rating of low-voltage equipment. 

The purpose of a short circuit study is to determine whether or not electrical equipment is rated properly for the maximum available fault current that the equipment may see. The study is performed using computer software first by modeling the system (conductors, transformers, generators, utility sources, etc.) and then by simulating faults.

X/R Ratio 

In the previous section, we used Ohm’s Law to say that if the voltage remains constant and the impedance decreases, the fault current increases. This is true. However, it does not take into account the dynamics of AC electrical systems. We must remember that a fault is a sudden event. Any time a sudden event occurs, the electrical system requires some time to adapt. Such a response is called a transient, which means that it lasts for only a short time.

In AC electrical systems, impedance has two components. The first is called reactance (X). Reactance depends on two things: (1) the inductance and (2) the frequency. Inductance reflects how hard it is to change the current. All conductors have some inductance, but a more useful example of a component having inductance is a coil of wire. Frequency is fixed at either 60 or 50Hz, depending upon where in the world the electrical system is, so the reactance is solely dependent upon the inductance. 

The second component of impedance is the familiar resistance (R). Resistance is a measure of how hard it is for current to flow. When current flows through a material having resistance, heat is transferred from the material to the surroundings.

The resistance and reactance of a circuit establishes a power factor. The power factor (p.f.) is given by the following equation: p.f. = cos(tan-1(X/R))

Please note that as power factor decreases, the X/R ratio increases.