Characteristics of Short Transmission Lines PDF

LESSON NO. 3 CHARACTERISTICS OF SHORT TRANSMISSION LINES LESSON OBJECTIVES: AT THE END OF THE LESSON, THE STUDENT WOULD BE ABLE TO 1. familiarize the parameters of short transmission lines 2. Construct the phase diagram of short transmission lines 3. Calculate th...

LESSON NO. 3 CHARACTERISTICS OF SHORT TRANSMISSION LINES LESSON OBJECTIVES: AT THE END OF THE LESSON, THE STUDENT WOULD BE ABLE TO 1. familiarize the parameters of short transmission lines 2. Construct the phase diagram of short transmission lines 3. Calculate the sending and receiving end voltage short transmission lines.  Voltage and Current Relations of Transmission lines The transmission lines are categorized as three types 1) Short transmission line– the line length is up to 80 km and the operating voltage is < 20 kV. 2) Medium transmission line– the line length is between 80 km to 160 km and the operating voltage is > 20 kV and < 100kV 3) Long transmission line – the line length is more than 160 km and the operating voltage is > 100 kV Whatever may be the category of transmission line, the main aim is to transmit power from one end to another. Like other electrical system, the transmission network also will have some power loss and voltage drop during transmitting power from sending end to receiving end. Due to smaller distance and lower line voltage, the capacitance effect are extremely small and can be neglected. Its performance depends on the resistance and inductance of the line.. Through in an actual line, the resistance and inductance are distributed over the whole length but in case of short lines, the total resistance and inductance are assumed to be lumped at one place. Unlike the electric machines studied so far, transmission lines are characterized by their distributed parameters: distributed resistance, inductance, and capacitance. The distributed series and shunt elements of the transmission line make it harder to model. Such parameters may be approximated by many small discrete resistors, capacitors, and inductors. The total series resistance, series reactance, and shunt admittance of a transmission line can be calculated as where r, x, and y are resistance, reactance, and shunt admittance per unit length and d is the length of the transmission line. The values of r, x, and y can be computed from the line geometry or found in the reference tables for the specific transmission line.  Short Transmission Lines For short length, the shunt capacitance of this type of line is neglected and other parameters like electrical resistance and inductor of these short lines are lumped, hence the equivalent circuit is represented as given in the next slide. For convenience, it is considered that the parameters of the conductors are lumped into one conductor, and the return conductor is assumed to have no resistance and inductive reactance. This circuit represents a three phase short transmission line if R and X represents the resistance and inductive reactance to neutral. I represent the current in one conductor, VR is the receiving end voltage to neutral while Vs is the sending end voltage to neutral and that the load is one phase. Short Transmission Line: Phasor Diagram (USING Vr AS REFERENCE) Using the phasor diagram with IR as the reference point The lower the voltage regulation, the better is it because low voltage regulation means little variation in receiving end voltage due to variation in load currents. The efficiency of transmission line is the ratio of power delivered at the receiving end to the power sent from the sending end. Mathematically, η = VR IR cos θR / VS IS cos θs OR η = VR IR cos θR / (VR IR cos θR + LINE LOSSES) In a summary: 1. If lagging (inductive) loads are added at the end of a line, the voltage at the end of the transmission line decreases significantly – large positive VR. 2. If unity-PF (resistive) loads are added at the end of a line, the voltage at the end of the transmission line decreases slightly – small positive VR. 3. If leading (capacitive) loads are added at the end of a line, the voltage at the end of the transmission line increases – negative VR Ferranti Effect In a medium or long transmission line when open circuited or lightly loaded the receiving end voltage is found more than the sending end voltage. This phenomenon of rise in voltage at the receiving end is called Ferranti effect owing to its first being observed on the Deptford mains laid down by S.Z. de Ferranti. This effect is due to voltage drop across the line inductance, due to charging current, being in phase with the applied voltage at the sending end of the line. Thus both capacitance and inductance are necessary to cause this phenomenon.  EXAMPLE NO. 4 1. A single phase line is transmitting 1100KW power to a factory at 11KV and at 0.8 lagging. It has a total resistance of 2Ω and a reactance of 3Ω. Determine the voltage at the sending end, percentage regulation and efficiency 2. A 10 mile, 60hz single phase TL using DOVE conductor equilaterally spaced with 5 feet spacing between centers. It delivers 2500KW at 13.8KV to a balance load. a. Determine the per phase impedance of the line b. What must be the sending end voltage when the power factor is 0.866 lagging, Unity power factor and 0.866 leading c. Determine the percent regulation of the line at different power factor d. Transmission efficiency of the line at different power factor Assume wire temperature to be 50oC Three phase short TL: The assumption on short 3 phase TL are 1. System is Y connected 2. Transmission is balance 3. Per phase basis Sending power, Ps = √3 Vs,LLIs,LLpfs (note that IΦ = ILL in Y ) Or Ps = 3 VSN Is pfs Receiving power = √3 VR,LL IR,LL pfR Or PR = 3 VRN IR pfR For Y connected, Is = IR VSN = Vs/ √3 VSN = sending end to neutral VRN = receiving end to neutral PLOSS = 3IS2 R 3. A short three phase transmission line of parameters R = 0.4Ω and X = 0.6Ω is delivering 2000KVA to a load at a power factor of 0.8 lagging at the receiving end of the line. If the load voltage is 3000V, determine the voltage regulation and the efficiency of the line. 4. A 20 mile, three phase transmission line is composed of 336.4MCM, 26/7 ACSR strand. The conductor are spaced horizontally with 3 ft between adjacent conductor. It is supplying a balanced load of 4000KW at 13.8KV with 0.8 lagging power factor at 60HZ a. Calculate the sending end voltage and the power factor b. Voltage regulation of the line c. Efficiency of the TL d. If a capacitor bank is connected in parallel with the load that draws a line current of 120A, calculate the sending end voltage and the sending end power factor. 5. Calculate the equilateral spacing between three phase line with sending end voltage of 8100V, 0.78 lagging and receiving end voltage of 7620V, 0.8 lagging per phase. If load voltage is used as reference and the sending end current is 60A. The radius of the conductor is 0.035 ft at a distance of 19.5Km 6. A balanced Y connected load of 300 + J100 ohms per phase is supplied by a 3 phase line 40Km long with an impedance of 0.6 + J0.7 ohms per Km. find the voltage at the receiving end when the supply voltage is 66KV. Find also the efficiency of the transmission. 7. A 13.8KV (nominal), three phase 60hz sub-transmission line 10Km from the utility’s substation, serves an industrial plant. The conductor used is PARTRIDGE, transposed, and spaced horizontally such that a-b = 2 meters and b-c = 1.2 meters. Determine the horsepower of the largest squirrel cage induction motor that can be started across the line (full voltage) without exceeding 2 percent voltage drop in order to avoid objectionable flicker. Assume the system reactance at the substation is 0.2 Ω the conductor working temperature is 500C. The effect of capacitance may be neglected and the efficiency and power factor of the motor are both 85% respectively.  ASSIGNMENT NO. 3 1. A short three phase transmission line connected to a 33KV, 50HZ generating station at the sending end is required to supply a load of 10MW at 0.8 lagging power factor at 30KV at the receiving end. If the minimum transmission efficiency is to be limited to 96% estimate the per phase values of resistance and inductance of the line. (VRN as reference vector) 2. A short three phase transmission line has an impedance of3 + J4 ohms per wire. At the receiving end are connected to a three phase inductive load of 3500KW at 13200V with 0.8 power factor and a capacitor bank drawing 150A line current. Calculate the sending end current, Is, the sending end voltage Vs and the sending end power factor. (VRN as reference vector) 3. A balance Y connected load of 250 + J100 ohms per phase is supplied by a three phase line 5KM long with an impedance of 0.1 + J0.2 ohms per KM. find the voltage at the receiving end whose sending voltage is 22KV. Calculate the efficiency of the transmission. (VRN as reference vector) Medium length transmission lines (nominal T) Medium lenght transmission line (nominal π)  EXAMPLE NO. 5 1. A 230KV three phase transmission line is supplying a substation that draws a line current of 120A at 0.866 lagging power factor. The line has the following characteristics A = 0.95∟0.980 B = 140∟760 C = 914X10-9∟900 Calculate the voltage regulation and the efficiency of the transmission using T and π network. 2. A 120km three phase TL is supplying a load that draws 180A at 100KV with 0.866 lagging. The conductors are spaced 6m horizontally between adjacent phases that uses 336.4MCM 30/7 strand. Assuming that the capacitance are lumped at the middle of the line. Determine a. The line constants b. Sending end voltage c. Sending end current d. Percent regulation