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EXPERIMENT NO: THREE AIM: Voltage Profile Enhancement of the Power System Theory: In a modern power system, electrical energy from the generating station is delivered to the ultimate consumers through a network of transmission and distribution. For satisfactory operation of motors, lamps and other loads, it is desirable that consumers are supplied with substantially constant voltage. Too wide variations of voltage may cause erratic operation or even malfunctioning of consumers’ appliances. To safeguard the interest of the consumers, the government has enacted a law in this regard. The statutory limit of voltage variation is ± 6% of declared voltage at consumers’ terminals. The principal cause of voltage variation at consumer’s premises is the change in load on the supply system. When the load on the system increases, the voltage at the consumer’s terminals falls due to the increased voltage drop in (i) alternator synchronous impedance (ii) transmission line (iii) transformer impedance (iv) feeders and (v) distributors. The reverse would happen should the load on the system decrease. These voltage variations are undesirable and must be kept within the prescribed limits (i.e., ± 6% of the declared voltage). This is achieved by installing voltage regulating equipment at suitable places in the power system. The purpose of this chapter is to deal with important voltage control equipment and its increasing utility in this fast-developing power system. Methods of Voltage Control There are several methods of voltage control. In each method, the system voltage is changed in accordance with the load to obtain a fairly constant voltage at the consumer’s end of the system. The following are the methods of voltage control in an A.C power system: 1) 2) 3) 4) 5) 6) By excitation control By using tap changing transformers Auto-transformer tap changing Booster transformers Induction regulators By synchronous condenser Voltage Control by Synchronous Condenser The voltage at the receiving end of a transmission line can be controlled by installing specially designed synchronous motors called synchronous condensers at the receiving end of the line. The synchronous condenser supplies wattless leading kVA to the line depending upon the excitation of the motor. This wattless leading kVA partly or fully cancels the wattles lagging kVA of the line, thus controlling the voltage drop in the line. In this way, voltage at the receiving end of a transmission line can be kept constant as the load on the system changes. For simplicity, consider a short transmission line where the effects of capacitance are neglected. Therefore, the line has only resistance and inductance. Let V 1 and V2 be the per phase sending end and receiving end voltages, respectively. Let I2 be the load current at a lagging power factor of cos φ2. (i) Without synchronous condenser: - Fig. 1 (i) shows the transmission line with resistance R and inductive reactance X per phase. The load current I 2 can be resolved into two rectangular components via Ip in phase with V2 and Iq at right angles to V2 [See Fig.1 (ii)]. Each component will produce resistive and reactive drops; the resistive drops being in phase with and the reactive drops in quadrature leading with the corresponding currents. The vector addition of these voltage drops to V2 gives the sending end voltage V1. Figure 1 (ii) With synchronous condenser: - Now suppose that a synchronous condenser taking a leading current Im is connected at the receiving end of the line. The vector diagram of the circuit becomes as shown in Fig. 2.2. Note that since I m and Iq are in direct opposition and that Im must be greater than Iq, the four drops due to these two currents simplify to: Figure 2 (𝐼𝑚 − 𝐼𝑞 ) R and in phase with Im (𝐼𝑚 − 𝐼𝑞 ) X in quadrature leading with Im From the vector diagram, the relation between V 1 and V2 is given by. 𝑂𝐸 2 = (𝑂𝐴 + 𝐴𝐵 − 𝐷𝐸 ) 2 + (𝐵𝐶 + 𝐶𝐷) 2 or 2 2 𝑉12 = [ 𝑉2 + 𝐼𝑝 𝑅 − (𝐼𝑚 − 𝐼𝑞 ) 𝑋] + [ 𝐼𝑝 𝑋 + (𝐼𝑚 − 𝐼𝑞 )𝑅] 𝑉1 From this equation, the value of Im can be calculated to obtain any desired ratio of 𝑉2 for a given load current and power factor. 3 𝑉2 𝐼𝑚 kVAR capacity of condenser = 1000 Calculations: Voltage Profile Enhancement using Synchronous Condenser A 3-phase overhead line has resistance and reactance per phase of 5Ω and 20Ω respectively. The load at the receiving end is 25MW at 66kV with power factor of 0.8 lagging. Find the capacity of the synchronous condenser required for this load condition if it connected at the receiving end and if the line voltage at both ends is to be maintained at 66kV. Present numerical solution and develop MATLAB program to fill relevant data in observat ion Table. Given: Load = 25MW; Line Voltage = 66kV; Power Factor = 0.8; R = 5Ω; X = 20Ω. Solution: 𝑃 𝐼2 = √3𝑉𝐿 𝑐𝑜𝑠𝜑 𝐼2 = 25 ∗ 106 √3(66000)( 0.8) 𝐼2 = 273.367𝐴 𝐼𝑝 = 𝐼2 𝑐𝑜𝑠𝜑2 = ( 273.367)( 0.8) = 218.693𝐴 𝐼𝑞 = 𝐼2 𝑆𝑖𝑛𝜑2 = (273.367)(0.6) = 164.02𝐴 Sending End Voltage: (V1 = Receiving End Voltage per phase = V2) 𝑉2 = 𝑉𝐿 √3 = 66000 √3 = 38.105𝑘𝑉 Let Im be the current taken by the synchronous condenser. Then, 2 2 𝑉12 = [𝑉2 + 𝐼𝑝 𝑅 − (𝐼𝑚 − 𝐼𝑞 ) 𝑋] + [ 𝐼𝑝 𝑋 + (𝐼𝑚 − 𝐼𝑞 )𝑅 ] (38.105𝑘𝑉 )2 = [(38.105𝑘𝑉 ) + (218.693 ∗ 5) − (20𝐼𝑚 − (20)164.02)]2 + [(218.693 ∗ 20) 2 + (5𝐼𝑚 − ((5)(164.02))] (38.105𝑘𝑉 )2 = [ 38.105𝑘𝑉 + 1093.465 − 20𝐼𝑚 + 3280.4] 2 + [4373.86 + 5𝐼𝑚 − 820.1]2 Now: 𝐼𝑚 = 233.369𝐴 And: Capacity of Synchronous Condenser: = = 3𝑉2 𝐼𝑚 106 𝑀𝑉𝐴𝑅 3 ∗ 38.105𝑘𝑉 ∗ 233.369 106 = 26.678 𝑀𝑉𝐴𝑅 MATLAB Program: close all clc kw=25e3; pf=0.8; v=66e3; r=5; x=20; i2=kw*1000/sqrt(3)/v/1000/pf; ip=i2*pf; iq=i2*sind(acosd(pf)); v1=v/sqrt(3); im=233.369; capacity=3*v1*im/10^6; fprintf("Load current = %d A \n", i2); fprintf("Ip = %.2 f A \n", ip); fprintf("Iq = %.2 f A \n", iq); fprintf("Sending end voltage per phase = %d V \n", v1 ); fprintf("Im = %d A \n", im); fprintf("Capacity of synchronous condenser = %.2f MVAR \n", capacity); Observation Table: Sr. No. Data Value Unit (V,A) 1. Load Current 273.367 A 2. Ip 218.693 A 3. Iq 164.02 A 4. Sending end voltage\phase 𝟑𝟖. 𝟏𝟎𝟓 kV 5. Im 233.369 A 6. Capacity of Syn. Condenser 26.678 MVAR Table 1 Conclusion: Voltage variations that are too large may cause consumer appliances to malfunction. The difference in voltage at the consumer's location is caused by a change in supply load. The system's load is inversely proportional to the voltage at the customers' terminals. The calculated results are like the simulated results. The load current, phase current, Iq, sending end voltage and Im are similar. Questions: 1. A synchronous condenser is generally installed at the receiving end of the transmission line. 2. The principal cause of voltage variation is the change of load on the system. 3. Describe the synchronous condenser method of voltage control for a transmission line. Illustrate your answer with a vector diagram. The voltage at the receiving end of a transmission line can be controlled by installing specially designed synchronous motors called synchronous condensers at the receiving end of the line. The synchronous condensers provide wattless reading KVA to the line depending upon the excitation of the motor. The wattless leading KVA then partly or fully cancels the wattless lagging KVA of the line, thus controlling the voltage drop in the line. This then results to voltage at the receiving end of a transmission line can be kept constant as the load on the system changes.