Unit 2 Reactive Power Management
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This document provides an overview of reactive power management in power systems. It discusses the power triangle and significance of positive and negative real and reactive power. Reactive power control is necessary to reduce losses, improve voltage regulation and increase transmission capacity. Sources of reactive power include synchronous machines, capacitors, and FACTS devices. Series and shunt compensation are used to improve voltage profiles and increase power transfer capabilities by reducing line reactance. Synchronous machines can generate or absorb reactive power through field excitation control.
Unit 2 Reactive Power Management
- 1. DEPARTMENT OF ELECTRICAL ENGINEERING JSPMS BHIVARABAISAWANTINSTITUTEOFTECHNOLOGYANDRESEARCH, WAGHOLI,PUNE A.Y. 2020-21 (SEM-I) Class: B.E. Subject: Power System Operation Control Unit No-2 Reactive Power Management Prepared by Prof. S. D. Gadekar Santoshgadekar.919@gmail.com Mob. No-9130827661
- 2. Content • Introduction • Power Triangle • The Significance of Positive and Negative P & Q • Necessity of Reactive Power Control • Advantages of Power Factor Improvement at Load End • Sources of Reactive Power • Synchronous Alternator as a Source of Reactive Power • Synchronous Motor as a Source of Reactive Power • Loading Capability curve of a Generator • Compensations in Power System • Problems Associated with Series Compensation • Comparison of Series and Shunt Compensation • Loading Capability Curve of Generator
- 3. Introduction The required power supply to an electric circuit depends on, Active power - real electrical resistance power consumption in circuit Reactive power - imaginary inductive and capacitive power consumption in circuit The required power supply is called the apparent power and is a complex value that can be expressed in a Pythagorean triangle known as Power Triangle.
- 4. Power Triangle Power Triangle is the representation of a right angle triangle showing the relation between active power, reactive power and apparent power. 𝐼 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 ∅ 𝐼 cos ∅ 𝐼sin∅ When each component of the above phasor diagram is multiplied by the voltage V, a power triangle is obtained shown in the figure below, ∅ 𝑉𝐼 𝑉𝐼 sin ∅ 𝑉𝐼 cos ∅ ∅ 𝑉𝐼 𝑉𝐼 sin ∅ 𝑉𝐼 cos ∅
- 5. When an active component of current is multiplied by the circuit voltage V, it results in active power.it is this power which produces torque in the motor, heat in the heater, etc. This power is measured by the wattmeter. When the reactive component of the current is multiplied by the circuit voltage, it gives reactive power. This power determines the power factor, and it flows back and forth in the circuit. When the circuit current is multiplied by the circuit voltage, it results in apparent power. From the power triangle shown above the power factor may be determined by taking the ratio of true power to the apparent power. 𝑃𝑜𝑤𝑒𝑟 𝐹𝑎𝑐𝑡𝑜𝑟 cos ∅ = 𝐴𝑐𝑡𝑖𝑣𝑒 𝑃𝑜𝑤𝑒𝑟 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 = KW KVA
- 6. The Significance of Positive and Negative P & Q P Positive- AC System supplies real active power to network. P Negative-AC network supplies real active power to a three phase ac system. Q Positive-AC system supplies lagging reactive power to a ac network. The network consists of elements which are predominantly inductive. Q Negative-AC system supplies leading reactive power to a ac network. The network consists of elements which are predominantly capacitive.
- 7. Necessity of Reactive Power Control 1. System losses due to reactive power flow The real power in three phase ac system is 3𝑉𝑙 𝐼𝑙 cos ∅ , 𝐼𝑙 = 𝑃 3𝑉𝑙 cos ∅ The current 𝐼𝑙 is minimum if cos ∅ is unity, as power factor cos ∅ becomes less than unity, the circuit current 𝐼𝑙 increases. Transmission Losses cos ∅ The system needs to transmit reactive power due to the fact that most of the loads operates at lagging power factor. Examples Induction motor, Transformer, arc lamps, welding equipment's.
- 8. Necessity of Reactive Power Control 2. To meet the load requirement at a low power factor, the capacity of power plant, transmission and distribution equipment has to be more than would be necessary if the load were demanded at unity power factor. G 𝐸′ < 𝛿 Bus 1 Bus 2 𝑃𝑚 𝑆𝑠 = 𝑃𝑠 + 𝑄𝑠 𝑆𝑟 = 𝑃𝑟 + 𝑄 𝑟 Unity Power Factor Load Case-1 Unity Power Factor Load ∅ = 𝟎 𝑆𝑟 = 𝑉𝐼 𝑄 𝑟 = 𝑉𝐼 sin ∅ = 0 𝑃𝑟 = 𝑉𝐼 cos ∅ = 𝑉𝐼 ∅ = 𝟎 𝑃𝑟 = 𝑉𝐼 = 𝑆𝑟
- 9. Necessity of Reactive Power Control 2. To meet the load requirement at a low power factor, the capacity of power plant, transmission and distribution equipment has to be more than would be necessary if the load were demanded at unity power factor. G 𝐸′ < 𝛿 Bus 1 Bus 2 𝑃𝑚 𝑆𝑠 = 𝑃𝑠 + 𝑄𝑠 𝑆𝑟 = 𝑃𝑟 + 𝑄 𝑟 Lagging Power Factor Load Case-1 Load At Lagging Power Factor 𝟗𝟎 > ∅ > 𝟎 𝑆𝑟 = 𝑉𝐼 𝑄 𝑟 = 𝑉𝐼 sin ∅ = 0.707𝑉𝐼 𝑃𝑟 = 𝑉𝐼 cos ∅ = 0.707𝑉𝐼 ∅ = 𝟒𝟓°
- 10. Necessity of Reactive Power Control 3. For the same active power operation of an existing power system at low power factor means overloading the equipment at times of full load. 4. For the same active power , a low power factor means a greater current and hence higher energy losses. 5. The low power factor causes the voltage regulation to be poor.
- 11. Advantages of Power Factor Improvement at Load End 1. Reduction in circuit current 2. Increase in voltage level at load 3. Reduction in copper losses in the system due to reduction in current 4. Reduction in investment in the system facilities per kW of the load demand 5. Improvement in power factor of the generators 6. Reduction in kVA loading of the generators and circuits 7. Reduction in kVA demand charges for large consumers
- 12. Sources of Reactive Power (VARS) 1. Synchronous Machines (Alternator & Motor) 2. Shunt Static Capacitors 3. Series Capacitors 4. Synchronous Condensers 5. FACTS Controllers
- 13. 1. Synchronous Alternator as a source of reactive power Consider the equivalent circuit of cylindrical rotor synchronous generator under steady state conditions. G𝐸 < 𝛿 XsR Vt 𝑬 = 𝑽 + 𝑰(𝑹 + 𝒋𝑿 𝒔) Where, E-Induced Emf R-Armature Winding Resistance per phase Xs − Synchronous reactance per phase I-Current per phase I
- 14. Vt𝛿 ∅ 𝑰𝑹 𝑰𝑿 𝒔 Case-1 E> Vt Over excitation At Lagging Power Factor Positive P & Positive Q Vt 𝛿 ∅ 𝑰𝑹 𝑰𝑿 𝒔 Case-2 E< Vt Under Excitation At Leading Power Factor Positive P & Negative Q
- 15. ∞ |𝑽| < 𝟎°G 𝑬 < 𝜹 Bus 1 Bus 2 𝑷 𝒎 𝑺 𝒔 = 𝑷 𝒔 + 𝒋𝑸 𝒔 𝑺 𝒓 = 𝑷 𝒓 + 𝒋𝑸 𝒓 Generalised Power System PF cos ∅ Ps MW Qs MVar 1 100 0 0.9 90 43 0.8 80 60 0.7 70 70 0.5 50 86.5 Rating of Synchronous Alternator is 100MVA 𝑽 𝒕
- 16. 1. Synchronous Motor as a source of reactive power Consider the equivalent circuit of cylindrical rotor synchronous motor under steady state conditions. M 𝐸 < 𝛿 XsR VSupply 𝑽 = 𝑬 + 𝑰(𝑹 + 𝒋𝑿 𝒔) Where, V-Supply AC Voltage E-Induced Emf in the motor R-Armature Winding Resistance per phase Xs − Synchronous reactance per phase I-Current per phase I ~
- 17. E𝛿 ∅ 𝑰𝑹 𝑰𝑿 𝒔 Case-1 E< Vt Under excitation At Lagging Power Factor 𝛿 ∅ 𝑰𝑹 𝑰𝑿 𝒔 Case-2 E> Vt Over Excitation At Leading Power Factor E
- 18. Synchronous Motor as a source of Reactive Power 1. When motor is under excited i.e power factor is lagging, the motor absorbs lagging VARs from the mains and delivers leading VARs. 2. When motor is over excited i.e power factor is leading, the motor absorbs leading VARs from the mains and delivers lagging VARs. 3. The synchronous motor can be made to deliver lagging or leading VARs to the system as per the system requirement. This can be done by controlling the excitation. 4. Synchronous motor which do not supply any mechanical load and are used for supply of VARs are known as synchronous condenser.
- 19. Compensations in Power System 1. Series Compensation It consists of capacitors connected in series with line at suitable locations. The effective reactance is given by 𝑋𝑙 = 𝑋 − 𝑋𝑐 Where 𝑋𝑙= Line Reactance 𝑋𝑐= Capacitor Reactance G1 𝐸′ < 𝛿1 |𝑉| < 0° 𝑋 Uncompensated Transmission Line 𝑃𝑒 = 𝐸′ |𝑉| 𝑋 sin 𝛿1
- 20. This results in improvement in performance of the system as a. Increase in Transmission Capacity 𝑃𝑒 = 𝐸′ |𝑉| 𝑋𝑙 sin 𝛿2 … … … . . This equation is called as power angle equation. The above equation shows that the power transmitted depends upon the transfer reactance and the angle between the two voltages. b. Voltage drop in the line reduces (gets Compensated) and thus it prevents voltage collapse. G1 𝐸′ < 𝛿2 |𝑉| < 0° 𝑋 𝑋 𝐶 𝐼
- 21. c. Improvement of System Stability For same amount of power transfer and same value of E and V, the δ in the case of series compensated line is less than that of uncompensated line. Compensated Transmission Line 𝑃𝑒 = 𝐸′ |𝑉| 𝑋𝑙 sin 𝛿2 Uncompensated Transmission Line 𝑃𝑒 = 𝐸′ |𝑉| 𝑋 sin 𝛿1 𝑃𝑒,E and V in both the cases are same. 𝐸′ |𝑉| 𝑋 sin 𝛿1 = 𝐸′ |𝑉| 𝑋𝑙 sin 𝛿2 sin 𝛿1 sin 𝛿2 = 𝑋 𝑋𝑙 A lower δ means better system stability.
- 22. Compensations in Power System 1. Shunt Compensation • For high voltage transmission line the line capacitance is high and plays a significant role in voltage conditions of the receiving end. • When the line is loaded then the reactive power demand of the load is partially met by the reactive power generated by the line capacitance and the remaining reactive power demand is met by the reactive power flow through the line from sending end to the receiving end. • When load is high (more than SIL) then a large reactive power flows from sending end to the receiving end resulting in large voltage drop in the line. • To improve the voltage at the receiving end shunt capacitors may be connected at the receiving end to generate and feed the reactive power to the load so that reactive power flow through the line and consequently the voltage drop in the line is reduced.
- 23. • To control the receiving end voltage a bank of capacitors (large number of capacitors connected in parallel) is installed at the receiving end and suitable number of capacitors are switched in during high load condition depending upon the load demand. • Thus the capacitors provide leading VAR to partially meet reactive power demand of the load to control the voltage. • During light load or no load conditions the voltage at the receiving end of the line may even exceed the sending end voltage. This is due to the charging current drawn by the shunt capacitance of the line. To limit this voltage rise shunt reactors have to be used. • Examples-Static Var Compensators(SVC), Static Synchronous Compensator(STATCOM), Synchronous Condenser.
- 24. Comparison of Series and Shunt Compensation Sr. No Series Compensation Shunt Compensation 1 In series capacitors the reactive power generation is proportional to square of the load current (𝐼2 𝑋𝑐). In series capacitors the reactive power generation is proportional to square of the voltage (𝑉2 /𝑋𝑐). 2 The cost of installation of series capacitor is higher due to the complicated protective equipment. The cost of installation of shunt capacitor or reactor is lower. 3 Comparatively small rating capacitor can be used to achieved the same amount of voltage improvement. For the same voltage improvement the rating of shunt capacitor will be higher. 4 Series capacitors are generally employed to improve the stability of the system. Shunt capacitors are generally employed to improve the power factor of the system.
- 25. Comparison of Series and Shunt Compensation Objective Series Compensation Shunt Compensation Improving Power Factor Secondary Primary Improving voltage level in overhead line system with low power factor Primary Secondary Improving voltage level in overhead line system with high power factor Not Used Primary Reduces line losses Secondary Primary Reduces voltage fluctuations Primary Not Used
- 26. Location of Series Capacitor a. Location along the line In this method the capacitor bank is located at the middle of the line. b. Location at one or both ends of line section on the line sides of in the switching station c. Location between bus bars within the switching station
- 27. Problems associated with series compensations 1. Sub synchronous resonance The natural frequency of oscillation for line elements series with series compensation is given by 𝐹𝑐 = 1 2𝜋 𝐿𝐶 𝐹𝑐 = 1 2𝜋 𝑋 2𝜋𝐹 ∗ 2𝜋𝐹𝐶 2𝜋𝐹 (𝑿𝒍 = 𝟐𝝅𝑭𝑳 & 𝑿 𝒄 = 𝟏 𝟐𝝅𝑭𝑪 ) 𝑭 𝒄 = 𝑭 𝑿 𝑪 𝑿 𝑳 Where F is a system Frequency The series capacitor introduces a sub synchronous frequency (proportional to the square root of the compensation) in the system.
- 28. Problems associated with series compensations 2. Ferro Resonance- When an unloaded or lightly loaded transformer is energized through a series compensation line, ferro resonance occurs. 3. Line Protection- Series compensation can lead to mal-operation of the distance relay of the line protection if the degree of compensation and capacitor location are not proper. 4. High Recovery Voltage- Capacitors bank produce high recovery voltages across the circuit breaker contacts.
- 29. Basics of Three Phase Synchronous Alternator Motor Generator Set- 2.2 kVA, 415V, 3.2 A, 220 V dc, Cylindrical Pole Alternator, 3 HP, 1500 rpm, 220 V, 12 A, DC Shunt Motor
- 30. Loading Capability Curve of a Generator The capability curve of a synchronous generator defines a boundary within which the machine can operate safely. The permissible region of operation is restricted to the following points given below. 1. The MVA loading should not exceed the generator rating. This limit is determined by the armature of stator heating by the armature current. 2. The MW loading should not exceed the rating of the prime mover. 3. The field current should not be allowed to exceed a specified value determined by the heating of the field winding. 4. For steady state or stable operation, the load angle 𝛿 must be less than 90°. The steady state stability limit occurs at 𝛿 = 90°.
- 31. The Continuous reactive power output capability is limited by three considerations, 1. Armature Current Limit- The armature current results in to an 𝐼2 𝑅 power loss and the energy associated with this loss must be removed so as to limit the increase in temperature of the conductor and its immediate environment. So the limitations on generator rating is the maximum current that can be carried by the armature without exceeding the heating limitations. Therefore on P-Q plane the armature current limit appears as the circle with centre at the origin and radius equal to the MVA rating. 𝑸 𝑷 −𝑷 −𝑸 Over excited Under excited Rated MVA 𝑸 𝑷 −𝑷 −𝑸 Over excited Under excited Rated MVA
- 32. The Continuous reactive power output capability is limited by three considerations, 1. Field Current Limit- The heat resulting due to an 𝐼2 𝑅 power loss, the field current also imposes a second limit on the operation of the generator. During this analysis the resistance is neglected. The phasor diagram will become, Vt 𝛿 ∅ 𝑰𝑿 𝒔 Case-1 E> Vt Over excitation At Lagging Power Factor Positive P & Positive Q ∅ 𝐼𝑋𝑠 sin ∅ 𝐼𝑋𝑠cos∅
- 33. Now multiply by 𝑉 𝑋𝑠 to each phasor, the phasor diagram of alternator at lagging power factor will become. 𝑉2 𝑋𝑠 𝛿 ∅ 𝑰𝑿 𝒔 𝑉 𝑋 ∗ 𝐼𝑋𝑠 sin ∅ 𝑜𝑟 𝑸 𝑉 𝑋 ∗ 𝐼𝑋𝑠 cos ∅ 𝑜𝑟 𝑷 O
- 34. 𝑇𝑎𝑘𝑒 𝐶𝑒𝑛𝑡𝑒𝑟 𝑎 ′𝑂′ mark the arc for minimum and maximum limit of field current Min 𝐼𝑓 Max 𝐼𝑓 𝛿 𝐿𝑖𝑚𝑖𝑡𝑎𝑡𝑖𝑜𝑛 Min 𝐼𝑓 Max 𝐼𝑓