Proceedings of the 2008 International Conference on Electrical MachinesPaper ID 1488 Asynchronous Starting Process of Hydro-generator Zlatko Maljković University of Zagreb, Faculty of Elec.Eng. and Comp. Unska 3, HR-10000 Zagreb, Croatia
[email protected] Abstract- Paper gives simulation analysis of starting process for two synchronous machines. Reasons for motor and compensator modes of work and for asynchronous starting are presented. Matlab Simulink model including synchronous machine, excitation, transformer, electrical grid, measuring units and circuit breaker is built. This paper also gives discussion about results of simulation, influence of parameters and compare to measured values. Marijo Šundrica Branko Tomičić KONČAR-KET KONČAR-GIM Fallerovo šet. bb, HR-10000 Zagreb, Croatia
[email protected] [email protected] ⎞ k f Lσf dψ d k L 1⎛ = −Um ⋅ sin⋅ (δ ) − ( XT + X M ) ⋅ id − '' ⎜ψ d − D ' σD ψ f − ' ψ D ⎟ + ωψq ⎜ ⎟ dt Tds ⎝ LfD LDf ⎠ dψ f kD LσD kd Lσs ⎞ 1⎛ = − '' ⎜ψ f − ' ψ d − ' ψ D ⎟ ⎟ dt Tf ⎜ LdD LDd ⎝ ⎠ ⎞ k f Lσf dψ D k L 1⎛ = − '' ⎜ψ D − ' ψ d − d ' σs ψ f ⎟ ⎜ ⎟ dt Td ⎝ Ldf Lfd ⎠ dψ q dt = −Um ⋅ cos (δ ) − ( XT + X M ) ⋅ iq − ⋅ dψ Q dt =− 1 (ψq − kQψQ ) −ωψd '' Tqs I. INTRODUCTION One way of starting synchronous machine is asynchronous starting. Its characteristics are machine connection to the grid from the beginning of the starting and the absence of mechanical torque during the starting process. In this work two characteristic examples of asynchronous starting are presented. The first one, “BKB1” (Bhavani-Kattalai Barrage 1) is a bulb type hydro-generator. Because of the drought period that lasts for several months in that area the machine is supposed to work also in compensator mode of work to do the reactive power voltage regulation on the electrical grid. It is impossible to change the mode of work from generator to compensator without extrusion of the water from the turbine. Because it needs time (measured in hours) for bulb type hydroaggregate to do that extrusion, during this process the machine cannot be connected to grid. Therefore, it is necessary to stop the aggregate, disconnect the grid, do the extrusion of water and then to come into compensator mode of work by the asynchronous starting of machine. Asynchronous starting is also applicable by the aggregates that should work in motor mode. The second example "Lepenica" (RHE Lepenica), reversible hydro power plant is one of them. Because of the economical electrical energy production the machine is working in motor mode of work during the periods of water pumping. To change the mode of work from generator to motor it is necessary to stop the machine, then the asynchronous starting is used to get into motor mode of work. II. MATHEMATICAL MODEL The calculation of asynchronous starting is based on mathematical description of the process. The main task, to model the synchronous machine, is done using rotating dq0 coordinate system. Step-up transformer is connected to machine and electrical grid to step-up transformer. By taking advantage of Park transformation equations connection of dq0 coordinate system to three phase grid system is done. The unknown variables of the nonlinear dynamic system are magnetic fluxes, angular velocity, and δ angle. Its final form is: 1 (ψQ − kqψ q ) Tq'' ⎤ ⎛1 1⎞ k f Lσf kQ dωel 1 ⎡kD LσD = ⎢ ' '' ψ f ψ q + ⎜ '' − '' ⎟ψ dψ q + ' '' ψ Dψ q − '' ψ Qψ d ⎥ ⎜L L ⎟ dt 2H ⎢ LfD Ld LDf Ld Lq ⎥T d ⎠ ⎝ q ⎣ ⎦ dδ = ωel −1 dt with id and iq: id = 1 ' L'd ⎛ ⎞ k L ⎜ψ d − kD LσD ψ f − f σf ψ D ⎟ ⎜ ⎟ L'fD L'Df ⎝ ⎠ 1 iq = '' (ψ q − kQψ Q ) Lq XT is transformer reactance and XM is grid reactance other parameters are well known in synchronous machine theory The system can be efficiently solved by many Maltab solvers like variable step solvers ode15s, ode45. Then, it is an easy task to get the values of stator, rotor and damper winding currents and electromagnetic torque. III. SIMULATION MODEL FOR BKB1 Simulation of asynchronous starting is done using software package Matlab Simulink. Simulink is simulation tool under MATLAB. Its library contains various blocks that can be used in simulation model. To analyze synchronous generator dynamics many types of synchronous machine blocks can be used. All of them give similar results. As given in the Fig.1 the machine is connected to excitation block and block for measurement of electrical and 978-1-4244-1736-0/08/$25.00 ©2008 IEEE 1 8 GVA.6/110 kV.u. J=702 tm2.614 ohm: synchronous reactance in d-axis: Xd 1.63 p.0301 s field winding open circuit: Tdo’ 2.33 p.0066 p. there are modeled transformer and circuit breakers with turn on and turn off timers.u.497 s damper winding in d-axis open circuit: Tdo’’ 0. Numerical calculation is done by the solver ode15s that is recommended for nonlinear equations. Un=6600 V.u. Time constants: field winding short circuit: Td’ 0.1800 MVA Fig.01146 s damper winding in q-axis short circuit: Tq’’ 0.Proceedings of the 2008 International Conference on Electrical Machines mechanical quantities. Un =110 kV 2 . Field winding is short circuited (or connected to additional resistor) and after the synchronization speed is exceeded circuit breakers change state to connect the machine to nominal voltage.02 p. synchronous reactance in q-axis: Xq 0. uk=10% between LV and HV by 17500 kVA Nominal values of electrical grid: S(3-phase short circuit)=1.0634 s Nominal values of step-up transformer: Sn=17500 kVA. subtransient reactance in d-axis: Xd’’ 0.804 s damper winding in d-axis short circuit: Td’’ 0.1 Simulation model for BKB1 IV. for BKB1 generator to be connected to the voltage twice lower then nominal during the starting process.25 p. resistance of armature winding Ra 0. 2p=84. if Te phimd <Stator current> <Field current if d (pu)> <Electromagnetic torque Te (pu)> <Mutual f lux phimd (pu)> <Damper winding current ikq1 (pu)> <Damper winding current ikd (pu)> is Continuous ism ikq ikd delta f(u) is (A rms) <Stator v oltage v d (pu)> <Stator v oltage v q (pu)> <Load angle delta (deg)> omega com A a b B C c ik f(u) <Rotor speed wm (pu)> <Output activ e power Peo (pu)> Step1 -KPeo (KW) power iA (A) Three-Phase Breaker2 0 Constant 1 v ref vd Vf vq m Pm A B Vf_ C Manual Switch1 + i - Step com A a b i mach B C c v stab Synchronous Machine pu Fundamental B C A Three-Phase Breaker1 Excitation System A a2 b2 c2 a3 b3 c3 10 kW B C N + v - Three-Phase Transformer (T hree Windings) Scope1 Voltage Measurement Scope A B C N Network 110kVrms VN . UnLV/UnMV/UnHV =3.0013 p.0474 s damper winding in q-axis open circuit: Tqo’’ 0. In the same time appropriate excitation is connected to field winding. Unit values system is used in such a way that each parameter is expressed as multiplier of base value Zb= 2. f=50 Hz.30 p.u.3/6. INPUT VALUES FOR BKB1 Nominal values of synchronous generator BKB1: Sn=16667 kVA. transient reactance in d-axis: Xd’ 0. subtransient reactance in q-axis: Xq’’ 0.u.u. Because it is supposed.u. In=1458 A. resistance of field winding Rf 0. 7 p. electromagnetic torque. In the Fig. Fig. stator field and damper winding current.4 p. one with filed winding short circuited and the other one with field winding connected to additional resistor [1]. and of damper winding current about 1. or 900 kNm. or 4100 A.u. 6 Damper current Id (p.Proceedings of the 2008 International Conference on Electrical Machines V. Fig. After about 35 seconds rotor will exceed synchronous speed. 3. of electromagnetic torque is about 0. 3 Electromagnetic torque Te (p. 2. 6 are given some of the results of simulation for BKB1: rotor speed.u.u. Fig. To obtain the SI values of field and damper winding current it is necessary to transform the base unit values to rotor and damper winding. 5. Connection of additional resistor makes the magnetic field penetrate into the field winding faster.u. Fig. Fig.) Fig.) Fig. The result is greater values of electromechanical torque and shorter time of starting process.u. 2 Rotor speed ω (p. 4.) Fig.) Fig. SIMULATION RESULTS FOR BKB1 There are made two options of starting.u..u. The maximum value of stator current is about 2 p. For dimensioning of additional resistor it is important not to exceed insulation level of the winding. 5 Field current If (p. Maximum value of field winding current is about 0.) 3 . 4 Stator current Is (p.u.1 p.u. Fig.0509. uk=6 % by 4000 kVA Nominal values of electrical grid: S(3-phase short circuit)=0. SIMULATION REZULTS FOR LEPENICA In the Fig.1861 leakage inductance of damper winding in d-axis: Xlkd 0. J=1. with a difference: voltage was full.) Fig.Proceedings of the 2008 International Conference on Electrical Machines VI. Damper winding current consists of ikd (Fig. 9.1773 magnetizing inductances in q-axis: Xq 0. Un =35 kV Unit values of step-up transformer have to be calculated regarding per unit system used by Simulink [2]. Unit values system is used in such a way that each parameter is expressed as multiplier of base value Zb= 25.622 leakage inductance of armature winding: Xla 0. f=50 Hz. Fig. SIMULATION OF LEPENICA Simulation of asynchronous starting of Lepenica was done with a model similar to BKB1 model. so the circuit breakers were omitted and two winding transformer was used.018 resistance of demper winding in d-axis rfkd 0. 10. Values of the damper winding current are calculated by the following expression: iD = i 2 kd + i 2 kq Fig.442 ohm: magnetizing inductances in d-axis: Xad 1.) Fig. 2p=10. electromagnetic torque.3/ 35 kV. 13) component. 9 Stator current (p. 12) and ikq (Fig.1479 leakage inductance of field winding: Xlf 0. stator. 8 Electromagnetic torque Te (p. Fig. value of ikq is about two times greater then ikd. In=143 A. Because of resistance of damper winding in q-axis rfkq that is about half a value of resistance in d-axis rfkd. 7.u.0965 resistance of demper winding in q-axis rfkq 0. 11 results of simulation for Lepenica: rotor speed.0964 leakage inductance of damper winding in q-axis: Xlkq 0.u. Nominal values of step-up transformer: Sn=4000 kVA. Fig. 8.752 tm2.u. field and damper winding currents are given. UnLV /UnHV =6. Nominal values of synchronous generator Lepenica: Sn=1560 kVA.) 4 . VII. not reduced to half of value like in BKB1.0509 resistance of armature winding Ra 0. 7 Rotor speed ω (p.5 GVA.01102 resistance of field winding plus additional resistor Rf 0. Un=6300 V. ) Fig.) 5 . Maximum value of field winding current is about 3 p. Except of in the following figure given rotor speed.85 p. and of damper winding current about 3. 14. or 39. The maximum value of stator current is about 4. 15.u. stator current and electromagnetic torque there is also known value of voltage drop (calculated as a difference of a measured value of voltage on machine before the asynchronous starting and at the starting) about 5886 V.u. Fig.. VIII.u. of electromagnetic torque is about 2 p. Field winding like in simulation was connected to additional resistor.u.3 p. 10 Field current (p.u. 12 Damper current ikd (p. 17.) Fig. 11 Damper current (p. or 700 A.COMPARISON OF SIMULATION AND MEASUREMENT FOR LEPENICA For hydro power plant Lepenica except of simulation results asynchronous process was recorded and the measured values are also given.u.u. Original values are given in the Fig.u. To obtain the SI values of field and damper winding current it is necessary to transform the base unit values to rotor and damper winding.8 kNm. and measured together with calculated values are given in the Fig. 13 Damper current ikq (p.) After about 4 seconds rotor will exceed synchronous speed. 16 and Fig. Fig. Simulation result of voltage drop is about 5900 V.Proceedings of the 2008 International Conference on Electrical Machines Fig. Consequently. Tomičić. CONCLUSION In both examples. www. Šundrica. voltage increase on field winding do not exceed designed value of winding insulation. Electrical machines and systems. stator current and rotor speed (original) measured calculated Fig. connection of additional resistor with ohmic resistance about ten times greater then field winding resistance shorted starting process.mathwork. Calculation has given acceptable results. Duration of starting process directly depends on moment of inertia of aggregate and electrical grid voltage. IEEE. Master’s Degree Project. 15 Measured and calculated values of rotor speed measured calculated [1] [2] [3] [4] 800 700 600 500 I (A ) 400 300 200 100 0 0 1 2 M. Na. X. Karlsson. B. R. 684-687. 2. “Simulation of asynchronous starting process of synchronous motors based on Matlab/Simulink”. Nov. “Evaluation of Simulink/SimPowersSystems and other Commercial Simulation Tools for the Simulation of Machine System Transients”. Stocholm. Vol. pp. pp. The only significant difference a value of electromechanical torque is result of difficulty to precisely determine damper winding parameters. 16 Measured and calculated values of stator current 6 . 14 Measured values of voltage. Sweden 2005 W. 1-7. 2007. “Calculation of asynchronous starting process of synchronous hydro-generator based on dynamical model”. Croatia. Nov. Duration is longer as transformer short-circuit voltage is greater and as electric grid is weaker. HRO CIGRE. In the Lepenica example characteristic values for stator current and calculated duration of starting process are almost the same as measured. Xiaoyuan. 17 Measured and calculated values of electromagnetic torque 700 600 500 n (rp m ) 400 300 200 100 0 0 1 IX. REFERENCES 2 time (s) 3 4 5 Fig. 2003. Cavtat.com “MATLAB/SIMULINK” time (s) 3 4 5 Fig. A.Proceedings of the 2008 International Conference on Electrical Machines measured calculated 45000 40000 35000 30000 T (N m ) 25000 20000 15000 10000 5000 0 0 1 2 time (s) 3 4 5 Fig. A1-25.