SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 TUTORIAL : SIMSEN OVERVIEW Table of contents page Introduction...2 2 Application fields...2 2. Electrical power networks...2 2.2 Adjustable speed drives...2 3 History and development...3 4 Main features...4 5 SIMSEN Users / Partners:...4 6 Application examples...5 6. Sub Synchronous Resonance (SSR)...5 6.2 Sudden short-circuit of a large power plant...7 6.3 Transient stability of a large HV power network... 6.4 HVDC transmission with SVC...3 6.5 Load Commutated Inverter (LCI) drive...7 6.6 VARSPEED Slip energy recovery drive with cyclo-converter cascade...2 6.7 Three-level Voltage Source Inverter (VSI) feeding an induction motor...23 6.8 Three-level UPFC (Unified Power Flow Controller)...28 6.9 Multi-level Voltage Source Inverter feeding induction motor...3 6. Doubly-fed induction motor/generator with 3-level VSI cascade...33 6. Induction motor fed by current converter...36 - -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Introduction This tutorial is an overview of the simulation software package SIMSEN. The development started in 992. The main goal was to develop a modular simulation package for the analysis of power networks and adjustable speed drives. These two domains represent the main application fields of SIMSEN. The next paragraphs explain you how and why the system has been developed. Finally, some examples show you what can be simulated and analyzed with SIMSEN. 2 Application fields The main application fields are electrical power networks and adjustable speed drives. In these fields, the main topics are: 2. Electrical power networks Electrical machines Electromagnetic transient in AC/DC networks Transient stability ON/OFF switching in power networks General fault analysis including earth faults Sub Synchronous Resonance (SSR) FACTS (Flexible Alternative Current Transmission Systems) HVDC (High Voltage DC transmission) SVC (Static Var Compensator) Control and regulation 2.2 Adjustable speed drives Special machines Power electronics converters Load-Commutated Inverter (LCI) Cyclo-converter Voltage Source Inverter (VSI) Multi level inverters Analog/digital mixed signals simulation Control and regulation - 2 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 3 History and development The development started in 992. The idea was to develop a modular system, which could be able to quickly simulate electrical power systems containing semiconductors and regulation parts. The whole development has been based on practical examples of power network and industrial drives. In both domains, the customer came with problems requiring the study of complex systems. SIMSEN has been tested and is regularly used in large industrial companies and in several technical schools. Summary 992 : Start of development. Many studies about HV power network stability have been performed. 994 : Introduction of power electronics elements. Studies about power drives have been required from ABB Industry. These studies involved complex converter topologies as LCI, cyclo-converter, Voltage Source Inverter. 995 : PhD about the SIMSEN simulation software. 996 : Extension for ABB Industry. On ABB requirements, many basic function blocs have been added in order to enhance the flexibility of the control schemes. 997 : SIMSEN became the official contract based simulation software for ABB Hydro Power Generation, specially for the Three-Gorges Project in China. 998 : Introduction of digital devices. This introduction permitted the simulation of digital control schemes. 999 : Calculation speed improvement. The reprogramming of the dynamic matrix system has improved the calculation speed (about 2 times faster). 2 : New version 2.2.. This version was the first upgraded version including many new features, as: output interface VISUAL, equation parser, automatic calculation parameters for synchronous machines, ON-LINE Fast Fourier Transform, user-defined DLL for control in C++, Fortran or PASCAL. 2 : Extension to hydraulic models. SIMSEN has been extended to the simulation of hydraulic elements (dam, penstock, turbine, etc ). This extension will allow the simulation of complete power generation systems. This great feature will be available in year 22. Other developments as the introduction of special regulation schemes for ALSTOM have also been performed. 22 : New version 2.3. This version is the second upgraded version. It includes the following new features: enhanced output interface VISUAL, BATCH processes, automatic parameters calculation for induction motors, linked inductors with variable coupling coefficients, enhanced editor function for large input files (on ABB Industry request). - 3 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 4 Main features One can summarize the main features as follows: Simple to use Input/output interface Modular structure with arbitrary topology No restriction on the network size Steady-state or transients operating modes can be calculated Electrical machines with mechanical shaft Semiconductors Events detection and back-tracking for more accuracy Initial conditions entirely, partly or not defined Additional Load-Flow program for power networks applications Stable operating point entirely saved Interactive read/write process to any parameters of the system Parameterization Results in SI (International System unit) or in per unit Harmonics analysis 5 SIMSEN Users / Partners: Alstom Power Generation Ltd. : Power generation : on site world wide license Alstom Power Generation Ltd. : Turbogenerators Alstom Power Generation Ltd. : Electrical and Power Plant Control ABB Industry : Power Electronics and Adjustable Speed Drives : on site swiss license ANSALDO Energia s.p.a. Italy : Power generation Biel School of Engineering and Architecture / Berner Fachhochschule Burgdorf School of Engineering and Architecture / Berner Fachhochschule ABB Industri AS Norway : Power Electronics and Adjustable Speed Drives WEIDMANN Transformerboard AG, Rapperswil, Switzerland - 4 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6 Application examples 6. Sub Synchronous Resonance (SSR) This example shows the possibilities of SIMSEN to take into account correctly the electrical and mechanical interactions in power systems. The Sub Synchronous Resonance (SSR) is an important problem in compensated power networks. Due to a change of topology or impedance of the compensated network, electrical resonance may match the mechanical resonance in the shaft of large generators. Such a resonance may destroy the whole shaft of generators. The studied circuit is represented in Figure 6.-. On the next page, the black curve presents the results obtain by a specific program developed to analyze SSR problems. Figure 6.- : Studied circuit for SSR - 5 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 tkt [p.u].3.2..9.8.7.6 2 3 4 Figure 6.-2 : Mechanical torque between rotor and turbine 6.3.22 ME2.VIS 5-6 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.2 Sudden short-circuit of a large power plant The studied circuit is represented in Figure 6.2-. From a steady-state operating point, the circuit breaker is switched on to generate a three-phase short-circuit. After a while, the circuit breaker is switched off to clear the fault. Therefore, it is possible to analyze the stability of the system. Figure 6.2- : Power plant including 4 turbo-generators - 7 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 ia [p.u] ib [p.u] ic [p.u] 5 4 3 2 - - 2-3 - 4-5.2.4.6.8 Figure 6.2-2 : Stator currents of a turbo-generator 4/ 7/ Sm.vis tem [p.u] tkt [p.u] n [p.u] 2nd 3. 2.5 -.95-2.9.2.4 Figure 6.2-3 : Air-gap torque, mechanical torque and speed of the rotor.6.8 4/ 7/ Me2.vis - 8 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 uf [p.u] if [p.u] 8 7 6 5 4 3 2.2.4.6.8 Figure 6.2-4 : Field voltage and current 4/ 7/ Sm.vis xad [%] xaq [%] 5 95 9 85 8 75.2.4.6.8 Figure 6.2-5 : Saturation effect 4/ 7/ Sat.vis - 9 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.3 Transient stability of a large HV power network The studied circuit is represented in Figure 6.3-. This example shows that SIMSEN can be used to analyze the transient stability of large power networks. From a steady-state operating point calculated with a Load-Flow program included in SIMSEN, a circuit breaker is switched on between the nodes CHAMOSON and ROMANEL, in the high voltage part of the network, to generate a two-phase short-circuit. The main goal of the study is to analyze the transient stability of the 3 large hydro-generators (465MVA each) at the node BIEUDRON after the fault clearing. Figure 6.3- : HV power network Although such studies could be made with simplified machine s models to save calculation time, it is nevertheless very important to take into account fast transient behavior of the synchronous machines, especially when the stability is depending on the voltage regulation. - -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Delta [deg] n [p.u] 2nd - 25.5-3. - 35.5-4.995-45.99-5 2 4 6 8 Figure 6.3-2 : Speed and load angle of a 465 MVA hydro-generator.985 4/ 7/ Ms2.vis Delta [deg] n [p.u] 2nd - 29-3 - 3-32 - 33-34 - 35-36 - 37..8.6.4.2.998.996.994.992.99 2 4 6 8 Figure 6.3-3 : Speed and load angle of a 8 MVA hydro-generator 4/ 7/ Ms.vis - -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6 5 uf [p.u] if [p.u] tem [p.u] 4 3 2 - - 2-3 2 4 6 8 4/ 7/ Ms2.vis Figure 6.3-4 : Field voltage and current, air-gap torque of a 465 MVA hydro-generator ia [p.u] ib [p.u] ic [p.u] 3 2 - - 2-3 - 4.5..5.2.25.3.35.4.45.5 Figure 6.3-5 : Stator currents of a 465 MVA hydro-generator 4/ 7/ Ms2.vis - 2 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.4 HVDC transmission with SVC The studied circuit is represented in Figure 6.4-. From a steady-state operating point with full power in the HVDC, the circuit breaker is switched on to generate a three-phase short-circuit on the rectifier side of the HVDC. After a while, the fault is cleared. The results show the recovery of the HVDC transmission. Figure 6.4- : HVDC transmission with SVC - 3 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Figure 6.4-2 : Rectifier control ug [p.u] ig [p.u].2..9.8.7.6.5.4.3.2..5..5.2.25.3.35.4.45.5.55.6.65.7.75.8.85.9.95 Figure 6.4-3 : Voltage and current of the HVDC 4/ 7/ Pg.vis - 4 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 y [] 3 2 9 8 7 6 5 4 3 2.5..5.2.25.3.35.4.45.5.55.6.65.7.75.8.85.9.95 Figure 6.4-4 : Extinguishing angle of the inverter 4/ 7/ Gamma.vis q [p.u] -.4 -.5 -.6 -.7 -.8 -.9 - -. -.2.5..5.2.25.3.35.4.45.5.55.6.65.7.75.8.85.9.95 Figure 6.4-5 : Provided reactive power of the SVC 4/ 7/ Tcomp.vis - 5 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 ila [p.u] ilb [p.u] ilc [p.u].5.5 -.5 - -.5.5.52.53.54.55.56.57.58.59.6.6 Figure 6.4-6 : HVDC transformer phase currents during the recovery.62.63.64.65.66.67.68.69 4/ 7/ Thvdc.vis Uth [V] Ith [A] 2nd 6 8 4 2 6 4 2-2 - 2-4 -4-6 -6.5.52.53.54.55.56.57.58.59.6.6.62 Figure 6.4-7 : Thyristor valve voltage and current during the recovery.63.64.65.66.67.68.69-8 4/ 7/ Conv.vis - 6 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.5 Load Commutated Inverter (LCI) drive The studied circuit is represented in Figure 6.5-. It represents a two channels current converter supplying a 6-phase synchronous machine. The 6-pulse converters are connected to a 4-windings transformer, which also supplies the excitation circuit. The mechanical shaft is modeled with two masses. Figure 6.5- : Wind tunnel LCI drive - 7 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 uan [p.u] ia [p.u].8.6.4.2 -.2 -.4 -.6 -.8 -.5..5.2.25.3.35 Figure 6.5-2 : Phase voltage and current of the synchronous machine 4/ 7/ Sm.vis.4 tem [p.u] n [p.u]..5.95.9.85.8.75.7.65.5..5.2.25.3.35 Figure 6.5-3 : Air-gap torque and speed of the synchronous machine 4/ 7/ Sm.vis.4-8 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Ia [A] Ib [A] Ic [A] 8 6 4 2-2 - 4-6 - 8.5..5.2.25.3.35.4 Figure 6.5-4 : Phase currents of the network 4/ 7/ Vs.vis Uth [V] Ith [A] 2nd 2 5 3 2 5-5 - - -2-5 -3-2.5..5.2.25.3.35.4 Figure 6.5-5 : Voltage and current of a rectifier valve 4/ 7/ Iconv.vis - 9 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.6 VARSPEED Slip energy recovery drive with cyclo-converter cascade The studied circuit is represented in Figure 6.6-. It contains a wound rotor induction machine with its stator connected to the network. The rotor windings are supplied through a cycloconverter, which is able to prescribe the frequency and amplitude of the rotor currents. The main advantage of this drive is to adjust the speed of the machine in a range depending on the power of the converter. Usually the range is about +- % of the synchronous speed. The drive is able to reach the optimal operating point in motor or generator modes and can even provide reactive power. The results show the behavior of the drive after a change of the reference set value of the speed from.95% to.5% with constant mechanical torque. Figure 6.6- : VARSPEED Slip energy recovery drive with cyclo-converter cascade - 2 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Figure 6.6-2 : Regulation part tem [p.u] n [p.u] 2nd..9.8.7.6.5.5..5.95.4.3.9.2..2.3.4.5.6.7.8.9..2.3.4.5.6.7.8.9 2 Figure 6.6-3 : Air-gap torque and speed of the induction machine 4/ 7/ Me.vis - 2 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 ia2 [p.u] ib2 [p.u] ic2 [p.u].5 -.5 -..2.3.4.5.6.7.8.9..2.3.4.5.6.7.8.9 2 Figure 6.6-4 : Rotor currents of the induction machine 4/ 7/ Mas.vis ia [p.u] ib [p.u] ic [p.u].2.8.6.4.2 -.2 -.4 -.6 -.8 - -.2.5.55.5.55.52.525.53.535.54 Figure 6.6-5 : Main transformer phase currents in steady-state 4/ 7/ Mas.vis - 22 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.7 Three-level Voltage Source Inverter (VSI) feeding an induction motor The studied circuit is represented in Figure 6.7-. It represents a three-level Voltage Source Inverter feeding a squirrel cage rotor induction motor. A 2-pulse rectifier supplies the DC-link of the frequency converter. The main characteristic of this drive is the control of the inverter. It is tuned through an efficient Direct Torque Control (DTC). This kind of control is based on a fine estimation of the stator flux of the machine. Figure 6.7- : 3-level VSI feeding induction motor - 23 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 uan [p.u] ia [p.u].5 -.5 -.5..5.2.25.3.35.4 Figure 6.7-2 : Motor phase voltage and current 4/ 7/ Mas.vis tem [p.u] n [p.u] tkt [p.u].8.6.4.2 -.2 -.4 -.6 -.8.5..5.2.25.3.35 Figure 6.7-3 : Air-gap torque, mechanical torque and speed of the motor 4/ 7/ Me.vis.4-24 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 t sta [p.u] t star [p.u].95.9.85.8.75.7.65.4.5.6.7.8.9.2 Figure 6.7-4 : Real torque and estimated torque.2 4/ 7/ Out.vis uab [p.u] ila [p.u].8.6.4.2 -.2 -.4 -.6 -.8 -.5..5.2.25.3.35 Figure 6.7-5 : Transformer line- to-line voltage and phase current 4/ 7/ T.vis.4-25 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Uth [V] Ith [A] 2nd 3 5 3 3 25 2 5 2 5 2 5 5 5.5..5.2.25.3.35 Figure 6.7-6 : Voltage and current on a GTO Thyristor valve.4 4/ 7/ Vu.vis 22 2 8 6 4 2 8 6 4 2 nb [] y [].5..5.2.25.3.35 Figure 6.7-7 : Pulse counter for switching frequency regulation 4/ 7/ Cpuls.vis.4-26 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 8 -+- y 5 ++- +- 4 2 9 7 3 -- ++ -+ +- + - 6 2 22 23 24 -++ ++ - + -- +-- +++ --- 26 25 x 4 8 3 -+ 5 -- + - ++ 9 +- 2 6 --+ -+ +-+ 7 Figure 6.7-8 : Inverter available switching states (voltage vector numbering) 2 y [] 26 24 22 2 8 6 4 2 8 6 4 2.5..5.2.25.3 Figure 6.7-9 : Vector numbering sequence in steady-state.35 4/ 7/ Dtcnpc.vis.4-27 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.8 Three-level UPFC (Unified Power Flow Controller) The studied circuit is represented in Figure 6.8-. It represents a three-level UPFC (Unified Power Flow Controller). The UPFC is a FACTS (Flexible Alternative Current Transmission System) device. It is able to maintain the voltage on the parallel AC bus (shunt connection) and to control separately the active and reactive power flow by inserting a series voltage in the transmission line. The simulation results present the dynamic response of the UPFC during changes of the reference set values of active and reactive power in the transmission line. Figure 6.8- : 3-level UPFC - 28 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 p [pu] q [pu]..9.8.7.6.5.4.3.2...2.3.4 Figure 6.8-2 : Active and reactive power of the transmission line 4/ 7/ Ames_ser.vis ia [p.u] ib [p.u] ic [p.u].8.6.4.2 -.2 -.4 -.6 -.8 -..2.3.4 Figure 6.8-3 : Phase currents of the transmission line 4/ 7/ Ln.vis - 29 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6.9 Multi-level Voltage Source Inverter feeding induction motor This example presents a multi level Voltage Source Inverter (VSI) supplying an induction motor, as displayed in Figure 6.9-. For medium voltage drive applications, the proposed topology has the advantage of reducing the voltage harmonics on the motor using a multi level inverter. A small DC voltage supplies each cell of the inverter. It is possible with the series connected cells to provide the motor with the desired phase voltage. The only inconvenient is the input supply transformer that needs many secondary windings as shown on the figure. This transformer has been modeled in details with linked inductors taking into account the special phase shifting angle of each secondary winding as well as the short circuit reactance of the transformer. This example demonstrates that SIMSEN can master a large number of semiconductors. Figure 6.9- : Multi-level VSI feeding induction motor - 3 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 uan [p.u] ia [p.u].5 -.5 -..2.4.6.8.2.22.24 6.3.22 IM.VIS Figure 6.9-2 : Induction motor phase voltage and current (black-measured, color-simulated).26-3 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Uan [V] Ia [A] 2nd 2 4 5 3 2 5-5 - - - 2-5 - 3-2.2.4.6.8.2.22.24.26-4.28 6.3.22 VS.VIS Figure 6.9-3 : Main transformer phase voltage and current (black-measured, color-simulated) - 32 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6. Doubly-fed induction motor/generator with 3-level VSI cascade This example, displayed in Figure 6.-, presents a Doubly-fed Asynchronous Machine (DASM). The rotor cascade is made of 2 3-level Voltage Source Inverter (VSI) for large pump storage plants. In comparison with the standard cyclo-converter cascade, the VSI cascade represents many advantages: less power components, harmonics reduction, high dynamic and reactive power compensation. The whole power circuit as well as the complete regulation part have been implemented in SIMSEN. The control part includes the transformer control: exchange of active and reactive power, the machine control: speed regulation, stator and rotor current controls and the DC-link voltages control. Both VSI are tuned with improved PWM shape. The simulation results present the behavior of the system after a % single-phase voltage drop at the high voltage side of the main transformer. SIMSEN appeared to be a powerful simulation system, especially when reconnecting the cascade transformer to the AC grid. This allows estimating correctly the global power plant current. Another important point of the control is the respect of the switching frequency limit of the new hard-driven GTO s. This has been taken into account in the control. Switching frequencies of 25 Hz on the transformer side and 5 Hz on the rotor side have been required. Even with these low switching frequency values, the calculated THD of both stator and main transformer currents lead to values lower than %. Figure 6.- : Doubly-fed induction motor/generator with 3-level VSI cascade - 33 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 tem [p.u] n [p.u] 2nd.5 -.5 - -.5-2.94.93.92.9.9.89.88.87.86.5..5.2.25.3.35.4.45 Figure 6.-2 : Induction motor/generator air-gap torque and speed.5 6.3.22 MAS.VIS ia2 [p.u] ib2 [p.u] ic2 [p.u] 3 2 - - 2-3.5..5.2.25.3.35.4.45.5 Figure 6.-3 : Induction motor/generator rotor currents 6.3.22 MAS.VIS - 34 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 ila [p.u] ilb [p.u] ilc [p.u] 3 2.5 2.5.5 -.5 - -.5-2 - 2.5.5..5.2.25.3.35.4 Figure 6.-4 : Main transformer primary side phase currents.45 6.3.22 TNET.VIS.5 U [V] U [V] 2 8 2 6 2 4 2 2 2 8 6 4 2.5..5.2.25.3.35.4.45.5 Figure 6.-5 : DC-link capacitors voltages 6.3.22 C.VIS + C2.VIS - 35 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 6. Induction motor fed by current converter This example, displayed in Figure 6.-, presents an induction motor fed by a current converter. This is a special frequency converter including additional capacitors in order to extinguish the current of the thyristors. This leads to very fast transients and to the typical form of terminal voltages on the motor side. To validate the accuracy of SIMSEN, measurements have been recorded on a real 28 kw drive. The results present the behavior of the system in steady state at 97% of the rated operating point. The red curves correspond to the SIMSEN computed results and the blue curves to the measurements. Due to the presence of the extinguishing capacitors, the voltage presents peaks during each commutation. The simulation matches the measurements with high accuracy. Figure 6.- : Induction motor fed by current converter - 36 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Uca [V] Uca* [V] 8 6 4 2-2 - 4-6 - 8.65.7.75.8 Figure 6.-2 : Motor line-to-line voltage (blue=measured, red=simulated).85.9.95 6.3.22 IM.VIS + u.vis. Ila [A] Ila* [A] 6 4 2-2 - 4-6.65.7.75.8.85 Figure 6.-3 : Motor phase current (blue=measured, red=simulated).9.95 6.3.22 IM.VIS + i.vis. - 37 -
SIMSEN 2.3 : Modular SImulation software for the analysis of ENergy conversion Systems 22 Tem [Nm] Tem* [Nm] 9 8 7 6 5 4 3 2.65.7.75.8.85 Figure 6.-4 : Motor air-gap torque (blue=measured, red=simulated).9.95 6.3.22 IM.VIS + tem.vis. The air-gap torque has been measured with a digital torque measurement device. This device needs only the phase voltages, the phase currents as well as the stator winding resistance. End of tutorial - 38 -