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COMBINED TORSIONAL AND ELECTROMECHANICAL ANALYSIS OF AN LNG COMPRESSION TRAIN WITH VARIABLE SPEED DRIVE SYSTEM by Paola Rotondo Senior Electrical Engineer GE Oil & Gas Florence, Italy Davide Andreo R&D Engineer ABB Medium Voltage Drives Turgi, Switzerland Stefano Falomi Ph.D. Student University of Florence, Italy Pieder Jörg Vice President Drives Projects ABB Medium Voltage Drives Turgi, Switzerland Andrea Lenzi Senior Engineer GE Oil & Gas Florence, Italy Tim Hattenbach Senior Principal Mechanical Engineer and Compressor Team Leader Bechtel Corporation Houston, Texas Duccio Fioravanti Design Engineer and Sergio De Franciscis Lead Electrical Engineer GE Oil & Gas Florence, Italy Paola Rotondo is currently a Senior Electrical Engineer and Variable Speed Drives Systems Team Leader in the Electrical Department of GE Oil & Gas, in Florence, Italy. She joined GE in 2005 and is involved in requisition activities, string test support, and system simulations for several projects. Before joining GE, she was a researcher at Centro Laser, Valenzano, Italy, where she worked on the development of numerical and experimental medical and industrial models by using rapid prototyping techniques. Dr. Rotondo received M.Sc. and Ph.D. degrees (Electrical Engineering) from Politecnico di Bari, Bari, Italy, in 2003 and 2007, respectively. Davide Andreo is an R&D Engineer at ABB Medium Voltage Drives, in Turgi, Switzerland. His main activities focus on electrical drive simulation and motor control software. Mr. Andreo received his M.Sc. degree (Mechatronics Engineering, 2008) from the Politecnico di Torino, Italy. Stefano Falomi is currently a Ph.D. Student at Florence University, sponsored by GE Oil & Gas. His activities focus on torsional vibrations of turbomachines and torsional interactions between compressor trains and electrical power systems. Mr. Falomi received his M.Sc. degree (Mechanical Engineering, 2007) from the University of Florence. 93 94 PROCEEDINGS OF THE THIRTY-EIGHTH TURBOMACHINERY SYMPOSIUM 2009 Pieder Jörg is Vice President Drives Projects, for ABB Medium Voltage Drives, in Turgi, Switzerland. He is responsible for the drive systems business. He joined ABB in 1995, starting at Corporate Research in the area of power electronics. In 2002 he joined the Medium Voltage Drives business unit as Head of Product Development. Since 2008 he has been responsible for the Drive Systems business and its products within Medium Voltage Drives. Mr. Jörg received his M.Sc. degree (Electrical Engineering) from the Swiss Federal Institute of Technology. Andrea Lenzi is a Senior Engineer in the Electrical Design Department at GE Oil & Gas, in Florence, Italy. He supports the electrical design department in risk review of critical jobs, system integration, reliability review, and supplier technical quality coordination. He covered the position of Project Engineer for North Sea projects from 2002 to 2006 and coordinated the development of a very large VSDS compressor application for the Ormen Lange project. He is also involved in implementation of Lessons Learned in GE Oil & Gas Electrical Drives Design. Mr. Lenzi received his M.Sc. degree (Chemical Engineering, 1997) from Pisa University. Timothy J. (Tim) Hattenbach is Senior Principal Mechanical Engineer and Compressor Team Leader with Bechtel Corporation in their Houston, Texas office. He has worked for Bechtel for 31 years and has 35 years of experience in the oil and gas industry. He has been the responsible engineer for full load string tests from 10 MW to 85 MW. Mr. Hattenbach has B.S. and M.S. degrees (Mechanical Engineering, 1972, 1974) from the University of Houston. He is a contributor to the Bechtel LNG Product Development Center and staff consultant on machinery issues. Mr. Hattenbach is the Taskforce Chairman for API Standards 670 (Machinery Protection Systems) and 616 (Gas Turbines), and is a member of the API 692 Taskforce for Compressor Gas Seals. Mr. Hattenbach is a registered Professional Engineer in the State of Texas. Duccio Fioravanti is a Design Engineer in the Mechanical Auxiliary Systems GEAR team for GE Oil & Gas, in Florence, Italy. He joined them in 2007, and his work mainly concerns gearboxes and coupling selections for different oil and gas applications. He has been a reviewer for international journals and conferences on robotic topics. Dr. Fioravanti received his M.Sc. degree (Mechanical Engineering, 2004) from the University of Florence and his Ph.D. degree (Applied Mechanics, 2008) from the University of Bologna. His research activities mainly concerned visual serving, robot control, and multibody dynamics in railway systems. Sergio De Franciscis is a Lead Electrical Engineer in the Electrical Department of GE Oil & Gas in Florence, Italy. He joined GE in 2007, working on several projects using variable speed electrical drives. Before joining GE, he worked for five years in the design of control systems and electronic hardware for power electrical conversion. Mr. De Franciscis received his M.Sc. degree (Electronics) from the Politecnico di Torino, Italy. ABSTRACT Nowadays variable speed drive systems (VSDS) are preferred to constant speed drives in the oil and gas industry because they can improve the efficiency of the process while avoiding the use of complex mechanical mechanisms (e.g., guide vanes) or plant recycling and throttling. However, the reputation of VSDS has not always been favorable since they can be a cause of torsional vibration problems. This is mainly due to the intrinsic nature of switching-based electrical systems to produce pulsating torque ripple on the shaft. In addition, closed-loop electromechanical interactions could lead to system instability. The aim of this paper is to introduce a new combined approach to deal with torsional phenomena, especially in high shaft-power applications such as liquefied natural gas (LNG) trains. Besides the conventional shaft-line modal analysis, a precise understanding of the electromechanical interactions is achieved through combined simulations between the shaft-line designer (compressor manufacturer) and the VSDS supplier together with a full-load-full-speed (FLFS) train string test. Simulations and string test results confirmed satisfactory torsional behavior and electromechanical stability of the overall system. INTRODUCTION One of the major improvements in the efficiency of plant operations in the oil and gas industry has been the use of variable speed drive systems (VSDS) where the Electric Motor speed can be adjusted to maximize the efficiency of the overall system, avoiding the use of complex mechanical mechanisms (e.g., guide vanes) or plant recycling and throttling (Baccani, 2007; Miranda and Brick, 2004). VSDS are employed mainly in the following oil and gas industry applications: LNG trains, pipelines, reinjection, storage recompression, subsea, and process gas compression. However, the use of VSDS is not free of concerns, in particular for high shaft-power applications. Disregarding specific issues typical of certain VSDS technologies (operability range, speed/torque control philosophy, etc.), two main critical aspects must be carefully considered: shaft torsional behavior and electromechanical interactions between the VSDS and the shaft-line. Typical problems of uncontrolled torsional vibrations are coupling failures, broken shafts, worn gears, fractured gear teeth, all of which result in undesired plant shutdowns (Kocur and Corcoran, 2008; Shimakawa and Kojo, 2007). The key to avoiding these consequences is designing the entire shaft-line employing a precise understanding of the forcing torsional phenomena, including the selection of couplings, gearboxes, and rotors from a torsional standpoint. Excitation of torsional natural frequencies may come from many sources that may or may not be a function of running speed (e.g., aerodynamic excitations, misalignment effects, etc.) (API 684, 2005). Moreover, systems including a VSDS, unlike those using conventional constant speed electrical equipment, show a pulsating torque ripple on the shaft-line that is created by the switching nature of the VSDS itself. This paper presents an overview of a new combined approach applied to an LNG application that includes a VSDS and is aimed at preventing torsional issues. Torsional phenomena are taken into account in the design phase of the shaft-line and the possible sources of torsional vibrations are simulated to assess the reliability of the design. The structure of this paper follows the main steps of this approach. The train configuration described in the SYSTEM DESCRIPTION section, is composed of a gas turbine, three centrifugal compressors (multistage, horizontally split type) and an induction motor fed by a converter. Shaft-line modal analysis, including evaluation of possible excitations within the operating range, is performed in the MECHANICAL MODEL DESCRIPTION section. The VSDS working principles and related phenomena are considered in the ELECTRICAL SYSTEM DESCRIPTION AND MODELING section. Open loop and closed loop electromechanical simulations are reported in the SYSTEM SIMULATIONS part. Finally, in the EXPERIMENTAL RESULTS AND DISCUSSION section, the torsional behavior of the compressor train is validated with string test experimental results. Some final remarks and future opportunities are discussed in the CONCLUSIONS. COMBINED TORSIONAL AND ELECTROMECHANICAL ANALYSIS OF AN LNG COMPRESSION TRAIN WITH VARIABLE SPEED DRIVE SYSTEM 95 SYSTEM DESCRIPTION The LNG train considered in this investigation consists of a 56,000 hp (42 MW) gas turbine, three centrifugal compressors, and a 9000 hp (6.6 MW) electric motor fed by a 9 MVA converter (rated torque ~ 10,000 lbf-ft (13,000 Nm), rated speed ~ 5000 rpm). For this specific application, the electric motor is needed as additional source of starting torque due to the high absorbed torque by the train during startup which is due to the considerable shaft-line length typical of a single shaft mechanical drive gas turbine. An overview of the train is shown in Figure 1. The specific components of the train identified in Figure 1 are defined in Table 1. Figure 2. Mode Shapes Related to the First Four TNFs: Normalized Amplitude Versus Train Section. MECHANICAL MODEL DESCRIPTION In order to describe the torsional behavior of the system, a lumped elements model was developed following the recommendations of API 684 (2008) and API 617 (2002). The train was divided into 60 rigid inertias connected by massless torsional springs. This allows a proper description of the stiffness of each shaft section, including coupling connections and shrink fits. Figure 1. LNG Train Overview. Table 1. Shaft-Line Abbreviations Used in this Paper. Modal Analysis Torsional natural frequencies of the system were calculated, performing an eigenanalysis on the equations of motion (modal analysis). In the modal analysis, damping is not considered since the low structural damping does not significantly affect the value of resonant frequencies and mode shapes (Walker, 2003). The equations, in matrix form, are the following: where [J] is the diagonal inertia matrix and [K] is the tridiagonal stiffness matrix. The vector contains the degrees of freedom of the system, which are the rotations G of each section about the shaft axis. The system is underconstrained, so there exists a zero solution, which is related to the rigid body motion of rotation. The nonzero solutions are the TNFs. The modal shapes related to the first four TNFs are plotted in Figure 3. (1) To better validate the closed loop behavior of the entire electromechanical system during the string test phase, both mechanical and electrical measurements were performed. A dedicated data acquisition system (DAS) was set up to acquire, record, and monitor in real time both electrical and mechanical parameters including the mechanical torque (average and ripple) acting on the train shafts. These data were used for post processing analysis and comparison with simulation results. Particular attention was focused on: Electric motor currents and voltages that were acquired by means of external probes and were used to calculate the motor air-gap torque (AGT). Mechanical torque on coupling C4 (measured with a strain gauge [Norton, 1982]) and on coupling C2 (measured using a phase shift method [Gindy]). The torque on coupling C4 was monitored since it is the torque transferred by the electric machine (EM) to the shaft-line. The torque on coupling C2 was monitored as well because it is where the first mode shape (which is usually the most problematic in electromechanical interactions [Lambrecht and Kulig, 1982]) has a nodal point (Figure 2). On the nodal point of each mode shape there is the highest pulsating torque response at the related torsional natural frequencies (TNF). Figure 3. Campbell Diagram. 96 PROCEEDINGS OF THE THIRTY-EIGHTH TURBOMACHINERY SYMPOSIUM 2009 The interaction in the operating range between TNFs and possible torsional mechanical excitation are represented in the Campbell diagram (Walker, 2003) of Figure 2. Torsional excitations included in this diagram are those at 1 rev (synchronous excitations due to centrifugal compressors) and 2 rev (related to misalignments of couplings). API Standards (API 684, 2005) require that TNFs of the full train are at least 10 percent above or 10 percent below any possible excitation frequency within the specified operating speed range (minimum operating speed [MOS], maximum continuous speed [MCS]). These limits are defined in Figure 2 by two dashed vertical lines labeled API LIMITS. The 2 rev crosses a TNF in this range (red circle in Figure 2). Fatigue verifications show that torsional stresses due to this excitation are considerably lower than the endurance limits of shafts and couplings. Couplings are selected to be the least stiff shaft-line components. As a consequence, the first four mode shape deformations are concentrated in the couplings, while the machines shafts are not significantly deformed. Therefore the first four TNFs are mainly a function of coupling stiffness and machine inertia (API 684, 2005). ELECTRICAL SYSTEM DESCRIPTION AND MODELING The electrical drive system used in this application is a medium voltage VSDS based on direct torque control (DTC) technology. A 36-pulse diode rectifier supplies three floating DC-links, which are combined via the insulated gate commutated thyristor (IGCT)-based inverter output bridge in series. This topology (Figure 4), combined with a particular switching concept, provides a nine-level line-to-line output waveform of 6.6 kv, which feeds a three-phase squirrel cage induction motor of 9000 hp (6.6 MW) nominal power and 5100 rpm rated speed. Forced Response In order to perform a forced analysis, a mechanical damping term is included by means of the damping matrix [C]. Vector T contains external torques applied on the shafts. G (2) Approximations of the Model The resulting model does not take into account damping nonlinearities, e.g., effects such as elastic saturation and torsio-flexural interactions. None of the secondary excitations described in API 684 (2005), e.g., aerodynamic forces and misalignments effects, are included, nor is the interaction with the train s speed regulator considered. Reduced Model A closed loop simulation of the electromechanical system would have a heavy computational burden if the entire lumped parameter model were to be included. A modal reduction model was created, replacing the physical state variables with the amplitude of vibration for each torsional mode. Using the mass normalized modal matrix (Gatti and Ferrari) and assuming that the damping matrix is a linear combination of the inertia and stiffness matrices, the equation of motion for the i th torsional mode is expressed as: where s i is the modal amplitude of vibration, i and i are the natural G frequency and mode shape for the i th vibration mode calculated from undamped analysis, and AF i is the modal amplification factor that was assumed based on experience on similar applications. The reduced model is limited to the first four flexible modes for the following primary reasons: The first four modes do not involve shaft deformations, so they are less damped than those at higher frequency (Walker, 2003). Only the modes below the maximum continuous speed were considered (Ooi, 1981). Only the TNFs below the bandwidth of the drive (~100 Hz) were considered. From the fifth to the eighth mode shapes, the amplitude of the deformed on the EM section is negligible, so they cannot be excited by electric motor torque components. Based on these criteria, modes higher than the fourth TNF were disregarded in the dynamics of the coupled electromechanical system included in this paper. (3) Figure 4. Functional Representation of the Electrical Topology of the Nine-Level Line-to-Line Output Inverter. The frequency converter controls the operation of the motor by variation of frequency and voltage. In order to control speed and power, the frequency converter receives a torque set point from the train s speed regulator. The drive control platform employs DTC technology. This control scheme allows field orientation without feedback using advanced motor theory to calculate the motor torque directly; the controlling variables are motor magnetizing flux and motor torque (Tiitinen, et al., 1995). Based on the actual status of the torque and flux in the machine, the best suited voltage vector is selected. The frequency at which the power elements switch is therefore variable. The switching frequency value mainly influences the thermal losses in the power stages and the quality of the output waveform. Its value is controlled defining a tolerance band in which the torque and flux are acceptable through the so-called hysteresis controllers. Figure 5 shows the basic principle of a hysteresis based controller: ht1 and hf1 define, respectively, the bands in which the torque and the flux are considered to be acceptable. Figure 5. Representation of the Hysteresis Based Strategy of the DTC. The main benefits of DTC technology are better torque response, torque control at low frequencies, and static and dynamic speed accuracy. Moreover, a fundamental feature in turbomachinery applications is that the produced air gap torque does not have any significant components in the low frequency range, thereby reducing the risk of exciting the torsional natural frequencies of the train. COMBINED TORSIONAL AND ELECTROMECHANICAL ANALYSIS OF AN LNG COMPRESSION TRAIN WITH VARIABLE SPEED DRIVE SYSTEM The investigation related to this paper makes use of a detailed model of the electric drive including the supply of the converter, the power stages, the squirrel cage induction machine with flux saturation and skin effect model, the DTC control, and the measurement of control signals. The model is definitely nonlinear, taking into account switching elements, saturations, hysteresis bands, measurement resolution, discrete implementation of control algorithms, etc. The model of a one-mass mechanical system (the motor rotor) together with a load model is also a part of the simulator. The latter allows the selection of a square, linear, or constant speed torque curve. Figure 6 shows the simulator structure where [v a v b v c ] are the three-phase voltages applied on the induction machine, [V DC i a i b i c ] are the measured values of the DC-link voltage together with inverter currents used by the control, [g u g v g w ] are the applied switching commands, T airgap is the air-gap torque produced by the induction machine, T load is the load torque obtained by the load model, motor is the motor speed, and Ref is the external reference for the electric drive that could be either speed or torque. In the application considered in this paper, the external reference is a torque set point. in simulation
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