Additional dc testbed components not presented in this 2 GENERATOR MODEL. study include As shown in Figure 3 the GS 1 generation system. 3 Generation system 2 GS 2 11 kW permanent magnet consists of the PM 1 prime mover emulator a SG 1. synchronous machine with voltage regulator 2 VR 2 synchronous generator a VR 1 voltage regulator a R 1 line. and an inverter serving as rectifier R 2 driven by a commutated rectifier a brushless exciter and an output low. four quadrant dynamometer prime mover emulator pass filter The synchronous generator is a 4 pole wound. 4 Power supply 1 PS 1 which steps down the 750 V rotor synchronous machine which is rated to supply 59 kW. primary dc bus to the 500 V port side dc distribution at 1800 rpm The output of the generator is rectified by a. bus three phase line commutated diode rectifier The brushless. 5 Power supply 2 PS 2 which feeds the 500 V exciter and VR 1 PI voltage regulator provides a 750 V. starboard side dc distribution fed by a 480 VAC utility nominal bus voltage The low pass LC output filter helps. grid connection prevent high frequency components mainly from switching. 6 Three dc distribution zones which include switchgear from propagating on to the dc bus. conversion modules inverter modules and load banks. 7 One pulsed power load PPL is designed to place a. load on the testbed which is representative of a pulsed. power weapon such as a radar or rail gun, Reference 2 provides a comprehensive description of the. dc tested including detailed models parameter values and. preliminary test results The test results included herein. supersede the preliminary test results in the reference. The dc testbed is an extension of prior U S Navy, funded research which included the establishment of a. Naval Combat Survivability NCS Testbed 3 The NCS, testbed contained an ac primary distribution bus feeding the. propulsion load as well as redundant port and starboard dc. zonal distribution buses converters switchgear and loads Figure 2 GS 1 controller. Research under this prior effort included the development of. advanced stability analysis tools power converter control The one line diagram of the GS 1 controller is depicted in. strategies new time domain simulation tools improvement. Figure 2 Therein v dc denotes the reference or, in multi level power conversion and electric drive. propulsion advanced methods of parameter identification commanded dc voltage v dc denotes the low pass filtered. and investigations into the system effects of pulsed power dc bus voltage with filter time constant fv and i dc denotes. the low pass filtered inductor current with filter time. constant fi The reference dc voltage is slew rate limited to. prevent excessive capacitor inrush currents on startup. Short circuit protection, is also included by, sharply reducing the. voltage command when, the current exceeds a, certain threshold The. droop term kd allows, multiple generators to, share the load Voltage. regulation utilizes a PI, control with anti wind, up The output of the. controller is the, commanded field current, into the brushless. exciter i fde, Figure 3 Generation source GS 1, The detailed GS 1 model employs a transfer function 3 PROPULSION DRIVE MODEL. model 5 6 in place of the equivalent circuit model The SPS ship propulsion system is composed of an. commonly found in the literature The simplified input LC filter PD propulsion drive controller and. synchronous machine model uses conventional modeling induction machine connected to a dynamometer which can. techniques 7 set forth in 8 The simplified brushless emulate 4 quadrant hydrodynamic loads The primary. exciter model uses a transfer function representation The components are presented in 11 The input filter has a. lumped parameters required for the simplified synchronous 1 kHz cut off The induction drive is a 4 pole 460 V. machine are obtained by curve fitting the frequency 60 Hz 50 Hp delta connected squirrel cage induction. response of the machine to the q and d axis transfer machine The overall control strategy for the propulsion. functions 5 The nonlinear AVM models are more drive is shown in Figure 5 The propulsion controls can. suitable for control design and dynamic response studies of operate in either torque or speed command modes and can. complex dynamically interdependent systems 9 The coordinate with a pulsed load The controller implements. average value model of GS 1 uses a reduced order model of the adaptive maximum torque per amp AMTPA control. the synchronous machine which neglects the stator described in 12 In commanded torque mode Te tc is. dynamics more detail is presented in 7 The average. value model of the rectifier is set forth in 8 The other processed by the torque trim controller which ensures. aspects of the GS 1 AVM model are similar to the detailed tracking between the commanded torque and the estimated. waveform model Complete models parameter data and torque Torque estimation based on the measured motor. simulations can be obtained from reference 10 or current and voltage as well as anti windup as documented in. www usna edu ESRDC 11 The propulsion controller contains a provision to. improve stability by modulating the torque command via. non linear stabilizing control NSC 13, This feature is disabled for the studies. presented herein The commanded torque, Te is slew rate limited and commanded. current is limited to protect the inverter The, output of this limiter is processed by the. synchronous current regulator described in, section 13 11 of 7 and delta hysteresis. modulation controls the inverter, The detailed waveform SPS model. includes all leakages and magnetizing, saturation The simplified waveform model. neglects saturation and replaces the AMTPA, control with constant slip MTPA control as set. forth in section 14 3 of 7 The primary, Figure 4 Propulsion drive primary components difference between the detailed waveform. model and the detailed non, linear average value model. NLAM is the use of a, synchronous reference frame, The simplified NLAM assumes. that the commanded current can, be tracked by the inverter. removing the current regulator, from simulation Also a reduced. order model for the induction, machine is used Complete. models and parameter data can, be obtained from the references. 11 14 and website, www usna edu ESRDC, Figure 5 Propulsion drive controller. 4 STABILITY ANALYSIS investigations and remains an active research tool 16 For. Power electronics based power distribution being a key the analysis herein the GS 1 system presented in Figure 3. technology in electric ships must be robust A shipboard provides the source impedance model Likewise the. isolated power system composed of fast power electronics propulsion system in Figure 4 provides the load admittance. coupled with transient loads and constant power loads of the model The gain margin and phase margin values used for. same order as the generation plant require an additional this analysis are 6 dB and 30 degrees respectively. level of analysis to guarantee that the system does not The application of the generalized immittance based. exhibit unstable operating points One such approach is that stability analysis to the system described in this paper. of generalized immittance based stability analysis 15 consists of analyzing two cases The base case will be. This analysis method represents components as generalized shown to be stable and a modified case that will be shown. immittances for example impedances or admittances to be unstable Figure 1 includes the testbed provisions to. which bound model behavior in the frequency domain A alternate between the two cases on the fly The base case is. significant advantage of this analysis is that it considers defined by the state of the two switches in the output filter. entire sets of equilibrium operating points at a time so that of the generation system and the two switches in the input. a single analysis can be used to explore the stability filter of the propulsion load being in a closed state This. properties of a system over its entire operating range results in an effective capacitance and ESR across the bus of. Another advantage is the potential to develop composable 1 5 mF and 0 0682 for the generation system and 1 5 mF. systems such as next generation integrated power systems and 0 1468 for the propulsion load The modified case. which guarantee system stability based on component only differs from the base case in that all four switches are. interface specifications opened This removes Cdc2 and rCdc2 from the generation. To illustrate the generalized immittance method 16 system and C and rESR from the propulsion load The. consider the simple source load system of Figure 6 Let the effective capacitance and ESR become 100 F and 0 752. small signal impedance characteristic of the source at an respectively for both the generation system and the. operating point x be denoted Z x and let the small signal propulsion load This modified case will be shown to be. admittance characteristic of the load be denoted Yx Let the unstable when the propulsion drive is operating at a full load. which corresponds to a torque command of 200 Nm at 1500. set Z represent the generalized impedance and the set Y. represent the generalized admittance Thus Z x Z and Figure 7 and Figure 8 depict the stability analysis. Y x Y for all operating points of interest The variation of results for the base case and the modified case Both figures. values stems both from nonlinearities as well as parameter contain a generalized source admittance constraint and. uncertainties generalized load admittance As can be seen in Figure 7 the. stable GS 1 and propulsion load base case contains no. intersection between the source constraint and the load. admittance This implies that across the entire frequency. range there is an argument for stability, Figure 6 Simple source load system. The next step is to select a stability criteria with a desired. gain margin GM and phase margin PM Using generalized. immittance analysis specification of a generalized source. impedance or load admittance constrains the allowable. load admittance or source impedance The constraint is. found such that if the generalized load admittance or source. impedance does not intersect the forbidden region then the. Nyquist contour of Z x Yx will not cross the stability criteria. boundary This in turn ensures that the Nyquist contour of. Z x Y x cannot encircle 1 which in turn ensures that all. operating points considered are locally stable, The generalized immittance based stability analysis was. conducted using the open source MATLAB based dc Figure 7 Stable GS 1 and propulsion load case. stability toolbox 17 which was developed under prior. The Figure 8 modified case distinctly shows an noise in the MHz regime and significant double. intersection between the source constraint and the load fundamental frequency ripple components associated with. admittance implying a possible instability at certain imbalances within the ac system Overall the correlation is. operating points Comparison of experimental stability very good. behavior with time domain simulation studies and, generalized immittance analysis is presented in the next. Figure 9 Study 1 Step change in resistive load, Figure 8 Unstable GS 1 and propulsion load case. 5 ACSL SIMULATION AND VALIDATION, The Advanced Continuous Simulation Language. ACSL is the primary simulation tool used in this, investigation The testbed simulations are numerically stiff. and contain many switching states ACSL has been found. to have one of the best solvers for this difficult class of. numerical problems Routines for the complete simulation. of the dc testbed have been developed using a modular and. systematic approach Two macro libraries are used in the. simulation the model library and the component library. The model library contains high level modules such as the. generator propulsion drive or induction motor This library. allows the user to easily instantiate various system Figure 10 Study 2 Step change in torque command. configurations The component library contains lower level. macro models which encapsulate the details of each 5 2 Study 2 Step Change in Torque Command. component model Together various system topologies can As in the first validation study the second study begins. be constructed using the concise model library modules with the system at steady state with the propulsion motor at. while the component library contains the detailed simulation half load condition with Te 100 Nm and rm 1500 rpm. building blocks Complete models can be obtained from the At t 2 3 s the commanded torque is stepped up from. reference 18 and website www usna edu ESRDC 100 Nm to 125 Nm while holding the speed constant. Figure 10 compares the detailed waveform simulation. 5 1 Study 1 Step change in resistive load results and measured testbed data Once again the. In the first validation study the system is at steady state experimental data contains higher harmonic content and. with the propulsion motor at half load condition with overall the correlation is very good Figure 11 compares. Te 100 Nm and rm 1500 rpm At t 0 20 s a shunt the detailed simulation waveform and measured testbed data. resistive load of Rshunt 60 2 is added to the system under steady state conditions Note the exce. Weapons amp Systems Engineering Department United States Naval Academy Annapolis MD 21403 USA zivi usna edu Keywords DC power system detailed waveform average value stability Abstract The modeling simulation and experimental validation of the primary bus components of a dc power system testbed are presented herein This reduced scale and

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