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The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

When using recently-developed active power factor correction (APFC) controllers in power systems comprised of dual-opposed free-piston Stirling convertors, a variety of configurations of the convertors and controller(s) can be considered, with configuration ultimately selected based on benefits of efficiency, reliability, and robust operation. The configuration must not only achieve stable control of the two convertors, but also synchronize and regulate motion of the pistons to minimize net dynamic forces. The NASA Glenn Research Center (GRC) System Dynamic Model (SDM) was used to study ten configurations of dual-opposed convertor systems. These configurations considered one controller with the alternators connected in series or in parallel, and two controllers with the alternators not connected (isolated). For the configurations where the alternators were not connected, several different approaches were evaluated to synchronize the two convertors. In addition, two thermodynamic configurations were considered: two convertors with isolated working spaces and convertors with a shared expansion space. Of the ten configurations studied, stable operating modes were found for four. Three of those four had a common expansion space. One stable configuration was found for the dual-opposed convertors with separate working spaces. That configuration required isochronous control of both convertors, and two APFC controllers were used to accomplish this. A frequency/phase control loop was necessary to allow each APFC controller to synchronize its associated convertor with a common frequency.

When using recently-developed active power factor correction (APFC) controllers in power systems comprised of dual-opposed free-piston Stirling convertors, a variety of configurations of the convertors and controller(s) can be considered, with configuration ultimately selected based on benefits of efficiency, reliability, and robust operation. The configuration must not only achieve stable control of the two convertors, but also synchronize and regulate motion of the pistons to minimize net dynamic forces. The NASA Glenn Research Center (GRC) System Dynamic Model (SDM) was used to study ten configurations of dual-opposed convertor systems. These configurations considered one controller with the alternators connected in series or in parallel, and two controllers with the alternators not connected (isolated). For the configurations where the alternators were not connected, several different approaches were evaluated to synchronize the two convertors. In addition, two thermodynamic configurations were considered: two convertors with isolated working spaces and convertors with a shared expansion space. Of the ten configurations studied, stable operating modes were found for four. Three of those four had a common expansion space. One stable configuration was found for the dual-opposed convertors with separate working spaces. That configuration required isochronous control of both convertors, and two APFC controllers were used to accomplish this. A frequency/phase control loop was necessary to allow each APFC controller to synchronize its associated convertor with a common frequency.

The Stirling Convertor System Dynamic Model developed at NASA Glenn Research Center is a software model developed from first principles that includes the mechanical and mounting dynamics, the thermodynamics, the linear alternator, and the controller of a free-piston Stirling power convertor, along with the end user load. As such it represents the first detailed modeling tool for fully integrated Stirling convertor-based power systems. The thermodynamics of the model were originally a form of the isothermal Stirling cycle. In some situations it may be desirable to improve the accuracy of the Stirling cycle portion of the model. An option under consideration is to enhance the SDM thermodynamics by coupling the model with Gedeon Associates Sage simulation code. The result will be a model that gives a more accurate prediction of the performance and dynamics of the free-piston Stirling convertor. A method of integrating the Sage simulation code with the System Dynamic Model is described. Results of SDM and Sage simulation are compared to test data. Model parameter estimation and model validation are discussed.

Free-piston Stirling convertors are being developed for potential use on NASA exploration missions. In support of this effort, the NASA Glenn Research Center has developed the Stirling convertor System Dynamic Model (SDM). The SDM models the Stirling cycle thermodynamics; heat flow; gas, mechanical, and mounting dynamics; the linear alternator; and the controller. The SDM s scope extends from the thermal energy input to thermal, mechanical, and electrical energy output, allowing one to study complex system interactions among subsystems. Thermal, mechanical, fluid, magnetic, and electrical subsystems can be studied in one model. The SDM is a nonlinear time-domain model containing sub-cycle dynamics, which simulates transient and dynamic phenomena that other models cannot. The entire range of convertor operation is modeled, from startup to full-power conditions.