The use of a direct-heated supercritical-CO2 (sCO2) closed Brayton cycle (CBC) in a Concentrated Solar Thermal (CST) power plant has the potential to deliver reductions in the costs of generated electricity through offering higher efficiencies and more compact power plants. Benefits provided by the sCO2 CBC arise from cycle operation in the vicinity of the critical point of CO2 where non-linear and abrupt increases in CO2 fluid properties are exhibited. The combination of dramatic CO2 fluid property changes, and fluctuations in solar heat energy and ambient-air temperatures used for cooling, make the cycle especially susceptible to performance deviations. Predictable, stable, and maximum power generation using the sCO2 CBC therefore requires an understanding of the dynamic behaviour of closed Brayton cycles and development of appropriate control strategies for predictable, stable, and maximum power generation using the cycle.
Design-point parameters for a direct-heated and recuperated 1-MWe sCO2 CBC in a parabolic-trough CST power plant are determined prior to dynamic simulation, using a first-law steady-state analysis. The required heat-exchange areas in the cycle are determined and the influence of CO2 specific heat variation with ambient air temperatures on the required heat-exchange area is also highlighted. A dynamic model of the sCO2 CBC is developed using mathematical models of heat exchangers and turbomachinery in Dymola®. Dynamic behaviour of the CBC is investigated for a power plant based at Longreach in Queensland, Australia, with ambient air and solar heat input fluctuations on representative summer and winter days. The effects of a range of hot and cold-side volume-ratios in the sCO2 CBC on dynamic performance of the cycle in the CST power plant, is also analysed using simulations on a representative summer day.
An extremum-seeking (ES) controller is proposed to maximise the power output of the CBC as the solar heat input and cooling-air temperature fluctuates given the difficulty in developing complete low-order models across all operating points of the CBC due to non-linearities in CO2 properties. This controller achieves this effect by manipulating the CO2 mass inventory in the CBC. Slack variables are introduced into the ES control performance metric to impose constraints on turbine inlet temperature and pressure to protect the CBC from damage. The performance of the proposed scheme is tested through simulations on representative summer and winter days. A low-pressure ideal-gas laboratory-scale CBC experimental-rig with CO2 as the working-fluid is constructed and used to gain an understanding of ideal-gas CBC dynamic characteristics, and for experimentation of potential CBC control strategies.
An optimum compressor inlet pressure which maximises power output exists for the sCO2 CBC. This is a result of the nonlinear and real-gas fluid characteristics of CO2 in the vicinity of the critical point. The optimum compressor inlet pressure varies with compressor inlet temperature and corresponds to the occurrence of pseudo-critical points at temperatures higher than the critical point temperature of CO2. Operating with the optimum compressor inlet pressure also delivers maximum cycle thermal efficiency and minimum required CO2 mass-flow rate. The occurrence of pseudocritical points in the supercritical-CO2 fluid region also significantly influences the required heat-exchange area for sCO2-to-air heat-exchange in the gas-cooler. Required sCO2 CBC gas-cooler and recuperator heat-exchange areas decrease when moving in a direction of increasing compressor inlet or ambient-air temperatures from the critical point of CO2.
Fluctuations in solar heat input and ambient air temperature causes movement of CO2 mass between the hot and cold-sides of the CBC in a direct-heated CST power plant. Hence fluctuations in these operating conditions eventually results in variations in CO2 mass-flow rate, pressures, temperatures, and net-power output throughout the day. The movement of CO2 mass between the hot and cold sides of the CBC also results in an imbalance in CO2 mass flow rates between the compressor and turbine. Turbine inlet temperatures reach excessive levels in summer due to the reduction in CO2 mass-flow rates resulting from a combination of changes in CO2 fluid properties and mass movement between the hot and cold sides of the cycle, when simulated with a fixed cycle inventory. A significant power output penalty is incurred for winter operation due to conditions at the compressor inlet becoming and remaining subcritical for most of the day.
Increasing the hot-to-cold-side volume-ratio in the sCO2 CBC results in slower dynamics in the system due to the delay associated with the larger magnitudes of CO2 mass movement in the CBC. A larger hot-to-cold-side volume-ratio in the sCO2 CBC also reduces fluctuations in pressures and temperatures, and reduces excessive turbine inlet temperature rises in summer. In comparison with a fixed inventory approach, the proposed ES algorithm demonstrated similar or better overall performance but required significantly less calibration effort. The ES controller is also able to maintain turbine inlet temperature and pressure close to or below the permissible limits and does not require retuning between seasons. Preliminary experimental investigations with the ideal-gas CO2 CBC has shown that the cycle possesses similar dynamic response characteristics to those of the sCO2 CBC.