## 1 Introduction  
Micro-gas turbines coupled with concentrated-solar power systems (CSP) can provide a viable solution for renewable energy generation. They have been shown to be ideally suited for small-scale standalone and off-grid applications [1]. However, micro-gas turbines experience larger losses in the system components, and hence achieve lower thermal efficiencies, compared to large-scale gas turbines. Thus, for a high thermal efficiency, in the range of 40 to 50%, the system needs to operate at high heat-source temperatures, above 600 \({}^{\circ}\)C. In comparison, cycles operating with supercritical carbon dioxide (sCO\({}_{2}\)) can achieve similar thermal efficiencies at more moderate temperatures. Therefore, sCO\({}_{2}\) can be considered as a potential candidate for concentrated-solar power applications, particularly for stand-alone solar dish units; offering a simple layout, high-power density and compact structures [2]. Despite the promising potential of sCO\({}_{2}\), sCO\({}_{2}\) turbomachine design is still a developing field. However, turbine performance is one of the main factors that affects the cycle performance; for example, a 2% increase in turbine efficiency has been shown to result in a 1% enhancement in the thermodynamic cycle efficiency [3]. This would have a significant impact on cost reduction of the solar power system through reduction in the size and the cost of the concentrator which typically represents over 60% of the total system cost.Therefore, several researchers have investigated advancing the state-of-the-art with regards to turbine design. [PERSON] et al. [4] discussed some design aspects for a 100 MW axial sCO\({}_{2}\) turbine for a direct sCO\({}_{2}\) recompression cycle. Aerodynamic and structural analyses were performed to determine the best design configuration as a function of the number of stages, radial tip clearance androtational speed. [PERSON] et al. [5] addressed the design of small radial turbomachinery with an output power ranging from 50-85 kW and an efficiency of 70%. Subsequent to that, [PERSON] et al. [6] presented a new insight for a sCO\({}_{2}\) radial turbine design for a power rating ranging between 100 and 200 kW through the integration of mean-line design with a loss model where an efficiency of 78-82% has been achieved. [PERSON] et al. [3] developed an algorithm that allows for the design of a sCO\({}_{2}\) radial turbine for CSP application rated at 10 MW. During the design process, a mean-line design tool that uses an enthalpy loss model, geometry optimisation and 3D RANS simulation were performed. As a result of the geometry optimisation, an enhancement in both the efficiency and power output of 5.34% and 5.30 % was achieved respectively [3]. In the same context, [PERSON] et al. [7] and [PERSON] et al. [8] proposed 300 kW and 1.5 MW radial sCO\({}_{2}\) turbine designs respectively. [PERSON] et al. [8] added a design of a 15 MW sCO\({}_{2}\) axial turbine to their study. They implemented CFD simulations to analyse the flow characteristics of sCO\({}_{2}\) turbine components. In the same year, [PERSON] et al. [9] developed an optimisation design approach for a radial-inflow turbine using sCO\({}_{2}\). This was done through combining a one-dimensional design method with an optimisation algorithm for both nominal and off design performance conditions for the stage inlet temperature, rotational speed and expansion ratio. Likewise, [PERSON] et al. [10] presented an optimal 10 MW three-stage sCO\({}_{2}\) axial turbine design using 3D model, optimisation methods and off design analysis. Considering the potential of sCO\({}_{2}\) fluid for small-scale systems, [PERSON] et al. [11] presented a comparative study between various turbine architectures for a small-scale 100 kW sCO\({}_{2}\) Rankine cycle. Single-stage radial-inflow, single-stage axial, and two-stage axial turbines were analysed to identify the most feasible turbine designs based on the limitations of the blade height.