## 2 Experimental Data and Machine Characterization  
An MGT MTT Enertwin was tested under various working conditions during experiments conducted at DLR, Stuttgart [18]. A schematic of the system and the instrumentation relevant for this paper is shown in Figure 1. At first, ambient air is compressed by the compressor (1) up to approximately 3 bars. Before entering the combustor (3), the air is pre-heated with hot exhaust gas in the recuperator (2). In the combustor, fuel (methane) is injected and oxidized and the hot exhaust gas is expanded through the turbine (4) and heats the compressed incoming fresh air in the recuperator (2). In the subsequent water heat exchanger (5), the thermal power (e.g., for use in heating systems) is coupled out. The compressor (1), turbine (4), and generator (7) are mounted on the same shaft (6). The oil pump and fuel pump are not shown in the scheme. The power needed to drive the compressor, \(P_{c}\), and the turbine power \(P_{t}\), can be calculated as:  
\[P_{c}=\dot{m}_{a}(h_{2c}-h_{1c}) \tag{1}\] \[P_{t}=(\dot{m}_{a}+\dot{m}_{f})(h_{1t}-h_{2t}), \tag{2}\]  
where \(\dot{m}_{a}\) is the mass flow rate of inlet air, \(\dot{m}_{f}\) is the mass flow rate of fuel, and \(h_{1c}\), \(h_{2c}\), \(h_{1t}\), and \(h_{2t}\) represent the enthalpy before and after the compression and the expansion (\(t=\) turbine), respectively. The MGT net shaft power, \(P_{MGT}\), is given by:  
\[P_{MGT}=P_{t}-P_{c}-P_{oil}-P_{f,pump}. \tag{3}\]The power consumption of the oil pump and fuel pump is 75 W and 300 W, respectively. In this layout, the turbine shaft is connected to a high-speed electric generator, and a frequency inverter is needed to convert the high-frequency output of the electric generator to the grid frequency. The net electric power output is:  
\[P_{el}=\eta_{gen}P_{MGT}, \tag{4}\]  
where \(\eta_{gen}\) takes into account the losses of the electric generator and inverter. The energy balance at the water heat exchanger can be written as:  
\[\frac{m_{a}+\dot{m}_{f}}{m_{H_{2}O}}=\frac{c_{p,H_{2}O}\Delta T_{H_{2}O}}{h_{ ex,2}-h_{ex,1}}, \tag{5}\]  
where \(\dot{m}_{H_{2}O}\), \(c_{p,H_{2}O}\), and \(\Delta T_{H_{2}O}\) are the water mass flow, specific heat, and temperature increase, respectively. \(h_{ex,1}\) and \(h_{ex,2}\) represent the enthalpy of exhaust gases before and after the heat exchanger. Finally, the thermal power produced by the CHP system is:  
\[P_{th}=\dot{m}_{H_{2}O}\ c_{p,H_{2}O}\ \Delta T_{H_{2}O}. \tag{6}\]  
At full-load, this system produces 3.2 kW electrical and 15.6 kW thermal power [19]. The built-in control software from MTT was modified and switched to manual mode (ProtoComm Manual Mode), so that the operators could test different maneuvers and operating points with more flexibility. The turbine outlet temperature is determined by the arithmetic average of three thermocouples (type K, tolerance class 2) with a measurement uncertainty of \(\pm\)5.9 K. All other thermocouples were type N with tolerance class 1 and a resulting uncertainty of \(\pm\)2.9 K. The MGT was controlled manually to a constant turbine outlet temperature of 1060 K by adjusting the fuel mass flow. The combustion chamber inlet temperature was in the range 725-734 \({}^{\circ}\)C with a gas turbine pressure ratio of about 3. The fuel mass flow was measured with an F-211 AV mass flow controller produced by Wagner-Bronkhorst with an accuracy of \(\pm\)0.5% as a percentage of reading, plus \(\pm\)0.1% full-scale. Fuel power is computed as:  
\[P_{f}=\dot{m}_{f}LHV, \tag{7}\]  
where \(\dot{m}_{f}\) is the fuel mass flow rate and \(LHV\) its Lower Heating Value. In this work, the MTT Enertwin works with methane with an \(LHV\) of 47.78 MJ/kg. Figure 1: The micro gas turbine MTT Enertwin in its combined heat and power configuration. The operating point of the EnerTwin is expressed by a number called the Setting Point (SP).