## 1 Introduction  
The demand for low fuel consumption and CO\({}_{2}\) generation vehicles over the last few years has popularly increased the necessity of downsizing and increasing the overall thermal efficiency of Internal Combustion (IC) engines. Downsizing is the process of reducing the volumetric capacity of an engine for reduced throttling and friction losses while its boosting capabilities need to be increased for higher specific heat. This can be achieved by the implementation of a boosting device (turbocharger or supercharger) for increased air pressure at the intake of the engine and therefore higher volumetric efficiency. A turbocharger is a device that recovers the waste energy from the engine's exhaust gasses and uses it to compress the air at the engine's intake. The level of compression is directly linked to the amount of air passing through the turbine, and it can be controlled by either bypassing part of the flow through a Wastegate (WG) or by changing the nozzle position of the turbine (VGT, Variable-geometry turbocharger). The proportion of the waste-gated flow can be up to 50% for high speed and load conditions, which imply a vast amount of unexploited energy. The drawback of this device is that due to the nature of the energy exchange between the engine and the turbocharger (filling of the intake and exhaust manifolds and low exhaust energy at low speeds/loads), the transient performance during engine load increase is relatively poor, which deteriorates the drivability of the vehicle [1]. On the other hand, a supercharger is a device mechanically driven by the engine to increase its volumetric efficiency. It has a very fast response time in transient conditions, but the power required for its operation is a parasitic loss for the engine; therefore, it is not widely used in recent technologies. The parallel use of a turbocharger and a supercharger could potentially improve the transient performance of the system during load increase while reducing the engine losses compared to a solely supercharger boosted system. However, this will increase the complexity, as a two-stage boosting system is required [2; 3]. An electrically-assisted turbocharger of a larger size and with higher efficiency could be used in case a simpler one-stage boosting system is needed. The motor can provide the electricity required at the periods of load increase for a faster response, while the turbocharger works as a conventional system during steady-state and tip-out conditions. [PERSON] et al. [4] investigated the influence of an electric motor attached to the turbo shaft on the transient response of a diesel engine. It was found that the time required to perform transient power increase was reduced from 3.9 s for the original conventional turbocharger down to 1.7 s. [PERSON] et al. [5] tested a hybrid turbo developed by Mitsubishi Heavy Industries under transient operating conditions. An improved engine peak torque and enhanced transient response compared to a conventional system was demonstrated. Torque was enhanced by 18% at low engine speeds, while the response time was reduced by 70% when 2 kW of turbo motor assistance was provided. [PERSON] et al. [6] investigated the potential of an electrically-assisted turbocharger for a heavy-duty diesel engine to evaluate the turbo-lag reductions and the fuel consumption savings that could be obtained in an urban bus at different operating conditions. The system allowed fuel consumption reductions of 6% to 1%, depending on the driving cycle, with lower values corresponding to congested traffic conditions. [PERSON] [7] applied various electric boosting systems to a gasoline and a diesel engine and evaluated their steady state and transient performance from the perspective of the air path. The author compared the performance characteristics of an electrically-assisted turbocharger with those of a two-stage system with an electrically-driven compressor placed before or after the main waste-gated turbocharger.