## 1 Introduction
Moreover, the use of dedicated modulation techniques, such as OFDM (orthogonal frequency division multiplexing), allows for a broadband transmission, hence, PLC is competitive in more than in economic terms. Some disadvantages have to be taken into consideration: power lines do not necessarily provide a sure support, due to the presence of different elements; the attenuation of the data could be a problem; the electrical noise on the line limits the speed of the data transmission. Designing the PLC system for the V2G needs a multi-objective optimization where some conflicting objectives should be considered: the communication capacity, the total transmission power, and the communication error probability. The multi-objective optimization process provides a set of equivalent solutions from which the designer makes the final choice, introducing further fitting criteria [14;15]. Figure 1: Vehicle-to-grid system. The optimization problem must be formalized depending on the modulation technique. Usually, to better exploit the available transmission band, the OFDM [8] system is assumed, which consists of splitting the transmission band into mutually orthogonal sub-carriers. Each one is used as a sub-carrier where the signal can be considered as if it were the only one in the channel. Every sub-carrier is loaded with a bit rate (\(BR\)) depending on the specific signal-to-noise ratio (\(SNR\)). OFDM is a modulation scheme commonly adopted in several application domains, such as mobile phones, digital TV and radio, and xDSL, each one having specific features and requirements. In particular, in the application presented in the present paper, different transmitters share the same channel, therefore, each sub-carrier must be assigned exclusively to one transmitter. The optimization of the modulation scheme works by allocating the bits to the sub-carriers, which is referred to as bit-loading [8] problem, and which depends on the properties of the channel and the requirements of the transmission. In the present paper, the optimal design of the modulation system in PLCs is formalized as a multi-objective optimization problem with the following three conflicting objectives: the \(BR\), to be maximized; the bit error rate (\(BER\)) and the interference on adjacent equipment, to be minimized [16; 17; 18]. The interference mostly depends on the power of the modulated signal and on its evolution in the time. The problem faced has its own specificity, since the transmissions of the charging stations travel through common branches of the grid. Consequently, they must share the same frequency band. However, each channel has its own frequency response and power spectral density of noise. Hence, the optimal solution of the design problem should consider all the channels simultaneously. Other applicative domains have the same specificity, for example, cellular phones or digital audio broadcasting (DAB) networks. In the proposed method, the OFDM symbols, to be sent by all the transmitters, are merged into one, which simultaneously travels in all the channels. A fictitious frequency response, called Chimera, is created which allows to perform the multi-channel optimization of the OFDM modulation scheme as if all the transmissions should be sent through a unique channel (named here Chimera channel). To define the Chimera frequency response an integer quadratic optimization problem is formalized whose aim is to assign band resources to the charging stations connected to the same feeder, depending on the number of supplied plugs, maximizing, at the same time, the overall capacity of the transmission. The rest of the paper is organized as follows. In Section 2, the problem at hand is outlined. In Section 3, the proposed Chimera algorithm is described. Section 4 reports the formalization of the multi-objective problem aiming to off-line design the PLC system. Results of the optimization procedure on a case study are reported in Section 5. Finally, in Section 6 some conclusions are given.