Due to the high penetration of renewable energy sources into the electrical power network, overcurrent relays coordination with highly sensitive and selective protection systems are now two of the most important power protection concerns. In this research, an optimal coordination strategy utilising a new hybrid tripping scheme based on current–voltage characteristics has been devised for overcurrent relays in a power network coupled to a photovoltaic system. This research develops and proves a new optimal coordination scheme based on two optimisation methods, the vibrating particles system and particle swarm optimisation algorithms, in consideration of the impact of renewable sources on fault characteristics. The new optimal coordination approach aims to improve the sensitivity and dependability of the protection system by reducing the tripping time of the overcurrent relays by employing a new hybrid tripping scheme. A specific case study, Conseil International des Grands Réseaux Electriques (CIGRE) distribution network connected to two photovoltaic systems is constructed and presented utilising Industrial software (namely ETAP), and the outcomes of the proposed optimal coordination scheme are compared with standard and recent characteristics from the literature. The hybrid tripping scheme and optimisation techniques are evaluated using different fault and power network model scenarios. The results show that the optimal hybrid tripping scheme provided successfully decreases the overall operating time of the overcurrent relays and increases the sensitivity of the relay during all fault scenarios. The reduction in overall time for the proposed hybrid tripping scheme was 35% compared to the literature for the scenario of a power grid with and without photovoltaic systems.

The bit error probability (BEP) of binary and quaternary PSK (BPSK and QPSK) signals over Rayleigh fading channel with imperfect carrier-phase recovery is derived. The channel is assumed to be slow and frequency-nonselective in which the received signal is constant over at least two symbol intervals. Numerical values for the average BEP are obtained by integrating the conditional BEP expression over the carrier-phase error distribution. The resultant integrands have only elementary functions, such as exponentials and algebraic power functions and can, therefore, be explicitly evaluated to any degree of accuracy. The accuracy of this approach is verified through proposing an efficient quazi-analytical simulation technique.

In this paper, we study the effect of cochannel interference (CCI) on the performance of partially coherent BPSK and QPSK in uncorrelated L-branch equal-gain combining systems. We consider a generalized propagation model wherein the desired and interfering signals undergo Nakagami-m or Rician fading with different amounts of fading severity. Further, the interfering signals are assumed to be asynchronous symbol timing with the desired signal, so that the effect of cross-signal intersymbol interference (ISI) is taken into account. Using a convergent Fourier series method, we derive extensive analytical results for the average bit error probability and the SNR gain penalty caused by the interference signals for different signal to-interference ratio levels. The numerical results presented in this paper demonstrate the system performance under very realistic propagation and detection conditions including CCI, carrier phase error recovery, cross-signal ISI, generalized fading channels, and AWGN. Hence our results are expected to be of significant practical use for such scenarios.

In this paper, we derive very tight lower bounds for the average bit error probability (BEP) of M-ary phase shift keying (MPSK) systems. For the first time, the bounds are obtained taking into consideration Nakagami-m wireless fading channel and Tikhonov-distributed carrier phase error. The bounds are shown to be tight and easy to evaluate for phase error noise parameters likely to be encountered in practice and for signal-to-noise ratio (SNR) that are needed in moderate fading environment. The accuracy of the derived bounds is illustrated by comparing the bound results to those obtained by exact solutions for M = 2 and M = 4.