For tolerating Byzantine faults of both the terminal and communication components in self-stabilizing clock synchronization, the two-dimensional self-stabilizing Byzantine-fault-tolerant clock synchronization problem is investigated and solved. By utilizing the time-triggered (TT) stage provided in the underlying networks as TT communication windows, the approximate agreement, hopping procedure, and randomized grandmasters are integrated into the overall solution. It is shown that with partitioning the communication components into 3 arbitrarily connected subnetworks, efficient synchronization can be achieved with one such subnetwork and less than 1/3 terminal components being Byzantine. Meanwhile, the desired stabilization can be reached for the specific networks in one or several seconds with high probabilities. This helps in developing various distributed hard-real-time systems with stringent time, resources, and safety requirements.

The authenticated broadcast is simulated in the bounded-degree networks to provide efficient broadcast primitives for building efficient higher-layer Byzantine protocols. A general abstraction of the relay-based broadcast system is introduced, in which the properties of the relay-based broadcast primitives are generalized. With this, fault-tolerant propagation is proposed as a building block of the broadcast primitives. Meanwhile, complementary systems are proposed in complementing fault-tolerant propagation and localized communication. Analysis shows that efficient fault-tolerant propagation can be built with sufficient initiation areas. Meanwhile, by integrating fault-tolerant propagation and localized communication, efficient broadcast primitives can be built in bounded-degree networks.

To improve the overall efficiency and reliability of Byzantine protocols in large sparse networks, we propose a new system assumption for developing multi-scale fault-tolerant systems, with which several kinds of multi-scale Byzantine protocols are developed in large sparse networks with high system assumption coverage. By extending the traditional Byzantine adversary to the multi-scale adversaries, it is shown that efficient deterministic Byzantine broadcast and Byzantine agreement can be built in logarithmic-degree networks. Meanwhile, it is shown that the multi-scale adversary can make a finer trade-off between the system assumption coverage and the overall efficiency of the Byzantine protocols, especially when a small portion of the low-layer small-scale protocols are allowed to fail arbitrarily. With this, efficient Byzantine protocols can be built in large sparse networks with high system reliability.

Silicon Carbide (SiC) MOSFETs are usually paralleled to increase the current capability for high power applications. While, the asymmetrical parasitic parameters of the wide-used laminated busbar can cause current imbalance for paralleled MOSFETs. The fast switching of SiC devices can further deteriorate the imbalance. However, the complex current paths and their mutual effects are seldom considered and effectively modeled for the parasitics of the busbar, which is not accurate enough to evaluate the current imbalance for the busbar connected with SiC devices. This paper proposes accurate modeling of the effective parasitic parameter of laminated busbars with paralleled SiC MOSFETs. The model incorporates not only the self-inductance and resistance but also the complex mutual coupling effect of all the current paths. Moreover, a switching period is divided into two durations for accurate effective parasitic models, in which the busbar can have different effective models regarding one physical structure. Furthermore, for easy evaluation of the current balance, a single effective model, namely equivalent model, is derived for a physical structure by replacing the complex mutual network. A specific laminated busbar for EV inverter is analyzed to prove the above theory, which is validated by simulation and experiment separately.