To enhance the reliability of converters, many fault-tolerant converters have been proposed in the literature. However, the design rule is seldom proposed. The converter is usually a switch circuit that can be described by the matrix; therefore, the design of a fault-tolerant converter can be transformed to the matrix design. The fault tolerance of a circuit is mainly determined by its alternative loops. In this study, minus-1 Boolean determinant is defined to establish a relationship between the matrix and the alternative loop. Then, the following proposition is proven: for a connection matrix of a circuit, the minus-1 Boolean determinant represents the sum of loops in the circuit, where each term of the minus-1 Boolean determinant represents a loop of the circuit. The asymmetric half bridge converter is the most commonly used converter of the switched reluctance motor (SRM). According to its connection matrix, its candidate fault-tolerant converters are listed, and with the proposition, their alternative loops are obtained, their fault tolerance performance is evaluated, and the optimal one is selected. Furthermore, the fault tolerance performance of the derived converter is tested by simulations and experiments on a 12/8 SRM.

为了提高转换器的可靠性，文献中提出了许多容错转换器。然而，很少有人提出设计规则。转换器通常是可以用矩阵来描述的开关电路；因此，容错转换器的设计可以转化为矩阵设计。电路的容错性主要由其替代回路决定。在这项研究中，定义了负 1 布尔行列式来建立矩阵和替代循环之间的关系。然后，证明以下命题：对于一个电路的连接矩阵，负1布尔行列式代表电路中回路的总和，负1布尔行列式的每一项代表一个回路。非对称半桥转换器是开关磁阻电机 (SRM) 中最常用的转换器。根据其连接矩阵，列出其候选的容错转换器，并根据该命题，获得它们的替代回路，评估它们的容错性能，并选择最优的。此外，衍生转换器的容错性能通过在 12/8 SRM 上的模拟和实验进行测试。