This paper investigates the influence of stator/rotor pole number combinations and permanent magnet (PM) numbers on electromagnetic performance of consequent-pole hybrid excited flux reversal machines (CP-HEFRMs), which have different numbers of PM poles and iron poles and concentrated AC and DC windings on the stator and a salient pole rotor. PMs in the slots of one stator pole are magnetized radially in the same direction, while opposite on adjacent stator poles. Magnetic field paths of DC, PM, and hybrid excitations are investigated. The phenomenon of flux cancellation, i.e., PM and DC MMFs in CP-HEFRMs are of opposite polarities in the flux-enhancing operating mode, is revealed and verified, for the first time, as the key feature that makes CP-HEFRMs different from other hybrid excited machines. Consequently, the saturation in stator pole and yoke can be mitigated and hence the overload capability of DC excitation is enhanced, which is verified by finite element analysis (FEA). Global optimizations are utilized to obtain the optimal rotor and stator pole number combinations and PM numbers for each stator pole. Torque, torque ripple, inductance, unbalanced magnetic force, and flux regulation capability are compared for different PM numbers and rotor pole numbers. Comparisons are made on consequent-pole and non-consequent-pole topologies in terms of torque capacity, flux regulation capability, and PM consumption to further illustrate the advantages of consequent-pole topology. A prototype machine is built and tested to validate the analyses.