  Pyroelectric energy converter is a functional capacitor using pyroelectric
material as the dielectric layer. Utilizing the first-order phase
transformation of the material, the pyroelectric device can generate adequate
electricity within small temperature fluctuations. However, most pyroelectric
capacitors are leaking during energy conversion. In this paper, we analyze the
thermodynamics of pyroelectric energy conversion with consideration of the
electric leakage. Our thermodynamic model is verified by experiments using
three phase-transforming ferroelectric materials with different pyroelectric
properties and leakage behaviors. We demonstrate that the impact of leakage for
electric generation is prominent, and sometimes may be confused with the actual
power generation by pyroelectricity. We discover an ideal material candidate,
(Ba,Ca)(Ti,Zr,Ce)O$_3$, which exhibits large pyroelectric current and extremely
low leakage current. The pyroelectric converter made of this material generates
1.95 $\mu$A/cm$^2$ pyroelectric current density and 0.2 J/cm$^3$ pyroelectric
work density even after 1389 thermodynamic conversion cycles.
