The only reference I know for precisely these matters is the handbook chapter

MR2768702. Koellner, Peter; Woodin, W. Hugh. *Large cardinals from determinacy*. In **Handbook of set theory. Vols. 1, 2, 3**, 1951–2119, Springer, Dordrecht, 2010.

(Particularly, section 7.)

For closely related topics, see also the work of Yong Cheng (and of Cheng and Schindler) on Harrington's principle.

First of all, $\mathsf{ZFC}+\mathsf{PD}$ proves the consistency of $Z_3+\mathsf{PD}$, and similarly $\mathsf{ZF}+\mathsf{AD}$ and $\mathsf{ZFC}+\mathsf{AD}^{L(\mathbb R)}$ prove the consistency of $Z_3+\mathsf{AD}$: (depending on your precise formulation of second- and third-order arithmetic), $(V_\omega,V_{\omega+1},V_{\omega+2},\in)^{L(\mathbb R)}$ is a model of the latter.

That said, however, (as pointed out by Andreas in a comment) there is a subtlety here in that $\mathsf{PD}$ is a single sentence. If instead we consider the infinite collection of axioms, the $n$th of which states the determinacy of boldface $\Sigma^1_n$-games, we should probably get equiconsistency, perhaps after some minor tweaking of the theories.

Section 7 of the reference above addresses these matters in reasonable detail for $\mathsf{ZFC}+$"there is a Woodin cardinal" and close variants, and $Z_2+$ lightface $\Delta^1_2$-determinacy, and close variants. For instance, from $Z_2+$ boldface $\Delta^1_2$-determinacy, they obtain (something stronger than) the consistency of $\mathsf{ZFC}+$"There is a Woodin cardinal". Note that the latter theory is equiconsistent with $\mathsf{ZFC}+$ lightface $\Delta^1_2$-determinacy which, in turn, implies the consistency of $Z_2+$ lightface $\Delta^1_2$-determinacy, so one needs to be careful here. They conjecture that $Z_2+$ lightface $\Delta^1_2$-determinacy is equiconsistent with $\mathsf{ZFC}+$"$\mathrm{ORD}$ is Woodin". In any case, from these results and the techniques in that chapter (particularly in section 6) one should obtain the equiconsistency results I suggested in the previous paragraph.

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