Renewable portfolio standards (RPSs) are popular market-based mechanisms for promoting development of renewable power generation. However, they are usually implemented without considering the capabilities and cost of transmission infrastructure. We use single-and multi-stage planning approaches to find cost-effective transmission and generation investments to meet single and multi-year RPS goals, respectively. Using a six-node network and assuming a linearized DC power flow, we examine how the lumpy nature of network reinforcements and Kirchhoff's Voltage Law can affect the performance of RPSs. First, we show how simplified planning approaches that ignore transmission constraints, transmission lumpiness, or Kirchhoff's voltage law yield distorted estimates of the type and location of infrastructure, as well as inaccurate compliance costs to meet the renewable goals. Second, we illustrate how lumpy transmission investments and Kirchhoff's voltage law result in compliance costs that are nonconvex with respect to the RPS targets, in the sense that the marginal costs of meeting the RPS may decrease rather than increase as the target is raised. Thus, the value of renewable energy certificates (RECs) also depends on the network topology, as does the amount of noncompliance with the RPS, if noncompliance is penalized but not prohibited. Finally, we use a multi-stage planning model to determine the optimal generation and transmission infrastructure for RPS designs that set multiyear goals. We find that the optimal infrastructure to meet RPS policies that are enforced year-by-year differ from the optimal infrastructure if banking and borrowing is allowed in the REC market.