The roll-out of distributed energy resources (DERs) challenges the current operating practice of distribution utilities due to increased volatility and uncertainty of nodal power injections. Furthermore, many DERs are independently-owned and, therefore, will likely be operated without cooperation with a local utility. This combination of uncertainty and self-interest can motivate DERs to act strategically in future distribution (retail) markets to maximize their payoff. Without assuming a particular distribution market design, this paper investigates engineering mechanisms for strategic behavior by independently-owned DERs in the context of radial and voltage-constrained distribution systems. We derive conditions that identify an exercise of market power by an independently-owned DER and propose a market power metric that accounts for AC power flow physics and uncertainty of nodal power injections. The case study illustrates a range of effects of market power on distribution system operations.