Conflict is an essential element of interesting stories. In this paper, we operationalize a narratological definition of conflict and extend established narrative planning techniques to incorporate this definition. The conflict partial order causal link planning algorithm (CPOCL) allows narrative conflict to arise in a plan while maintaining causal soundness and character believability. We also define seven dimensions of conflict in terms of this algorithm's knowledge representation. The first three-participants, reason, and duration-are discrete values which answer the "who?" "why?" and "when?" questions, respectively. The last four-balance, directness, stakes, and resolution-are continuous values which describe important narrative properties that can be used to select conflicts based on the author's purpose. We also present the results of two empirical studies which validate our operationalizations of these narrative phenomena. Finally, we demonstrate the different kinds of stories which CPOCL can produce based on constraints on the seven dimensions.