Analyzing students' written solutions to physics questions is a major area in PER. However, gauging student understanding in college courses is bottlenecked by large class sizes, which limits assessments to a multiple-choice (MC) format for ease of grading. Although sufficient in quantifying scientifically correct conceptions, MC assessments do not uncover students' deeper ways of understanding physics. Large language models (LLMs) offer a promising approach for assessing students' written responses at scale. Our study used an LLM, validated by human graders, to classify students' written explanations to three questions on the Energy and Momentum Conceptual Survey as correct or incorrect, and organized students' incorrect explanations into emergent categories. We found that the LLM (GPT-4o) can fairly assess students' explanations, comparable to human graders (0-3% discrepancy). Furthermore, the categories of incorrect explanations were different from corresponding MC distractors, allowing for different and deeper conceptions to become accessible to educators.