This paper presents a comprehensive reliability-constrained economic dispatch model with an analytical formulation of operational risk evaluation (RCEED-AF) to address the operational risk problem in power systems. The model integrates reliability indices and constraints into the economic dispatch (ED) decision-making process, aiming to optimize both reliability and cost for day-ahead economic dispatch. The key contributions of the paper are: 1. **Model Development**: A reliability-constrained economic dispatch model (RCED-AF) is proposed, which incorporates an analytical formulation of operational risk evaluation. This model efficiently optimizes reliability and cost by avoiding computationally expensive evaluation procedures. 2. **Operational Reliability Evaluation**: An operational reliability evaluation model is designed to accurately assess system behavior under various renewable production changes. The model considers day-ahead operational decisions, wind power scenarios, and component contingencies. 3. **Computational Efficiency**: A computationally efficient scheme is developed to update risk indices for each ED decision by approximating the reliability evaluation procedure with an analytical polynomial function. This significantly reduces the computational cost while maintaining accuracy. The paper also includes case studies on modified RBTS, IEEE RTS-79, and modified IEEE 118-bus systems to demonstrate the effectiveness and accuracy of the proposed RCEED-AF model. The results show that the model can provide accurate optimization results and improve operational reliability, even in the presence of demand uncertainty and high wind penetration levels. The computational efficiency of the RCEED-AF model is highlighted, particularly in scenarios with a large number of wind power scenarios.This paper presents a comprehensive reliability-constrained economic dispatch model with an analytical formulation of operational risk evaluation (RCEED-AF) to address the operational risk problem in power systems. The model integrates reliability indices and constraints into the economic dispatch (ED) decision-making process, aiming to optimize both reliability and cost for day-ahead economic dispatch. The key contributions of the paper are: 1. **Model Development**: A reliability-constrained economic dispatch model (RCED-AF) is proposed, which incorporates an analytical formulation of operational risk evaluation. This model efficiently optimizes reliability and cost by avoiding computationally expensive evaluation procedures. 2. **Operational Reliability Evaluation**: An operational reliability evaluation model is designed to accurately assess system behavior under various renewable production changes. The model considers day-ahead operational decisions, wind power scenarios, and component contingencies. 3. **Computational Efficiency**: A computationally efficient scheme is developed to update risk indices for each ED decision by approximating the reliability evaluation procedure with an analytical polynomial function. This significantly reduces the computational cost while maintaining accuracy. The paper also includes case studies on modified RBTS, IEEE RTS-79, and modified IEEE 118-bus systems to demonstrate the effectiveness and accuracy of the proposed RCEED-AF model. The results show that the model can provide accurate optimization results and improve operational reliability, even in the presence of demand uncertainty and high wind penetration levels. The computational efficiency of the RCEED-AF model is highlighted, particularly in scenarios with a large number of wind power scenarios.