In city-integrated energy systems containing electric–thermal multi-energy sources, the uncertainty of renewable energy sources and the fluctuation of loads challenge the safe, efficient, economic and stable operation of the integrated energy systems. This paper introduces a novel approach for the operation of a carbon capture plant/CHP with PV accommodation within a city-integrated energy system. The proposed strategy aims to maximize the utilization of photovoltaic (PV) power generation and carbon capture equipment, addressing issues related to small-scale CHP climbing constraints and short-term output regulation. Additionally, this paper presents a multi-timescale optimal scheduling strategy, which effectively addresses deviations caused by PV fluctuations and load changes. This was achieved through a detailed analysis of the CHP climbing constraints, carbon capture equipment operation and real-time characteristics of PV power generation. This paper introduces a fully distributed neural dynamics-based optimization algorithm designed to address multi-timescale optimization challenges. Utilizing rolling cycles, this algorithm computes both day-ahead and real-time scheduling outcomes for urban integrated energy systems. Theoretical analyses and numerical simulations were conducted to validate the precision and efficacy of the proposed model and algorithm. These analyses quantitatively evaluate the scheduling performance of PV power generation and carbon capture CHP systems across various timescales.