Abstract: This paper takes a retired 135 MW unit as the research object and proposes a bi-level optimization model for the configuration and operation of a Carnot battery, considering variable-load performance. First, off-design models of turbomachinery and heat exchangers are established, and the performance curves of the Carnot battery during the charging process are obtained. An NSGA-II optimization model is constructed with "upper-level capacity configuration optimization and lower-level operational dispatch optimization", combined with the 8760-hour nodal electricity prices from a location in Shandong Province. Results show that COP exhibits a negative correlation with the electric heating share. For every 10% increase in the electric heating share, the COP decreases by approximately 0.038. The initial investment is 579.5559 million CNY, the average annual net profit arrives 91.4481 million CNY. The dynamic payback period is 9.42 years, and the levelized cost of electricity as low as 0.59 CNY/kWh. The system dispatch exhibits a "deep charging and deep discharging within a single day" pattern to maximize peak-valley price arbitrage. Sensitivity analysis indicates that the current capacity compensation mechanism plays a fundamental role in enabling the commercial deployment of long-duration energy storage. If this mechanism is completely abolished, the dynamic payback period would extend to 10.59 years.