## 1 Introduction
As for energy storage systems, [PERSON] et al. [20] designed a compressed carbon dioxide energy storage (CCES) system test rig and applied a data reconciliation algorithm for it to improve the precision of exergy analysis. Such research has proved the practicability of the data reconciliation method in different types of energy systems. Despite its successful usage, the standard data reconciliation method is facing an important challenge: gross errors of the measurements. Usually, a measurement with gross error means its error exceeds its supposed random distribution, which means the measurement does not follow the supposed distribution (e.g., a standard normal distribution). This may happen when instrument failure or leakage exists in the system. Though the data reconciliation algorithm may still try to correct the errored measurements (as we have explored in the previous study [21]), its excessive error may spread to relating measurements and make them unreliable as well, which is referred to as the \"smearing effect\" [22]. To overcome the challenge, the concept of the robust data reconciliation method was proposed by [PERSON] and [PERSON] [23], with a contaminated normal distribution for the measurements with gross errors. Under the robust data reconciliation framework, different forms of objective functions, rather than the standard least-square function, is applied in the data reconciliation optimization problem. These objective functions are called robust estimators, and they represent the supposed error distribution other than standard normal distribution. It can be regarded as the direct application of robust regression theory in the data reconciliation method. [PERSON] and [PERSON] [24] proved that robust data reconciliation can effectively reduce both random errors and gross errors, without the categorization of the measurements into normal ones and errored ones. This also means that the smearing effect can be reduced under robust data reconciliation. Successively, various robust estimators have been proposed to improve the correction effect, as well as the augmented algorithms, to cope with these nonlinear objective functions. [PERSON] et al. [25] carried out a comparative analysis for eight robust estimators, and they pointed out the superiority of the [PERSON] [26] and [PERSON] estimators. Besides theoretical studies, several works focused on the application of robust data reconciliation in industrial systems. For example, [PERSON] et al. [27] utilized their newly proposed robust estimator in the evaporation process of alumina production, showing its effectiveness in gross error correction. [PERSON] et al. [28] developed a robust data reconciliation analysis framework for a double-flash smelter system and eventually programmed their algorithm into a metal balance software system. These cases prove the feasibility of applying robust data reconciliation in the industrial scene. As for energy systems, however, the application of robust data reconciliation is still rare. Such works include the one by [PERSON] and [PERSON] [29], where they combined the robust data reconciliation method with the particle swarm optimization algorithm and applied it to a simple turbine plant model, as well as a reactor. However, the systems analyzed in their work were rather simple, where most sensors were for mass flow, so the system was almost linear. [PERSON] et al. [30] constructed a performance estimation model for an entrained-flow pulverized coal gasification system, based on the data reconciliation method enhanced with several machine learning techniques. In their model, the standard least-square target function was applied, which limited its performance facing gross errors. As for the S-CO\({}_{2}\) system, no existing studies have implemented robust data reconciliation.