_Applied_  
_sciences_  
_Article_  
Uncertainty Quantification for Thermodynamic Simulations  
with High-Dimensional Input Spaces Using Sparse Polynomial Chaos Expansion: Retrofit of a Large Thermal Power Plant  
[PERSON] 12,2* (c), [PERSON] 3, [PERSON] 4, [PERSON] 4 and [PERSON] 12,2  
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While co-firing of biomass with fossil fuels is intensely researched nowadays [17; 18; 19], it is more difficult to find studies about full coal-to-biomass conversions [20; 21; 22]. Assessing the future thermodynamics performance of retrofitted heat and power production plants is, however, not straightforward. It requires a detailed modeling of complex processes and their components. In this paper, the impact on the performance of a retrofit of a coal-fired power plant into a biomass combined heat and power (CHP) and the working method is discussed. In [23], we modeled and optimised the retrofit of a large-scale ultra-supercritical (USC) coal-fired power plant into a biomass-fired CHP unit using a deterministic thermodynamic model made of 180 components, 285 links, and 1500 variables. Key performance indicators (KPIs) were defined and assessed. A shortcoming of the deterministic comparison between 100% coal and 100% biomass CHP for different loads and different temperatures of the heat-to-heat clients is that uncertainties were not taken into account. A widely employed technique for uncertainty quantification (UQ) is the fundamental Monte Carlo simulation method. This approach involves the random generation of scenarios based on input parameter distributions until a sufficient quantity, typically ranging from \(10^{4}\) to \(10^{5}\), of output values is accumulated. This dataset serves as a robust statistical distribution of potential outcomes [24]. However, this method encounters challenges when the system model requires more than a few seconds to produce results for each scenario [25]. To enhance computational efficiency, surrogate-assisted UQ leverages a surrogate model of the system. This surrogate model simplifies the system's representation within the bounds defined by the various input parameter distributions. Examples of surrogate models encompass Kriging [26], support vector machines [27], analysis of variance (ANOVA) [28], and polynomial chaos expansion (PCE) [29]. PCE, for example, enables the analytical derivation of distribution parameters and sensitivity indices, such as Sobol' indices, from the surrogate model's coefficients. Ref. [30] describes a probabilistic comparison between an USC coal-fired power plant before and after a conversion to biomass. In this paper, the possibility of uncertainty quantification (UQ) polynomial chaos expansion (PCE) is investigated to avoid the issue of unknown parameters. PCE was applied on two unknown parameters related to heat transfer in the furnace of the boiler. In traditional PCE, the truncation set contains multivariate polynomials, many of which represent interactions between input variables.