Non-Iterative Calculation of Quasi-Dynamic Energy Flow in the Heat and Electricity Integrated Energy Systems

Abstract

PDEPartial differential equation. SASSemi-analytical solution. SOE Second-order explicit scheme. TVD Total variation decreasing. B. Operators diag(•)Transform a column vector into a diagonal matrix. ⊗ Convolution. 𝑿 (0 : 𝑘) Linear combination of 𝑿 (0), 𝑿 (1), • • • , 𝑿 (𝑘). C. VariablesThe capitalized/bold forms of these variables denote the DT/vector of these variables respectively.𝑚/ 𝑚 in Pipe/node injection mass flow rate. 𝜏 s/r Node supply/return temperature. 𝜏 in/out,s/r Inlet/outlet temperature of supply/return pipes. 𝜏 amb Ambient Temperature. 𝜙 Node power. 𝑒/ 𝑓 Real/imaginary part of bus voltage. 𝑝/𝑞 Active/reactive power. D. Coefficients 𝛾 Cross-sectional area. 𝜌 Density. 𝐻 Length of pipe. 𝐶 p Thermal capacity of mass flow. 𝜆 Overall heat transfer coefficient. 𝐾 Resistance coefficient. 𝑍 Trade-off between heat supply and electric power. 𝑐 m1 Heat-to-power ratio. 𝜂 e Electrical efficiency. 𝐹 in Fuel input rate of steam turbine. Δ𝑥/Δ𝑡 Spatial/temporal step sizes. 𝜃 Parameter that balances the dissipative/dispersive errors in PDE solutions. 𝑉/𝐿 Node/loop incidence matrix. 𝐺/𝐵 Conductance/susceptance matrix. E. Superscripts/Subscripts D Diagonal matrix generated by diag(•).

Modeling and analysis method for carbon emission flow in integrated energy systems considering energy quality

“…The power of nonequilibrium nodes is usually a known quantity in the analysis of IES 32 . In this scenario, the multi‐energy power flow calculation method is used to calculate parameters such as power flow, gas flow rate, water flow rate, and water temperature 33 .…”

“…The power of nonequilibrium nodes is usually a known quantity in the analysis of IES. 32 In this scenario, the multi-energy power flow calculation method is used to calculate parameters such as power flow, gas flow rate, water flow rate, and water temperature. 33 Based on this, the exergy flow distribution of the system is solved by the exergy flow calculation model, 19 and then the carbon emission flow distribution is solved using the carbon emission flow calculation model considering energy quality.…”

An accurate and efficient quasi-dynamic simulation method of electricity-heat multi-energy systems

“…However, the heterogenous forms of energy, which are depicted by disparate mathematical models, complicate the underlying operational law of MES. Several analysis methods have been put forward in literature to tackle this, including the steadystate energy flow computation (EFC) (Liu et al, 2016;Zhang et al, 2021b;Li et al, 2022), the quasi-dynamic EFC (Pan et al, 2016;Qin et al, 2019;Yao et al, 2021;Yu et al, 2022;Zhang et al, 2022) and the combined dynamic simulation (Shen et al, 2020;Wang et al, 2022). Among these methods, the quasi-dynamic EFC can plot the temperature variations precisely while demonstrates moderate modelling complexity, which has drawn much attention.…”

“…Chen et al have further proposed an enhanced node method, the water mass method, to eliminate the integer variables in optimization applications (Chen et al, 2019), which sheds light on the more complicated hydraulic-thermal cooperative operation optimization of MESs (Lu et al, 2020). It has been pointed out by Yu et al that the node method is fairly accurate when depicting thermal dynamics but also suffer non-convergence issues in variable mass flow scenarios (Yu et al, 2022).…”

“…Huang et al have applied the Levenberg-Marquardt-form Newton method to improve the convergence and efficiency of EFC (Huang et al, 2023). Yu et al have proposed to derive time polynomials, which are called semi-analytical solutions, of unknown variables with a differential-transformation-based method (Yu et al, 2022). An adaptive time window strategy has also been developed to speed up the quasi-dynamic EFC and ensure convergence.…”