Conventional carbon emission flow (CEF) calculation methods for power systems face challenges regarding unfair network loss allocation and difficulty in quantifying renewable energy's carbon reduction contributions. Existing studies often allocate network losses entirely to the load side or neglect the actual carbon reduction effects of renewable energy, leading to inequitable carbon emission responsibility distribution. To address these issues, this study proposes a simulation-based teaching method for CEF calculation grounded in power decomposition.

To overcome these limitations, the proposed method decomposes the actual power network into a basic power network and a power deviation network. Virtual nodes are introduced into transmission branches to distribute network losses equally between the generation side and the load side. We treat renewable energy units as negative-valued loads to quantify their carbon reduction contributions by calculating the difference in injected carbon flow rates. Finally, an IEEE 57-node system compares carbon flow rate differences under four allocation modes and simulates the impact of real power fluctuations on actual carbon flows.

Experimental results demonstrate that: 1) Under the bidirectional allocation mode, branch carbon flow rates fall between those of generator-side allocation and load-side allocation, validating the rationality of shared responsibility between generation and load sides. 2) When renewable energy unit G2 is treated as a negative load, its carbon reduction contribution increases from 66.49 t/h in the basic power network to 92.74 t/h in the power deviation network. This accurately reflects the impact of renewable power variability on carbon emission reduction within the system.

The proposed power decomposition-based CEF calculation method provides a fair and precise carbon emission measurement tool for power system low-carbon transitions. The teaching framework successfully integrates theoretical knowledge with simulation experiments, enhancing students' understanding of CEF-related theories while cultivating their low-carbon awareness and research literacy.

As one of many uncertain optimization methods, the robust optimization method does not need a specific probability distribution function. Instead, it only needs to master the range of uncertainty to realize the reliable operation of a system. Two-stage robust optimization dynamically adapts decisions in response to evolving uncertainties. This approach significantly enhances the conservative nature of day-ahead decisions, providing an effective scheme to solve the problem of the optimal scheduling of new energy uncertainty. Nonetheless, the advanced and intricate nature of two-stage robust optimization for regional integrated energy systems (RIESs) makes its fundamental principles and practical applications difficult to impart through conventional teaching methods. Its complexity and steep learning curve hinder the effective fulfillment of teaching aims.

To address this pedagogical challenge, this study develops a simulation experimental teaching platform tailored for RIES. It introduces an experimental scheme based on two-stage robust optimization for such systems. The first optimization stage accounts for the costs associated with starting and stopping units. It aims to optimize both the start–stop cycles of equipment and the energy interactions within the system, thereby establishing the operational states and energy exchanges of the units. Subsequently, the second optimization stage refines the equipment output based on the first stage's scheduling outcomes, seeking the most adverse scenario amidst the fluctuations of uncertain variables. Ultimately, the column-and-constraint generation algorithm is employed iteratively to resolve the two-stage conundrum, deriving the optimal resolution for the original problem. This ensures the system's optimal performance, even when faced with variable uncertainties.

The RIES two-stage robust optimization experiment shows the following: 1) Implementing virtual heat storage within the system yields a 4.3% cost reduction compared with systems lacking this feature. The heat pipeline serves as a thermal reservoir, storing inexpensive heat during periods of low demand and releasing it during peak demand. This capability effectively adapts to heat load fluctuations, provides additional resources for system scheduling, facilitates timely heat energy transfer, and enhances the system’s operational flexibility and economic efficiency. 2) The two-stage robust control strategy allows for a fine-tuned balance between system conservatism and cost-effectiveness by modulating the uncertainty budget. System operators seeking more conservative outcomes can increase the uncertainty budget to achieve this equilibrium. Conversely, a reduced uncertainty budget leads to more cost-efficient scheduling outcomes.

The two-stage robust optimization experimental platform for RIES establishes a robust foundation for both educational and research pursuits in the realm of RIES optimal scheduling amidst the uncertainties of new energy production. From an educational standpoint, this platform enables students to emulate the optimal operational procedures of RIES, thereby allowing them to gain proficiency in pertinent theoretical concepts and practical skills. It allows for the analysis of system performance and optimization strategies, fostering the enhancement of engineering practices and the cultivation of innovative thinking. In the context of scientific inquiry, the platform serves as a conduit for researchers to engage in design modeling, case studies, and optimization control related to RIES. It provides a venue for the exploration and integration of novel technologies, methodologies, and paradigms, thereby elevating the caliber of scientific research and the capacity for innovation.