*2.1. Low-Carbon Power*

To achieve a low-carbon operation of a power system, extensive studies were devoted to addressing the environmental economic dispatch (EED). In EED, the minimization of emissions [25] is generally designed as one part of the objective function. To further improve the operation economy, the uncertainty of wind power was considered in [26,27], in which the power output of a wind turbine was evaluated based on a probability distribution function of the wind speed. Besides, a modified EED, by combining heat and power economic dispatch, was presented in [28], which can achieve an optimal operation for the heat and power system simultaneously. Furthermore, a coordinated operation of an integrated regional energy system with various energies (e.g., a CO2-capture-based power) was proposed in [29], while the demand response was also introduced in EED. To further reduce carbon emissions, the CO2 emission trading system was combined into the daily operation of an energy system. In [30], a decentralized economic dispatch was proposed by considering the carbon capture power plants with carbon emission trading. Moreover, the power uncertainty of wind and photovoltaic energy was fully taken into account in [31,32] based on carbon emission trading. For the purpose of clarifying the internal relation between energy consumption and carbon emissions from power grids, the concept of carbon emission flow is put forward for the first time in reference [33]. On this basis, the authors of [34–36] carried out a theoretical analysis and case verification on the carbon emission flow calculation and the carbon flow tracking of a power system, respectively.

#### *2.2. Application of Meta-Heuristic Algorithms*

In fact, the optimal low-carbon operation of a power system faces with various complex and di fficult optimization problems, e.g., EED. Hence, various meta-heuristic algorithms have been employed for these optimization problems due to their strong searching ability and high application flexibility. In [25], an improved PSO combining the di fferential evolution algorithms was designed for EED. In [26], a so-called exchange market algorithm was used for EED due to its fast convergence and strong global searching ability. In [27], a population-based honey bee mating optimization with an online learning mechanism was presented. Inspired by the well-known tag-team game in India, the novel Kho-Kho optimization algorithm [28] with an excellent optimization performance was proposed for EED. To achieve a distributed optimization for real-time power dispatch, a novel adaptive distributed auction-based algorithm with a varying swap size was proposed in [37]. On the other hand, the reinforcement learning-based optimization attracted many investigations for optimal operations of power systems. In [23], a distributed multi-step Q(λ) learning was proposed for the complex OPF of a large-scale power system. To satisfy the requirement of multi-objective optimization, an approximate ideal multi-objective solution Q(λ) learning was presented in [36] via a design of multiple *Q* matrices for di fferent objective functions.

## **3. OCECF Mathematical Model**
