## 1 Introduction  
On 15 March 2015, the Communist Party of China's (CPC's) Central Committee and State Council proposed opinions on further deepening the reforms of the electric power system, marking the beginning of a new round of electricity market reform in China [1], after a series of reforms in 1985, 1996, and 2002 [2]. This new round of reform aims to break the monopoly, introduce competition, and achieve optimum allocation of power resources in a broader scope. Over the past four years, most provinces and regions have been actively trying to get involved in the reform and have continuously improved the market operation rules. Although the market is still constrained by many factors, the hydropower plants in some provinces of southwestern China have successfully participated in the yearly and monthly electricity markets [3; 4]. It is foreseeable that a competitive and stable electricity market environment will be formed in the future. With extremely rich hydropower resources, many huge cascaded hydropower plants have been constructed in southwestern China. As the main sending end for the West-to-East Electricity Transmission (WEET) Project, these hydropower plants face a special multi-market environment. They not only have to supply the load for the local provincial market, but also need to deliver electricity to the central and eastern load centers in the external market [5], which has a direct impact on the supply and demand balance of the two markets and, as a result, the electricity prices of the two markets are closely correlated. Under such circumstances, optimizing the generation scheduling for cascades in different markets, improving the overall benefits, and coping with the market risks is a practical problem to be solved by the hydropower enterprises. However, this problem becomes much more complicated due to the uncertainty of electricity prices and the correlation of prices in different markets. In addition, the hydraulic and market constraints of the cascade hydropower plants increase the complexity further [6]. The generation scheduling for hydropower plants is a typical multi-variable and non-linear problem [7; 8], especially for cascade hydropower plants. It has close internal cascade dependency, indicating that the water release from the upstream reservoir is the inflow of the downstream reservoir [9]. In the deregulated market, which is different from a conventional centralized operation, producers most important objectives are to generate power with more benefits [10; 11] and lower market risks [12]. To get hydropower producers involved in the electricity market, scholars have carried out many studies and have made great achievements. The electricity price policies, such as the market clearing price (MCP), peak-valley price, time-of-use (TOU) price, and so on, are considered in the generation scheduling models of hydropower plants [13; 14], as the electricity prices directly affect the market benefits. Accordingly, an uncertainty description of electricity prices is also proposed to improve the robustness of the models, in which the electricity prices are treated as variables rather than fixed constants [15; 16; 17]. At the same time, with the expansion of wind power, for photovoltaic power, and other distributed energy sources, the uncertainties in the power system have increased dramatically, and research on uncertainty-based models [18] and stochastic models [19] have drawn more and more attention. Corresponding to the hydropower generation scheduling models, some scholars have introduced market risk constraints to further improve the reliability of optimizing the trading strategies [20; 21]. Overall, from the perspective of the time horizon, most existing studies focus on optimization in the daily market, and, as a result, the medium- and long-term studies are in a small quantity [22]. Price uncertainty has been included in the generation scheduling models, but it is mainly for a single market and the correlation of stochastic prices between multiple markets has not been considered.