This paper proposes a stochastic bilevel optimization approach to owners of pumped hydro storage systems (PHSSs) to participate in pay-as-bid power market and provide optimal bids and offers. The price offering of other generation units is modeled by stochastic programming. The upper-level of the proposed bilevel programming seeks maximization of the profit of the PHSS arbitrage, where the lower-level assures the optimal system dispatching (and market-clearing), and keeps the network security. The bilevel optimization is then transferred into a single-level equivalent via Karush-Kuhn-Tucker (KKT) complementarity conditions. The equations of the KKT conditions are linearly modeled using special ordered sets of type 1 (SOS1) variables. Furthermore, the bilinear objective function of the upper-level is approximated using McCormick envelopes relaxation method, in order to obtain the solutions as fast as possible and making the problem as mixed-integer linear programming. The proposed method is verified on the IEEE 24-bus reliability test system (RTS) considering different cases. The operation of a single PHSS is assessed in the network's normal and congested conditions. The results show that the PHSS achieve more revenue in a limited network as the offered prices go up to price cap in some periods. In the studied cases, the profit of energy arbitrage by the PHSS increases from $ 3302 in a normal network, to $ 8170 in a limited network. Moreover, the effect of wind generation uncertainty on the arbitrage problem is investigated using five sub-scenarios dedicated to wind generation. It is shown that the arbitrage profit is more sensitive on generation cost uncertainty rather than wind generation uncertainty. Furthermore, it is revealed that the expected profit in the presence of wind turbines is slightly lower than that without wind turbines. This is due to the fact that the wind generation power is always accepted and dispatched in the market and lowers the load demand and deteriorates the arbitrage opportunity. In this case the expected profit of the PHSS is decreased from $ 3302 to $ 3288. Furthermore, the effects of three PHSS units in the mentioned network is investigated. For a particular PHSS in the studied system, it is found that the increase of PHSS units in the network decreased the expected profit from $ 3302 to about $ 3176. Also, the location of PHSS units is deduced as an influential factor on profitability of merchant storage facilities.

本文为抽水蓄能系统（PHSS）的所有者提出了一种随机双级优化方法，以参与按需付费电力市场并提供最佳投标和报价。其他发电单元的价格提供是通过随机规划建模的。所提出的双层编程的上层寻求最大化PHSS套利的利润，而下层则确保最佳的系统调度（和市场清理），并保持网络安全。然后，通过Karush-Kuhn-Tucker（KKT）互补条件将双级优化转换为单级等效项。KKT条件的方程式使用类型1（SOS1）变量的特殊有序集进行线性建模。此外，使用McCormick包络松弛方法对上层的双线性目标函数进行逼近，以便尽可能快地获得解，并使该问题成为混合整数线性规划问题。考虑到不同的情况，该方法在IEEE 24-bus可靠性测试系统（RTS）上得到了验证。在网络的正常和拥塞情况下评估单个PHSS的运行。结果表明，由于所提供的价格在某些时期达到了价格上限，PHSS在有限的网络中获得了更多的收入。在研究的案例中，PHSS进行能源套利的利润从正常网络中的3302美元增加到有限网络中的8170美元。此外，使用五个专门用于风力发电的子场景研究了风力发电不确定性对套利问题的影响。结果表明，套利利润对发电成本的不确定性比对风力发电的不确定性更为敏感。此外，揭示了在有风力涡轮机的情况下的预期利润略低于没有风力涡轮机的情况。这是由于这样的事实，即风力发电总是在市场上被接受和分配，并且降低了负荷需求并且恶化了套利机会。在这种情况下，PHSS的预期利润从3302美元减少到3288美元。此外，还研究了上述网络中三个PHSS单元的影响。对于所研究系统中的特定PHSS，发现网络中PHSS单位的增加使预期利润从$ 3302降低到约$ 3176。