## 1 Introduction
The total cost is reduced significantly when considering pump-storage units. However, the above models only studied the optimal dispatch in the energy market but rarely discussed on the ancillary service. As for frequency stability, reserve capacity is required by each generator to deal with uncertainty from wind power generation outputs, as well as temporary outages of generation units. As a result, several types of reserves have been developed and applied in power system to smooth the output of renewable energy in an economically efficient way. Reserves can be classified by their usages as regulating reserve and spinning reserve. Specifically, the regulating reserve is used to balance any instantaneous power mismatch caused by load and generation output fluctuations. In contrast, the spinning reserve is used to compensate the shortage of active power when an outage of a generator occurs. Obviously, the more reserve there is in a power system, the higher its reliability will be. Nevertheless, too much reserve capacity in the generators may lead to a higher cost. Therefore, the question as to how to balance the generation dispatch and reserve capacity is very important. To deal with this issue, several methods of energy and reserve dispatch were proposed, e.g., a merit order based dispatch method [14], a sequential dispatch method [15], and a joint dispatch approach [16; 17; 18]. For the methods in [14; 15], the energy dispatch and ancillary service dispatch are optimized separately according to their priorities. However, they may be suboptimal or even infeasible, which may result in insufficient supply for the lower priority commodity [16; 17]. By contrast, the joint dispatch model presented in [18] is based on a formulation in the context of the constrained optimization model. The normal energy and reserve joint dispatch method usually aims to minimize the total costs of energy and reserve to obtain an economically optimal dispatch schedule, together with a consideration of the equation of power balance, generator ramp rate limits, the constraints of transmission line capacity, and minimum reserve requirements [19]. For this reason, Midcontinent ISO (MISO) has operated in this joint market since 2009, where the energy and reserve dispatch are considered as competitive commodities and then co-optimized in the real-time deregulated market every 5 min [20; 21; 22]. According to the rule of market mechanism in energy and ancillary markets, references [23; 24] presented comprehensive models and pricing mechanisms using the robust co-optimization approach in the day-ahead market and real-time market, respectively. Note that the reliability and deliverability of energy and reserves are very important. Those should be considered into the optimization model, especially under contingencies when the network congestion is particularly remarkable. Zonal reserve constraints can guarantee the minimum requirement for reserves of each zone to be satisfied, and therefore overcome the problem of network congestion. As a result, the zonal reserve constraints can be incorporated into the conventional security constraints to maintain deliverability of reserves in the system. In [23], the ISO New England market clearing framework for the co-optimized real-time energy-reserve market was discussed, and reserve deliverability for nested reserve zones was recognized. A security-constrained unit commitment model for energy and ancillary services auction was proposed in [24], where reserve requirements are optimized in electricity markets by simulating contingencies rather than specifying the requirements as fixed system constraints. Furthermore, to manage and increase the integration of renewable energy in the power system, an innovative procedure is needed for both normal and abnormal conditions. In this sense, a model incorporated an N-k security criterion, by which the power balance is guaranteed under any contingency state comprising the simultaneous loss of up to \(K\) generation units, was formulated in [25].