**1. Introduction**

In recent years, flexible loads have become a research hotspot for scholars due to their corresponding speed, low carbon footprint, and low cost [1–3]. The continuous development of energy managemen<sup>t</sup> technology has resulted in an increasing trend in the flexible load participation in demand response (DR) projects [4–6]. Many countries are allowing qualified, large consumers, or flexible load aggregators to participate directly in the electricity market [7,8]. In the study [9], authors propose a model for flexible aggregators flexibility provision in distribution networks, the model takes advantage of load flexibility resources allowing the re-schedule of shifting/real-time home-appliances to provision a request from a distribution system operator or a balance responsible party. In the mature stage of the spot market, the transition from the unilateral quotation to bilateral quotation mode will allow the flexible load to directly participate in the power market. In addition, due to the flexible variability in the time and space of the flexible load, the flexible load can also participate in the auxiliary service market [10,11]. Under the bilateral quotation model, how to participate in the market clearing of flexible loads and how to perform a safety checking of the power dispatching agency when the line overrun occurs as a result of the market clearing are issues that need to be resolved for the flexible load participation in the electricity market.

In order to maximize the benefits of integrated energy companies in an increasingly complex multi-participant energy market, some researchers [12] classified loads into three categories based on the elastic characteristics of the loads: reducible loads, convertible loads, and shiftable loads. The three types of loads participate in the demand response project, so that integrated energy companies ge<sup>t</sup> more benefits. In the work of [13], the authors proposed an innovative economic and engineering coupled framework to encourage typical flexible loads or load aggregators, such as parking lots with a high penetration of electric vehicles, to participate in the real-time retail electricity market based on an integrated e-voucher program directly. In order to integrate the flexible load in the distribution network, a new pricing mechanism was proposed in the literature [14]. The price can be calculated through the two-tier local distribution network market. Flexible load aggregators act as the price receiver, and the system operator is the manager; the proposed method can save the cost of the flexible load aggregator. Researchers have proposed a market clearing mechanism to minimize the costs (both the day-ahead and real-time adjustments) and maximize the social benefits in terms of the market clearing; this mechanism took into consideration the uncertainty of wind power generation and load forecasting [15]. Another market clearing mechanism was proposed in a di fferent study [16], where the pricing uncertainty and generation reserve were determined by the uncertainty marginal price (UMP). At the same time, energy is priced by locational marginal price (LMP), and the uncertainty of the load is borne by the unit in the day-ahead market. UMP and LMP can be obtained through the robust optimization method. In the work of [17], the researchers adopted a two-stage market clearing method to weaken collusion among the power producers, established a causal relationship and a quantitative relationship between the bidding process of the power producers and the market clearing, and evaluated the e ffectiveness of the method using system dynamics.

The above-mentioned studies examined the flexible load and market clearing, and the related research is su fficient. However, there is very little research on the flexible load participation in market clearing. In the study [18], researchers assumed that users can participate in market competition (such as on the power generation) directly; they established a market equilibrium model that considered the DR and studied the impact of the DR implementation on the power market. However, in this literature, the classification of flexible loads is not specific, and the impact of flexible loads on the model is not analyzed. In order to ensure the safety of the market clearing results, the dispatching agency needs to perform the safety checking process. During the safety checking process, when the transmission line power exceeds the limit, the output of the line is generally adjusted by adjusting the output of the unit. In the safety checking of the power generation plan, the combined optimization technology is used to solve the power grid safety checking problem and the power generation plan in each time period, and it is widely used in the day-ahead market [19,20].

In this paper, we propose a market clearing and safety checking method for multi-type units that considers the flexible load. First, using the characteristics of the power load, the flexible load was divided into reducible loads, convertible loads and shiftable loads, and we created three mathematical models of the flexible load. In the day-ahead market, generators and demanders submit quotation curves separately, and so we established the market clearing model that considers the convertible loads. The power managemen<sup>t</sup> agency executed the clearing process to obtain the clearing results; when the line transmission power breaks out as a result of clearing, the flow of the branches and sections can be eliminated by adjusting the output of the generator set and reducing the flexible loads at the same time.

The remainder of this paper is organized as follows: Section 2 discusses the three mathematical models of the flexible load and its mechanism. Section 3 includes the market clearing model that considers the convertible loads. In addition to conventional units, the model also considers the pumped storage and nuclear power units. In this section also discusses a safety checking model that considers the reducible loads. Section 4 introduces the solution method and steps of the model. Section 5 evaluates the e ffectiveness of the method proposed in this paper through actual cases.

#### **2. Flexible Load Modeling and Its Mechanism**

## *2.1. Flexible Load Modeling*

In this paper, the flexible load is divided into reducible loads, convertible loads, and shiftable loads. The power consumption law of the flexible load can be accurately sensed by a real-time monitoring device, and the load control technology can be used to realize the interruption and translation of the load in a specific time period. From the perspective of the demand response, the flexible load can participate in the demand side managemen<sup>t</sup> (DSM) and DR projects of the grid by adjusting its own power demand, and it can be dynamically adjusted with the balance of the supply and demand [21–24]. When the flexible loads participate in the control and responds to the demand, the load model can be expressed as:

$$P\_{\rm LD} = \left(t\_\prime P\_{\rm re}, P\_{\rm convert}, P\_{\rm shift}\right) = P\_{\rm s}(t) + P\_{\rm fl}(t, P\_{\rm re}, P\_{\rm convert}, P\_{\rm shift}) \tag{1}$$

where *P*LD is the total load demand, *<sup>P</sup>*s(*t*) is the normal load demand, *P*fl is the flexible load, *P*re is the load demand reduction, *P*convert is the convertible load demand, and *P*shift is the translatable load demand.
