## 1 Introduction  
When the primary energy is far from the load center, transmitting large amounts of power with minimum losses is necessary. In China, large energy bases such as coal resources, wind and photovoltaic energy resources are mainly distributed in the northwestern provinces, while the load centers are in the eastern coastal areas. In order to transmit large-capacity power to load centers over long distances, several high-voltage direct current (HVDC) transmission lines have been built in China in recent years [1]. The high proportion of HVDC transmission operation power to the total demand of the receiving-end power grid replaces many synchronous generators, leading to the decline of system inertia [2, 3]. A disturbance with the same amount of power loss can cause a larger rate of change of frequency and a larger frequency deviation under low inertia conditions [4, 5]. In recent years, several HVDC blocking disturbances occurred. For example, in September 2015, a \(\pm 800\) kV HVDC bipolar blocking disturbance caused the power system frequency to drop to 49.56 Hz in the East China Power Grid [6, 7]. To prevent large frequency deviations caused by large power losses, emergency frequency control (EFC) is adopted to prevent the frequency from falling below the under-frequency load-shedding threshold [8]. For a HVDC blocking disturbance, the event-driven EFC can act immediately after disturbance to quickly reduce the active power imbalance and ensure system frequency stability [9]. For the receiving-end power grid with multi-infeed HVDC, EFC measures include HVDC emergency power support, cutting out any -pumped-storage pump, and emergency load shedding (ELS) [10]. There are massive distributed energy resources (DERs) on the demand side, such as electric vehicles (EV) and thermostatically controlled loads (TCLs); the latter usually include air conditioners (AC), water heaters (WH), and refrigerators [11; 12]. As the proportion of electric energy in the terminal energy consumption increases, the scale of controllable DERs is increasing. Controllable DERs can store electricity or heat, and therefore they can alter their active power for a short time while not affecting the user comfort [13; 14]. The controllable DERs can be aggregated and coordinated, controlled through a virtual power plant (VPP), which can provide huge regulation capacity for frequency control [15; 16]. If the DER device acts quickly enough, the VPP will have the ability of emergency power regulation and can be a new control resource for EFC [17]. ELS is the most common resource for EFC in the receiving-end power grid. An ELS model is proposed to minimize the total load-shedding cost while meeting constraints on transient rotor angle stability and voltage/frequency deviation security [18]. For a HVDC blocking disturbance, an ELS model is created to minimize the total load-shedding amount [19]. Most of the existing ELS for a HVDC blocking disturbance directly cut off the outlet of the substation, leading to a large area of power outages, and the control cost is high [20]. To reduce the control cost, an EFC with multi-resource coordination has been studied recently. A two-stage EFC scheme is proposed, where the control resources include HVDC modulation, energy storage, and load shedding in both stages and wind farms only for the first stage [21]. A two-stage EFC control for online decision-making is proposed, where the ELS is adopted in the first stage to prevent a large frequency drop, and the coordination of demand response and ELS is adopted in the second stage for frequency recovery while reducing the control cost [22]. A real-time coordinated control method for EFC is proposed, where control resources include emergency demand response, HVDC modulation, and energy storage [23]. Recently, demand-side DERs or VPPs participating in emergency control for frequency stability have been studied.