## 1 Introduction  
In order to fulfil the growing demand for energy, there has been a rapid expansion of renewable energies such as wind power and solar power in recent years [1]. Renewable energies are rapidly emerging and showing significant value in the entire energy system with the advantage of sustainable, less pollution, and reducing the costs of mitigating climate change [2]. However, renewable energies are easily affected by weather conditions and have features of intermittent generation. When the distributed generation (DG) of renewable energies is integrated to the grid, the voltage and frequency of the grid will fluctuate due to the intermittent output of DG [3]. If the voltage exceeds the allowable range, electrical equipment will operate at an over-voltage or under-voltage condition, which will cause the insulation of electrical equipment to accelerate aging, increase the power loss of the distribution network and may result in voltage collapse, and partial power grid collapse. The frequency deviation in the power system adversely affects the operation of users and power plants. For example, a frequency deviation of power system will change the speed and the power of motors, resulting in a change in the output of the transmission machinery and affecting the production efficiency. Traditionally, traditional generators' droop control is a typical method to address the frequency issues in the power system. The droop control uses the real power output of a generator to calculate the ideal operating frequency. This relaxing of a stiff frequency allows the grid to dampen the fast effects of changing loads, increasing the stability of the system [4]. However, traditional generatorsmay be phased out in the future due to the constraint of the greenhouse gas emissions on a global scale, making the traditional generators insufficient to deal with the increasing requirements of frequency regulation [5]. The change of the load's operating power can provide frequency regulation service when the system frequency fluctuates [6]. Moreover, the operating power of the Demand-side resource can be regulated rapidly, while the generator regulates its power generation through a series of processes, such as the speed governor process and the reheat steam turbine process, leading to a larger inertia compared with Demand-side resource [5]. In terms of voltage, different types of regulators are used to maintain the voltage within an acceptable range in traditional distribution systems, such as, on-load tap changer (OLTC), step voltage regulators (SVRs), and shunt capacitors (SCs) [7; 8; 9; 10; 11; 12]. The tap operation of an OLTC and an SVR can directly regulate the distribution system voltage from the system operator [13]. SCs can solve a series of problems caused by electrical loads' reactive power consumption, which can improve the voltage profile and reduce system losses. However, when the penetration of grid-integrated DGs is getting large, those types of regulators are not efficient enough to regulate the voltage in the fast nonlinear dynamics [14]. Moreover, frequent switching operation will reduce regulating efficiency. PV inverters can inject or absorb reactive power, in order to mitigate the overvoltage problems [15]. In addition, it is necessary to splits distribution networks into several separate control areas to control the voltage profile of each area in an admissible time calculation for online operation [16]. Because the resistance/reactance (R/X) ratio is relatively large in a low-voltage distribution system, the effectiveness of reactive power in voltage control is limited. As a result, active power adjustment should be considered for the voltage control of distribution systems. In addition, demand response is an effective way to keep the voltage in a permissible range [17]. Demand response changes consumers' inherent power consumption mode, reduce or shift the power load for a certain period of time, thus ensuring the stability of the power grid.