**2. Hierarchical Voltage Control Architecture**

In this paper, the voltage control strategy is based on a hierarchical architecture (Figure 1), where the main controller has been already proposed and utilized in several countries [46,47]. Therefore, the proposed strategy is based on an already implemented algorithm. Indeed, in the last 30 years this algorithm has proved its simple implementation, while at the same time it is scalable to transmission networks of different size and topology. For all these reasons, the application of such an algorithm has been extended to HV networks populated by nonprogrammable energy resources. The proposed architecture presents an external loop and a cluster of internal controllers, where the RPR behaves as a central control unit for coordinating the reactive power from each generator. Such a regulation is therefore adopted to obtain the voltage control on a peculiar pilot bus, named point of connection (POC). By implementing this control structure, the so-obtained reactive power regulation is actually similar to what is achieved by the SVR on transmission grids [48].

The control structure is explained in the scheme of Figure 1. Particularly, the network operator forwards the voltage reference to the control system, while the POC of the RES generation plant is operating as a pilot bus (as defined in SVR). In traditional fossil fuel power plants, all the generators are normally connected through a busbar, while in a more general case all generators are connected through any kind of grid, thus without any topology regularity. In the proposed architecture, the busbar voltage regulator (BVR) plays a crucial role, being responsible for the pilot bus voltage control (time constant *Tb* near ten seconds). Based on a classical PI (proportional-integral) functionality, the BVR can impose a level of reactive power *qliv* (between −1 and +1) to be applied by each generator [48] for getting the requested voltage regulation. For particular cases in which the TSO implements a remote regional voltage control architecture, the TSO excludes the BVR function by directly sending an external *qliv* reference signal to the reactive power control loop (i.e., switch in Figure 1). In both cases, the so-obtained *qliv* signal is the input for the RPR, where the *qliv* is multiplied by each generator reactive power limit to define the vector of reactive power references *Qre f* . The vector components are then compared to the actual reactive power *Q* values of each generator, thus determining a vector of errors Δ*Q*. The latter is therefore multiplied by the dynamic decoupling (DD) matrix, whose outputs constitute the inputs for the generator reactive power regulators (GRPRs) [49], thus obtaining the reactive power control loop (i.e., the time constant *TQ* is approximately few seconds). The reason for adopting the DD matrix is demonstrated by observing the MIMO (multiple-input-multiple-output) characteristic, which is typical of the generator reactive power control loop (i.e., several PI regulators, one for each generator). Instead, the dynamic decoupling matrix is capable of compensating for the mutual interactions, thus decoupling the MIMO reactive power control loop and consequently simplifying the control system design. Thus, the DD application allows the MIMO system to broken down into *n* single-input-single-output (SISO) loops, where the *n* generators are modeled by the same transfer function [49].

**Figure 1.** Synoptic scheme of secondary voltage control applied to a general case where all generators are connected by means of a distribution grid with a given topology.

The control signals calculated by GRPRs are the references Δ*Vre f* for each generator, which is represented as static frequency converter SFC and synchronous generators AVR in Figure 2. For what regards the control functionality ensured by BVR and RPR blocks, the related regulator parameters are to be set not only for decoupling internal and external control cycle but also for ensuring a voltage time response with an equivalent time constant of about 50 s. This value is chosen similar to what is usually required in conventional HV production power plants [50]. DGs are thus modeled as "voltage actuators" in terms of a first order mathematical model in d and q-axis coordinates. The time constant *Tv* of voltage control loops is fast enough compared to that one of the outer reactive power loop *TQ* (i.e., under the second), so Δ*Vi* can be assumed equal to Δ*Vi*\_*re f* . This model can be used for suitably studying the transient stability of the proposed hierarchical voltage control coupled with a simplified RES generator model (Figure 2) [51]. In the past, several studies have investigated the possibility of controlling the reactive power of a voltage source converter (VSC) independently from the active power. For instance, [52] not only shows the reactive power transient response in the presence of a changing in reactive power reference but also points out the P and Q injection decoupling. On the other hand, [53] exhibits a fast response for the reactive power control. This control algorithm can be applied on generation plants with different production technologies, coordinated by the same TSO. The application of the same control scheme allows a sort of uniformity in the dynamic responses of all generators. This control algorithm can be adopted in the case of generation plants with different production technologies, coordinated by the same TSO. Some examples are shown in [54–56], a cluster of hydropower plants, wind, and PV farms.

**Figure 2.** Distributed Generator model.

#### **3. Power Plants Modeling**

By observing Figure 1, the importance of the DD matrix appears undeniable, being capable of subdividing the initial system into *n* independent SISO subsystems. In this regard, the calculation of DD matrix is firstly shown in Section 3.1 for a generic distribution grid connecting all the generators (suitable for distributed RES production power plants). Then, the matrix is provided in Section 3.2 for the standard case, where large traditional generators are connected to the HV busbar through their step-up transformers (i.e., as in traditional large fossil fuel power plants).
