**1. Introduction**

Renewable energy sources (RESs) of solar and wind type are characterized by a non-predictable intermittency of power generation. When many RESs of these types contribute to the grid power, the uncertainty on their output power a ffects the power quality of the power system, with the occurrence of harmonics, voltage excursions, flickers, and even with the possible collapse of the power system [1,2]. An electric spring (ES) is a new power compensation device that provides a solution to the problem of grid power uncertainty. Indeed, it changes the traditional operation mode of the power system, whereby the load consumption determines the power generation, into a new one, whereby the automatic matching between power generation and load demand is implemented. Therefore, ES represents an e ffective solution to the large grid power fluctuations expected when RESs of solar/ wind type penetrate the grid on a large scale [3–6].

The keystone of the ES approach is to divide the loads of a user into two groups with di fferent requirements: one is critical load (CL), and the other one is non-critical load (NCL). CL requires highly stabilized supply voltage and/or uninterrupted supply to work correctly, and it may operate in frequent situations at nearly the rated power; examples of CL are machine rooms and medical equipment. NCL allows its supply voltage -and, hence, its absorbed power- to vary within a larger range, and can even be cut o ff for a certain period of time when the total power supply is not enough to ensure the required voltage for the CL supply; examples of NCL are water heater and other heating equipment. Both CL and NCL are connected at the same grid node, called the point of common coupling (PCC), but in a di fferent way: CL in a direct way while NCL through the interposition of ES.

An ES is made of a voltage direct current (DC) source, a voltage source inverter (VSI) and an alternating current (AC) output inductor-capacitor pair; the capacitor, placed between PCC and NCL, constitutes the ES output whilst the inductor plays the role of filtering the VSI output current. By suitably controlling the capacitor voltage, the NCL voltage is adjusted such that the grid-incoming power fluctuations are transferred to the NCL so that CL is supplied at the required voltage [3]. By this reason, the branch constituted by the capacitor and NCL is called the smart load (SL).

Two basic ES versions exist. One version utilizes a capacitor as voltage DC source, and the ES exchanges only reactive power with the SL branch to stabilize the CL voltage; this version is commonly referred to as ES-1. The other version utilizes a bidirectional DC source like a battery as voltage DC source, and the ES exchanges both active and reactive power with the SL branch to stabilize the CL voltage; this version is commonly referred to as ES-2. Besides stabilizing the CL voltage, ES-2s have the capabilities of executing other tasks such as the correction of the power factor (PF) of the user [7] or the suppression of the frequency [8] and voltage [9] excursions of the power system. Due to their capabilities, hereafter only the ES-2s are considered.

Various strategies have been developed for the ES control. The δcontrol, proposed in [10], instantaneously adjusts the phase angle δbetween the PCC and line voltages to regulate the magnitude of the CL voltage and, at the same time, to keep the user PF compliant with the standards. The radial-chordal control strategy, proposed in [11], decomposes the ES output voltage into its chordal and radial components. Then it adjusts the chordal component to regulate the magnitude of the CL voltage ad the radial component to control the power angle of the SL. The active and reactive power control, proposed in [12], simplifies the ES control by using independent loops to adjust the CL voltage and the active power exchanged by the ES. Regarding the strategies for the control of multiple ESs, the droop control, presented in [13], manipulates the modulation index of the ES-embedded VSI to regulate the CL voltage at each node, which makes the solution appropriate for the ES-1 version. The consensus control, presented in [14,15], processes the voltage information coming from the adjacent ESs to calculate the reference voltage of the local ES; clearly, this control needs communication means to work.

There are other studies related to the control of multiple ESs. The simplified ES model established in [16] is intended to the simulation of a large-scale system endowed with the ESs. The modular dynamic model of the ES established in [17] is tailored for the integration of sophisticated control algorithms, reducing the order of the model by help of experimental measurements. In [18], the distributed voltage control attained with multiple ESs in a power system is compared to the single node voltage control done with the Static Synchronous Compensator (STATCOM); from the comparison executed under di fferent voltage excursion situations, it emerges that the ESs provide a better voltage regulation than the STATCOM. The e ffect that the ES operation combined with an energy managemen<sup>t</sup> strategy exerts on the suppression of the voltage and frequency excursions in microgrids is examined in [19]. In [20], hybrid ESs for grid-tied power control and storage reduction in AC microgrids is discussed. In [21], a method to stabilize a set of multiple ESs is presented, based on the small signal modeling of their behavior.

As a new paradigm of load demand managemen<sup>t</sup> enabled by a power compensation device, the ES has outstanding advantages in adapting to the future distributed system when compared with the traditional centralized devices of reactive power compensation. However, the sizing power of a single ES is often limited. For the stabilization of the loads of a power system to take place, the joint e ffort of multiple ESs is requested, as exemplified in Figure 1. When multiple ESs are tied to di fferent nodes of a power system, the node voltages are unable to reach the nominal value simultaneously (e.g., 220 V) due to the inherent voltage drop of the transmission line. Therefore, the adoption of an overall control strategy of the ESs becomes necessary to appropriately modify the local reference voltage of the ESs during the transients. The role of the strategy is to provide for a coordinate operation of the ESs while

maintaining stabilized voltage across the associated CLs. Some papers have shown that the popular droop control is a useful tool on which to build up the strategy [22–26].

**Figure 1.** Microgrid with three ES-2 (electric springs (ES) exchanging both active and reactive power with the smart load (SL) branch to stabilize the critical load (CL) voltage and frequency).

The existing popular hierarchical control is well illustrated in [25] which is derived from the international standard for the integration of enterprise and control systems (ISA-95) and electrical dispatching standards to endow smartness and flexibility to Microgrids (MGs). With such control, the MGs are able to work at both islanded or stiff-source-connected modes, as well as to achieve a seamless transfer from one mode to another. Besides, multiple MG clusters can be performed to constitute a smart grid. Moreover, the system becomes more flexible and expandable, and consequently, more and more MGs could be integrated without changing the local hierarchical control system associated to each MG. Compared to the hierarchical control in [25], traditional droop control has many disadvantages which need to be improved. For instance, it is not suitable when the paralleled system must share non-linear loads due to harmonic currents, frequency deviation, accuracy sharing between active and reactive power under islanded mode. The hierarchical control proposed in [25] consists of three levels: (1) the primary control is based on the droop control; (2) the secondary control allows the restoration of the deviations obtained by the primary control; and (3) the tertiary control manages the power flow between the MG and the external electrical distribution system. Although it has so many advantages, it is complicated and hard to build prototype in a laboratory with limited resources and space. Considering the simple structure of ES system, and in order to avoid the disadvantages of the traditional droop control and to take the advantage of the hierarchical control in [25], a simplified hierarchical control only containing the droop control and the inner control loops is adopted in this paper. Another contribution is that it is proposed that the power decoupling control with fast dynamic responses is adopted at the ES level. In details, the hierarchical control is structured into two levels: primary and secondary. Compared to the existing primary control solutions, a novel scheme is developed that enhances both the dynamics and the robustness of the ES operation. After discussing the inconveniences of multiple ESs working independently, their coordinate operation is accomplished by the secondary control; besides modifying the CL reference voltage at the different nodes by using droop characteristics, it is designed to cope with the frequency excursions that often arise in the islanded operation of a microgrid. Finally, the effectiveness of the novel ES control scheme as well as of the proposed hierarchical control is verified by simulation.

The organization of the paper is as follows. Section 2 shortly reviews topology and model of an ES-2. Section 3 illustrates the proposed coordinated control for multiple ESs tied to a microgrid and explains how the control steers the ESs. Section 4 presents and discusses the results of some significant simulations carried out on a set of three ESs governed with the proposed control. Finally, Section 5 concludes the paper.

#### **2. Electric Spring (ES-2) Operating Principles**
