**1. Introduction**

As a demand-response technique, the electric spring (ES) has been proposed initially in [1] to ensure the stabilization of the supply voltage of loads when the grid power fluctuates, which today is more frequent than in the past since the grid power is mostly or entirely generated by renewable energy sources (RESs). Based on the ES concept, two types of equipment have been developed: One is named the AC electric spring (ACES) [2,3] and is intended to stabilize the supply voltage of AC appliances; the other one is named the DC electric spring (DCES) [4,5] and is intended for DC appliances. ACESs have been investigated first and actually many topologies and control strategies are available for their implementation [2,6].

Instead, there is much to explore on DCESs as the research interests on this topic date back only a few years. The overall system with the photovoltaic (PV) systems, fuel cells, and batteries that are inherently of a DC nature can be fully integrated in the DC form without any DC/AC or AC/DC converters, which contribute to a higher efficiency and reliability [7]. However, similar to the AC grids, there are also some drawbacks in the DC microgrid due to the intermittent RES, such as the power imbalance among the power sources and load, the bus voltage instability, and fluctuation. Existing solutions include the line-regulating converter [8], control for the coordinating the demands and supplies [9], and droop control strategies [10]. However, these solutions commonly suffer from

additional communication system or poor regulation performances. Considering the deficiencies of the DC power system with the RES, the concept of a DC electric spring is firstly proposed in [11], for the regulation of the bus voltage and power in a DC microgrid.

According to the ES concept, the loads of a DC microgrid are sorted into critical loads (CLs) and non-critical loads (NCLs). According to the sorting terminology, CLs are critical with respect to the supply voltage in the sense that they require a well-stabilized voltage to operate correctly, while NCLs do not require it. In order to stabilize the CL voltage, the DCES transfers some of the grid power fluctuations from the DC microgrid to NCLs, and forces the remaining power fluctuations to be borne by a DCES-embedded battery, thus enabling fast and flexible energy storage with a reduced battery usage.

There are two kinds of existing versions of the topology of the DCES [4,5], which can be sequenced as DCES-1 and DCES-2. The configuration of DCES-1 is the same as the original version of ACES. Since the low-pass filter inside the ACES has a big volume, the power density of such circuit is pretty low. In contrary, DCES-2 is realized by pure DC/DC converters to avoid the disadvantage introduced by the filter with a big volume. However, there are three di fferent power converters inside it, which leads to a more complex control and lower reliability.

To avoid these disadvantages, an improved DCES topology has been proposed lately [12], which circumvents the inconvenience of the series connection of the NCL and ES. Moreover, in the proposed DCES, the CL and NCL are isolated from each other and are both in parallel with the DC bus, which is consistent with the traditional connection type in power systems.

The topology is comprised of a DC/DC three-port converter (TPC) [13] and an energy storage unit (ESU). The TPC input port is fed by RES (or by a RES-prevalent grid), whilst the two output ports supply the NCL and CL separately. The ESU, in turn, is connected in parallel to the CL and is comprised of a bi-directional buck-boost converter (BBC) [14] and a battery; its task is to ensure the stabilization of the CL supply voltage while keeping the state-of-charge of the battery within predetermined limits. Hereafter, this DCES topology is referred to as a CL-paralleled (CLP)-ESU.

This paper focuses on DCESs and is aimed at investigating the regulation performance of a set of topology-novel DCESs when they are controlled by means of a distributed cooperative system.

Cooperative control systems of a multi-stage appliance can be classified into three categories, denoted as centralized, decentralized, and distributed [15]. A centralized system necessitates of communication between a central controller and the local controllers to control an appliance. A decentralized system dispenses from a central controller and the local controllers operate on the basis of information that they are able to find individually, like the droop control for a power system; as a counterpart, it may not be e ffective in the full and/or optimal utilization of the resources of the appliance [16]. A distributed system also dispenses from a central controller, but is di fferent from a decentralized system, in which the local controllers exchange information with the other controllers through a communication network to control the appliance.

A distributed cooperative control proposed in [17], including the voltage and current controller, is based on a consensus algorithm [18], which refers to all components reaching a certain common agreemen<sup>t</sup> after the distributed control. In [19], the distributed cooperative control is used to establish a primary/secondary control framework for the DC microgrid. The *V*-*I* droop mechanism in [19] is used in the primary control for enabling a decentralized coordination of distributed energy resources. Moreover, the consensus algorithm is used in the secondary control for the DC-bus voltage regulating and battery state-of-charge (SOC) balancing. The distributed cooperative control applied in the series and shunt DCESs is proposed in [20], whilst the primary and secondary control can achieve an average DC-bus voltage consensus and SOC balance among the di fferent DCESs.

In this paper, a distributed cooperative system is developed to control a set of multiple DCESs with a CLP-ESU topology [12]. The system has two control levels, primary and secondary, whose joint action allows the concurrent achievement of the following objectives: Local voltage stabilization, local power allocation, consensus on the DC bus voltage of the CL of each DCES, and consensus of the

state-of-charge (SOC) of the battery of each DCES. The system level with the primary control is of a decentralized type and includes the phased-shift control of TPC ports, the decoupling voltage control of CLs, the adaptive droop settling of CLs, and the charging and discharging control of the batteries. In turn, the system level with the secondary control is of a distributed type and includes the voltage control of the CL DC buses and the SOC control of the batteries.

In short, the organization of the paper is as follows. Section 2 reviews the topology and operation of DCES utilized in the paper. Section 3 illustrates the distributed cooperative system arranged for the control of multiple DCESs. Section 4 shows the steady state analysis of the proposed control method. Section 5 presents the simulations carried on a study case of multiple DCESs and discusses the results. Section 6 concludes the paper.

## **2. DCES Topology and Operation**

This paper utilizes DCESs with the CLP-ESU topology drawn within the dashed line of Figure 1. The photovoltaic (PV) array, NCL and CL are connected to the ports of the TPC, which is essentially a two-output DC/DC converter isolated by means of a high frequency transformer and equipped with a full AC/DC bridge at each port. The battery is used for voltage regulation, and is paralleled to the CL DC bus through the BBC, which can be thought of as a version of the boost DC/DC converter, modified to support the bi-directional power flow. Compared to the existing DCES ones, the CLP-ESU topology keeps the supply of the CL and NCL isolated from each other. This circuital layout is compliant with the traditional way of connecting loads with di fferent requirements in a power system [12]. More broadly, it can be envisaged that each output port in the figure supplies a distinct DC bus with connecting as many CLs and NCLs as per the DCES sizing power.

**Figure 1.** Critical load paralleled-energy storage unit (CLP-ESU) topology of the DC electric spring (DCES).

The typical operating modes of the DCES are three, designated as the battery-balancing mode, battery-discharging mode, and battery-charging mode.

In the battery-balancing mode (mode 1), the power delivered by the RES is enough to supply CL at the specified value. The RES power fluctuations are forced by the ESU to flow almost entirely from the RES to the NCL, whilst the remaining small part of them flows into the battery to keep the CL voltage stabilized.

In the battery-discharging mode (mode 2), the RES power is in-su fficient to supply CL at the rated value even if the NCL voltage is adjusted to consume less power than the rated one. In this mode, the battery discharges to provide the deficit of power to the CL.

At the battery-charging mode (mode 3), the RES power exceeds the power consumption of CL even if the NCL voltage is adjusted to consume more power than the rated one. In this mode, the battery is charged and stores the excess of power.

The structure of multiple DCESs in a DC microgrid is schematized in Figure 2. The figure shows that the CL DC buses (henceforth briefly referred to as the DC buses) of each DCES are connected to each other by transmission lines, whose resistances are denoted with *RL*1, *RL*2, *RL*3, and *RL*4. The link of the four DCESs together forms a typical DC microgrid.

**Figure 2.** Structure of multiple DCESs.
