Complexity

Volume 2019, Article ID 5376360, 12 pages

https://doi.org/10.1155/2019/5376360

## Steady-State Analysis and Output Voltage Minimization Based Control Strategy for Electric Springs in the Smart Grid with Multiple Renewable Energy Sources

^{1}School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China^{2}College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China

Correspondence should be addressed to Michael Z. Q. Chen; moc.kooltuo@nehcqzm

Received 21 February 2019; Revised 1 April 2019; Accepted 8 April 2019; Published 9 May 2019

Guest Editor: Chun Wei

Copyright © 2019 Yun Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a general steady-state analysis and proposes a minimal compensating voltage (MCV) control scheme for the second generation of electric springs (ES-2) in the power system with substantial penetration of intermittent renewable energy sources. For the steady-state analysis, the relationship among the fluctuating part of the supply voltage, the voltage at the point of common-coupling (PCC), and the compensating voltage provided by ES-2 is derived, which implies that the phase angle related to the PCC voltage can be used as a degree of freedom for the control design to obtain a minimal compensating voltage in a given system. Such a fact is utilized in the control design to obtain the reference of PCC voltage by tuning the above-mentioned phase angle. Once the phase angle of the PCC voltage is chosen, the maximal compensating voltage can be estimated based on the fluctuating part of the supply voltage which can be estimated* a priori*. Such a fact can be used to design suitable electric springs with appropriate compensating capacity to avoid overcapacity. Numerical simulations are conducted to verify the effectiveness of the steady-state analysis and the proposed control scheme for ES-2.

#### 1. Introduction

In recent years, due to the energy crisis and the increasingly severe environmental issues, renewable energy sources are attracting more and more attention. Nowadays, wind [1–3] and solar energies are the two most widely used renewable energy sources for distributed generation [4–6]. However, due to the highly intermittent and unpredictable natures, renewable energy power generation brings a series of challenges to the power grid. Imbalance between the power supply and demand is one of the most prominent problems [7], which will cause the fluctuations of frequencies and voltages. Therefore, demand-side management has become a significant topic in the smart grid with intermittent renewable energy sources [8, 9].

Electric spring (ES) was first introduced in 2012 as a new generation of smart grid [10, 11] technology aiming to automatically balance the power generation and load demand without relying on the information and communication technology [12]. Generally speaking, ESs can be mainly divided into two categories. The first type called ES-1 works as a purely reactive power compensator to regulate the PCC voltage, while keeping the power consumption at the load side to be consistent with the power generation in real time. Examples of relevant research work on ES-1 are as follows. Dynamic modeling of ES and the influence of load ratios on compensation effects are described in [13]. Hardware and control implementation based on theoretical analysis are illustrated in [14]. Droop control and consensus control used to regulate the voltage by distributed ESs in the future smart grid are introduced in [15] and [16], respectively. However, just as a physical spring has limits for tension and compression, ES-1 also has its own compensation limits, exceeding which ES-1 will be invalidated. ES-2, which can provide six more operating modes in addition to the capacitive and inductive modes [17], can make up for these shortcomings. The difference in the topological structure between ES-1 and ES-2 is that the DC-link capacity in ES-1 is replaced by energy storage systems (such as batteries) on the DC side of the inverter in ES-2, thus the voltage phase angle of ES-2 is not restricted to be 90 degrees with respect to its current. At present, some research results of theoretical analysis and control schemes for ES-2 have been obtained. Regulating voltage and improving power quality (e.g., power factor correction and harmonics reduction) at the same time by ES-2 are introduced in [18], which are not possible with ES-1. In [19], a novel control strategy named control is proposed to obtain the instantaneous phase of PCC voltage to achieve specific power factor correction and constant power compensation. In [20], a radial-chordal decomposition (RCD) approach for ES-2 to regulate the PCC voltage is introduced, which can concurrently realize power factor correction by independent control of active and reactive powers.

However, these control strategies ignore the effect on ES-2 its own output value while focusing on the compensation functions. Note that it is meaningful to avoid overcapacity in terms of cost reduction in practice, and for ES-2, the relationship among the fluctuating part of the supply voltage, the PCC voltage, and the voltage provided by ES-2 is significant for determining the compensation capacity of electric springs. Therefore, in this paper, a general steady-state analysis for ES-2 is carried out to algebraically derive this relationship, which is depicted in a vector diagram. Based on the vector diagram, the detailed impact on compensating voltage caused by the fluctuating part of the supply voltage and a specific phase angle related to the PCC voltage is analyzed. Moreover, a control strategy to obtain the minimal compensating voltage (MCV) is proposed, the effectiveness of which is demonstrated by numerical simulations. These constitute the main contributions of this paper.

The rest of this paper is organized as follows. In Section 2, the operating principle of ES for the future smart grid is described. Sections 3 and 4 analyze the steady-state based on the vector diagram and propose a control scheme for ES-2, respectively. Numerical simulations are presented in Section 5 to verify the effectiveness of the analysis and the control scheme. Section 6 draws the conclusions.

#### 2. Operation Principles of Electric Springs

Figure 1 shows a simplified schematic of the power system that is composed of an ES, noncritical loads, critical loads, a fluctuating AC voltage source, and transmission lines. One thing to note is that the noncritical loads can withstand a wide range of voltage fluctuation, while the critical loads are sensitive to voltage fluctuation. The ES shown in the red dashed box of Figure 1 mainly consists of an energy storage system (represented by batteries), a single-phase inverter [21–26], and an LC filter as a second-order low-pass filter to reduce the switching harmonics. The output of the ES is connected to the noncritical load to form a smart load. The critical load and the smart load connect to the supply voltage source through the line impedance . The voltages across the noncritical load and the filter capacitor are represented as and , respectively. denotes the current flowing through the noncritical load. The supply voltage source denoted by in Figure 1 can be represented as follows:where represents the voltage corresponding to the power generated by the power plant, which is stable and controllable, while denotes the fluctuating part of the supply voltage caused by intermittent renewable energy sources, which is unstable and unpredictable. As the proportion of renewable energy connected to the power grid increases, will increase correspondingly. Due to the requirements of being grid-connected, and will have the same frequency and phase angle.