Research Article  Open Access
Yun Zou, Michael Z. Q. Chen, Yinlong Hu, Yun Zou, "SteadyState Analysis and Output Voltage Minimization Based Control Strategy for Electric Springs in the Smart Grid with Multiple Renewable Energy Sources", Complexity, vol. 2019, Article ID 5376360, 12 pages, 2019. https://doi.org/10.1155/2019/5376360
SteadyState Analysis and Output Voltage Minimization Based Control Strategy for Electric Springs in the Smart Grid with Multiple Renewable Energy Sources
Abstract
This paper presents a general steadystate analysis and proposes a minimal compensating voltage (MCV) control scheme for the second generation of electric springs (ES2) in the power system with substantial penetration of intermittent renewable energy sources. For the steadystate analysis, the relationship among the fluctuating part of the supply voltage, the voltage at the point of commoncoupling (PCC), and the compensating voltage provided by ES2 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 abovementioned 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 steadystate analysis and the proposed control scheme for ES2.
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, demandside 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 ES1 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 ES1 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, ES1 also has its own compensation limits, exceeding which ES1 will be invalidated. ES2, 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 ES1 and ES2 is that the DClink capacity in ES1 is replaced by energy storage systems (such as batteries) on the DC side of the inverter in ES2, thus the voltage phase angle of ES2 is not restricted to be 90 degrees with respect to its current. At present, some research results of theoretical analysis and control schemes for ES2 have been obtained. Regulating voltage and improving power quality (e.g., power factor correction and harmonics reduction) at the same time by ES2 are introduced in [18], which are not possible with ES1. 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 radialchordal decomposition (RCD) approach for ES2 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 ES2 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 ES2, the relationship among the fluctuating part of the supply voltage, the PCC voltage, and the voltage provided by ES2 is significant for determining the compensation capacity of electric springs. Therefore, in this paper, a general steadystate analysis for ES2 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 steadystate based on the vector diagram and propose a control scheme for ES2, 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 singlephase inverter [21–26], and an LC filter as a secondorder lowpass 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 gridconnected, and will have the same frequency and phase angle.
Because of the randomness of renewable energy, the power delivered to the network is unstable. When exceeding the demand, the PCC voltage will be over the rated value, vice versa. For a change in , ES will provide a corresponding compensating voltage to keep the PCC voltage stable. In this way, the power generation and load demand can be balanced automatically, which is different from the existing control paradigm that the power generation should follow load demand.
Note that the ES2 as shown in Figure 1 is equipped with batteries on the DC side of the inverter. The phase angle of the voltage provided by ES2 is not limited to 90 degrees (lag or lead) with respect to the phase angle of . Therefore, active power can be provided in addition to reactive power. And for this reason, ES2 has a larger compensation rang compared to ES1. Consequently, new control strategies are required due to the structural change mentioned above, which will be described in detail in Section 4.
3. SteadyState Analysis of Electric Springs for Minimal Compensating Voltage
From Figure 1 and Kirchhoff’s voltage and current laws, one obtainswhere and are the equivalent resistance and inductance of the transmission lines, respectively.
Solving (1)–(3), one obtainswhere and are determined by the parameters of the circuit elements which can be treated as constant values for a given system.
Equation (5) can be represented in the phasor form aswhere and are the magnitude and the displacement angle of (), respectively. , , , and are the rootmeansquare (RMS) values of , , , and , respectively, and , , and are the phase angles of , , and , respectively. denotes the difference between and , which is related to and due to the fact that and are constants in a given system. The vector diagram among , , , and is depicted in Figure 2. Since the PCC voltage (i.e., ) is maintained at its nominal reference level (e.g., 220 V), then is a constant as the circle 1 showed in Figure 2. Similarly, on the circle 2 represented by the solid line OA can be treated as a constant as well. The fluctuating part of the source voltage () multiplied by is represented by the dashed line AB. For a constant , if changes from point A to point B, the compensating voltage will change from line OC to line OD, correspondingly.
From Figure 2, one sees that , are the two essential factors for . Especially, if , namely, and have the same phase angle, a maximal will be obtained as shown in Figure 3(a). In contrast, a minimal can be obtained with as shown in Figure 3(b).
(a)
(b)
To quantitatively show the influence of and on , the parameters in Table 1 are employed. A threedimensional representation among , , and is given in Figure 4, where one sees that the minimal value of is obtained at . Table 2 shows some representative values of , and the corresponding based on the parameters in Table 1. One sees that is highly influenced by . For example, when changes from to 0, the variation percentages of are up to 2177.64 for the cases =0. All the variation percentages shown in Table 2 are based on the values obtained at , where positive values indicate increment.
 
Parameters come from [27] 

In conclusion, has a significant influence on . In other words, is so sensitive to the phase angle , which implies that the phase angle of should be carefully selected when designing the proper control law for ES2. If an appropriate phase angle has been chosen, then is only determined by . Since the proportion of the intermittent renewable source injected to the power grid is limited, will fluctuate within a certain range. Once can be estimated in advance, the required voltage can also be estimated. This provides guidelines for designing suitable ESs with appropriate compensating capabilities to avoid overcapacity.
4. Control Design for ES2
The aim of control design is to minimize the error between the PCC voltage and its reference by a minimal ES voltage. In this paper, to show the effectiveness of the analysis in the Section 3, a minimal compensating voltage (MCV) based control strategy is proposed for ES2 and a proportional resonant (PR) controller is employed because of the characteristic that PR control can track a sinusoidal signal with a zero steadystate error.
Figure 5 shows the system block diagram, where the red dotted box at the bottom of the figure shows how to obtain the reference signal . As can be seen from the steadystate analysis in Section 3, the magnitude of is related to and , so can be treated as a degree of freedom for control design to obtain a minimal value of . Since is related to the phase angle of (see (9)–(11)), the key point of the proposed control strategy is transformed to select an appropriate phase angle of . The supply voltage signal is obtained by a sensor, and a singlephase lock loop (PLL) is used to acquire its phase angle . Then can be calculated through (9)–(11) based on the circuit parameters and . One remark is that the value of arctan function belongs to the interval , which is corresponding to the argument of a complex number whose real part is positive. If the real part of the complex number is negative, then one need to add when calculating the argument of a complex number, where care should be taken when calculating and . Thus, the complete reference signal can be obtained by combining the magnitude and the phase angle . The expression of the PR controller used in this paper is as follows:where is the angular frequency of the grid and and are the proportionality coefficient and resonance coefficient, respectively.
Equation (14) is an ideal PR controller, which has an infinite gain at angular frequency , but no phase transition and gain at other frequencies. Therefore, it can realize tracking a sinusoidal signal without any steadystate error. For this reason, a PR controller is introduced to regulate the PCC voltage () to its reference level by driving the difference between reference voltage and measured voltage to zero. In addition to PR control, many other control methods, such as slidingmode control [28, 29], robust control [30], model predictive control [31, 32], and eventtriggered control [33] can also be considered in future studies based on the control strategy mentioned above.
5. Simulations and Discussions
To double verify the effectiveness of the aforementioned analysis and the MCV control strategy, simulations are conducted by using MATLAB/Simulink and LabVIEW/PXI based on the parameters shown in Table 1. Without loss of generality, the RMS of is assumed to be V.
5.1. The Simulations Conducted on MATLAB/Simulink
5.1.1. Voltage Support Mode with ΔU = 0 V
In this case study, the effect of different on for voltage boosting is investigated. is set 0 to simulate insufficient output of power generation, so it can be seen that the RMS of the line voltage is less than 220 V with the ES2 deactivated from Figure 6. In order to restore back to 220 V, ES2 should play the role of voltage support. In the voltage support mode, different values of are employed to verify the influence of on . The RMS of the compensating voltage provided by ES2 to regulate at 220 V are considerably different as shown in Figure 7 for different , which are consistent with the algebraic calculations shown in Table 2. Taking the red line shown in Figure 7 as an example, the RMS is about 4600 V in the steadystate which is consistent with the value obtained from (13).
5.1.2. Voltage Suppression Mode with
In this case study, the effect of different on for voltage suppression is investigated. Figure 8 shows the RMS of the line voltage with ES2 activated and deactivated when , which is used to simulate the overvoltage conditions. When , the RMS of the line voltage is about 230 V with ES2 deactivated. However, under the action of the ES2, is effectively controlled at 220 V. Similarly, for different , the compensating voltage injected to the power system is considerably different as shown in Figure 9. The simulation results correspond to the analyses mentioned in Section 3. As previously mentioned, for ES1, the compensating capability is limited [19]. For example, by using the parameters in Table 1, it has been described in [27] that the variation range of is 215.8 V to 236.7 V, which means that, if is out of the range mentioned above, ES1 cannot regulate at 220 V. When V, that is to say is 210 V, one can intuitively see that ES1 can just adjust the voltage to 214 V as shown in Figure 10. Similarly, when V, which means that the supply voltage is higher than the upper compensation limit of ES1, ES1 can just adjust the voltage to 223 V in the best case. Such a fact indicates that ES2 has a larger compensation range than ES1. In some cases where the voltage fluctuation is large, ES1 may fail to regulate the line voltage , whereas ES2 does.
5.1.3. ES1 vs ES2 within the Effective Regulation Range of ES1
In this case study, ES voltage, compensation modes, and real and reactive powers are compared between ES1 and ES2 within the effective regulation range of ES1. From Figure 11(a), one can see the ES voltages of ES1 and ES2 with the supply voltage V, respectively, where the voltage of ES2 (about 140 V) based on the MCV control strategy is less than the voltage of ES1 (about 162 V) to regulate the line voltage to 220 V. If one carefully observes the phase relationships in Figures 11(b) and 11(c), one will find that the ES1 voltage lags its current about 90 degrees for capacitive compensation. Therefore, the real and reactive power of ES1 are about 0 and 3000 Var as shown in Figures 11(d) and 11(e), respectively. For ES2, its voltage lags its current by more than 90 degrees for negative resistive plus capacitive compensation. Therefore, ES2 injects about 3600 Var reactive power, while injecting about 1200 W real power at the same time to regulate the line voltage to its rated value as shown in Figures 11(d) and 11(e).
(a)
(b)
(c)
(d)
(e)
Similarly, ES1 and ES2 are also compared in voltage suppression mode within the effective regulation range of ES1. The ES voltages of ES1 and ES2 are about 97 V and 70 V with the supply voltage V as shown in Figure 12(a). As can be seen from Figures 12(b) and 12(c), the ES2 voltage leads its current by more than 90 degrees for negative resistive plus inductive compensation, while ES1 is in inductive compensation mode to suppress voltage. Figures 12(d) and 12(e) show the corresponding real and reactive power injected into the power grid. One remark is that the ES currents in Figures 11(b), 11(c), 12(b), and 12(c) are enlarged for the ease of comparison while maintaining the phases.
(a)
(b)
(c)
(d)
(e)
The simulation results not only verify the effectiveness of the steadystate analysis and the MCV control scheme, but also show that ES2 has a remarkable ability to regulate the PCC voltage. Theoretically, ES2 has a wider range of compensation with respect to ES1, in the sense that for any , there always exists a corresponding to regulate at its nominal level. In addition to this, the ES2 voltage is less than the ES1 voltage within the effective regulation range of ES1 at the expense of some real power.
5.2. The Simulations Conducted on LabVIEW/PXI
To further verify the effectiveness of the steadystate analysis in Section 3 and the MCV control strategy in Section 4, hardware in the loop (HIL) simulations are conducted based on LabVIEW/PXIe1071. For convenience, the ES currents shown in the following simulation results are actually the voltages across the noncritical roads. Since the current and the voltage of the resistive load are in the same phase, it does not affect the verification of the phase relationship.
5.2.1. The Influence of on
In this case study, the influence of on with V and V is further analyzed. From Figures 13(a), 13(c), and 13(e), we can see intuitively the sine waveforms of voltage , whose RMS values are 4.587 V, 3.29 V, and 207.7 mV with , , and when V, respectively. It is worth noting that RMS values here are reduced by 1000 times due to the fact that HIL output constraint is V. Similarly, when , the corresponding RMS values are 4.901 V, 3.431 V, and 114.0 mV as shown in Figures 13(b), 13(d), and 13(f), respectively. The results of the HIL simulations and the Matlab simulations as well as the theoretical calculations are basically consistent, which means that is extremely sensitive to . Moreover, it further indicates the necessity of MCV control strategy for ES2 to regulate the line voltage due to the fact that DC side voltage of ES2 is constrained.
(a)
(b)
(c)
(d)
(e)
(f)
5.2.2. Comparing ES1 with ES2 out of the Effective Regulation Range of ES1
From the perspective of power electronics, ES1 is a special reactive power compensator used to regulate the line voltage in the future smart grid with multiple renewable energy sources. However, due to the limitation of its compensation modes, only reactive power is exchanged with the power grid; thus ES1 has compensation limits. In other words, once the supply voltage changes beyond a certain range, ES1 will fail. With the introduction of real power for voltage regulation, ES2 can well overcome this disadvantage. In this case study, the supply voltage is set at V, which is out of the effective regulation range of ES1. Figures 14(a) and 14(b) show the line voltage with ES1 and ES2 activated, respectively. The RMS values, 4.47 V and 4.39 V, in Figures 14(a) and 14(b) are reduced by 50 times, which show that the ES1 is unable to adjust to its rated value. The phase relation in Figure 14(c) indicates ES1 is in inductive compensation mode, while ES2 is in negative resistive plus inductive compensation mode as shown in Figure 14(d).
(a)
(b)
(c)
(d)
5.2.3. ES1 and ES2 for Voltage Boosting within the Effective Regulation Range of ES1
ES1 and ES2 are compared for voltage boosting within the effective regulation range of ES1 in this case study. The supply voltage is set at V, which is within the effective regulation range of ES1 and used to simulate undervoltage conditions. The phase relationships of ES1 and ES2 are shown in Figures 15(a) and 15(c), while the corresponding output voltages of ES1 and ES2 are shown in Figures 15(b) and 15(d), respectively. The simulation results show that the ES2 based on the MCV control strategy has a smaller output voltage relative to ES1 at the expense of injecting some real power to the power grid for voltage boosting.
(a)
(b)
(c)
(d)
5.2.4. ES1 and ES2 for Voltage Suppression within the Effective Regulation Range of ES1
Similar to the voltage boosting mode, ES1 and ES2 are compared for voltage suppression within the effective regulation range of ES1 in this case study. The supply voltage is set at V, which is within the effective regulation range of ES1 and used to simulate overvoltage conditions. As can be seen from Figure 16(a), the ES1 voltage and ES1 current are almost orthogonal and ES1 voltage leads ES1 current by almost 90 degrees for inductive compensation to suppress voltage, while the corresponding ES1 voltage is shown in Figure 16(b). ES2 works in negative resistive plus inductive compensation mode based on the MCV control strategy as shown in Figure 16(c), while its output voltage injected to the power grid is shown in Figure 16(d). In the same way, ES2 based on the MCV control strategy has a smaller output voltage relative to ES1.
(a)
(b)
(c)
(d)
6. Conclusion
ES1 has compensation limits because of the constraints of its structure, while ES2 can effectively remedy this defect at the expense of injecting real power. In this paper, ES1 and ES2 were compared in detail within and out of the effective regulation range. Moreover, for ES2, the steadystate analysis was provided and a PRbased MCV control strategy was proposed to regulate the PCC voltage. For steadystate analysis, the relationship among the fluctuating part of the supply voltage, the PCC voltage, and the compensating voltage provided by ES2 was derived, which implied that the phase angle of the PCC voltage could be used as a degree of freedom for control design to obtain a minimal compensating voltage in a given system. Once the phase angle of the PCC voltage was chosen, the maximal compensating voltage could be estimated based on the fluctuating part of the supply voltage which could be estimated a priori. Such a fact could be used for designing suitable electric springs with appropriate compensating capacity. Numerical simulations were conducted to demonstrate the effectiveness of the steadystate analysis and the control scheme.
Data Availability
All data can be accessed in the Simulation Studies section of this article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this article.
Acknowledgments
This research was supported by the National Natural Science Foundation of China [grant number 61873129].
References
 Y. Zhao, C. Wei, Z. Zhang, and W. Qiao, “A review on position/speed sensorless control for permanentmagnet synchronous machinebased wind energy conversion systems,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 1, no. 4, pp. 203–216, 2013. View at: Publisher Site  Google Scholar
 Q. Guo, Z. Sun, Y. Zhang, and W. Xu, “Timedelayed feedback control in the multiple attractors windinduced vibration energy harvesting system,” Complexity, vol. 2019, Article ID 7973823, 11 pages, 2019. View at: Publisher Site  Google Scholar
 F. Cheng, L. Qu, W. Qiao, C. Wei, and L. Hao, “Fault diagnosis of wind turbine gearboxes based on dfig stator current envelope analysis,” IEEE Transactions on Sustainable Energy, 2018. View at: Publisher Site  Google Scholar
 T. Kang, S. Kim, C. Hyoung, S. Kang, and K. Park, “An energy combiner for a multiinput energyharvesting system,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 62, no. 9, pp. 911–915, 2015. View at: Publisher Site  Google Scholar
 K. T. Tan, X. Y. Peng, P. L. So, Y. C. Chu, and M. Z. Q. Chen, “Centralized control for parallel operation of distributed generation inverters in microgrids,” IEEE Transactions on Smart Grid, vol. 3, no. 4, pp. 1977–1987, 2012. View at: Publisher Site  Google Scholar
 H. E. Espitia, I. MachónGonzález, H. LópezGarcía, and G. Díaz, “Proposal of an adaptive neurofuzzy system to control flow power in distributed generation systems,” Complexity, vol. 2019, Article ID 1610898, 16 pages, 2019. View at: Publisher Site  Google Scholar
 Z. Yang, J. Xiang, and Y. Li, “Distributed consensus based supplydemand balance algorithm for economic dispatch problem in a smart grid with switching graph,” IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 1600–1610, 2017. View at: Publisher Site  Google Scholar
 M. Pedrasa, T. Spooner, and I. MacGill, “Scheduling of demand side resources using binary particle swarm optimization,” IEEE Transactions on Power Systems, vol. 24, no. 3, pp. 1173–1181, 2009. View at: Publisher Site  Google Scholar
 Z. Luo, J. Zhao, R. Yao, and Z. Shu, “Emergybased sustainability assessment of different energy options for green buildings,” Energy Conversion and Management, vol. 100, pp. 97–102, 2015. View at: Publisher Site  Google Scholar
 L. Xi, Y. Li, Y. Huang, L. Lu, and J. Chen, “A novel automatic generation control method based on the ecological population cooperative control for the islanded smart grid,” Complexity, vol. 2018, Article ID 2456963, 17 pages, 2018. View at: Publisher Site  Google Scholar
 H. Zhong, D. Du, C. Li, and X. Li, “A novel sparse false data injection attack method in smart grids with incomplete power network information,” Complexity, vol. 2018, Article ID 8503825, 16 pages, 2018. View at: Publisher Site  Google Scholar
 S. Y. Hui, C. K. Lee, and F. F. Wu, “Electric springs  a new smart grid technology,” IEEE Transactions on Smart Grid, vol. 3, no. 3, pp. 1552–1561, 2012. View at: Publisher Site  Google Scholar
 N. R. Chaudhuri, C. K. Lee, B. Chaudhuri, and S. Y. R. Hui, “Dynamic modeling of electric springs,” IEEE Transactions on Smart Grid, vol. 5, no. 5, pp. 2450–2458, 2014. View at: Publisher Site  Google Scholar
 C. K. Lee, B. Chaudhuri, and S. Y. Hui, “Hardware and control implementation of electric springs for stabilizing future smart grid with intermittent renewable energy sources,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 1, no. 1, pp. 18–27, 2013. View at: Publisher Site  Google Scholar
 C. Kwan Lee, N. Ray Chaudhuri, B. Chaudhuri, and S. Y. R. Hui, “Droop control of distributed electric springs for stabilizing future power grid,” IEEE Transactions on Smart Grid, vol. 4, no. 3, pp. 1558–1566, 2013. View at: Publisher Site  Google Scholar
 X. Chen, Y. Hou, and S. Y. Ron Hui, “Distributed control of multiple electric springs for voltage control in microgrid,” IEEE Transactions on Smart Grid, vol. 8, no. 3, pp. 1350–1359, 2017. View at: Publisher Site  Google Scholar
 S.C. Tan, C. K. Lee, and S. Y. Hui, “General steadystate analysis and control principle of electric springs with active and reactive power compensations,” IEEE Transactions on Power Electronics, vol. 28, no. 8, pp. 3958–3969, 2013. View at: Publisher Site  Google Scholar
 S. Yan, S.C. Tan, C.K. Lee, B. Chaudhuri, and S. Y. R. Hui, “Use of smart loads for power quality improvement,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 1, pp. 504–512, 2017. View at: Publisher Site  Google Scholar
 Q. Wang, M. Cheng, Z. Chen, and Z. Wang, “Steadystate analysis of electric springs with a novel δ control,” IEEE Transactions on Power Electronics, vol. 30, no. 12, pp. 7159–7169, 2015. View at: Publisher Site  Google Scholar
 K.T. Mok, S.C. Tan, and S. Y. R. Hui, “Decoupled power angle and voltage control of electric springs,” IEEE Transactions on Power Electronics, vol. 31, no. 2, pp. 1216–1229, 2016. View at: Publisher Site  Google Scholar
 L. Diao, H. Du, Z. Shu, Y. Xue, M. Li, and S. M. Sharkh, “A comparative study between AIHM and SPDHM for railway auxiliary inverter with pulsating DC link,” IEEE Transactions on Industrial Electronics, vol. 65, no. 7, pp. 5816–5825, 2018. View at: Publisher Site  Google Scholar
 X. Liu, A. M. Cramer, and F. Pan, “Generalized average method for timeinvariant modeling of inverters,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 64, no. 3, pp. 740–751, 2017. View at: Publisher Site  Google Scholar
 X. Yan, Z. Shu, and S. M. Sharkh, “Hybrid modelling and control of singlephase gridconnected NPC inverters,” in Proceedings of the IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 2223–2228, IEEE, Long Beach, CA, USA, 2016. View at: Publisher Site  Google Scholar
 J. Zeng, W. Qiao, C. Wei, and L. Qu, “A softswitched threeport singlestage inverter for photovoltaicbattery systems,” in Proceedings of the IEEE Energy Conversion Congress and Exposition, pp. 4568–4573, IEEE, Montreal, QC, Canada, 2015. View at: Publisher Site  Google Scholar
 X. Yan, Z. Shu, S. M. Sharkh, and T. Chen, “Outputfeedback switching control of DCDC cuk converters using multiple sampling,” in Proceedings of the International Automatic Control Conference (CACS), pp. 1–6, Yilan, Taiwan, 2015. View at: Publisher Site  Google Scholar
 J. Xiang, F. Ji, H. Nian, J. Zhang, and H. Deng, “Seamless transfer of singlephase utility interactive inverters with a synchronized output regulation strategy,” Journal of Power Electronics, vol. 16, no. 5, pp. 1821–1832, 2016. View at: Publisher Site  Google Scholar
 X. Wei, Y. Liu, Z. Zhang, and J. Wang, “Steadystate analysis of electric spring for smart grid,” in Proceedings of the 12th World Congress on Intelligent Control and Automation (WCICA), pp. 905–909, Guilin, China, 2016. View at: Publisher Site  Google Scholar
 S. Wen, T. Huang, X. Yu, M. Z. Q. Chen, and Z. Zeng, “Slidingmode control of memristive chuas systems via the eventbased method,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 1, pp. 911–915, 2017. View at: Google Scholar
 C. Wei, W. Qiao, and Y. Zhao, “Slidingmode observerbased sensorless direct power control of DFIGs for wind power applications,” in Proceedings of the IEEE Power and Energy Society General Meeting, (PESGM), IEEE, Denver, CO, USA, 2015. View at: Google Scholar
 Y. Tang, H. Gao, and J. Kurths, “Distributed robust synchronization of dynamical networks with stochastic coupling,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 61, no. 5, pp. 1508–1519, 2014. View at: Publisher Site  Google Scholar  MathSciNet
 Y. Xue, D. Meng, S. Yin et al., “Vectorbased model predictive hysteresis current control for asynchronous motor,” IEEE Transactions on Industrial Electronics, 2018. View at: Publisher Site  Google Scholar
 K. T. Tan, P. L. So, Y. C. Chu, and M. Z. Q. Chen, “Coordinated control and energy management of distributed generation inverters in a microgrid,” IEEE Transactions on Power Delivery, vol. 28, no. 2, pp. 704–713, 2013. View at: Publisher Site  Google Scholar
 L. Zhang, M. Z. Chen, H. Su, and G. Chen, “Eventbased asynchronous communication and sampled control for synchronization of multiagent networks with input saturation,” International Journal of Robust and Nonlinear Control, vol. 28, no. 5, pp. 1871–1885, 2018. View at: Publisher Site  Google Scholar  MathSciNet
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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.