Power System Small-Signal Stability as Affected by Grid-Connected SmartPark

Large-scale smart charging stations can effectively satisfy and control the charging demands of tremendous plug-in electric vehicles (PEVs). But, simultaneously, their penetrations inevitably induce new challenges to the operation of power systems. In this chapter, damping torque analysis (DTA) was employed to examine the effects of the integration of smart charging station on the dynamic stability of the transmission system. A single-machine infinite-bus power system with a smart charging station that denoted the equivalent of several ones was used for analysis. The results obtained from DTA reveal that in view of the damping ratio, the optimal charging capacity is better to be considered in the design of the smart charging station. Under the proposed charging capacity, the power system can achieve the best maintained dynamic stability, and the damping ratio can reach the crest value. Phase compensation method was utilized to design the stabilizer via the active and reactive power regulators of the smart charging station respectively. With the help of the stabilizers, damping of the system oscillation under certain operating conditions can be significantly improved, and the power oscillation in the tie-line can be suppressed more quickly.


Introduction
The growing concern of carbon dioxide emission, greenhouse effect, and rapid depletion of fossil energy drives the demand for the revolutionary changes in the automobile industry. Much effort has been put into developing a new highefficient, environment-friendly, and safe transportation vehicle that can replace the conventional ones. The utilization of plug-in electric vehicles (PEVs) as the most suitable solution has been promoted in many countries. China is expected to have 5 million electric vehicles (EVs) by 2020 according to its Development Plan for Energy-saving and Renewable Energy Vehicles. However, a prediction by State Grid Corporation of China (SGCC) illustrates that the number will be 5-10 million due to the fast development of EVs at present in China. As EV-related technologies have been making progress and many national and local incentives have been created for EV purchases, the total number of EVs is likely to be 30 million by 2030 [1][2][3].
the optimal charging capacity is better to be considered during the design of the smart charging station. In Section 4, the phase compensation method is utilized to design the stabilizer via the active power and reactive power (RP) regulators of the smart charging station, respectively. A single-machine infinite-bus power system integrated with a smart charging station is presented as an example in Section 5. Results of numerical computation, non-linear simulations, and eigenvalue calculations at different system operating conditions are given. These simulations and results demonstrate and confirm the presented theoretical analysis, and verify the effectiveness of the designed stabilizer. Another four-machine power system is employed to show that the conclusions obtained in the singlemachine power system are also available in the multi-machine power system. Conclusions are summarized in Section 6.

A linearized model of single-machine infinite-bus system with a smart charging station
The local electricity generation systems, besides supporting the regional loads, can be used to charge a smart charging station under usual conditions. Comparing with 1000-million-kilowatt capacity of outer power systems, the abundant active power generation with 10,000-kilowatt capacity in a regional system can be simplified as an equivalent synchronous machine. The inertia of the equivalent synchronous machine denotes the dynamic stability of the regional system. Because every individual smart charging station has the same dynamic behavior during the transient procedure, the smart charging stations can be regarded as an equivalent one with higher active power and reactive power capacities. A smart charging station usually is connected to the transmission system through a step-up transformer, which is seen as a reactance in this chapter.
In this chapter, the research focuses on the power oscillation which lasts for mostly 10-20 s. Uncertainties during EV charging such as the alternations of charging strategies or vehicle numbers have little effect on this analysis. EV charging demand or discharging supply during this dynamic procedure is considered as determinate power from the start time and following seconds. For a simple analysis, a constant power charging/discharging strategy is utilized to estimate the optimal EV charging numbers for smart charging station design. Figure 1 shows the configuration of a single-machine infinite-bus power system, where a smart charging station is connected at a busbar denoted by subscript s. The linearized models of network equations and synchronous machine are presented in [18,22,23]. Here, U s is the voltage at the high-voltage-level busbar where the smart charging station locates; U b and U c are the voltages at infinite busbar and the low-voltagelevel busbar connected with the smart charging station; I ts , I s , and I sb are the line currents as indicated in Figure 1; and X ts , X sb , and X s are line reactances as indicated in Figure 1.
The control strategy of smart charging stations is shown in Figure 2.
The objective control is to command the currents corresponding to the fast change in demanded active and reactive power. The equations of smart charging stations according to Figure 2 are obtained as: > > > > > > > : where P PEV and Q PEV are the demanded active and reactive power by the smart charging station and s are the proportional-integral controllers in the smart charging station.
Control strategy of a smart charging station.
While this chapter focuses on the analysis of the impact from the grid-connected smart charging station to the system small-signal stability, linearized processes and expressions for coefficients are not specifically listed.

Analysis of damping torque contribution from the Phillips-Heffron model
The Phillips-Heffron model of a smart charging station, which is based on the linearization of the system and describes the relationships between all variables, assessed to the single-machine infinite-busbar (SMIB) power system can be obtained as Figure 3, where the Phillips-Heffron model of SMIB only is referred to Refs. [22][23][24]. From Eqs. (2) and (3), the model of the smart charging station and its control strategy can be obtained as Figure 4.
From Figures 3 and 4, we have: Figure 3. Phillips-Heffron model of the single-machine infinite-busbar system with a smart charging station.
Figures 3 and 4 clearly show the dynamic interaction between the smart charging station and the conventional synchronous generator. Figure 3 is very similar to the conventional Phillips-Heffron model based on which the DTA was proposed and developed. It shows that the smart charging station interacts closely with the generator by contributing the electric torque to the electromechanical oscillation loop of the generator. The contribution of electric torque is comprised of two parts, viz. ΔT et-sp which relates to Δδ and directly affects the oscillation loop, and ΔT et-ex which relates to ΔE′ q and functions through the excitation system, as indicated in Figure 3. According to DTA, the electric torque can be decomposed into two components, viz. the synchronizing torque and the damping torque as shown in Eq. (7). The damping torque contributions ΔT dt-sp , ΔT dt-ex, and ΔT dt determine the influences on the damping of power system oscillation.
With certain output power of the synchronous machine and absorbed or injected power of the smart charging station, the bus voltages and currents of the corresponding operation condition can be determined. The damping torques ΔT dt-sp , ΔT dt-ex, and ΔT dt are dependent on the output power of the synchronous machine and the absorbed or injected power of the smart charging station.
From Eqs. (5)- (7), the conclusions can be summarized as follows: 1. The proportional controls K p in the smart charging station mainly induce the synchronous torque into the oscillation loop, while for ΔT et-sp in Eq. (5), only its real part is related to Δδ; and the majority of damping torque is introduced by integral controls K i /s, because 1/s induces the imaginary part in ΔT et-sp relating to Δω.
2. Because the signals ΔU dc and ΔU qc through path a and path b in Figure 3 are significantly attenuated by lag loops before they form one part of the damping torque through the excitation system [24], the damping torque contribution from them can be neglected for simplified analysis. ΔT dt-sp represents the main damping torque supplied by the smart charging station in damping torque analysis, and ΔT dt-ex mainly expresses the torque supplied by the excitation system of the synchronous machine.
3. In this chapter, the 'À' sign indicates the vehicles are selling power to the grid, that is, they are in discharging mode and the '+' sign indicates that they are buying power from the gird, denoting that the vehicles are in charging mode.
The optimal operation point when the system has the biggest damping torque can be calculated as: When the output power of the synchronous machine is fixed, the positive or negative damping torque supplied by the excitation system of the synchronous machine is only slightly changed. At the optimal operation point, the total damping torque ΔT dt of the system and ΔT dt-sp contributed from the smart charging station both reach their maximum values.
When the active power in the tie-line is fixed, the output power of the synchronous machine is changed corresponding to the absorbed or injected power of the smart charging station. Both damping torques contributed by the smart charging station and the excitation system need to be considered. The total damping torque ΔT dt of the system and ΔT dt-sp contributed from the smart charging station reach their maximum values at different operation points.

Design for the stabilizer attached to the smart charging station
Under the operation conditions that the total damping torques supplied by the smart charging station and the excitation system are not enough to suppress the oscillations, additional damping torques need to be added. Compared with the installation and coordinated parameter setting for power system stabilizers (PSSs) in synchronous machines, smart charging stations can be simply utilized to suppress the grid's active power oscillation with little infrastructure cost. Only a centralized stabilizer will be required at the smart charging station to maintain system stability.
The stabilizer added via the active power (AP) or reactive power (RP) control loop is shown in Figure 5.
The forward path function which describes the way from output signal of the stabilizer to the additional damping torque into the electromechanical oscillation loop can be obtained: where, F pssp or F pssq is corresponding to the utilized output signal of the stabilizer u pssp or u pssq .
K sp-U dc u pssp , K sp-U qc u pssp , K sp-U dc u pssq and K sp-U qc u pssq are obtained from the linearization of the control strategy with the output signals of the stabilizer considered.
The active power P b in the tie-line is chosen for the feedback signals of the stabilizers via the active power regulator and the reactive power regulator. From the linear system control theory, the active power P b can be written as a function of the rotor speed of the generator. where q and K E ′ q δ are related to the reconstruction of this feedback signal.
Considering Eqs. (9) and (10), the electric torques contributed by the stabilizer via active and reactive power regulators, respectively, are expressed as: where G PEVP (s) and G PEVQ (s) are the transfer function of the stabilizer via active and reactive power regulators respectively. The transfer function of the stabilizer is The stabilizers are designed to compensate the lagging or leading angle of the forward path, in order to supply maximum positive damping into the system. The phase compensation method is used to design the parameters of the stabilizers.

Case description
Two example cases are employed in this section. From Case A to Case D, a single-machine infinite-busbar power system is used. The parameters of the system are given in Appendix A.1. Under different capacities of the smart charging station, computational results of the damping torque contribution from the smart charging station and the excitation system to the electromechanical oscillation loop of the single synchronous generator are obtained and confirmed by the eigenvalue of the system's oscillation mode. The critical point in which the system has the biggest damping torque is highlighted. In Case E, a four-machine power system is presented. The parameters are given in Appendix A.2. The eigenvalue related to the inter-area oscillation mode is concerned under different capacities of the smart charging station.  Table 1, when only P control is utilized in the smart charging station. From Table 1, it can be concluded that: 1. The total damping torque contribution ΔT dt is approximately equal to the damping torque from the excitation system ΔT dt-ex . The change of ΔT dt is mainly induced by ΔT dt-ex which is the impact from the excitation system of the synchronous machine under different output power. The smart charging station only with the proportional control functions as an adjustable load in charging mode or as a regulator generator in discharging mode.

Case
2. Integral control in the smart charging station not only helps to reduce the steady-state error and accelerate the smart charging station to the steady operation point, but also supplies either positive or negative damping torque into the system. It demonstrates conclusion (1) obtained in Section 3.

Case B: utilizing PI control in the smart charging station and fixing output power of the synchronous machine
A comparison of the damping torques is made under different charging or discharging power capacities of the smart charging station with the fixed output power of the synchronous machine. The computational results of the example system are shown in Table 2, when active power supplied by the synchronous machine is fixed at 10 MW. From Table 2, it can be concluded that: 1. While the output of the synchronous machine is constant, the damping torque from the excitation system of the synchronous machine is nearly unchanged. The signals ΔU dc and ΔU qc through path a and path b only contribute slight changes to ΔT dt-ex . The variety of total damping torque contribution ΔT dt is mainly induced from ΔT dt-sp which comes from the smart charging station and directly affects the oscillation loop. It demonstrates conclusion (2) obtained in Section 3.
2. The damping torque from the smart charging station changes at its different charging or discharging capacity, which is either positive or negative. The smart charging station can help to improve the damping with certain charging capacity which is between the lower and upper threshold. In charging mode, the smart charging station is preferred to operate around 10 MW which is nearly the same as 10 Table 2. Computational results of the example system when active power supplied by the synchronous machine is fixed at 10 MW.
torque and damping torque from the smart charging station coincided at the same point. It demonstrates conclusion (3) obtained in Section 3. Under this operation point, the smart charging station just consumes the electricity generated by the equivalent synchronous machine. There is no active power exchange in the tie-line. Beyond or below this point, the damping ratio of the system will decrease because of the increased load burden in the tie-line either from the synchronous machine to the infinite bus or vice versa. Considering each vehicle can draw AE3.5 kW of active power [25] and always around 60% personal vehicles in the parking lots need to be charged [26], roughly 5000 personal vehicles are optimal to be accepted in this equivalent smart charging station.
3. During the discharging process, the damping of the system tends to deteriorate with the increasing power injected from the smart charging station to grid.  Table 3.
From Table 3, it can be concluded that: 1. The total damping torque contribution ΔT dt is simultaneously influenced by ΔT dt-sp which relates to Δδ and directly affects the oscillation loop, and ΔT dt-ex which relates to ΔE′ q and functions through the excitation system.
2. The damping torque supplied from the smart charging station and the excitation system of the synchronous machine respectively is complementary during the charging process. Compared with Table 1, the positive damping torque supplied by the smart charging station helps the system to improve the low damping capacity from 5 to 15 MW in charging mode of the smart charging station. This conclusion can be confirmed by the analysis from Eqs. (5) and (6). When the charging power of the smart charging station is between 0 and 30 MW, the product of ΔT dt-sp and ΔT dt-ex is negative.  Table 3. Computational results of the example system when load-flow in the tie-line is fixed at 10 MW.
3. The impact of the damping torque from the synchronous machine also needs to be considered. With this impact, the highest total damping torque and damping torque from the smart charging station are obtained at different points. In this case, the optimized operation point reaches 25 MW which is nearly the same as 24.6 MW calculated by Eq. (8). It demonstrates conclusion (3) in Section 3. Under the operating conditions that the absorbed power of the smart charging station varies from 20 to 25 MW, although the smart charging station supplies the negative damping torque into the grid, the total damping torque is still positive and keeps increasing with the compensation of the damping torque from the excitation system. The smart charging station at the optimal operation point is also charged by the electricity generated by the equivalent local synchronous machine.
4.The damping of the system tends to deteriorate with the increasing power injected from the smart charging station to the grid during the discharging process.

Case D: stabilizer design
While the operation condition for the smart charging station varies stochastically, the stabilizer is designed and attached to the smart charging station to supply additional damping torques into the system.
The stabilizer via the active and reactive power loops is designed respectively under the condition that the equivalent synchronous machine supplies 20 MW and the smart charging station consumes 10 MW of active power. A three-phase shortcircuit fault happens in Bus s at 0.5 s and lasts for 0.1 s.
The forward path is: The parameters of the designed stabilizer attached to active and reactive power regulators, respectively, are ( Table 4).
With the designed stabilizer, the eigenvalue of the system with the smart charging station can be obtained as that, the effectiveness of the designed stabilizers is verified by the time-domain simulation in Figure 6 and eigenvalue calculation in Table 5. From Table 5 and Figure 6, it can be seen that the designed stabilizer attached to the smart charging station can not only help to reduce the power fluctuations for PEV charging, but also suppress the power oscillation in the tie-line.

Case E: analysis in the four-machine power system
The power system integrated with the smart charging station is shown in  oscillation frequency f critical and its corresponding attenuation factor α critical are extracted. The eigenvalue of the critical oscillation mode is λ critical = α critical + j2πf critical .
With the load-flow in the tie-line L 6-7 fixed at 70 MW, a comparison is done between the proportional controlled smart charging station and the adjustable load/ generator connected at Bus 7, respectively. The eigenvalue related to the inter-area oscillation mode is a concern. From Table 6, only the proportional controlled smart charging station functions as the adjustable load during charging period and as the regulable generator in discharging mode in view of the damping ratio.
Proportional control of the smart charging station only supplies the synchronous torque and integral control that introduces the damping torque into the grid. With the stabilizer via active power regulator À0.759 0 + j10.816 9 With the stabilizer via reactive power regulator À0.651 1 + j10.847 1 Table 5.  Conclusion (1) obtained in the single-machine infinite-busbar power system is also available in the multi-machine power system. Both proportional and integral controls are utilized in the smart charging station. A comparison is done under different charging or discharging power capacities of the smart charging station when the load-flow in the tie-line is fixed at 70 MW. The eigenvalue related to the inter-area oscillation mode is concerned. The results are shown in Table 7.
From Table 7, the optimal charging point with the highest damping ratio in the single-machine power system can be obtained by Eq. (8) and verified by the damping torque calculation; and it also exists in the multi-machine power system. But, because of the complex interconnection of the synchronous machines and the   Table 7.
Comparison of eigenvalue related to the inter-area oscillation mode utilizing PI control of the smart charging station.
smart charging station, it is difficult to calculate the optimal charging point in theory (Figure 8).

Conclusion
The chapter investigates the impacts of a grid-connected smart charging station on power system's small-signal stability based on a simple single-machine infinitebus power system integrated with a smart charging station. Damping torque analysis (DTA) is employed to examine the contribution from the smart charging station to the electromechanical oscillation loop of the generator in theoretical analysis. The analysis has concluded that, the smart charging station affects power system's smallsignal stability in light of its interaction with the synchronous machine. The proportional controls in the smart charging station mainly induce the synchronous torque into the oscillation loop and the majority of damping torque is introduced by integral controls. The damping torque supplied by the smart charging station is mainly directly induced into the oscillation loop, and the damping torque from the excitation system is almost from the synchronous machine itself. The optimal operation condition of the smart charging station is the moment when the system has the highest damping ratio. In this chapter, such an optimal operation condition is defined, indicating that the optimal charging capacity is considered for smart charging station design.
Results of the damping torque computation of a single-machine power system integrated with a smart charging station, confirmed by eigenvalue calculations of system oscillation mode, are presented in the chapter. The conclusions obtained from the theoretical analysis are demonstrated and verified by these results. Under the optimal operation condition, the total damping torque supplied from the smart charging station and synchronous machine reaches its maximum value. During the discharging process, the damping of the system tends to deteriorate with the increasing power injected from the smart charging station to the grid. Another fourmachine power system is employed to manifest that the conclusions obtained in the single-machine power system are also available in the multi-machine power system.
The stabilizer is designed and attached to the active or reactive power regulator of the smart charging station to supply additional positive damping into the system. The phase compensation method is used here. The effectiveness is confirmed by the Comparison of damping ratio related to inter-area oscillation mode utilizing the P and PI control of the smart charging station, respectively.

Author details
Cai Hui State Grid Jiangsu Economic Research Institute, Nanjing, P.R. China *Address all correspondence to: caihui300@hotmail.com © 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.