Small Signal Modeling and Networked Control of a PHEV Charging Facility

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1 Small Signal Modeling and Networked ontrol of a PHEV harging Facility uis Herrera, Ernesto Inoa, Feng Guo, Hanning Tang, and Jin Wang Department of Electrical and omputer Engineering The Ohio State University olumbus, OH herrera.46@osu.edu Abstract The introduction of communication systems to power system controllers have brought in another layer of complexity in their design and operation. In this paper a Plugin Hybrid Electric Vehicle (PHEV) charging facility is studied. A linearized model of the facility is built including both the dc/dc and dc/ac converters of the Distributed Energy Resources (DER). In addition, a control strategy that includes both local and networked loops is proposed to monitor and control the dc bus voltage of a ocal Energy Storage (ES) unit. This dc bus voltage is crucial to the self-sustaining capabilities of the system. Impacts of different communication factors to the system stability are analyzed. astly, the small signal model, control strategy, and stability analysis are verified with real time simulations. I. INTRODUTION With the need to supply clean, renewable energies, integrations of Distributed Energy Resources (DERs) into Plugin Hybrid Electric Vehicle (PHEV) charging facilities are expected. One key aspect of this integration is the introduction of communication systems to multiple power units in the facility, including both sources and loads. This presents both opportunities and challenges in the control and optimization strategies to provide highest efficiency and ancillary services such as frequency and voltage regulation, VAR compensation, etc. [1]. In a typical charging facility, charging stations need to be equipped with local controllers and communication systems. For example, it is necessary for the charging facility to know the state of the grid in terms of demand, pricing, and health status in order to better estimate optimal charging schedules. In [2], an overview of different communication methods applicable to PHEV charging stations such as Power ine arriers (P), IEEE (Zigbee), ZWave, and cellular networks were summarized and compared. While in [3], a Zigbee based platform for testing optimization parameters in a PHEV charging station was proposed. The reliability of the charging facility can be considered to depend on two modes of operation: grid connected and islanded. Several papers have addressed optimal strategies and the stability of microgrids by studying the small signal model of the system. In these papers, inverter based models of microgrids have been constructed assuming the dc and This work is supported by U.S DOE Graduate Automotive Technology Education (GATE) enter of Excellence, DE FG26 5NT42616 ac voltage sources are ideal [4], [5]. For instance, in [5], a systematic approach for small signal stability analysis of an inverter based microgrid with simplified dc input was proposed and verified. However, to boost voltage and increase system level efficiency, a boost converter is often added between the dc source and the dc/ac inverter. In addition, depending on the control strategy of the dc/dc and dc/ac converters, the simplification of the dc side cannot be applied to all cases. Furthermore, the introduction of communication as an integral part of a controller is known as a Networked ontrol System (NS) [11]. In this case, a stability analysis needs to be performed under different communication factors such as delay, packet losses, etc. In [6], the authors have studied the operation of parallel dc/dc converters using wireless signals to transmit sensor data. In [7], a NS for wide area power systems was designed and simulated. In this paper, an instance of networked control of a PHEV charging facility is developed and analyzed. In Section II, the small signal model of the charging facility, including multiple DER with two stge (dc/dc cascaded by dc/ac) power inverters is built. Utilizing this linearized model, an approach of applying NS to the charging facility is proposed in Section III. The model and stability analysis are then verified using real time simulations in Section IV. The conclusion and a summary of future work are presented in Section V. Figure 1. Topology of the charging facility. II. MODEING OF THE HARGING FAIITY The PHEV charging facility discussed in this paper has two integrated DER units: a ocal Energy Storage (ES) and a Photovoltaic (PV) plant. The structure of this facility is shown /12/$ IEEE 3411

2 in Fig. 1. As a starting point, the modeling and analysis of an islanded charging facility is presented in this paper. this system one extra state variable is needed: ξ 1P = ĩ, (5) and the duty cycle becomes: d i = ĩ kp + ξ 1P ki. (6) Figure 2. ES and PV dc/dc converter. (a) ES dc/dc controller. (b) PV dc/dc controller. Figure 3. Dc/dc closed loop controllers for ES and PV respectively. A. Dc-dc converter Although the dc/dc converter of both the ES and PV is a bi-directional boost converter as shown in Fig. 2, the control strategy of these two converters is quite different. For the ES, it is desired that the output of the boost converter to be a constant voltage, while for the PV, the boost converter is controlled to achieve a desired input current to realize Maximum Power Point Tracking (MPPT). Fig. 3 shows the control diagrams of the dc/dc converters for ES and PV plant. State space averaging is used in order to model the open loop boost converter [8]. The average differential equations are given by The closed loop state variables for the PV converter are x = [ĩ, ṽ, ξ 1P ] T. As an example, the linearized equations for the ES boost converter can be written as d ĩ ṽ ξ 1 ξ 2 = R l R md 1 (1 D ) (1 D ) 1 R 1 1 kp v ki v + Ṽ dc + V c I Rm I ĩ ṽ ξ 1 ξ 2 d, (7) and by plugging (4) into (7) one obtains the closed loop system. The small signal models of both ES and PV converters were verified by performing a circuit simulation to compare against the linearized model. For example, the validation of the ES boost converter is shown in Fig. 4 where a disturbance in Ṽdc was introduced. ẋ = (da on + (1 d)a off ) x + (db on + (1 d)b off ) V dc ẋ = f(x, d, V dc ). (1) The system is then linearized around an operating point := {{X }, D, Vdc } by defining a new variable x := x x x = f x + f d + f x d dc, (2) Ṽ V dc where the state variables are the inductor current and the capacitor voltage x = [ĩ, ṽ ] T. 1) ES dc/dc controller: In order to write the linearized closed loop system, the Proportional and Integral (PI) controllers for the ES converter can be represented by adding two state variables to the system ξ 1 = ṽ ξ 2 = kp v ṽ + ki v ξ 1 ĩ. (3) Thus, the closed loop state variables are x cl = [ĩ, ṽ c, ξ 1, ξ 2 ] T and the input is d = ( kp v ṽ + ki v ξ 1 ĩ )kp i + ξ 2 ki i. (4) 2) PV dc/dc controller: The same idea is used to derive the linearized equations for the PV boost converter. However, in Figure 4. Verification of the linearized ES boost converter. Although the equations presented in this subsection assume that there is a resistor at the load side of the boost converter, this resistor can replaced by a current source in order to interconnect the dc/dc and dc/ac converters. The new equation for the capacitor voltage ṽ can be derived as: ṽ = (1 D ) where ĩ o is the new input current. B. Dc-ac inverter i 1 ĩo I d, (8) A typical three phase inverter is shown in Fig. 5. The modeling of the dc/ac inverter involves the analysis of the 3412

3 R low pass filter, the coupling inductance, line resistance, and the controllers. Prior to deriving the differential equations 1) ES dc/ac controller: In order to model the closed loop converter for the ES, three additional state variables are introduced to account for the integrals in the controller ξ 1 = ṽ fd ξ 2 = ṽ fd kp v + ξ 1 ki v ĩ d ξ 3 = ĩ q. (12) Figure 5. Dc/ac inverter used in the charging facility. for the open loop inverter, the power invariant abc to transformation is used to simplify the analysis. The nonlinear differential equations for the inverter are then given as follows: di d = R f i d + ω n i q 1 v fd + 1 d d v f f f di q = ω ni d R f i q 1 v fq + 1 d q v f f f dv fd dv fq di cd di cq = 1 f i d + ω n v fq 1 f i cd = 1 f i q ω n v fd 1 f i cq = 1 c v fd R c c i cd + ω n i cq 1 c v gd = 1 c v fq ω n i cd R c c i cq 1 c v gq, (9) where ω n is the nominal fundamental frequency of the inverters. To simplify notation, we can refer to the previous set of equations in the following form: ẋ = f(x, d, v, v g ), (1) where the vector x = [i d, i q, v fd, v fq, i cd, i cq ] T, d = [d d, d q ] T and v g = [v gd, v gq ] T. The linearized { system around an operating point given by := {X }, {D }, V, {V g } } can be written as x = f x x + f d d + f v ṽ + f v g g. (11) ṽ The controllers for the ES and PV inverters have different goals. Since the ES inverter is assumed to have a constant dc input voltage, the control goal is to maintain a constant ac bus voltage, while for the PV system, the aim of the controller is to maintain a constant dc bus voltage, inject active power and provide reactive power compensation. These two controllers are shown in Figs. 6 and 7. Figure 6. ES dc/ac controller. Based on these new variables, the modulation factors in both the d and q axes can be derived as d d = ( ṽ fd kp v + ξ 1 ki v ĩ d )kp i + ξ 2 ki i ṽ fd ĩ q ω n f d q = ĩ q kp q + ξ 3 ki q + ĩ d ω n f. (13) 2) PV dc/ac controller: It is important to note that in the control system for the PV, the boost converter is operating as a current source and the inverter is maintaining a constant dc bus voltage. Therefore, the dc/dc side of the PV plays a very important role and should not be ignored. Figure 7. PV dc/ac controller. The controller shown in Fig. 7 can be modeled by introducing the following three state variables and the modulation factors are ξ 1P = ṽ ξ 2P = ṽ kp v + ξ 1P ki v ĩ d ξ 3P = ĩ q, (14) d d = (ṽ kp v + ξ 1P ki v ĩ d )kp i + ξ 2P ki i ṽ fd ĩ q ω n f d q = ĩ q kp q + ξ 3P ki q + ĩ d ω n f. (15) The closed loop system for each inverter, ES and PV, is built in a similar way as the dc/dc converters shown in the previous sub-section.. oads and connections In order to link the small signal models of the dc/dc converter and dc/ac inverter together, the relationship between the voltages and currents of the two circuit stages can be written as [9] v id = v d d (16) v iq = v d q (17) i o = i d d d + i q d q. (18) Although (16) and (17) were already taken into account in (1), (18) can be connected to the dc/dc converters by 3413

4 linearizing ĩ o = I d d d + I q d q + ĩ d D d + ĩ q D q (19) and linking (19) to (8). Since the inverters are modeled on a rotating reference frame, the ES inverter is chosen as reference. In this case, the PV inverter outuput current variables have to be rotated to the ES reference frame if there is an angle θ difference between the two [1] ( ) cos(θ) sin(θ) T s :=. (2) sin(θ) cos(θ) Similarly, any input states to the PV system have to be translated to the PV s rotating angle by using Ts 1. In order to have a well defined voltage value v g shown in Fig. 5, [5] explains the addition of a virtual resistance, r N, in both the d and q axes. In the case of the charging facility shown in Fig. 1, this resistance corresponds to the critical loads. The PHEV batteries along with their chargers are modeled as R loads. The interconnection voltage is then written as (ĩ ṽ gd = r N d + ĩ P ) D ĩ Batd ṽ gq = r N (ĩ q + ĩ P Q ĩ Batq ), (21) where stands for ES, P for PV, and the capital letter D and Q assumes the currents have been transformed using (2) to the proper reference frame. The complete large scale state space system is then in the following form: x dc x ac x Pdc x Pac x Bat A ES dc Bi ES o x dc Bv ES A ES dc/ac Bi P B B i x ac = A PV dc Bi PV o x Pdc Bi P Bv PV A PV dc/ac BB P i x Pac Bi B Bi P B A Bat x Bat B V dc Bî Ṽdc ES + B V P dc Ṽ PV dc, (22) BîP Î BîB where Î is an intentional disturbance added to the system at the load side used to represent PHEV battery connections and validate the small signal model. Fig. 8 shows the verification of the linearized model by comparing the analysis results with a circuit simulation of the charging facility in Matlab Simulink. The main parameters of the simulation are shown in Table I. TABE I. SIMUATION PARAMETERS PV V dcmppt 437 V PV i MPPT 7.6 A ES, PV v 8 V Ac Bus V gd 24 V rms ES V dc 212 V ritical oad r N 1 Ω oad Dist. Îd A Fund. Frequency 6 Hz (a) (b) Figure 8. Small signal model validation based on circuit simulation. III. NETWORKED ONTRO OF THE HARGING FAIITY For the charging facility presented in section II, there are several reasons for the involvement of communication networks: ontrol the power output based on the status of the batteries (So, T, etc.). During grid connected mode, decide the best charging times based on a price signal from the grid. Monitor power output of the ES system for power balancing between the DERs and PHEVs. Therefore, networked control can be used to determine how communication parameters such as latency and packet losses impact the operation of the charging facility. A. Proposed ontroller In this paper, a control strategy for power balance is proposed based on monitoring the output voltage of the ES boost converter, v. This dc bus voltage is an indication of the power handling capacity of the charging facility. It is assumed that the PV is supplying maximum power at any given time; therefore, the rest of the active loads will be supplied by the ES. If v cannot be maintained to a desired value, there is more active power demanded than supplied by the ES and PV. This voltage can be used in deciding whether vehicles should be connected or disconnected, or reduce their charging 3414

5 power. The system diagram with communication is shown in Fig. 9. Figure 9. harging facilitiy including communication infrastructure. In this charging facility, the networked controllers are envisioned to be composed of local and remote control units. Fig. 1 shows a diagram of the proposed controller where the inner loop controls the current and the outer loop incorporates a communication link to monitor and control the v voltage. In addition, τ sc and τ ca represent the sensor-to-controller and controller-to-actuator delays respectively. Figure 1. Proposed controller to monitor and control v. B. NS Modeling Two of the main concerns in NS are the communication delay and packet losses. As a start point, this paper focuses on studying the impact of the communication delay in the controller shown in Fig. 1 to the entire system. In [11], a straightforward approach to model this delay was illustrated based on the assumption that the total delay τ := τ sc + τ ca is bounded and of the following form: τ = lt s mt s, (23) where l N, m (, 1) and fixed network sampling time T s R >. The entire system is modeled as in (22), with the exception that i is left for feedback in the ES dc/dc converter: d = i k p ĩ k p. (24) Therefore, (22) is modified to include the inner control loop shown in Fig. 1, and the new input to the ES boost converter becomes i. The new linearized model for the charging facility is then written as x = A x + b i i + Bµ, (25) where µ = [Ṽ dc, Ṽ dc P, Î ] T and B are the same disturbances and matrix as in (22). For simplicity, we assume that there are no external disturbances, i.e. µ. The solution to (25) is of the following form: x(t) = e A(t t) x(t ) + t t e A(t η) b i i (η)dη. (26) et t := kt s, t := (k + 1)T s, and η := β + kt s to discretize the solution: x ((k + 1)T s ) = e ATs x(kt s ) + Ts e A(Ts β) b i i (β + kt s )dβ. (27) Assuming that the l = 1 then the delay is bounded within one time step, τ = (1 m)t s, and as such, we can separate the integral in (27) into two parts: one for the previous input i ((k 1)T s) and the other one for the current input i (kt s): x ((k + 1)T s ) = e ATs x(kt s ) + Φ 1 i ((k 1)T s ) + Φ 2 i (kt s ), (28) where Φ 1 := pt s e A(Ts β) dβ b i, Φ 2 := T s pt s e A(Ts β) dβ b i and p := (1 m). Using a controller of the form i (k) = K N x(k), we can obtain the closed loop system: ( ) ( ) ( ) x(k + 1) e AT s Φ 2 K N Φ 1 x(k) i (k) =. (29) K N i (k 1). Stability Analysis In this subsection, the stability of the charging facility with respect to network sampling time and delay is studied. In general, we can deduce that the linearized model of the charging facility is ocally Exponentially Stable about the operating point x if the state matrix denoted by A cl in (29) is Hurwitz, i.e. λ < 1, λ σ(a cl ). Using a network sampling time of T s = 1 ms, the stability regions for which the PHEV charging facility is ocally Exponentially Stable based on the networked control parameter and delay is shown in Fig. 11. Figure 11. ocal stability regions based on a network sampling time and outer proportional constant K of controller in Fig. 1. IV. REA TIME SIMUATION BASED VERIFIATION In order to verify the stability analysis, a Real Time (RT) simulation of the charging facility with networked control was carried out. The RT simulation platform is shown in Fig. 3415

6 (a) Ts = 1 ms, τ = 2 ms, kpv = 1.5. (b) Ts = 1 ms, τ = 7 ms, kpv = 2. Figure 12. Real Time simulation results for stable and unstable NS during load change. 13. The simulation of the electrical system of the charging facility was realized using Opal-RT [12] RT targets, while the communication network was built using OPNET s Systemin-the-oop (SIT) package [13][14]. These two simulators are linked through Ethernet links. In OPNET, the sensor and actuator of the NS are separated by different IP addresses and routed through the communication network to obtain the desired total delay τ. Figure 13. Real Time Simulation setup. The real-time simulation results are shown in Fig. 12. Fig. 12a corresponds to the point in Fig. 11 located in the stable region. The yellow trace represents a load change disturbance added to the system to verify the local stability properties. The other signals correspond to actual voltages and currents in the facility. In Fig. 12b, the unstable region of the system was simulated where it can be seen clearly that the RT simulation is also unstable. Several other points from Fig. 11 were also confirmed with RT simulations. V. ONUSION In this paper, the small signal analysis and proposed NS of a PHEV charging facility were presented. It can be concluded that in NS, the delay is crucial to the operation of the facility. Based on a network sampling time of Ts = 1 ms, boundaries of operation based on delay and control parameters were validated using real time simulations. This work represents a starting point in the analysis of NS applied to DER based PHEV charging facilities. In the future, more in-depth analysis of sophisticated control schemes for charging facilities involving Multiple Input Multiple Output (MIMO) NS as well as optimal control will be analyzed following a similar approach as the one presented in this paper. R EFERENES [1] J. Tomic and W. Kempton, Using fleets of electric-drive vehicles for grid support, Journal of Power Sources, Vol. 168, No, 2, pp , June 27. [2] T. Markel, M. Kuss, and P. Denholm, ommunication and control of electric drive vehicles supporting renewables, in IEEE Proc. Vehicle Power and Propulsion onference, 29, pp [3] P. Kulshrestha, K. Swaminathan, M. how, and S. ukic, Evaluation of ZigBee communication platform for controlling the charging of PHEVs at a municipal parking deck, in IEEE Proc. Vehicle Power and Propulsion onference, 29, pp [4] F. Katiraei, M. Iravani, and P. ehn, Small-signal dynamic model of a micro-grid including conventional and electronically interfaced distributed resources, IET Gener. Transm. Distribution, Vol. 1, No. 3, pp , May 27. [5] N. Pogaku, M. Prodanovic, and T. Green, Modeling, analysis and testing of autonomous operation of an inverter-based microgrid, IEEE Trans. On Power Electronics, Vol. 22, No. 2, pp , March 27. [6] S. Mazumder, M. Tahir, and S. Kamisetty, Wireless PWM control of a parallel dc-dc buck converter, IEEE Trans. On Power Electronics, Vol. 2, No. 6, pp , November 25. [7] S. Wang, X. Meng, and T. hen, Wide-area control of power systems through delayed network communications, IEEE Trans. On ontrol Systems Technology, Vol. PP, No. 99, pp. 1-9, March 211. [8] R. D. Middlebrook and S. uk, A general unified approach to modelling switching-converter power stages, in 1976 IEEE Power Electronics Specialist onference, 1976, pp [9]. Rim, D. Hu, and G. ho, Transformers as equivalent circuits for switches: general proofs and d-q analyses, IEEE Trans. On Industry Applications, Vol. 26, No. 4, pp , July/August 199. [1] J. Undrill, Dynamic stability calculations for an arbitrary number of interconnected synchronous machines, IEEE Trans. On Power Apparatus and Systems, Vol. PAS-87, No. 3, pp , March [11] M. Branicky, S. Phillips, and W. Zhang, Stability of networked control systems: explicit analysis of delay, in Proc. Of the 2 American ontrol onference, 2, pp [12] Opal-RT Technologies [online]. Available: [13] OPNET [online], 211. Available: [14] F. Guo,. Herrera, R. Murawski, E. Inoa, P. Beauchamp, E. Ekici, and J. Wang, omprehensive real time simulations of smart grid, IEEE Industry Applications Mag., accepted in Dec