Plug-in HEV Charging for Maximum Impact of Wind Energy on Reduction of CO 2 Emissions in Propulsion

Transcription

1 Plug-in HEV Charging for Maximum Impact of Wind Energy on Reduction of Emissions in Propulsion Rakesh Patil, Jarod Kelly, Hosam Fathy, Zoran Filipi Abstract This paper studies the reduction in resulting from synergistic interaction of PHEVs with an electric grid containing significant amount of wind power. A combined optimal charging and optimal power management approach is used to rigorously quantify the optimal reduction impact. This approach produces results that show that inclusion of any amount of wind power on the grid results in reduced from transportation. The results also account for the temporal variation in wind power. Furthermore, since it is not practical to implement a different control strategy for days with different amounts of wind, we quantify the loss of optimality resulting from this variability in wind. T I. INTRODUCTION HIS paper investigates the reduction in total emissions resulting from PHEV charging on the grid with significant wind penetration. We use a rigorous optimal control framework to quantify this reduction from transportation. Recent forecasts suggest that the electric grid will include a significant amount of renewable power sources [1]. A PHEV is considered a key enabler in clean transportation through charging from a cleaner grid. Studies suggest significant reduction of emissions resulting from a grid with higher penetration of renewable resources [2, 3]. In this paper we analyze in detail the emissions impact of using PHEVs with a cleaner grid. There is an obvious emissions benefit of charging a PHEV from a grid with more renewable sources and using this energy for transportation. However there are two major challenges to be addressed. First, the intermittency of renewable sources will require more storage and regulation on the grid. Using PHEV batteries for storage and regulation has been previously studied [4, 5, 6,7]. Secondly, achieving maximum synergy requires optimized charging and driving of a PHEV considering total emissions [5, 6]. In this paper we will address the second challenge by using a global optimal control approach for fair comparison of cases rather than simplistic approaches in preliminary studies [5]. There is significant amount of research on optimal PHEV charging and its on-road power management, but the problems are typically considered separately. Optimal charging refers to the problem of finding a State-of-Charge This work was supported in part by the U.S. NSF under Grant # Rakesh Patil and Zoran Filipi are with the Department of Mechanical Engineering, University of Michigan, Ann Arbor,MI 4819 USA ( rakeshmp@umich.edu; filipi@umich.edu). Hosam Fathy is with the Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 1682, USA ( hkf2@psu.edu). (SOC) trajectory that minimizes some environmental or economic objective for a given PHEV. The goal is typically to minimize the cost of electricity consumed by the PHEV, minimize emissions, or provide V2G services [8, 9]. Optimal power management refers to the problem of delivering power to a PHEV s wheels in the most effective manner. Objectives in power management are minimization of gasoline consumption and dollar costs associated with a given trip [1, 11]. Current studies on optimal charging and optimal power management typically assume or require the PHEV battery to be full at the onset of a given driving. Our work relaxes this assumption to enable a full exploration of tradeoffs and synergies between these two problems. The proposed approach of considering the two major PHEV operations (charging on the grid and driving on the road) in a single framework has the following advantages. The solution considers the inter-dependence between the optimal charging and optimal power management problems, thereby providing a "combined optimal". This approach also allows us to explore the impact that PHEV activity on the grid has on its energy management for propulsion. For example, this approach accounts for the grid during PHEV charging and uses that information to decide whether to use gasoline or electricity during driving. Equivalently, the power generation mix in the grid will affect the optimum blending of electric energy and gasoline during driving. Previous studies regarding grid integration of PHEVs assume PHEV population numbers and complete control over all PHEV batteries when not being used on the road [4, 7]. These studies are extremely relevant to understand the total load and controllability aspects of the load. However, our studies focus on a single PHEV's 24 hour charging opportunities. In other words, this study focuses on the optimal control strategies that should be implemented in a PHEV, or to be followed by a consumer, for that individual PHEV owner to have the least impact. Deterministic Dynamic Programming (DDP) is used to obtain optimal control solutions in this paper. This reasons for this choice of optimal control algorithms are twofold. First, this approach provides a globally optimal solution. Second, the output of this process is a supervisory control trajectory that can be used to gain important physical insights. We do not use a stochastic approach as the resulting trajectory would be optimal only in an average sense. However, we recognize that there is significant differences in daily wind patterns. For this purpose, we compare our deterministic daily optimal solutions to that of a 'yearly average' solution, and analyze the differences.

2 The contributions of this paper are - 1) application of a Deterministic Dynamic Programming (DDP) based framework for the combined optimal control problem of charging and power management. 2) Quantification of reduction depending on wind penetration on the grid through PHEV propulsion. The major challenges in this work are the integration of two problems with different dynamics and time scales into a single optimal control framework, and the computational time required to obtain solutions. Next, we briefly discuss the models and the optimal control framework used in the study. Particular importance is given to the wind power data used to obtain the results. Section III describes the framework which obtain a combined optimal charging and optimal power management solution. Finally, the results present the impact of wind penetration on reduction in production for PHEVs. II. MODEL REPRESENTATION The optimal control problem is solved to obtain optimal trajectories of the states and inputs related to PHEV charging and on-road power management. In this section, we briefly present the PHEV powertrain model and the electric grid dispatch model. Finally, wind power traces and the corresponding traces for which the optimal control solutions are calculated are presented. A. PHEV powertrain A series hybrid electric powertrain model is considered for this study. It is schematically shown in Fig. 1 and the component sizes are listed in Table I. The dashed lines in Fig. 1 indicate electrical connections and the solid lines indicate mechanical connections. The power electronics are a parallel bus which splits the electric current between the generator, battery and the motor. Power Electronics Engine Generator Battery Motor Final Drive and Wheels Fig. 1. Series hybrid powertrain model The Engine, Generator and the Motor are modeled using static maps obtained from the Powertrain System Analysis Toolkit (PSAT). These maps provide the efficiency of each component as a function of the component s operating speed and torque. The maps for battery voltage and internal resistance are based on the Li-ion battery chemistry and are also obtained from PSAT. Equations governing the powertrain model dynamics are represented as nonlinear ODEs. This powertrain model has 2 states: engine speed (ω e ) and battery state-of-charge (SOC), i.e. x = {ω e, SOC} is the state variable whose optimal trajectory will be obtained. The two inputs used to control the model are the fuel flow rate to the engine ( ) and the torque demand from the generator (τ g ) i.e. u = {, τ g }. System equations are not presented here to keep this section brief but the model is presented in detail in [1]. Component TABLE I COMPONENT SPECIFICATIONS OF THE POWERTRAIN Specification Engine Based on MY4 Prius 1.5 L gasoline, 57 kw, 11 Nm max torque at 4 RPM. Generator Permanent magnet. 4 Nm max torque, 58kW peak power Battery Li-ion, 7.35Ah 75 cell SAFT model scaled by current capacity to 13.3 kwh total energy Motor Permanent magnet. 715 Nm max torque, 13 kw peak power Final Drive Ratio = 3.7 Resistance f = 88.6 N, f 1 =.14 N-s/m, f 2 =.36 N-s 2 /m 2 Coefficients The powertrain model has constraints related to the ratings of the components and to the power flow between the components. For example, the battery has limits on its charging and discharging power available, depending on its SOC and its capacity. In addition, there are physical constraints on the states and inputs denoted respectively by the sets Z and U below. e,min e e,max Z SOCmin SOC SOC m f m f,max ( e) U g g,max ( g ) max (1. a-b) The chosen engine model has a maximum speed rating of 45 RPM. The SOC is restricted to be within.9 and.3 at all times. The engine fueling rate ( ) has a maximum value which varies with engine speed and the maximum generator torque output is also a function of its speed. These constraints are different from that during charging, as there are only constraints on battery operation during charging. B. Electric Grid Dispatch To quantify the grid emissions associated with PHEV charging (i.e., the emissions associated with generating the electricity supplied to the PHEV), we employ an economic grid dispatch model developed by Kelly et al. in [12]. This dispatch model contains a list of power plants arranged in ascending order of generation costs ($/kwh). Data for these power plants were obtained from the EPA EGrid database. The model simulates grid dispatch for a given total power demand profile, and outputs the resulting dollar costs and emissions associated with grid power generation. The model is also capable of accommodating PHEV power demand and wind power input in this simulation process. All the available wind power input is supplied to the demand by

3 Power [MW] Wind Power [MW] dispatching it first. More information about the wind power traces used in our study is presented in the next subsection. In our studies, we assume that the traces produced from the grid are not affected by a PHEV's charging patterns. A 1-15% market penetration of PHEVs is assumed and a corresponding grid load is calculated and used in the grid dispatch model. This means that there is a one way connection, in which the PHEV owner is aware of the grid level, whereas his actions do not change the produced by the grid. More details on the grid load from the PHEVs are presented in [13]. In this paper, our goal is to understand optimal charging and driving patterns for a PHEV from the PHEV manufacturer and consumer standpoint. Hence, we are only interested in obtaining a meaningful trajectory from the grid. For this reason, we will obtain optimal charging and power management trajectories for a chosen grid mix and assume that the PHEV's charging activities do not affect the grid in turn. We will look at several grid mixes representing different levels of wind penetration, thereby providing a range of solutions and thereby make the results more meaningful. A different set of dynamics and constraints affect the PHEV during grid charging than during on-road operation. The model has one state variable, x = {SOC} and one input, u = {P b } in comparison with the 2 states and 2 inputs for the complete powertrain during driving. The charging outlet considered is rated at 11 V and 15 A. Thus the charging power can be a maximum of 1.65 kw. Battery SOC is constrained to be between.3 and.9, the same as for PHEV on-road usage. The battery cannot discharge power to the grid. These constraints, together with (1), form the sets Z and U in (2c) presented in section III. 18 One Year Averaged Power from all sites potential. In our work, projected wind power from offshore wind in the state of Michigan is used. Due to significant variability in wind speeds over time and space, it is not practical to obtain optimal charging and power management trajectories for one specific chosen wind power trace. Figure 3 shows a graph of wind power output, which is summed up over all offshore locations (21 sites), and averaged over all days of the year. The datasets show that the wind output has significant temporal variability, but averaging over all days of the year produces identical 24- hour wind traces for the 3 years. We call these the Yearly Averaged Traces. In our study, we use data for only 24, and will focus on that particular yearly averaged trace Fig 4. Wind Power traces on different days compared to the yearly averaged trace Wind Power on chosen days Yearly Average High Day Medium Day Low Day Wind Power and Energy Penetration (%) Max(%) Min(%) Energy(%) Fig 3. Wind Power trace summed over all sites and averaged over all days of a year (Yearly Averaged Traces). C. Wind Power Data The wind power data used in our studies are obtained from the Eastern Wind Integration and Transmission Study (EWITS) [14]. AWS-Truewind created this dataset with assistance from NREL/DOE. This data consists of three years (24-26) of 1-minute time step wind speeds. The study evaluated potential sites for wind power development and forecasted wind power output at sites with high 5 High Med Low Avg. Yr. Fig 5. Amount of power and energy supplied by wind in different cases to satisfy grid power demand To assess the performance of an average optimal solution on different days, three days with different levels of wind power are considered. A day with 85 percentile wind energy content was selected as a "high wind" day. The "medium day" has 5 percentile and the "low day" is chosen as a day with 15 percentile wind energy content. Figure 4 shows the wind traces corresponding to these days along with the yearly averaged trace. The actual amount of power and energy supplied by wind power to satisfy the grid demand is shown in Figure 5. It is observed that that on the high wind day, up to 18% of the grid energy is from wind, compared to

4 Vehicle Velocity [mph] Grid Grid only 4% on the low wind day. Figure 5 also shows that even on the day with lowest wind, at some point during the day, wind power supplied close to 15% of the demand. Hence all these scenarios describe wind penetration levels that are currently not observed in the Michigan grid. Finally, Figure 6 shows the traces resulting from the different amounts of wind supplied during a particular day. These traces impact the optimization algorithm's decision to charge from the grid as it might beneficial to charge from the grid at different times depending on the grid mix. optimality in achieving minimum, the framework shown in Figure 8 is used. This framework proceeds backwards in time, starting at the end of the 24 hour period under consideration as illustrated by Fig. 7. The essence of the framework is that it accounts for the different dynamics of charging and driving at the appropriate time steps, while implementing the HBJ equation. The value function V, is converted to different dimension matrices as explained in Fig. 8. Essentially the loop in Fig. 8 is followed twice starting with the initialization block Daily traces from different wind patterns Average Wind High Wind Medium Wind Low Wind No Wind i i j j V( k, x ( k)) min{ c( x ( k), x ( k 1)) V( k 1, x ( k 1))} X ( k1) (3) 24 hours and vehicle velocity Fig 6. traces produced by a grid mix with different amounts of wind III. OPTIMAL CONTROL The optimal control problem is formulated as follows: Minimize 24 CO 2 CO2 J * mf * tdr * Pb * tch gal kwh subject to x f ( x, u), (2. a-c) xz, u U where the optimization objective, J, is the total amount of produced during a 24-hour period. This is produced by both driving fuel usage (the first term in the expression for J) and grid charging (the second term). Gasoline consumption is gallons per time step during driving ( ). Battery charging power is given by P b in kw and the charging time step is. It is important to note that the dynamics and constraints given in the above equations are different depending on whether the PHEV is driving or charging. The states and inputs of the system are x and u respectively. The state and input variables are different for charging and driving. These are the variables in the control optimization. The admissible ranges of x and u are the sets Z and U respectively, which are also different for charging and driving as discussed in sections II.A and II.B The Hamilton-Bellman-Jacobi (HBJ) equation for dynamic programming (DP) is used to ensure global optimality. To integrate the two optimal problems, but still use the HBJ equation given by (3) to guarantee global 1 5 Charging Driving Fig 7. Illustrates the 24 hour cycle for which the optimization is performed V = R n xr m cost to go for each SOC and ω e Execute HJB equation with vehicle model x { SOC, } e u{ g, mf} x f ( x, u) V = R n xr m cost to go for each SOC and ω e Fig 8. Complete Optimal Framework Charging Driving Charging Proceeds backward in Time Modify V by extraction. Only ω e = is allowed at start of trip V V () Modify V by concatenation. Same function for all ω e V1.. V2 n.. V1 Initialize V for each SOC V = Rm cost to go for each SOC Execute HJB equation with grid charging model x { SOC} u { P b } x f ( x, u) i i j j V( k, x ( k)) min { c( x ( k), x ( k 1)) V ( k 1, x ( k 1))} X ( k1) V = R m cost to go for each SOC m = 45 SOC grid points n = 3 ω e grid points V - Value function In this framework, SOC is a state variable that is common to both system's dynamics and this approach ensures its continuity. Since battery usage should not be unduly rewarded, we impose an additional constraint that the initial and final SOC has to be same. This framework is computationally feasible due to the use of a backward

5 Grid Charging Cumulative [kg] Fuel [kg] SOC Grid Charging cumulative [kg] SOC looking model and the interpretation of the HJB equation as presented in (13). Please refer to [1] for a more detailed discussion on the DP implementation and [13] for a more detailed explanation of the framework given in Fig. 8. IV. RESULTS AND DISCUSSION Five different grid mixes are considered in our study corresponding to days with high, low and medium wind, yearly averaged and no wind. In each case 7 optimization problems are solved corresponding to an initial and final SOC ranging from.3 to.9 in steps of.1. Since we consider the Michigan grid, there is a considerable amount of coal resulting in higher per unit energy. The results are specific to the assumptions on wind power, grid mix and driving behavior, hence we present a qualitative analysis of interesting trends rather than focusing on the numbers. The results we present will be the optimal trajectories for an individual PHEV which interacts with the grid and follows driving pattern as described in section II. The results are highly sensitive to the driving requirements and the grid mix. However, our goal is to analyze each optimal solution in detail and learn from these 'best case' scenarios. The following are the highlights of the results 1. Total emissions decrease due to inclusion of wind power (even in the case of lowest wind power) 2. Due to our integrated charging and power management framework, we capture the impacts of temporal variation of wind. It is shown that the optimal trajectories vary significantly depending on the wind penetration. 3. We quantify the loss of optimality resulting from wind variability in Figure 7 by providing a comparison of the 'yearly average' optimal solution to the other solutions. Next, we explain each of these results in more detail. It is obvious that adding large quantities of wind will result in reduced per unit energy produced on the grid (Fig 5). It is less straightforward to understand the impact of increased wind power on reduction in produced from transportation. Total emissions decrease due to inclusion of wind power (even in the case of lowest wind power). First, we compare two cases, one without any wind power on the grid and the other with a low amount of wind power on the grid (low amount of wind power refers to the low day as described in section II.C). Fig. 9 presents the resulting produced over 24 hours due to the PHEV's transportation needs in the two cases. The observations from this figure are that there is a small reduction in (2%) due to inclusion of wind power (in this case of lowest wind power) and the optimal SOC trajectories in the two cases are different. The difference is observed in the first few hours, when the output of the grid is lower due to wind. For the low day, there is an insignificant amount of wind for the rest of the day. Thus even though a higher amount of grid energy used for driving in the case with low wind (and a higher amount of gasoline used in the case with no wind), the amount of produced differs only by 2%. Comparison of Optimal Trajectories for days with no wind and low wind No wind Low Wind Fig 9. Optimal Trajectories for days with no and low wind A comparison of optimal trajectories for the three days with different levels of wind penetration was performed. Fig. 1 shows the difference in optimal trajectories related to the three days with different amounts of wind. The differences are due to - 1) the tradeoffs between the produced by gasoline fuel and electricity and 2) due to varying amounts of wind throughout the day, resulting in different from the grid at different times. Thanks to a combined approach, we can capture these differences. For example, in the medium wind case (Fig. 7), we observe that higher grid (due to low wind) during hours 1-16 results in the optimal solution using some gasoline for the second trip rather than charging before the second trip. Such tradeoffs between gasoline usage and charging are seen in all the cases depending on the produced by the chosen grid mix. Comparison of Optimal Trajectories for days of different Wind Penetration Low Wind Day Medium Wind Day High Wind Day Fig 9. Optimal Trajectories for days of high, low and medium wind As mentioned in section II.C on wind data, it is not practical to implement optimal solutions for every single day

6 Optimal per day [kg] due to wind variability. So we obtain an optimal solution for the yearly average wind case. Comparing its performance to the optimal solutions on the days with high, low and medium wind, we quantify the loss of optimality resulting from wind variability in Figure 1. In particular, there is a maximum loss of ~1% amongst the cases considered. Looking at the variation in wind power in Fig. 5 and in the wind penetration in Fig. 6, it can be observed that despite such variations, the final loss (of optimality) as compared to an average case is 1% in the worst case. This is due to the narrower range of variations in the resulting produced by the grid in all the cases, as seen in Fig. 6. Quantifying the penalty stemming from variability of wind energy is a unique finding of this study. This showcases the opportunities to develop control rules for different grid mixes and eventually obtain stochastic optimal results Average wind optimal High wind optimal Low wind optimal Low wind with Avg optimal High wind with Avg optimal No wind optimal Optimal produced in different cases [4] Han Sekyung, Han S., Sezaki Kaoru, "Development of an Optimal V2G Aggregator for Frequency Regulation", IEEE Trans. on Smart Grid, 1, 1, 21, pp [5] W. Short, P. Denholm, "A preliminary assessment of plug-in hybrid electric vehicles on wind energy markets", NREL Technical Report TP , April 26 [6] Kashyap, A., Callaway, D.S., Controlling distributed energy constrained resources for power system ancillary services, 11 th International Conference for Probabilistic Methods Applied to Power Systems. [7] Chiao-Ting Li, Changsun Ahn, Huei Peng, and Jing Sun, "Decentralized Charging of Plug-In Electric Vehicles," ASME Dynamic Systems and Control Conference, Arlington, VA, 211 [8] K Clement, E. Haesen, J. Driesen, "Coordinated charging of multiple plug-in hybrid electric vehicles in residential distribution grids", IEEE Power Systems Conference and Expo, 29, Seattle, WA. [9] A. Y. Saber, G. K. Venayagamoorthy, "Intelligent unit commitment with vehicle-to-grid A cost-emission optimization", Journal of Power Sources, 195, 3, 21, pp [1] R. Patil, Z. Filipi, H. K. Fathy, "Comparison of optimal supervisory control strategies for a series plug-in hybrid electric vehicle", ASME Dynamic Systems and Control Conference, 211, Washington D.C. [11] S. Stockar,; V. Marano, G. Rizzoni, L. Guzzella, "Optimal control for Plug-in Hybrid Electric Vehicle applications" Proceedings of the 21 American Control Conference, Baltimore, MD. [12] J. Kelly, G. Keoleian, I. Hiskens, " Evaluation of economic and capacity factor electricity dispatch models for estimating air pollutant emissions", in review. [13] R. Patil, Z. Filipi, H. K. Fathy, " Framework for the Integrated Optimization of Charging and Power Management in Plug-in Hybrid Electric Vehicles", American Control Conference, 212 [14] Eastern Wind Integration and Transmission Study (EWITS), % - Loss of Optimality Initial SOC (at 1 AM) Fig 1. Comparison of loss of reduction for different cases V. CONCLUSIONS A rigorous optimal control approach of considering combined charging and power management of a PHEV with a DP algorithm ensures the synergistic interaction of the PHEV with the grid. Three different cases of varying amounts of wind power on the electric grid were considered. The results show that this approach produces results that account for the temporal variation in wind power. Since it is not practical to implement optimal solutions for every single day due to wind variability, a comparison of loss of optimality resulting from using average optimal solutions is also presented. REFERENCES [1] Ali Ipakchi, Farrokh Albuyeh, "Grid of the Future", IEEE Power and Energy Magazine, 7, 2, 29, pp [2] Thomas H. Bradley, Andrew A. Frank. "Design, demonstrations and sustainability impact assessments for plug-in hybrid electric vehicles", Renewable and Sustainable Energy Reviews, 13, 29, pp [3] W. Kempton, J. Tomic, "Vehicle-to-Grid power fundamentals: Calculating capacity and net revenue", Journal of Power Sources, 144, 1, 25, pp