ENERGY DISPATCH SCHEDULE OPTMIZATION IN GRID-CONNECTED, PHOTOVOLTAIC-BATTERY SYSTEMS: A COST-BENEFIT ANALYSIS FOR DEMAND SIDE APPLICATIONS

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1 ENERGY DISPATCH SCHEDULE OPTMIZATION IN GRID-CONNECTED, PHOTOVOLTAIC-BATTERY SYSTEMS: A COST-BENEFIT ANALYSIS FOR DEMAND SIDE APPLICATIONS Anders Nottrott, Jan Kleissl, Byron Washom UC San Diego 9500 Gilman Dr, EBUII La Jolla, CA jkleissl@ucsd.edu ABSTRACT A linear programming (LP) routine was implemented to model optimal energy storage dispatch schedules for demand charge management in a grid-connected, combined photovoltaic-battery storage system (PV+ system). The LP leverages PV power output and load forecasts to minimize peak loads subject to elementary dynamical and electrical constraints of the PV+ system. We simulated a broad range of PV+ designs (in terms of battery storage capacity and peak load reduction target) and performed a cost-benefit analysis to quantify the net present value (NPV) of the battery storage system. We compared the financial benefits of our optimized energy storage dispatch schedule with simple off-peak charging/on-peak discharging and real-time load response dispatch strategies that were not informed by net load forecasts. The NPV of the battery array increased significantly (in the range $150k - $450k) when the battery was operated on the optimized schedule compared to the off-peak/on-peak schedule. The NPV of the battery array also increased (in the range $100k - $400k) when the battery was operated on the optimized schedule instead of the realtime dispatch schedule. These trends were attributed to increased battery lifetime and reduced demand charges attained under the optimized dispatch strategy. We estimated that Lithium-ion batteries can be a financially viable energy storage solution in demand side, energy cost management applications at an installed cost of about $200 - $500 per kwh (approximately 1/5 to 1/2 of 2011 market prices). 1. INTRODUCTION Adoption of advanced energy storage technologies as a means integrate renewable energy resources into electric grids will increase significantly in the next decade. 28 states in the USA have enacted mandatory renewable portfolio standards (RPS) and 5 additional states have adopted voluntary RPSs. RPSs require electricity providers to obtain a minimum percentage of their power from renewable energy resources by a certain date. The state of California has set an ambitious RPS of 33% renewable electricity generation by the year 2020 (CA Senate Bill 2, Simitan Energy, 2011) and has passed legislation to determine energy storage procurement targets for both privately and publicly owned utilities (CA Assembly Bill 2514, Skinner, 2010). Although critical applications for large scale energy storage (and the associated costs, benefits and market potentials) have been clearly identified (Eyer & Corey, 2010; Rastler, 2010), dispatch strategies for stored energy that maximize the financial value of combined renewable generation and energy storage systems (hereafter RSS) are not well quantified or understood in an operational context (Abele et al, 2011). Many models have been developed to determine optimal scheduling for stored energy dispatch in RSSs. The objective of these modeling studies can be broadly classified in two categories, utility side applications and demand side applications (Divya & Østergaard, 2009). Utility side applications focus on optimizing properties of the RSS power output that are economically beneficial to electric utilities (e.g. transmission and distribution upgrade deferral, transmission support, etc.). Demand side applications typically focus on optimizing economics of the RSS when the storage system is installed behind the meter. In this 1

2 case economic benefits are usually quantified in terms of energy bill savings for the RSS owner who purchases power paper we focus on quantifying the economics of demand side applications for grid connected combined photovoltaic (PV) and battery energy storage systems (hereafter PV+ systems). 1 We will demonstrate that significant financial benefits are realized when PV power output and load forecasts are used to inform energy storage dispatch strategies for PV+ systems. A number of studies have investigated optimal energy storage capacity and dispatch scheduling, and economics for PV+ systems. Su et al (2001) implemented a closed-loop control system to modulate power output from a PV+ system for demand charge management, time-of-use (TOU) energy cost management, emergency power supply and transmission support. Su et al concluded that the economic viability of PV+ systems is site specific and depends on the end user load shape, utility rate schedule, PV+ capacity and choice of application. Hoff et al (2007) studied the economic benefits of PV+ for emergency power supply and demand charge management applications for typical industrial customers. Hoff et al found that financial benefits from emergency power supply exceeded benefits from demand charge management. Shimada & Kurokawa (2006) modeled annual energy bill savings for a PV+ system over a range of battery capacities using insolation and load forecasts to determine the amount of night time charging required to minimize the cost of energy purchased by the customer from an electric utility in the following day. Shimada & Kurokawa found that the value of the PV+ system was significantly increased by using insolation and load forecasts to inform the energy storage dispatch scheduling algorithm and identified optimal battery capacities in terms of end user peak load and annual energy bill reductions. Ru et al (2011) developed a mixed integer linear program (MILP) to determine optimal battery energy capacity for a PV+ system, in the context of marginal energy cost reductions, by considering TOU energy tariffs to minimize the net cost of energy purchased by the customer. Ru et al used only historical data (i.e. no PV output or load forecast information was used for the battery capacity optimization) and did not account for capital costs or interest rates in the determination of optimal battery capacity so the range of feasible (profitable) battery capacities could not be determined. In a similar application to the one presented herein Riffonneau et al (2011) developed a realistic electrical model of a PV+ system implemented in a dynamic programming (DP) algorithm. The objective was to optimize the PV+ energy dispatch for a peak shaving application at the lowest energy cost to the 1 The term PV+ was coined by Hoff et al (2007) and refers to combined photovoltaic and battery energy storage systems where the battery is placed behind the meter. from an electric utility (e.g. time-of-use energy cost management, demand charge management, etc.). In this customer using PV output and load forecasts to inform the optimization. Riffonneau et al demonstrated significant performance and financial gains from their optimized energy dispatch schedule over a simple rule-based dispatch schedule. Riffonneau et al estimated a 13% reduction in energy bill costs for a single 24 hour period, although a longer simulation time is necessary to quantify the financial value of the energy storage. The most comprehensive model to quantify the economic value of a general RSS in demand side applications is the Distributed Energy Resources Customer Adoption Model (DER-CAM; Stadler et al, 2008). DER-CAM minimizes the operating costs of on-site generation considering different combinations of distributed generation technologies, which can be dispatched in a variety of demand side applications under different electrical tariffs. Stadler et al (2009) used DER-CAM to study demand charge management and CO 2 emissions minimization strategies in PV+ systems. Their results showed that for demand charge management, it is most economically efficient to charge batteries from the electric grid during off-peak hours, while for CO 2 minimization, charging batteries directly from zero emissions PV generation results in extraordinarily high energy costs to the customer. In this paper we consider an idealized PV+ system in which a PV array and a Lithium-ion battery array are connected to the utility electric grid via a lossless bidirectional inverter (Fig. 1). The goal is to determine the optimal dispatch schedule for the battery energy storage to achieve a preset amount load peak shaving (i.e. demand charge management). The optimization algorithm is formulated as a linear program (LP) and leverages day-ahead PV power output and load forecasts with regular updates to determine the best time to charge or discharge the battery subject to basic dynamical and electrical performance constraints of PV+ system. Using model output data we estimated the financial benefits of operating the battery under the optimized energy dispatch schedule in terms of annual energy bill savings. These savings were used to estimate the net present value (NPV) of the battery at the time of installation and were compared to NPV attained under a simple off-peak/on-peak and real-time dispatch schedules that were generated without any knowledge of future PV power output or customer load. 2. METHODOLOGY 2.1 LP Model We modeled an idealized PV+ system in which a PV array and a Lithium-ion battery array are connected to the utility electric grid (Fig. 1). The PV array and battery array 2

3 generate DC power, which is converted to AC power via a lossless bidirectional inverter, and all power electronics (e.g. DC-DC converters and battery management systems) are assumed to be 100% efficient. The charging/discharging response of the battery is assumed to be instantaneous so that energy from the battery may be dispatched on demand. This assumption is justified because the response time of Li-ion type batteries is O(ms) and energy dispatch from the battery was modeled on 15 min intervals. The battery is treated as a black box within the model, meaning that the charging and discharging efficiency of the battery does not depend on P s, and P s can take any values within the specified limits of the nominal battery performance. unrestricted during off-peak periods. 2 The condition P lf n > P pf n provides neutral incentive for battery charging and discharging when the forecasted PV power output meets or exceeds the forecasted load. No cost is associated with selling or purchasing power from the electric grid in the LP (i.e. the model does not explicitly leverage price arbitrage between the on-peak and off-peak energy markets). Eqs. 2a,b are energy conservation (Kirchhoff s Law) and system dynamic respectively. Eqs. 2a,b are enforced as equality constraints in the LP. Eq. 3a requires that the energy stored in the battery is bounded within the capacity of the battery. Eqs. 3b constrains the battery charging and discharging rate within the specified limits of the battery performance. Eqs. 3a,b are modeled as inequality constraints. The discrete-time LP system is solved in MATLAB. 2.2 Receding Horizon Time Advancement Fig. 1: Schematic of the system model illustrating the important components and power flows; the PV+ system is delineated by the dashed line. Because the inverter is assumed to be lossless it is not shown in this diagram. The battery management system is included in the battery, which allows black box treatment of complex electrical dynamics and transients within the battery. The model is formulated as a discrete-time, linear optimization problem. In Eqs. 1-3 E and P are energy and power. Variables with subscript s are related to the battery array, subscript pf refers to the PV power output forecast, subscript lf is the load forecast, subscript o denotes power flows to and from the grid and 0 indicates an initial condition. Integer superscript n is the current timestep, Δt is the timestep size and N denotes the maximum number of timesteps in the forecast horizon (i.e. N = 96 for a 24 h forecast horizon at 15 min sampling rate). Superscripts min and max indicate performance limits of the battery (i.e. maximum and minimum capacity or charging/discharging rate). Eq. 1 minimizes net PV+ system power output (P o ) levels that fall below the forecast customer peak load. In Eq. 1 f is a scalar valued objective function (or cost function) that corresponds to the energy shortage between the forecast customer load P lf and the forecast PV power output P pf. The condition P lf n 0 ensures that battery charging and discharging is PV power output forecasts (P pf ) and load forecasts (P lf ) are available for a finite time horizon N Δt and are continuously updated on an interval t update. Forecast updates are denoted by the integer subscript m Z = [0,m]. This type of information about future system output motivates a receding horizon approach for time advancement. Initially an optimization is performed to compute the best dispatch schedule for the energy stored in the battery {P s } m=0 using all available information about the initial state of the system and PV power output and load forecasts. At the initial starting time (n = 1, m = 0) the only requirement for the storage device is the amount of energy stored in the {E 0 } 0 battery (Eq. 3a) and {P s 1 } 0 is allowed to take any value between P s min and P s max. The system operates on this initial schedule until t update when a new forecast is available. At that point the optimization is repeated using new PV output and load forecast data, and additional equality constraints are imposed in the LP to ensure that {P s 1 } m in the current optimization is equal to {P s n_update } m-1 from the previous optimization (i.e. continuity of the storage dispatch schedule P s is required between forecast updates). The initial energy storage for the m th iteration is set to, The system operates on the updated schedule for n update = t update /Δt timesteps until a new forecast is obtained. This procedure is repeated for M optimization iterations to generate an optimal energy dispatch schedule for the battery. 2 In the context of Eq. 1 off-peak periods are determined from the peak load forecast and are not necessarily the same as the utility defined off-peak time-of-use rater period defined in Table 1. 3

4 2.3 Battery Charge State Management and Dynamic, Realtime Response PV power output and load forecasts inherently contain uncertainties that are primarily attributed to weather and human behavior. If stored energy is dispatched solely according to forecast information, forecast errors will result in PV+ output shortages or surpluses relative to the optimal dispatch schedule. It is more important to minimize PV+ output shortages than surpluses from both the demand side and utility side perspectives. In the case of an output shortage the utility must balance the load with spinning reserves and the customer will incur high energy and/or demand charges, while for an output surplus the utility may curtail the PV+ output and the customer incurs a relatively small financial loss from reduced energy sales profits. For this reason it is beneficial to ensure that the battery is fully charged during the off-peak rate period, which provides the best capability to respond to a worst case PV+ output shortage scenario caused by a large forecast error during the on-peak rate period. The assumption of instantaneous battery response permits the incorporation of real time PV output and load data which is leveraged to improve the PV+ system performance during the forecast update interval t update. At the forecast valid time the optimal stored energy dispatch schedule is computed over the entire forecast horizon according to Eqs. 1-3 using only forecast information and the current state of the battery. The actual PV output and load are monitored in real time and the battery responds on-demand to compensate for forecast errors. During off-peak periods 2 this approach amounts to a renewables capacity firming application for the battery. After a period t update new forecast information is available and the optimal dispatch schedule is recalculated over the new forecast horizon. Conceptually one can interpret this procedure as a continuous perturbation of the optimal solution arising from forecast errors. At each forecast valid time the charge and output states of the battery are perturbed from their expected states under the optimized solution due to real time compensation for forecast errors. 2.4 PV+ System Cost Analysis There are three PV+ system design parameters in our model: PV array DC nameplate rating, energy storage capacity of the battery and peak load reduction target. In order to evaluate feasible PV+ system designs a cost analysis was performed to determine the net present value (NPV) of the battery storage system by calculating energy bill savings attained over the lifetime of the battery relative to capital costs of the storage system, annual operation and maintenance (O&M) costs and interest rates. The net present value is estimated from where A is the value of annual energy bill savings extrapolated from 2009 data, OM is the annual O&M cost for operating the storage system (including energy costs for active cooling of the battery array), r is the interest rate, t is the current year and T is the total lifetime of the battery in years. For t = 0, OM is equal to the capital costs incurred on the purchase and installation of the storage array and A = 0. Annual energy bill savings are attributed solely to the use of energy storage in the PV+ system. Energy bill savings are assessed in terms of the difference between the annual energy costs with and without the application of battery energy storage. Electric utilities assess TOU energy pricing and demand charges for industrial customers. The energy bill was calculated using the San Diego Gas & Electric (SDGE) AL- TOU rate schedule for industrial customers. The AL-TOU tariff includes basic service fees, seasonal and peak demand charges and TOU energy pricing (Table 1; SDGE, 2011). TABLE 1: SDGE TIME-OF-USE RATE PERIODS In order to quantify the advantages of our optimization strategy we compared our optimized dispatch schedule with a basic off-peak/on-peak, charge/discharge schedule and a real-time dispatch schedule. In the off-peak/on-peak schedule the battery undergoes one full charge cycle at 80% depth of discharge (DoD) per day. Charging and discharging rates are constant over the off-peak and on-peak periods defined in Table 1. In the real-time dispatch schedule the battery is fully charged at a constant rate over the off-peak period (Table 1) and then discharged in real time to meet the actual daily load until the energy stored in the battery is exhausted. The battery undergoes on full charge cycle per day only if the energy capacity of the daily load exceeds the energy capacity of the battery. 3. INPUT DATA AND MODEL PARAMETERS 3.1 PV Power Output Forecast One year (2009) of 15 min DC power output data from EBU2 building rooftop PV array on the University of California, San Diego campus was used as the basis for P p and P pf. The PV array has a DC nameplate rating of 7.5 kw DC and the data was scaled to approximate the output of a larger system with a rating of P p DC rating = 500 kw DC. This signal was filtered using a 45 min moving average window to generate an idealized solar forecast P pf which was 4

5 provided as input to the LP model. This method of filtering was applied in order to simulate the expected characteristics of a real solar forecast. During clear and overcast conditions P p (the actual PV power output) and P pf (the forecast PV output) are generally equal, but in cloudy conditions P p fluctuates quasi-randomly about P pf, and the two signals maintain strong seasonal and diurnal correlations. After each forecast update timestep the new PV power output forecast is perturbed using a Monte Carlo technique to simulate a forecast that is continuously updated with new information. 3.2 Load Forecast A load forecast was generated using UCSD campus historical load data from Uncertainty in the load forecast was simulated by incorporating random, normal fluctuations with a standard deviation of 5% of the magnitude of the load. The peak load reduction target (P l target ) for the PV+ system is a parameter in the model. In order to explore a broad range of possible designs for the PV+ system we simulated peak load reduction targets in the range P l target = kw for the results presented in this report. New load forecasts are also perturbed after each forecast update timestep using the same Monte Carlo method that is applied to randomize PV output forecast updates. 3.3 Battery Array The energy storage device is Sanyo DCB-102 Lithium-ion battery array. A single Sanyo DCB-102 has nominal energy storage capacity of 1.59 kw and minimum lifetime rating of 3000 cycles at 80% DoD. The DCB-102 has a maximum charging power of P s min = 340 W and a maximum discharging power of P s max = 720 W. The capital cost of the battery array was assumed to be $1000/kWh including installation costs. The number of charge cycles at 80% DoD over a period of N timesteps was calculated from Eq. 7. In Eq. 7 NCC is the number of charge cycles and E s total is the total energy capacity of the battery. To avoid overcharging or overdrawing of the battery array the model parameters E s min and E s max in Eq. 3a are set to 0.2E s total and 0.99E s total, respectively. In order to investigate the financial viability of different combinations of battery capacity and energy dispatch capacity for the PV+ system we simulated battery array capacities in the range E s total = kwh. 4. RESULTS AND DISCUSSION PV+ system performance was simulated for a wide range of peak load reduction targets ( kw), battery storage capacities ( kwh) and a PV array with a fixed nameplate rating of P p DC rating = 500 kw DC in order to evaluate model performance and quantify the financial benefits that are realized when PV and load forecasts are applied to optimize the charge/discharge schedule of the battery. 4.1 Time Series of Model Output Fig. 2 shows exemplary timeseries of model output data from July 18 th, 2009 for P l target = 1020 kw and E s total = 1270 kwh. Figs. 2a,d,g show PV+ system power flows, battery charge state and net load on the electric grid for the offpeak/on-peak dispatch schedule, Figs. 2b,e,h are the PV+ output for the real-time dispatch schedule and Figs. 2c,f,i are the PV+ output for the optimized dispatch schedule. Figs. 2c,f,i illustrate superior performance of the optimized schedule over the dispatch schedules that do not leverage forecast PV output and load forecasts. For all three dispatch schedules the battery undergoes one complete charge cycle over the one day period shown in Fig. 2. Using off-peak/onpeak strategy the energy stored in the battery is dispatched concurrently with the peak load, but the output power of the battery is too low during that time. Using the real-time strategy the battery discharges too quickly and the battery is completely discharged by the beginning of the on-peak rate period. Using the optimized strategy the shape of the battery discharge curve closely approximates the shape of the peak load, and the net load during the on-peak rate period is relatively constant when compared with the off-peak/onpeak and real-time strategies (Fig. 2i). Figs. 2g,h,i show that the maximum net load on the electric grid during the on-peak rate period (i.e. when demand charges are assessed by the utility) is reduced under the optimized schedule. For the data shown in Fig. 2 the optimization algorithm reduced the maximum on-peak, net load by 34% (119 kw) when compared with the offpeak/on-peak schedule, and 53% (262 kw) when compared with the real-time storage dispatch. 5

6 Fig. 2: Sample timeseries of model output data on July 18 th, 2009 illustrating PV+ system power flows (a,b,c), the battery charge state (d,e,f) and the net load on the electric grid (g,h,i). Figs. 2a,d,g show model output when energy storage is dispatched according to the offpeak/on-peak strategy, Figs. 2b,e,h show model output for the real-time dispatch strategy and Figs. 2c,f,i show model output for the optimized dispatch strategy. Power flows in Figs. 2a,b,c are relative to the PV+ system so that P o > 0 indicates net generation by the PV+ system and P o < 0 indicates reverse power flow from the grid (i.e. the battery is charging). The fine dashed lines in Figs. 2a,b,c, indicates the maximum charging and discharging power of the battery array. The net load plotted in Figs. 2g,h,i is relative to the electric grid so that (P l P o ) > 0 indicates power flow from the grid to the customer, while (P l P o ) < 0 indicates net generation from the PV+ system to the grid. The dash-dotted line in Figs. 2g,h,i indicate the range of the on-peak period as defined in Table NPV of the Battery Array Operating under the assumption that 2009 PV power output and load data are representative of a typical year, results from 2009 model output were extrapolated over the lifetime of the battery to estimate the NPV of the battery array. Fig. 3 shows the difference between the NPV of the optimized dispatch schedule, and the off-peak/on-peak (Fig. 3a) and real-time (Fig. 3b) dispatch schedules for different battery capacities that were tasked with broad range of peak load reduction targets (P l target ). Total battery array capacity (E s total ) is plotted on the horizontal axis and the ratio of peak load reduction target to PV array DC nameplate rating (P l target / P p DC rating ) is plotted on the vertical axis. The grayscale represents the NPV of the battery array at the time of capital investment in US dollars. Fig. 3 shows that operating the battery on the optimized dispatch schedule is more profitable than operating on the off-peak/on-peak or real-time schedules for most battery sizes and peak load capacities modeled in this study. The optimization strategy 6

7 always improve the NPV of the battery array over the offpeak/on-peak and real-time strategies for P l target / P p DC rating > 1. Fig. 3: Difference between the net present value (NPV; Eq. 6) of the optimized dispatch schedule and (a) the off-peak/on-peak schedule; (b) the real-time dispatch schedule. The NPV difference for broad range of battery capacities (E s total ) and peak load reduction targets (P l target ) are shown. The PV array nameplate rating was set to P p DC rating = 500 kw DC. The units of the grayscale are $USD. provides significantly more value than the off-peak/on-peak strategy, especially in the range E s total > 700 kwh and P l target / P p DC rating < 1.25, which is attributed to superior load following and reduced battery cycling under the optimized dispatch schedule (Fig. 3a). When compared with the realtime dispatch strategy (Fig. 3b) the optimized dispatch schedule significantly increases the value of the battery array for E s total > 700 kwh and P l target / P p DC rating > 1.5. These gains occur because the optimization strategy leverages PV output and load forecasts to distribute the stored energy dispatch over the entire duration of the peak load period, even when the energy capacity of the peak load exceeds the energy capacity of the battery array. In the range P l target / P p DC rating < 1 the performance of the optimization and realtime dispatch strategies is similar because the energy capacity of the battery is greater than the energy capacity of the peak load so the amount of energy storage is sufficient to eliminate the peak load throughout the year, and the dispatch schedules for both strategies are similar. It is important to note that P l target / P p DC rating is not scale invariant in P p DC rating, so a change in the nameplate capacity of the PV array will change the trends observed in Fig. 3. Neverthe-less it is expected that the optimization strategy will Another way to interpret Fig. 3 is to consider the increased NPV attained under the optimized dispatch strategy in the context of PV output and load forecasts. If the PV+ system is already installed then there is no additional cost to the system owner associated with implementing the optimized dispatch strategy over the off-peak/on-peak and real-time strategies (according to the assumptions of the basic battery model). Therefore the NPV shown in Fig. 3 may be interpreted as the financial value of the PV output and load forecasts in the PV+ application. As an extension of this reasoning one could consider that the current state of the art for load forecasting is significantly more advanced than that for solar forecasting, especially in terms of forecast accuracy. Thus errors arising in the computation of the forecast net load (P lf P pf ) are more likely to occur due to errors in P pf than errors in P lf. This argument loosely permits the assumption that, because an accurate load forecast is already attainable, the NPV presented in Fig. 3 can be interpreted as the value of developing an accurate solar forecast for demand side, energy bill management application. Fig. 4 illustrates the NPV (at the time of capital investment) of the battery array when operated under the optimized dispatch strategy assuming different costs for the storage. Fig. 4a shows the battery NPV assuming a cost $1000/kWh, which is representative of the current (2011) market price for large scale, stationary lithium ion battery arrays. At a price of $1000/kW all battery sizes have a negative NPV indicating that lithium ion type batteries are not a financially viable technology in demand side applications if energy bill savings for the utility customer are the only value proposition considered in the valuation of the storage array. The results of Fig. 4a raise an interesting question: At what price do lithium ion batteries become a financially viable? We estimated this price within our model framework by varying the capital cost in Eq. 6. Fig. 4b shows the NPV of the battery array at a cost of $200/kWh, the maximum price at which the NPV > 0 for nearly all PV+ system designs modeled in this study. It is worth noting that the NPV of the battery array became greater than zero for a limited range of PV+ designs at a price as high as $500/kWh. This result is particularly relevant for the 2 nd life battery industry, which holds promise for developing large scale Lithium-ion, battery energy storage systems from used EV batteries at a lower cost than new batteries. 5. CONCLUSION We developed a linear programming routine to optimize the energy storage dispatch schedule for a grid-connected 7

8 6. ACKNOWLEDGEMENTS The authors gratefully acknowledge Yu Ru (UC San Diego) and Mike Chen (York University) for their helpful comments and input at the early stages of this research. This project was motivated by discussion among the members of the EPRI subgroup during the 2011 Sustainability Problems Workshop hosted at the American Institute of Mathematics in Palo Alto, CA, USA. This material is based upon work supported by the United States Department of Energy under Award Number EE and Sanyo Electric Corporation. 7. REFERENCES Fig. 4: The NPV of the battery array operated on the optimized dispatch schedule assuming a capital cost for storage of (a) $1000/kWh and (b) $200/kWh. The units of the grayscale are $USD and the dashed white line delineates the $0 contour. combined photovoltaic-battery storage system (PV+ system). The optimization strategy targets demand charge management and leverages PV power output and load forecasts to determine the best trajectory for the battery storage output power in order to minimize demand charges. We simulated a broad range of PV+ system designs and performed a cost analysis to compare the financial benefits of our optimized energy storage dispatch schedule with basic off-peak/on-peak charging/discharging and real-time dispatch strategies. The performance and value of the optimization method were quantified in terms energy bill savings attainable over the lifetime of the battery array. We conclude that significant financial value is derived from using PV power output and load forecasts to compute the energy storage dispatch schedule for the PV+ system. The net present value (NPV) of the battery array increased significantly (in the range $100k - $450k for some PV+ configurations) when energy storage was dispatched on the optimized schedule. These gains are attributed to increased battery lifetime and reduced demand charges attained under the optimized dispatch schedule. We estimate that the Lithium-ion batteries can be a financially viable energy storage solution in demand side, energy cost management applications at an installed cost of about $200 - $500 per kwh. (1) CA SB 2, Simitan Energy: Renewable energy resources (2) California AB 2514, Skinner (3) J. Eyer and G. Corey, Energy Storage for the Electricity Grid: Benefits and Market Potential Assessment Guide, SANDIA Report SAND , 2010 (4) Electric Energy Storage Technology Options: A White Paper Primer on Applications, Costs, and Benefits, EPRI, Palo Alto, CA, (5) A. Abele, E. Elkind, J. Intrator, B. Washom, et al (University of California, Berkeley School of Law; University of California, Los Angeles; and University of California, San Diego) 2011, 2020 Strategic Analysis of Energy Storage in California, California Energy Commission. Publication Number: CEC (6) K. C. Divya and J. Østergaard, Battery energy storage technology for power systems An overview, Electric Power Systems Research, vol. 79, pp , 2009 (7) W.-F. Su, C.-E. Lin and S. J. Huang, Economic analysis for demand-side hybrid photovoltaic and battery energy storage system, IEEE Transactions on Industry Applications, vol. 37, pp , 2001 (8) T. E. Hoff, R. Perez and R. M. Margolis, Maximizing the value of customer-sited PV systems using storage and controls, Solar Energy, vol. 81, pp , 2007 (9) T. Shimada and K Kurokawa, Grid-connected photovoltaic systems with battery storages control based on insolation forecasting using weather forecast, in Proc. Renewable Energy 2006, pp (10) Y. Ru, J. Kleissl and S. Martinez, Storage size determination for grid-connected photovoltaic systems, IEEE Trans. Sustainable Energy, arxiv: v1 [math.oc] (11) Y. Riffonneau, S. Bacha, F. Barruel and S. Ploix, Optimal power flow management for grid connected PV systems with batteries, IEEE Trans. Sustainable Energy, vol. 2, No. 3, pp , July 2011 (12) M. Stadler, H. Aki, R. Firestone, J. Lai, C. Marnay and A. Siddiqui, Distributed Energy Resources on-site optimization for commercial buildings with electric and thermal storage technologies, LBNL, Environmental Energy Technologies Division, May 2008 (13) M. Stadler, C. Marnay, A. Siddiqui, J. Lai and H. Aki, Integrated building energy systems design considering storage technologies, LBNL, Environmental Energy Technologies Division, April 2009 (14) SDGE AL-TOU Rate Schedule, Accessed 11/25/11 8