This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6%.
The microgrid concept has recently gained significant attention from academia, equipment vendors, and energy companies alike. A microgrid can be defined as a group of interconnected loads and distributed energy resources within clearly defined electrical boundaries that acts as a single controllable entity with respect to the grid, and can connect and disconnect from the grid, enabling it to operate in both grid-connected and islanded-modes [1]. Microgrids can contribute to ensure reliable, low cost, and environmentally friendly energy by taking advantage of distributed energy resources (DER) (including renewable sources), small-scale yet efficient fossil-fired combined heat and power technology (CHP), and both mobile and stationary storage technologies [2], [3] and [4]. Furthermore, microgrids can provide locally high power quality and reliability (PQR) to sensitive loads and/or critical infrastructure [5]. By increasing the number of supply sources, microgrids are prone to a high degree of operational complexity, particularly when storage technologies are used under time dependent energy tariffs and peak pricing [6] and [7]. Because loads are inevitably quite variable in small systems, it is crucial to tightly control sources so that loads are reliably served, particularly under uncertainty and if islanded operation is a goal.
The microgrid planning and scheduling problem has been previously addressed using different approaches. Most models found in the literature use linear or mixed integer linear programming [8], [9], [10] and [11], while a few adopt nonlinear programming [12] and [13]. However, little work has been published considering uncertainty [14] and [15], suggesting a need for the contributions introduced with this work.
This paper follows on previous work on the problem of optimal scheduling of a reconfigurable (4 MWh–1 MW or 2 MWh–2 MW) lithium-iron-phosphate (LFP) battery, considered for use at the Santa Rita Jail (SRJ), given the output uncertainty of a legacy fuel cell [16].
This almost 3 MW peak facility is located in Dublin, California, and houses up to 4500 inmates. During the past decade, it has installed a series of efficiency and DER technologies to reduce its energy consumption, including a 1.2 MW rooftop photovoltaic (PV) system and a 1 MW molten carbonate fuel cell (MCFC) operating as a CHP unit [16]. The fuel cell has proven unreliable and is frequently out of service. These assumed random outages combined with time variable tariffs for both energy and power demand incurs significant potential financial penalties [16]. Fuel cell outages result in increased utility electricity purchases, significantly higher peak power demand charges, and losses of heat supply replaced by natural gas purchase. Please note that heat loads are not explicitly addressed in this work, so all natural gas purchases are tied to MCFC generation and not to replace its foregone waste heat. In part to mitigate this unreliability problem, the Jail has added local electrical storage in the form of an LFP battery.
This paper adds to previous work by expanding on the Operations version of the Distributed Energy Resources – Customer Adoption Model (Operations DER-CAM) by introducing stochastic linear programming and introducing uncertainty in MCFC availability, which determines an adjusted battery schedule.
DER-CAM [17], is a mixed integer linear programming algorithm (MILP) developed at the Lawrence Berkeley National Laboratory (LBNL) written and implemented in GAMS. It has two main versions that may be used to size and/or schedule the optimal DER capacity for a given site: (1) I + P-DER-CAM (Investment and Planning) picks optimal microgrid equipment combinations and the corresponding dispatch, based on 36 or 84 typical days representing a year of hourly energy loads and technology costs and performance, fuel prices, existing weather data, and the utility tariff; (2) Operations DER-CAM as applied in this study is used for the optimization of the detailed dispatch in a microgrid for a given period, typically a week ahead, with a time resolution of 5 min, 15 min, or 1 h, assuming the installed capacity is known, and using weather forecasts from the web to forecast requirements.
This paper analyzes the generic implementation of stochastic programming in Operations DER-CAM. Its use is illustrated by addressing the optimal scheduling of a reconfigurable LFP battery considered for installation in the Santa Rita Jail microgrid. The output uncertainty of a legacy 1 MW MCFC, which has often proven unreliable, justifies the Jail's interest in batteries.
Results are obtained from separately running deterministic scenarios and ones applying the stochastic approach. The implementation of stochastic linear programming followed the standard formulation of a two-stage recourse problem, and given the specific conditions of the problem under study the deterministic equivalent program was formulated.
Several sets of runs have been made. A few deterministic runs provide basic information on the range of costs obtainable by using the MCFC, or the LFP battery, or both together. Introducing uncertain MCFC availability in the DER-CAM model and comparing results obtained by the deterministic and stochastic methods demonstrates how uncertainty impacts the LFP scheduling.
Results indicate that the LFP schedule found by the stochastic method always outperforms the schedule given by the deterministic approach. Expected deterministic total weekly energy costs calculated this way exceed those calculated with the stochastic LFP schedule by $1170 up to $3781, depending on the scenario outcome.
Results indicate that using a stochastic approach can both increase the reliability of microgrid operations and improve its economic performance, which also illustrates the advantages of using an integrated modeling approach with a model such as DER-CAM.
