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At least 127 records · Page 7

A novel large-scale EV charging scheduling algorithm considering V2G and reactive power management based on ADMM

Electric vehicle aggregators (EVAs) that utilize vehicle-to-grid (V2G) technologies can function as both controllable loads and virtual power plants, providing key energy management services to the distribution system operator (DSO). EVAs can also balance the grid’s reactive power as a virtual static VAR compensator (SVC) and provide voltage stability by utilizing advanced electric vehicle (EV) chargers that are capable of four-quadrant operations to provide reactive power management. Finally, managed charging can benefit EVAs themselves by minimizing power factor penalties in their electricity bills. In this paper, we propose a novel EV charging scheduling algorithm based on a hierarchical distributed optimization framework that minimizes peak load and provides reactive power compensation for the DSO by collaboration with EVAs that manage both the active and the reactive charging and discharging power of participating EVs. Utilizing the alternative direction method of multipliers (ADMM), the proposed distributed optimization approach scales well with increased EV charging infrastructure by balancing active and reactive power while decreasing computational burden. In our proposed hierarchical approach, each EVA schedules the active and reactive EV charging and discharging power for 1) reactive power compensation in order to minimize power factor penalty and electricity cost accrued by the EVA, 2) satisfaction of each EV’s energy demand at minimal charging cost, and 3) peak shaving and load management for the DSO. When compared with an uncoordinated charging model, the efficacy of this proposed model is successfully demonstrated through a 300% decreased peak EV load for the DSO, 28% lower electricity costs for EV users, and 98.55% smaller power factor penalty, along with 17.58% lower overall electricity costs, for EVAs. The performance of our approach is validated in a case study with 50 EVs at multiple EVAs in an IEEE 13-bus test case and compared the results with uncoordinated EV charging.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Performance Demonstration of an Occupancy Sensor-enabled Integrated Solution for Commercial Buildings

Traditionally, a single-loop fixed-gain controller is applied to supply fan (SF) and cooling coil (CC) valve controls while a fixed-damper position control is applied to outdoor air (OA) damper control at air handling units (AHUs) in commercial buildings. With the increasing application of occupancy sensors, the information generated by occupancy sensors is applied to not only reduce the electricity loads from lighting and controllable plug loads, but also reset OA intake and minimum supply airflow setpoints. Meanwhile, these intermittent operation actions greatly elevate the dynamics of AHU systems, which may introduce unstable SF and CC valve operations and inaccurate OA flow control at AHUs and consequently degrade maximum energy efficiency gains. With virtual fan and valve flow meter technologies, two advanced controls, including cascade control and gain scheduling control, can be implemented on both the SF and CC valve, and an advanced control using a virtual OA flow meter can be implemented on OA damper integrated with occupancy sensors. The goal of this project is to demonstrate the savings, cost, and performance of an integrated solution that integrates the three advanced HVAC controls with occupancy sensors to allow accurate and stable AHU operations in real buildings. The project objectives are to: 1) develop and validate an advance SF control algorithm; 2) develop and validate an advanced CC valve control algorithm; 3) validate an algorithm to implement a virtual OA flow meter; and 4) demonstrate the savings, cost, and performance of the integrated solution in real buildings. The technical approaches are to: 1) select a test system at the University of Oklahoma; 2) develop and implement the algorithms of advanced SF and CC valve controls and validate the performance; 3) develop and implement the advanced OA control using a virtual OA flow meter and validate the performance; 4) demonstrate the savings, cost, and performance of the proposed integrated solution with and without three advanced HVAC controls; and 5) disseminate the project results through publications and presentations. For the SF control, both the gain scheduling and cascade controls can improve the fan energy performance by reducing the fan power during the transient period and the fan control performance at lower speeds by reducing fan speed variation. Moreover, the gain scheduling control provides a simple and low-cost solution and is recommended. The fan power savings can reach 30% in a transient period. For the CC valve control, the gain scheduling control can considerably reduce the supply air temperature oscillation range and frequency under both higher and lower load conditions and the control valve response is much more stable. As a result, the gain scheduling control is recommended. The projected pump energy consumption can be reduced by 68.5%. With the developed virtual OA flow meter, the OA can be accurately controlled at its setpoint, which is determined based on the actual number of occupants in the building provided by occupancy sensors. The RMSE of the proposed OA control is 15.9 L/s. The energy data shows that the fan power and CC cooling energy were significantly reduced. On the other hand, the energy savings majorly results from the occupancy sensors and the energy savings by the advanced HVAC controls is minimal because that the controllers in the test AHU were tuned with very slow response. An annual technical savings potential is estimated as 0.5 quads in the commercial sector.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Nontargeted vs. Targeted vs. Smart Load Shifting Using Heat Pump Water Heaters

Deployment of CTA-2045–enabled devices is increasing in the U.S. market. These devices allow utilities or third-party aggregators to control appliance energy use in homes, and could also be applied to end uses in small commercial buildings. This study focuses on a field study using CTA-2045–enabled water heaters to shift electric load off the peak and toward periods when renewable resources are more prevalent (e.g., near noon for solar resources and near midnight for wind resources). The following load shifting strategies were compared to understand effects on the aggregate load-shifting capabilities of Heat Pump Water Heaters (HPWHs) and on consumer hot water supply: non-targeted (traditional), targeted (grouped, with different shifting schedules) and “smart” (adaptive control commands). The results of this study show that targeted and smart control strategies yield significantly more load-shifting potential from a population of water heaters than the non-targeted approach without sacrificing hot water supply to occupants. However, as control commands become more aggressive, aggregators may face challenges in meeting consumer hot water demand. Furthermore, the findings and lessons learned can benefit electric utilities and inform updates to manufacturer controls and communications standards. The data collected may also be useful for developing and validating HPWH models.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints

Abstract Mixed integer linear programming (MILP)–based distributed energy management for networked microgrids embedded modern distribution systems is proposed. Considering the diverse ownership of microgrids, distributed energy resources (DERs) that interface directly with utilities and responsive loads, an alternating direction method of multipliers–based distributed framework was formulated for the scheduling of networked microgrids embedded modern distribution systems by adjusting nodal price signals iteratively. In addition, to make the formulated optimization problems resolvable through more accessible and popular MILP solvers, different linearisation techniques were employed to transform the nonlinear terms into linear or mixed integer linear formats. The proposed MILP‐based distributed method preserves all participants' autonomy (e.g., microgrids, DERs that interface directly with utilities and responsive loads), while incentivising them to actively participate in the distribution system operation with price signals. The proposed method is validated with results of numerical simulation using a modern distribution system consisting of multiple networked microgrids, DERs that interface directly with utilities, as well as responsive loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Model predictive control for voltage restoration in microgrids using temporal logic specifications

Power system operation will encounter numerous voltage variabilities as the proliferation of renewable energy continues. Real-time monitoring and communication technologies can potentially improve voltage stability by enabling the rapid detection of voltage deviations and the implementation of corrective actions. These corrective actions will only be effective in restoring stability if they are chosen in a timely and scalable manner. This paper considers the problem of power systems’ load voltage control in order to simultaneously address both magnitude and time voltage specifications. In order to comply with grid codes and avoid unnecessary relay protection actions, a model predictive control (MPC)-based control strategy employing temporal logic specifications (TLSs) is proposed. The TLSs strategy is introduced as a formalism to control the voltage variation at a critical load bus against operational bounds over time. The control objective is to schedule optimal control input signals from the available supportive energy storage systems, which provide reactive power injections, leading to satisfying the specified finite-time restoration described by the TLSs with minimal control efforts. The simulation results display that the TLSs strategy for power systems’ voltage control synthesis is extremely significant.

24 POWER TRANSMISSION AND DISTRIBUTION↗

RLScheduler: An Automated HPC Batch Job Scheduler Using Reinforcement Learning

Today’s high-performance computing (HPC) platforms are still dominated by batch jobs. Accordingly, effective batch job scheduling is crucial to obtain high system efficiency. Existing HPC batch job schedulers typically leverage heuristic priority functions to prioritize and schedule jobs. But, once configured and deployed by the experts, such priority functions can hardly adapt to the changes of job loads, optimization goals, or system settings, potentially leading to degraded system efficiency when changes occur. To address this fundamental issue, we present RLScheduler, an automated HPC batch job scheduler built on reinforcement learning. RLScheduler relies on minimal manual interventions or expert knowledge, but can learn high-quality scheduling policies via its own continuous ‘trial and error’. We introduce a new kernel-based neural network structure and trajectory filtering mechanism in RLScheduler to improve and stabilize the learning process. Through extensive evaluations, we confirm that RLScheduler can learn high-quality scheduling policies towards various workloads and various optimization goals with relatively low computation cost. Moreover, we show that the learned models perform stably even when applied to unseen workloads, making them practical for production use.

Zhang, Di↗

Evaluating the Grid Impact of Oregon Offshore Wind [Slides]

This analysis used high-resolution offshore wind data and a detailed production cost model (PCM) of the Western Interconnection to explore the value and operational impact of integrating offshore wind along Oregon's coastline. Leveraging local technical stakeholder expertise and input, we determined a set of scenarios to explore. These scenarios vary both offshore wind capacities and the Western Interconnection generation and transmission infrastructure. From the scenario modeling and analysis, we identified the following key findings. In addition, we simulated a subset of the scenarios for a range of historical weather years (2007-2013), to understand the robustness of our findings to different weather conditions. Trans-coastal transmission constraints and congestion are the key drivers to the curtailment of Oregon offshore wind. Once power can be delivered into the Willamette Valley, there are few system constraints that lead to a significant curtailment of offshore wind off the coast of Oregon. Approximately 2.6 GW of installed offshore wind capacity can be integrated into Oregon's power system without major upgrades to trans-coastal transmission while avoiding significant curtailment. The system value provided by offshore wind ranges between $\$65$ /MWh and $\$85$ /MWh across the various scenarios considered. Offshore wind heavily influences the flow of the cross Cascade transmission. Across all scenarios, we found a robust relationship of approximately 500-550 MW decrease in the hourly flow of the cross Cascade transmission for every 1,000 MW of hourly offshore wind generation. However, we also found there was not a strong relationship between the highest cross-Cascade transmission flow hours and high offshore wind generation, limiting the extent to which offshore wind can be considered a non-wires alternative to cross cascade transmission. Depending on the meteorological year, 880-1,580 MW and 1,650-3,100 MW can be counted on to serve coastal loads with 2.6 GW and 5 GW of offshore wind capacity, respectively. Offshore wind allows for more optimal daily and hourly scheduling of hydropower, while still complying with various technical and regulatory constraints on the water resource. Oregon offshore wind has the potential to contribute to the evening net load peak in California (i.e., mitigate duck curve challenges), however transmission congestion between California and Oregon limits this contribution. Co-located storage at the point of interconnection for offshore wind reduces curtailment when trans-coastal transmission is not upgraded, providing a non-wires alternative to increase offshore wind capacity beyond 2.6 GW.

17 WIND ENERGY↗

An MILP-Based Distributed Energy Management for Coordination of Networked Microgrids

An MILP-based distributed energy management for the coordination of networked microgrids is proposed in this paper. Multiple microgrids and the utility grid are coordinated through iteratively adjusted price signals. Based on the price signals received, the microgrid controllers (MCs) and distribution management system (DMS) update their schedules separately. Then, the price signals are updated according to the generation–load mismatch and distributed to MCs and DMS for the next iteration. The iteration continues until the generation–load mismatch is small enough, i.e., the generation and load are balanced under agreed price signals. Through the proposed distributed energy management, various microgrids and the utility grid with different economic, resilient, emission and socio-economic objectives are coordinated with generation–load balance guaranteed and the microgrid customers’ privacy preserved. In particular, a piecewise linearization technique is employed to approximate the augmented Lagrange term in the alternating direction method of multipliers (ADMM) algorithm. Thus, the subproblems are transformed into mixed integer linear programming (MILP) problems and efficiently solved by open-source MILP solvers, which would accelerate the adoption and deployment of microgrids and promote clean energy. The proposed MILP-based distributed energy management is demonstrated through various case studies on a networked microgrids test system with three microgrids.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Integration of a Smart Outlet-Based Plug Load Management System with a Building Automation System

The growth of and reliance on renewable energy necessitate a multi-pronged approach to achieve grid reliability and economics. As they represent a notable portion of U.S. energy consumption, commercial buildings must play an active role in this effort. Conserving energy and responding to grid conditions through demand flexibility can be achieved through the integration of major building systems. Integration of plug and process loads with lighting and heating, ventilation, and air conditioning systems maximizes the effectiveness of integrated building energy management. In this research, we demonstrate the integration of smart outlets into a building automation system. We cover the installation process as well as the architecture required for smart outlets to communicate data to the building automation system and to receive commands back. After recording power measurements for one week as a baseline, we configured the building automation system to turn the smart outlets on and off according to a set schedule. This resulted in energy savings of 66% during 1 week on 25 plug loads. This work demonstrates that grid-interactive efficient buildings are achievable through building system integration.

building automation system↗

Grid-connected heat pump water heater benefits for low-income households in the Southeastern United States

Energy efficient heat pump water heaters (HPWHs) reduce customer energy costs; grid-connected controls further increase HPWH value by enabling energy storage and shifting demand to cheaper, off-peak periods. However, a HPWH’s first cost premium can put it out of reach for low-income customers. This paper will present results of an ongoing study exploring the benefits of load shifting HPWHs for 24 low-income households, aiming to support increased product deployment in this demographic. The study uses EcoPort modules to shift HPWH load for a study sample consisting primarily of low-income adults and seniors in North Carolina. Building upon prior studies, the study’s HPWH operating schedules are designed to maximize shifted energy and minimize participant electricity costs based on local time-of-use rates. The study documents load profiles of grid-connected HPWHs in a less-studied demographic group and explores how certain groups may have particularly flexible loads due to their unique usage profiles. The results are relevant for HPWH product performance in the Southeast. The study will quantify HPWH load shifting performance during North Carolina’s hot summer, temperate shoulder, and occasionally sub-freezing winter seasons, and the study includes installations in conditioned, semi-conditioned, and unconditioned spaces. Finally, study results will also explore how controlled HPWHs can provide value to the regional grid by reducing seasonal peaks via demand response. Lessons learned include HPWH acceptance for low-income and senior users, best practices for maintaining HPWH connectivity among users without prior product experience, and strategies to leverage remote monitoring to ensure optimal operation and enhance HPWH reliability.

Urigwe, Daniela↗

Usage Pattern Analysis for the Summit Login Nodes

High performance computing (HPC) users interact with Summit through dedicated gateways, also known as login nodes. The performance and stability of these login nodes can have a significant impact on the user experience. In this study, the performance and stability of Summit’s five login nodes are evaluated by analyzing the log data from 2020 and 2021. The analysis focuses on the computing capability (CPU average load, users and tasks) and the storage performance, along with the associated job scheduler activity. The outcome of this study can serve as the foundation of a predictive modeling framework that enables the system admin of an HPC system to preemptively deploy countermeasures before the onset of a system failure.

Eiffert, Brett↗

Adaptive PID Gain Scheduling Control for Hydropower Turbine Using Neural CDE and Stochastic Distribution Shaping

This paper introduces a gain-scheduling PID controller design strategy for hydroturbine frequency control mode. This scheme first uses real data to learn the nonlinear dynamics of the hydroturbine using neural controlled differential equations and then perturbs the obtained nonlinear system at different equilibrium points, based on which a static output feedback adaptive dynamic programming algorithm is then used to optimize the PID gains for each equilibrium point. Moreover, a continuous-time version of stochastic distribution control is proposed to further fine-tune the optimized PID gains. Finally, the controller is obtained by implementing linear interpolation between the optimized PID control gains. The simulation results show that the proposed gain-scheduling PID controller can control a larger range of operation points compared with the given fixed PID controller and the baseline method. Compared with the given fixed PID controller, the proposed gain-scheduling PID controller can regulate hydroturbine frequency against disturbances induced by power-load variation with over 50% less overshoot for some operation points.

13 HYDRO ENERGY↗

Technology Development and Field Monitoring in nZEB - US Country report IEA HPT Annex 49 Task 3

The International Energy Agency (IEA) Heat Pumping Technologies (HPT) Annex 49, “Design and Integration of Heat Pumps for Nearly Zero Energy Buildings,” deals with the application of heat pumps (HPs) as a core component of the HVAC system for nearly or net-zero energy buildings. This report covers the Task 3 activities of the US team. Three institutions are involved on the US team and have worked on the following projects. 1) Oak Ridge National Laboratory (ORNL) summarized development activities since the conclusion of IEA HPT Annex 40 for several integrated HP (IHP) systems - electric ground-source IHP and air-source IHP versions and engine-driven AS-IHP version. 2) The University of Maryland partnered with ORNL and Blue Bear Management to develop a personal cooling device called RoCo that can provide personalized conditioned air to occupants in inadequately or unconditioned environments. With RoCo, building facility management can elevate the HVAC thermostat settings without compromising occupants’ thermal comfort. Researchers have found that a 4°F increase in thermostat settings can save 12–30% energy savings. Therefore, RoCo is a promising technology that can help reduce building energy consumption and facilitate achievement of net-zero energy building performance. 3) The National Institute of Standards and Technology (NIST) is working on a field study effort on the NIST Net-Zero Energy Residential Test Facility. Two air-source split-system HPs were installed in a residential, net-zero energy home that was constructed as a laboratory on the NIST campus in Gaithersburg, Maryland. The first HP was a two-stage, 7 kW (2 ton), 15.8 seasonal energy efficiency ratio (SEER), 9.05 heating seasonal performance factor (HSPF) conventionally ducted system; the second HP was a variable-speed, 10.6 kW (3 ton), 14 SEER, 8.35 HSPF, high-velocity ducted system. These two systems operated side by side, using separate supply ducts and a common return duct, on a weekly alternating schedule to condition the home that was operated with very consistent simulated thermal loads. The team wanted to determine whether the high-velocity system could provide comparable energy-use efficiency to the conventional system. The results of this study showed that it did meet the required loads and had slightly greater efficiency; the average cooling coefficient of performance (COP) was (0.40 ± 0.11) higher, and the average heating COP was statistically equal. A new firmware was provided at the end of the heating season that greatly improved the performance of the high-velocity system; its average heating COP went from (1.8 ± 0.9) to (2.5 ± 1.1) at a 95% confidence level. The new firmware heating COP averaged (1.05 ± 0.23) higher than the old firmware over the same outdoor temperatures. The defrost performance is very different for these two systems, yet they consumed equivalent energy per HDD. The conventional system uses a timed-initiate, temperature-terminate algorithm with auxiliary electric resistive heating, whereas the high-velocity system uses calculated evaporator parameters with a hot-gas bypass before a full reverse-cycle defrost with no supplementary resistive heat.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Coupling thermal energy storage with a thermally anisotropic building envelope for building demand-side management across various US climate conditions

Here, the thermally anisotropic building envelope (TABE) is a novel active building envelope that enhances energy efficiency and thermal comfort in buildings by transferring heat and cold between building envelopes and hydronic loops. When coupled with thermal energy storage (TES) units, the TABE + TES enables the storage of both heat and cold energy captured by the TABE roof or exterior walls. This stored energy can be later released by the TABE floor for indoor heating and cooling, benefiting both the grid and the end user. This paper evaluates the merits of TABE + TES for building demand-side management across various US climate conditions, focusing on peak load shaving, annual energy savings, and cost savings under time-of-use (TOU) electric rate schedules. Simulations were conducted by integrating time-of-day–informed, rule-based control strategies in MATLAB, TABE components and TES units in COMSOL Multiphysics, and whole-building energy analysis in EnergyPlus. A case study using the US Department of Energy’s prototype single-family detached house model in Birmingham, Alabama; Los Angeles, California; Oak Ridge, Tennessee; and Denver, Colorado, showed that the TABE + TES system achieved (1) 70 % peak load shaving in Los Angeles and Denver and 20 % in Birmingham and Oak Ridge; (2) significant peak electricity savings of 351–497 kWh, reducing peak energy consumption by 38 %–78 %; and (3) annual heating cost savings of 0.79 $\$$/m2–1.17 $\$$/m 2 and cooling cost savings of 0.60 $\$$/m 2 –1.17 $\$$/m 2 using a normal utility rate or low-TOU rate. The benefits of employing the TABE + TES system are even more significant under high TOU rates.

25 ENERGY STORAGE↗

A data-driven linear formulation of the optimal demand response scheduling problem for an industrial air separation unit

Demand response (DR) has become a key element in balancing the power grid as the contribution of time-varying renewable power generation increases. Chemical plants are appealing candidates for DR programs as they offer large, concentrated and flexible loads. DR participation calls for frequent production rate changes over time scales that overlap with the dominant dynamics of the plant. Production scheduling should therefore consider the process dynamics explicitly. Here we present a data-driven approach for modelling the scheduling-relevant dynamics based on historical closed-loop operating data using autoregressive with extra inputs (ARX) models. We introduce a new, linear scheduling problem formulation based on the ARX representation, and demonstrate its implementation on an industrial air separation unit.

42 ENGINEERING↗

A Framework to Evaluate the Grid Impacts of EV Fleet Charging Solutions

Growing Electric vehicle (EV) adoption in residential and commercial applications is driving the need for the charging infrastructures required to fulfill the charging needs. The resulting increase in demand for electric power will add a significant load to the electric grid, which could negatively impact the grid operation. EVs are power electronic loads and draw harmonic currents which can lead to a host of power quality issues. Therefore, it is crucial to assess the grid impacts and management of EV charging loads to ensure the reliable operation of the electric grid. In this paper, we develop a framework to help determine power-quality impacts given an EV charging schedule on the system. We compare the performance of unmanaged and managed charging solutions on factors like voltage drop, flicker, harmonic distortion and the peak site load - based on the EV depot in Hazelwood school district. The results allow insights into operation and site design of EV depots.

ADVANCED PROPULSION SYSTEMS,POWER TRANSMISSION AND↗

Evaluation of supply air temperature control performance with different control strategies at air handling units

Due to its nonlinear feature, supply air temperature control systems at air handling units using single-loop fixed gain control frequently suffer unstable response under dynamic conditions. This paper is aimed at identifying a more effective control strategy to stabilize the valve control and achieve desirable supply air temperature response under various operation conditions by evaluating three control strategies, cascade, gain scheduling and cascade plus gain scheduling controls. Firstly, a control-oriented model is developed and calibrated through open-loop tests. Then, the control issues with single-loop fixed gain control are evaluated through simulations and field tests, which indicates that the system has more aggressive response or becomes unstable under lower load conditions when the chilled-water flow rate is less than 0.1 L/s. Finally, three control strategies are proposed and evaluated. Further, the results reveal that all three proposed controls can achieve better robustness with the integral square error of supply air temperature decreased to 16%, 47% and 5%, respectively, under lower load condition. However, since high-frequency oscillation of the control valve occurs with cascade and cascade plus gain scheduling control, the gain scheduling control is recommended considering a trade-off among the supply air temperature response, valve lifetime and implementation complexity.

42 ENGINEERING↗

Ice storage model-predictive control in an office building with PV: scenario, error and sensitivity analysis

Thermal energy storage (TES) can enable more building-sited renewable electricity generation and lower utility bill costs for buildings owners and occupants, especially when there are high demand and variable time-of-use (TOU) charges. A model predictive control (MPC) strategy can offer additional savings over a schedule-based control with added complexity and reliance on forecasts. Here, this study examines savings for medium office buildings with chiller plants in three locations with building-installed solar photovoltaics (PV) to understand the impact of MPC. Control setpoints are fixed by a schedule-based control or optimized by nonlinear MPC. These control setpoints are actuated within EnergyPlus building models to simulate the utility cost of the chiller plant. NLP solutions can be unstable or unrealistic, but our results show that by regularizing the NLP, the solutions can be reasonably followed by the building model. MPC models make simplifications that lead to errors once the controller is participating in and changing the operation of the building. These errors average 9 % across the cases, showing that the most important parts of the system are represented. The no-thermal load costs are computed to show that the optimization can in some cases achieve both the minimum TOU and minimum monthly demand costs by demand management while reducing TOU energy costs by energy arbitrage. The MPC saves 35–66 % in the annual chiller plant operating costs, which is an additional savings above the schedule by 1–33 %. PV and TES are complementary and mostly independent, but a load with PV often results in better performance for the schedule. Our case study and sensitivity analysis show the importance of modeling and optimization for complex rates, but also the circumstances wherein a simpler strategy achieves the same performance with less potential for error.

14 SOLAR ENERGY↗