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This paper presents one of the first real-life demonstrations of coordinated and distributed resource control for secondary frequency response in a power distribution grid. A series of tests involved up to 69 heterogeneous active distributed energy resources consisting of air handling units, unidirectional and bidirectional electric vehicle charging stations, a battery energy storage system, and 107 passive distributed energy resources consisting of building loads and solar photovoltaic systems. The distributed control setup consists of a set of Raspberry Pi end-points exchanging messages via an Ethernet switch. Actuation commands for the distributed energy resources are obtained by solving a power allocation problem at every regulation instant using distributed ratio-consensus, primal-dual, and Newton-like algorithms. The problem formulation minimizes the sum of distributed energy resource costs while tracking the aggregate setpoint provided by the system operator. We demonstrate accurate and fast real-time distributed computation of the optimization solution and effective tracking of the regulation signal over 40 min time horizons. An economic benefit analysis confirms eligibility to participate in an ancillary services market and demonstrates up to $\$ $ 53k of potential annual revenue for the selected population of distributed energy resources.

Forecast errors can cause sub-optimal solutions in resource planning optimization, yet they are usually modeled simplistically by statistical models, causing unrealistic impacts on the optimal solutions. In this paper, realistic forecast errors are prescribed, and a corrective approach is proposed to mitigate the negative effects of day-ahead persistence forecast error by short-term forecasts from a state-of-the-art sky imager system. These forecasts preserve the spatiotemporal dependence structure of forecast errors avoiding statistical approximations. The performance of the proposed algorithm is tested on a receding horizon quadratic program developed for valley filling the midday net load depression through electric vehicle charging. Throughout one month of simulations the ability to flatten net load is assessed under practical forecast accuracy levels achievable from persistence, sky imager and perfect forecasts. Compared to using day-ahead persistence solar forecasts, the proposed corrective approach using sky imager forecasts delivers a 25% reduction in the standard deviation of the daily net load. It is demonstrated that correcting day-ahead forecasts in real time with more accurate short-term forecasts benefits the valley filling solution.

This paper presents a comparative analysis of the different forecasting techniques (Statistical method (ARIMA)), Machine Learning method (Multivariate Linear Regression) and Deep Learning method (LSTM)) for short term load forecasting. The forecasting model for each of these techniques takes into account the historical load (annual), site temperature data and US calendar data as input features. The model is trained on the first nine months of data and then tested for accuracy on the remaining three months. A case study using the load profile of a commercial building (amusement park) in San Diego, California is presented, where the performance of the above forecasting techniques is compared. The error metric used for comparison is the Root Mean Squared Error (RMSE) value. The results indicate that LSTM model offers the best performance in terms of forecasting accuracy. The designed LSTM model can be deployed as part of Energy Management System (EMS) for smart grids. The robustness of the LSTM model is further explored by comparing the above LSTM encoder-decoder architecture with a standard LSTM architecture. In addition to the above dataset, both architectures were tested on two more datasets- one for an office building and another for an operations center building located in San Diego. Both architectures were trained on first 9 months of load data and tested on the remaining 3 months. The encoder-decoder architecture performed better than the standard architecture across all the datasets.

Large ramps and ramp rates in photovoltaic (PV) power output are of concern and sometimes even explicitly restricted by grid operators. Battery energy storage systems can smooth the power output and maintain ramp rates within permissible limits. To enable PV plant and energy storage system design and planning, a method to estimate the largest expected ramps for a given location is proposed. Because clouds are the dominant source of PV power output variability, an analytical relationship between the worst expected ramp rate, cloud motion vector, and the geometrical layout of the PV plant is developed. The ability of the proposed method to bracket actual ramp rates is assessed over 10 months under different meteorological conditions, demonstrating an average compliance rate of 98.9% for a 2 min evaluation time window. The largest observed ramp of 29.7% s(-1)is contained with the worst case estimate of 34.3% s(-1). This method provides a convenient yet economical approach to worst-case PV ramp rate modeling and is compatible with solar irradiance measured at coarse temporal resolution. Juan Bosch was financed in part by Project No. PID2019-108953RB-C21, funded by the Ministerio de Ciencia e Innovación and co-financed by the European Regional Development Fund. In addition, Iñigo de la Parra was partially supported by the Spanish State Research Agency (AEI) and FEDER-UE under Grant Nos. DPI2016-80641-R and DPI2016-80642-R.

In many jurisdictions, policy-makers are seeking to decentralize the electric power system while also promoting deep reductions in the emission of greenhouse gases (GHG). We examine the potential roles for residential energy storage (RES), a technology thought to be at the epicenter of these twin revolutions. We model the impact of grid-connected RES operation on electricity costs and GHG emissions for households in 16 of the largest U.S. utility service territories under 3 plausible operational modes. Regardless of operation mode, RES mostly increases emissions when users seek to minimize their electricity cost. When operated with the goal of minimizing emissions, RES can reduce average household emissions by 2.2-6.4%, implying a cost equivalent of $180 to $5160 per metric ton of carbon dioxide avoided. While RES is costly compared with many other emission-control measures, tariffs that internalize the social cost of carbon would reduce emissions by 0.1-5.9% relative to cost-minimizing operation. Policy-makers should be careful about assuming that decentralization will clean the electric power system, especially if it proceeds without carbon-mindful tariff reforms.

International audience; Cloud height information is crucial for various applications. This includes solar nowcasting systems. Multiple methods to obtain the altitudes of clouds are available. In this paper, cloud base heights derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) and three low-cost and low-maintenance ground based systems are presented and compared against ceilometer measurements on 59 days with variable cloud conditions in southern Spain. All three ground based systems derive cloud speeds in absolute units of [m/s] from which cloud heights are determined using angular cloud speeds derived from an all-sky imager. The cloud speed in [m/s] is obtained from (1) a cloud shadow speed sensor (CSS), (2) a shadow camera (SC) or (3) derived from two all-sky imagers. Compared to 10-min median ceilometer measurements for cloud heights below 5000 m, the CSS-based system shows root-mean squared deviations (RMSD) of 996 m (45%), mean absolute deviations (MAD) of 626 m (29%) and a bias of −142 m (−6%). The SC-based system has an RMSD of 1193 m (54%), a MAD of 593 m (27%) and a bias of 238 m (11%). The two all-sky imagers based system show deviations of RMSD 826 m (38%), MAD of 432 m (20%) and a bias of 202 m (9%). The ECMWF derived cloud heights deviate from the ceilometer measurements with an RMSD 1206 m (55%), MAD of 814 m (37%) and a bias of −533 m (−24%). Due to the multi-layer nature of clouds and systematic differences between the considered approaches, benchmarking cloud heights is an extremely difficult task. The limitations of such comparisons are discussed. This study aims at determining the best approach to derive cloud heights for camera based solar nowcasting systems. The approach based on two all-sky imagers is found to be the most promising, having the overall best accuracy and the most obtained measurements.

The main contributor to spatio-temporal variability in the solar resource is clouds passing over photovoltaic (PV) modules. Cloud velocity is a principal input to many short-term forecast and variability models. In this paper spatio-temporal correlations of irradiance data are analyzed to estimate cloud motion. The analysis is performed using two spatially and temporally resolved simulated irradiance datasets generated from large eddy simulation. Cloud motion is estimated using two different methods; the cross-correlation method (CCM) applied to two or a few consecutive time steps and cross-spectral analysis (CSA) where the cloud speed and direction are estimated by cross-spectral analysis of a longer time series. CSA is modified to estimate the cloud motion direction as the case with least variation for all the velocities in the cloud motion direction. To ensure reliable cloud motion estimation, quality control (QC) is added to the CSA and CCM analyses. The results show 33% (52°) and 21% (6°) improvement in the cloud motion speed (direction) estimation using the modified CSA and CCM over the original methods (without QC), respectively. In general, CCM results are accurate for all the different cloud cover fractions with average relative mean bias error (rMBE) of cloud speed and mean absolute error of cloud direction equal to 3% and 3°, respectively. For low cloud cover fractions, CSA estimates the cloud motion speed and direction with rMBE and mean absolute error equal to 10% and 11°, respectively. However, for high cloud cover fractions and unsteady cloud speed, CSA results are not reliable for 3–4 h time series; however, splitting the whole time series into shorter time intervals reduces the rMBE and mean absolute error to 15% and 16° respectively.

The intra-hour intermittency of solar energy and demand introduce significant design challenges for microgrids. To avoid costly energy shortfalls and mitigate outage probability, islanded microgrids must be designed with sufficient distributed energy resources (DER) to meet demand and fulfill the energy and power balance. To avoid excessive runtime, current design tools typically only utilize hourly data. As such, the variable nature of solar and demand is often overlooked. Thus, DER designed based on hourly data may result in significant energy shortfalls when deployed in real-world conditions. This research introduces a new, fast method for optimizing DER investments and performing dispatch planning to consider intra-hour variability. A novel set of constraints which operate on intra-hour data are implemented in a mixed-integer-linear-program microgrid investment optimization. Variability is represented by the single worst-case intra-hour fluctuation. This allows for fast optimization times compared to other approaches tested. Applied to a residential microgrid case study with 5-minute intra-hour resolution, this new method is shown to maintain optimality within 2% and reduce runtime by 98.2% compared to full-scale-optimizations which consider every time-step explicitly. Applicable to a variety of technologies and demand types, this method provides a general framework for incorporating intra-hour variability into microgrid design.

Whole sky imagers are commonly used for forecasting irradiance available for solar energy production, but validation of the forecast models used is difficult due to sparse reference data. We document the use of Large Eddy Simulations (LES) and a 3D Radiative Transfer Model to produce virtual clouds, sky images, and radiation measurements, which permit comprehensive validation of the sky imager forecast. We then use this virtual testbed to investigate the primary sources of sky imager forecast error on a cumulus cloud scene. The largest source of nowcast (0-min-ahead forecast) errors is the converging-ray geometry implied by use of a camera, while longer-term forecasts suffer from overly-simplistic assumptions about cloud evolution. We expect to use these findings to focus future algorithm development, and the virtual testbed to evaluate our progress.

We develop a new convex optimization (CO)-based charge/discharge scheduling algorithm for distributed energy storage systems (ESSs) co-located with solar photovoltaic (PV) systems. The CO-based scheduling algorithm minimizes the monthly electricity expenses of a customer who owns an ESS and incorporates both a time-of-use volumetric tariff and a demand charge tariff. Further, we propose the novel idea of a “supply charge” tariff that incentivizes ESS customers to store excess solar PV generation that may otherwise result in reverse power flow in the distribution grid. By means of a case study we observe the CO-based daily charge/discharge schedules reduce (1) peak net demand (that is, load minus PV generation) of the customer, (2) power fluctuations in the customer net demand profile, and (3) the reliance of the customer on the grid by way of promoting energy self-consumption of local solar PV generation. Two alternate methods for behind-the-meter ESS scheduling are considered as benchmarks for cost minimization, peak net demand reduction, and mitigation of net demand fluctuations. The algorithm is tested using real 30-min interval residential load and solar data of 53 customers over 2-years. Results show that the CO-based scheduling algorithm provides mean peak net demand reductions between 46% and 64%, reduces mean net demand fluctuations by 25–49%, and increases the mean solar PV self-consumption between 24% and 39% when compared to a customer without an ESS. Introduction of a supply charge reduces the maximum solar PV power supply to the grid by 19% on average and does not financially impact ESS owners.

As urbanization progresses, more realistic methods are required to analyze the urban microclimate. However, given the complexity and computational cost of numerical models, the effects of realistic representations should be evaluated to identify the level of detail required for an accurate analysis. We consider the realistic representation of surface heating in an idealized three-dimensional urban configuration, and evaluate the spatial variability of flow statistics (mean flow and turbulent fluxes) in urban streets. Large-eddy simulations coupled with an urban energy balance model are employed, and the heating distribution of urban surfaces is parametrized using sets of horizontal and vertical Richardson numbers, characterizing thermal stratification and heating orientation with respect to the wind direction. For all studied conditions, the thermal field is strongly affected by the orientation of heating with respect to the airflow. The modification of airflow by the horizontal heating is also pronounced for strongly unstable conditions. The formation of the canyon vortices is affected by the three-dimensional heating distribution in both spanwise and streamwise street canyons, such that the secondary vortex is seen adjacent to the windward wall. For the dispersion field, however, the overall heating of urban surfaces, and more importantly, the vertical temperature gradient, dominate the distribution of concentration and the removal of pollutants from the building canyon. Accordingly, the spatial variability of concentration is not significantly affected by the detailed heating distribution. The analysis is extended to assess the effects of three-dimensional surface heating on turbulent transfer. Quadrant analysis reveals that the differential heating also affects the dominance of ejection and sweep events and the efficiency of turbulent transfer (exuberance) within the street canyon and at the roof level, while the vertical variation of these parameters is less dependent on the detailed heating of urban facets.

This work explores the allocation question of battery energy storage systems (BESS) in distribution systems for their voltage mitigation support in integrating high penetration solar photovoltaics (PV). A genetic algorithm (GA)-based bi-level optimization method is developed that reduces the voltage fluctuations caused by PV penetration through deploying BESS among permitted nodes of a distribution system while accounting for their capital, land-of-use and installation costs using a qualitative cost model. The optimization problem considers BESS capacity and installation points in the distribution system as decision variables. Each BESS operation is determined using a linear programming (LP) routine that minimizes the daily coincident peak demand. A comprehensive validation study is carried out through exhaustive enumeration with the IEEE 8500-Node test feeder showing that the proposed method results in consistent decisions that appear to be globally optimal. Further sensitivity studies are conducted to showcase the behavior of the method under varying sizing costs, siting costs and PV penetrations.

Sky imaging systems are commonly used for aerosol characterization, cloud detection, and solar forecasting. We present an algorithm for measuring full-sky radiance with a range that exceeds the normal dynamic range of the camera system in question. Extended dynamic range over most of the sky is achieved with multiple exposures and High Dynamic Range (HDR) imaging, while solar beam intensity is estimated using CCD smear. Smear measurements are calibrated to match reference GHI based on pixel position on the sensor, and resulting irradiance measurements are validated. Global horizontal irradiance RMSE (root-mean-square error) for a year-long data set is in the 9–11% range for per-image data and 6–9% for hourly-averaged data when compared against a solid-state pyranometer. In addition, Direct Normal Irradiance (DNI) measurements for clear skies during a five-month period are compared to a non-co-located SPN1 DNI sensor, with RMSE of 8%.

Smart PV inverter functions have the potential to allow integrating increased PV penetration levels without the need of costly distribution upgrade measures. This paper evaluates the effectiveness of using California Rule 21 Phase I and Phase III smart inverter functions to increase PV hosting capacity. In particular, Volt-var, Volt-watt, and Limit Maximum Real Power functions are analyzed to increase PV hosting capacity by 25% on five real California distribution feeders. Comprehensive simulations are performed on each function over a range of settings, PV/load conditions, and feeder characteristics. Detailed analysis is shown to assess the impact that the settings have on numerous feeder metrics. Volt-var function with var priority is shown to be successful in improving hosting capacity with minimal PV energy curtailment. Additionally, smart inverter functions are compared against the distribution upgrade measures that would otherwise be required to increase the hosting capacity.

This paper develops a new microgrid investment planning model that determines cost-optimal investment and operation of distributed energy resources (DERs) in a microgrid. We formulate the problem in a bilevel framework, using particle swarm optimization to determine investment and the DER-CAM model (Distributed Energy Resources Customer Adoption Model) to determine operation. The model further uses sequential Monte Carlo simulation to explicitly simulate power outages and integrates time-varying customer damage functions to calculate interruption costs from outages. The model treats nonlinearities in reliability evaluation directly, where existing linear models make critical simplifying assumptions. It combines investment, operating, and interruption costs together in a single objective function, thereby treating reliability endogenously and finding the cost-optimal trade-off between cost and reliability - two competing objectives. In benchmarking against a version of the DER-CAM model that treats reliability through a constraint on minimum investment, our new model improves estimates of reliability (the loss of load expectation) by up to 600%, of the total system cost by 6%-18%, of the investment cost by 32%-50%, and of the economic benefit of investing 27%-47%. Improvements stem from large differences in investment of up to 56% for natural gas generators, solar photovoltaics, and battery energy storage.

Historical observations from radiosondes, buoys, and satellite images are used to generate an analog ensemble (AnEn) solar forecast. In coastal California, Stratocumulus (Sc) clouds appear most frequently during late spring and summer months. Sc clouds form at night and begin to dissipate after sunrise, limiting solar energy generation in the morning hours. The AnEn method categorizes cloudy (as either well-mixed or decoupled) and clear events at the forecast initial time and uses several meteorological variables to find the closest analogs. The AnEn forecast is tested at the NKX weather station in San Diego, CA during May to September 2014-2017. The AnEn forecast has a lower root mean square error than a numerical weather prediction model and 24-hour persistence forecasts. The error is lowest for the clear cases and largest for the cloudy decoupled cases. The AnEn forecast is able to capture Sc dissipation for the well-mixed cases in the early morning, but decoupled cases display higher variability throughout the day and are much harder to predict as a result.

The proliferation of distributed generation on distribution feeders triggers a large number of integration and planning studies. Further, the complexity of distribution feeder models, short simulation time steps, and long simulation horizons rapidly render studies computational burdensome. To mend this issue, we propose a methodology for reducing the number of nodes, loads, generators, line, and transformers of p -phase distribution feeders with unbalanced loads and generation, non-symmetric wire impedance, mutual coupling, shunt capacitance, and changes in voltage and phase. The methodology is derived on a constant power load assumption and employs a Gaussian elimination inversion technique to design the reduced feeder. Compared to previous work by the authors, the inversion reduction takes half the time and voltage errors after reduction are reduced by an order of magnitude. Using a snapshot simulation the reduction is tested on six additional publicly available feeders with a maximum voltage error 0.0075 p.u. regardless of feeder size or complexity, and typical errors on the order of $1\times 10^{-4}$ p.u. For a day long quasi-static time series simulation on the UCSD A feeder, errors are shown to increase with changes in loading when a large number of buses removed, but shows less variation for less than 85% of buses removed.

Open-source, high resolution power consumption data are scarce. We compiled, quality controlled, and released publicly a comprehensive power dataset of parts of the University of California, San Diego microgrid. The advanced microgrid contains several distributed energy resources (DERs), such as solar power plants, electric vehicles, buildings, a combined heat and power gas-fired power plant, and electric and thermal storage. Most datasets contain 15-min averages of real and reactive power from 1 January, 2015 until 29 February, 2020. We also include Python codes to fill missing data and flag and replace potentially erroneous data. The extensive dataset of conventional and new DERs is designed to accelerate research and development work in the area of sustainable microgrids.

The University of California, San Diego, has responded to the growth of Electric Vehicle (EV) ownership by continually adding charging stations all around campus over the past five years. In March 2020, the coronavirus pandemic caused a massive decline in EV charging as shelter-in-place orders were issued and the campus closed except for the medical centers. Overall, EV charging energy demand decreased by over 73%. But the decrease was uneven as direct current fast charger (DCFC) stations and the charging stations at the university's medical centers took on a larger percentage of the total campus load. Charging energy provided at the nonmedical stations decreased by 84%, while it decreased 50% at medical stations and 67% at DCFC stations. DCFC showed the strongest recovery in charging energy during the shutdown. The distribution of charging energy during the day and the charging duration did not change during the shutdown, while the plug-in duration increased. Implications for decarbonizing the transportation and electrical power systems are discussed.

Some potential adverse impacts of high photovoltaics (PV) penetration on the power grid are an increasing number of tap operations, over-voltages, and large and frequent voltage fluctuations and PV power ramps. The ability to create realistic PV input profiles with high spatial and temporal resolution is crucial to assess these impacts. This paper proposes a unique method to improve the accuracy of feeder hosting capacity studies using (1) high resolution PV generation profiles from sky imagers, (2) quasi-steady state distribution system simulation, and (3) distribution models created from utility data. Solar penetration levels, defined as ratio of peak PV output to peak load demand, from 0% to 200% and various cloud conditions are considered. Three conclusions were drawn: (1) the impacts of high PV penetration depend on feeder topology and characteristics; (2) the use of a single PV generation profile overestimates the tap operation number up to 260% resulting from an overestimation of power ramp rates and magnitudes – therefore, multiple realistic profiles should be used; and (3) distributed PV resources increase the feeder hosting capacity significantly compared to a centralized setup.

Mixed Integer Linear Programming (MILP) optimization algorithms provide accurate and clear solutions for Microgrid and Distributed Energy Resources projects. Full-scale optimization approaches optimize all time-steps of data sets (e.g., 8760 time-step and higher resolutions), incurring extreme and unpredictable run-times, often prohibiting such approaches for effective Microgrid designs. To reduce run-times down-sampling approaches exist. Given that the literature evaluates the full-scale and down-sampling approaches only for limited numbers of case studies, there is a lack of a more comprehensive study involving multiple Microgrids. This paper closes this gap by comparing results and run-times of a full-scale 8760 h time-series MILP to a peak preserving day-type MILP for 13 real Microgrid projects. The day-type approach reduces the computational time between 85% and almost 100% (from 2 h computational time to less than 1 min). At the same time the day-type approach keeps the objective function (OF) differences below 1.5% for 77% of the Microgrids. The other cases show OF differences between 6% and 13%, which can be reduced to 1.5% or less by applying a two-stage hybrid approach that designs the Microgrid based on down-sampled data and then performs a full-scale dispatch algorithm. This two stage approach results in 20–99% run-time savings.

Detonation of a nuclear weapon differs significantly from traditional chemical blasts in a number of well documented ways. However, at time of detonation, it is not easy to detect which type of blast actually occurred. Conventional forensics rely on collection of measurement which are either not well suited for surface detonations or require a lot of processing time at which it may be too late to have an accurate sense of battle awareness or enact defense mechanisms. We propose a novel approach which uses the power output of solar PV panels with the thermal radiation produced from the explosion as a signature. We extend the methodology to determine the effect on the powerflow in a nearby distribution feeder circuit rich with PV panels in both the steady and dynamic states. Our simulations show that the blast causes a saturation in every PV inverter and causes a large rapid increase in voltage on the feeder. The voltage increase was discussed to be generally non-reproducible through natural operation.

High penetration and intermittency of solar resources drive the development of distributed energy storage in microgrid. The adoption of electric vehicles (EV) encourages solar self consumption and carries a significant potential owning to cost and environmental considerations. Previous deterministic valley filling algorithms for EV charging scheduling are extended to consider the stochastic nature of EV schedules. The uncertainties in EV availabilities are studied through sampling coupled with ${k}$- means clustering methods formulated specifically for a real- world EV database. Then a scenario-based approach is proposed for modeling probabilistic EV charge events. The stochastic objective function is realized by considering uncertain EV charging in form of scenarios as true, which is known as deterministic equivalent problem. The resulting net load profiles are transformed into quantile distribution considering their probabilities of occurrence. The final output mustrates probabilistic EV charging strategies and associated grid net load profiles to assist operators in proactively managing grid load.

Integration of solar energy forecasts into the electric network is becoming essential because of the continually increasing penetration level of solar energy. Three-dimensional numerical weather prediction (NWP) models predict the weather based on the current weather conditions (called initialization) and simulate the ensuing atmospheric processes. The accuracy of forecasts therefore depends, in part, on the accuracy of the model initializations. Data assimilation is recognized as the most widely used technique to improve the initialization into NWP models. In this study, meteorological observations from the surface and upper-air in-situ networks over the southern California coast are assimilated into the advanced research version of the Weather Research and Forecasting (WRF) model using a three dimensional variational data assimilation technique (3DVAR). A single observation test was conducted to tune-up the length scale and variance scale along with the regional domain-dependent background error statistics. A customized version of 3DVAR data assimilation was deployed with two sets of cyclic data assimilation with 6-h and 1-h assimilation windows along with the cold-start mode. The cyclic data assimilation experiments consistently outperformed the cold-start data assimilation and WRF for intra-day Global Horizontal Irradiance (GHI) and Clear Sky Index (CSI) forecast. Hourly cyclic assimilation showed the highest forecast skill score against ground measurements and satellite measurements. Even at the coastal stations with more challenging meteorological conditions, the hourly cyclic assimilation consistently outperformed the 24-h persistence forecast. The average (mean of four case studies) hourly cyclic data assimilation showed the highest forecast skill score in GHI and CSI intra-day forecast with reference to 24-h persistence forecast up to 39.4% and 40.7% respectively at the coastal stations. The spatial distributions of GHI biases estimated against SolarAnywhere satellite measurements showed that the hourly cyclic assimilation consistently improved the stratocumulus cloud coverage, thickness, and life time over the coastal region, but biases are still present further inland.

Quasi-static time-series simulations (QSTS) of distribution feeders are a critical element of distributed solar PV integration studies. QSTS are typically carried out through computer simulation tools, such as OpenDSS. Since a typical feeder contains thousands of buses, for long investigation periods or at fine time scales such simulations are computationally costly. Simulation times are reduced in this paper through a reduction of the number of buses in the model. The feeder reduction algorithm considers p -phase distribution feeders with unbalanced loads and generation, unbalanced wire impedance, and mutual coupling, while preserving the spatial variation of load and generation. An extensive Monte Carlo sensitivity analysis was performed on a real feeder from a California utility. All bus voltage differences are found to be less than 1.13% with a root mean square error of 0.21%. Simulation time savings were up to 96% when only one bus is selected to remain in the model. Example applications of the proposed algorithm are interconnection studies of utility-scale photovoltaic system to the distribution grid, siting analyses of other distributed energy resources and dynamic behavior of devices in large systems, such as smart inverters on distribution grids.

A method for retrieving cloud optical depth (τc) using a UCSD developed ground-based sky imager (USI) is presented. The radiance red–blue ratio (RRBR) method is motivated from the analysis of simulated images of various τc produced by a radiative transfer model (RTM). From these images the basic parameters affecting the radiance and red–blue ratio (RBR) of a pixel are identified as the solar zenith angle (θ0), τc, solar pixel angle/scattering angle (ϑs), and pixel zenith angle/view angle (ϑz). The effects of these parameters are described and the functions for radiance, Iλτc, θ0, ϑs, ϑz, and RBRτc, θ0, ϑs, ϑz are retrieved from the RTM results. RBR, which is commonly used for cloud detection in sky images, provides non-unique solutions for τc, where RBR increases with τc up to about τc = 1 (depending on other parameters) and then decreases. Therefore, the RRBR algorithm uses the measured Iλmeasϑs, ϑz, in addition to RBRmeasϑs, ϑz, to obtain a unique solution for τc. The RRBR method is applied to images of liquid water clouds taken by a USI at the Oklahoma Atmospheric Radiation Measurement (ARM) program site over the course of 220 days and compared against measurements from a microwave radiometer (MWR) and output from the Min et al. (2003) method for overcast skies. τc values ranged from 0 to 80 with values over 80, being capped and registered as 80. A τc RMSE of 2.5 between the Min et al. (2003) method and the USI are observed. The MWR and USI have an RMSE of 2.2, which is well within the uncertainty of the MWR. The procedure developed here provides a foundation to test and develop other cloud detection algorithms.

A detailed derivation of stratocumulus cloud thickness and liquid water path tendencies as a function of the well-mixed boundary layer mass, heat, and moisture budget equations is presented. The derivation corrects an error in the cloud thickness tendency equation derived by R. Wood to make it consistent with the liquid water path tendency equation derived by J. J. van der Dussen et al. The validity of the tendency equations is then tested against the output of large-eddy simulations of a typical stratocumulus-topped boundary layer case and is found to be in good agreement.

Techniques for estimating cloud motion and stability for intra-hour forecasting using a ground-based sky imaging system are presented. A variational optical flow (VOF) technique was used to determine the sub-pixel accuracy of cloud motion for every pixel. Cloud locations up to 15 min ahead were forecasted by inverse mapping of the cloud map. A month of image data captured by a sky imager at UC San Diego was analyzed to compare the accuracy of VOF forecast with cross-correlation method (CCM) and image persistence method. The VOF forecast with a fixed smoothness parameter was found to be superior to image persistence forecast for all forecast horizons for almost all days and outperform CCM forecast with an average error reduction of 39%, 21%, 19%, and 19% for 0, 5, 10, and 15 min forecasts respectively. Optimum forecasts may be achieved with forecast-horizon-dependent smoothness parameters. In addition, cloud stability and forecast confidence was evaluated by correlating point trajectories with forecast error. Point trajectories were obtained by tracking sub-sampled pixels using optical flow field. Point trajectory length in mintues was shown to increase with decreasing forecast error and provide valuable information for cloud forecast confidence at forecast issue time.

Accurate forecasting of the spatio-temporal variability of solar power is a critical enabler of economical grid-integration of large amounts of solar power. A new physically-based endogenous method to forecast power output and ramps a few minutes ahead is presented. This cloud speed persistence method consists of advecting the current distribution of power output across the plant using endogenous measurements of cloud motion vectors. The method was validated at a 48 MW photovoltaic power plant in south-western Nevada, USA. Excluding clear days and in terms of the percentage root mean squared error the new method outperformed persistence by 16.2% at 20 s, 10.6% at 60 s, and 4.0% at 120 s forecast horizon. Given plant dimensions (1807 × 539 m) and cloud motion vectors at the site, the method can be applied out to forecast horizons of 65 s, on average.

Opportunities to develop commercial microgrids are emerging, but investors need analytical tools to assess the economics of microgrid business cases. A large part of the business case for microgrids in the real world is reliability based; yet in academic literature most tools analyze economics based on energy sales to customers or the macro grid. This work offers a new model, based on Monte Carlo simulation (MCS), that stacks both values streams — and hence makes it possible to develop business cases for microgrids which improve reliability as well as sell electricity. The tool is analytical and can be used to study the effect many real-world parameters, such as utility reliability, generator availability, gas prices or carbon taxes, have on operating costs and revenue. We demonstrate the tool in a case study based in Texas, and showcase its analytical features that can aid in developing a sound and robust business model.

Stratocumulus clouds play an important role in climate cooling and are hard to predict using global climate and weather forecast models. Thus, previous studies in the literature use observations and numerical simulation tools, such as large-eddy simulation (LES), to solve the governing equations for the evolution of stratocumulus clouds. In contrast to the previous works, this work provides an analytic closed-form solution to the cloud thickness evolution of stratocumulus clouds in a mixed-layer model framework. With a focus on application over coastal lands, the diurnal cycle of cloud thickness and whether or not clouds dissipate are of particular interest. An analytic solution enables the sensitivity analysis of implicitly interdependent variables and extrema analysis of cloud variables that are hard to achieve using numerical solutions. In this work, the sensitivity of inversion height, cloud-base height, and cloud thickness with respect to initial and boundary conditions, such as Bowen ratio, subsidence, surface temperature, and initial inversion height, are studied. A critical initial cloud thickness value that can be dissipated pre- and postsunrise is provided. Furthermore, an extrema analysis is provided to obtain the minima and maxima of the inversion height and cloud thickness within 24 h. The proposed solution is validated against LES results under the same initial and boundary conditions.

Despite the increase of modern residential rooftop solar PhotoVoltaic (PV) installation with smart inverters, islanded operation during grid blackouts is limited for most PV owners. This paper presents an optimization method to construe an resource sharing algorithm for islanded operation during blackouts by using shared PV energy. The optimization methods determine if rooftop PV power is either used directly or distributed to neighbors within a residential subsystem. Residential customers, each with a fixed size rooftop PV system are assumed to be connected by a single point of common coupling to a distribution network. The algorithm derives the optimal power distribution to improve the reliability of electricity supply to each residential customer and the results are benchmarked against the isolated self-consumption only mode. In addition, an energy storage system (ESS) is added to quantify the improvement in reliability, whereas a comparison is made between a distributed and centralized ESS deployment strategy.

Battery Energy Storage Systems (BESS) can mitigate effects of intermittent energy production from renewable energy sources and play a critical role in peak shaving and demand charge management. To optimally size the BESS from an economic perspective, the trade-off between BESS investment costs, lifetime, and revenue from utility bill savings along with microgrid ancillary services must be taken into account. The optimal size of a BESS is solved via a stochastic optimization problem considering wholesale market pricing. A stochastic model is used to schedule arbitrage services for energy storage based on the forecasted energy market pricing while accounting for BESS cost trends, the variability of renewable energy resources, and demand prediction. The uniqueness of the approach proposed in this paper lies in the convex optimization programming framework that computes a globally optimal solution to the financial trade-off solution. The approach is illustrated by application to various realistic case studies based on pricing and demand data from the California Independent System Operator (CAISO). The case study results give insight in optimal BESS sizing from a cost perspective, based on both yearly scheduling and daily BESS operation., Accepted at IFAC 2017 World Congress, Toulouse, France

The variability of solar energy in off-grid systems dictates the sizing of energy storage systems along with the sizing and scheduling of loads present in the off-grid system. Unfortunately, energy storage may be costly, while frequent switching of loads in the absence of an energy storage system causes wear and tear and should be avoided. Yet, the amount of solar energy utilized should be maximized and the problem of finding the optimal static load size of a finite number of discrete electric loads on the basis of a load response optimization is considered in this paper. The objective of the optimization is to maximize solar energy utilization without the need for costly energy storage systems in an off-grid system. Conceptual and real data for solar photovoltaic power production is provided the input to the off-grid system. Given the number of units, the following analytical solutions and computational algorithms are proposed to compute the optimal load size of each unit: mixed-integer linear programming and constrained least squares. Based on the available solar power profile, the algorithms select the optimal on/off switch times and maximize solar energy utilization by computing the optimal static load sizes. The effectiveness of the algorithms is compared using one year of solar power data from San Diego, California and Thuwal, Saudi Arabia. It is shown that the annual system solar energy utilization is optimized to 73% when using two loads and can be boosted up to 98% using a six load configuration., Comment: Accepted to Solar Energy Journal

Intra-hour solar generation and ramp forecasting with sky imagers benefits from fast, frequent and accurate cloud base height (CBH) calculation. Using two sky imagers, CBH is determined using a two dimensional (2D) method for single homogeneous cloud layers and an enhanced three dimensional (3D) method to provide CBH of the cloud field with high resolution. The 2D method is based on georeferenced projection and statistical correlation of two sky images from the pair of sky cameras. The 3D method utilizes the epipolar technique to determine CBH for each cloud pixel. The 2D method was validated against ceilometer CBH measurements on four days. Several technical considerations for the set up of the sky cameras for CBH calculation, as well as strength and weaknesses of the proposed methods are discussed.

A battery storage dispatch strategy that optimizes demand charge reduction in real-time was developed and the discharge of battery storage devices in a grid-connected, combined photovoltaic-battery storage system (PV+ system) was simulated for a summer month, July 2012, and a winter month, November 2012, in an operational environment. The problem is formulated as a linear programming (LP; or linear optimization) routine and daily minimization of peak non-coincident demand is sought to evaluate the robustness, reliability, and consistency of the battery dispatch algorithm. The LP routine leverages solar power and load forecasts to establish a load demand target (i.e., a minimum threshold to which demand can be reduced using a photovoltaic (PV) array and battery array) that is adjusted throughout the day in response to forecast error. The LP routine perfectly minimizes demand charge but forecasts errors necessitate adjustments to the perfect dispatch schedule. The PV+ system consistently reduced non-coincident demand on a metered load that has an elevated diurnal (i.e., daytime) peak. The average reduction in peak demand on weekdays (days that contain the elevated load peak) was 25.6% in July and 20.5% in November. By itself, the PV array (excluding the battery array) reduced the peak demand on average 19.6% in July and 11.4% in November. PV alone cannot perfectly mitigate load spikes due to inherent variability; the inclusion of a storage device reduced the peak demand a further 6.0% in July and 9.3% in November. Circumstances affecting algorithm robustness and peak reduction reliability are discussed.

The performance of the Total Sky Imager (TSI) and University of California, San Diego Sky Imager (USI) instruments has been evaluated using correlation and dispersion metrics applied to clear sky index. The TSI was located at a 48MW PV plant in Nevada, USA, and the USI was located at the UCSD campus in San Diego, USA. Distributed pyranometer measurements over several square kilometers were available at both locations to provide spatial averages of irradiance. Clear sky index was forecast for a 15 minute horizon at 30 sec. intervals, and the correlation and Euclidean dispersion were evaluated. A persistence forecast was generated for each location to provide a reference for comparison. For the aggregate dataset, the forecast performance of the USI exceeded that of persistence beyond the 10 minute forecast horizon, whereas the TSI did not show skill over persistence. For the period of study, the USI gave correlations of clear sky index between 0.70 and 0.82, whereas the TSI provided correlations between 0.55 and 0.69. Overall, the mean value and the trend of the correlation results were more consistent for the USI than the TSI on the days evaluated. It is concluded that the USI is a more reliable solar resource assessment instrument for the wide range of atmospheric conditions evaluated.

Of the estimated 1.6-2 billion people who lacked access to electricity at the end of the last millennium, millions have gained access to basic indoor lighting through off grid solar PV home systems with lead acid battery storage over the last decade. In Nepal, through government subsidy programs and INGO/NGO projects, around 350,000 solar PV home systems have been installed since 2001, mainly in remote, high altitude Himalayan communities. The author's field experience shows that within 6-24 months, 50-70% of the solar PV home systems are either not properly functioning, or not working at all. This is mainly due to substandard equipment, lack of user awareness, inability to maintain their systems, as well as the nonexistence of after sales services. Thus, an estimated 250,000 “dead”, flooded lead-acid batteries are either unsafely disposed of or lying around, posing huge potential hazards for people and the unique yet fragile Himalayan ecosystem. The research conducted demonstrates that by tapping into more than one renewable energy resource, converting the local available solar and wind resources into electricity through a solar PV - wind turbine hybrid RAPS (Remote Area Power Supply) system, the lead-acid battery bank capacity can be minimized by 57%, compared to an equivalent energy generating solar PV RAPS system, without jeopardizing, or reducing the village's load demands. This project shows that wind and solar resources are complimentary to each other over several hours in an average day. Thus, by utilizing both of the local wind and solar resources and converting them into electricity to meet the loads directly or to store into the lead-acid battery bank, it allows an average of 3-4hours longer electricity generation per day. This enables the design of smaller battery bank capacities for hybrid RAPS systems without limiting the end users’ energy services. Hence, long-term health risks to the people, as well as environmental damage to the delicate and exceptional Himalayan flora and fauna through disposed “dead” lead-acid batteries, is reduced.

In this paper, we study battery sizing for grid-connected photovoltaic (PV) systems. In our setting, PV generated electricity is used to supply the demand from loads: on one hand, if there is surplus PV generation, it is stored in a battery (as long as the battery is not fully charged), which has a fixed maximum charging/discharging rate; on the other hand, if the PV generation and battery discharging cannot meet the demand, electricity is purchased from the grid. Our objective is to choose an appropriate battery size while minimizing the electricity purchase cost from the grid. More specifically, we want to find a unique critical value (denoted as E max c ) of the battery size such that the cost of electricity purchase remains the same if the battery size is larger than or equal to E max c , and the cost is strictly larger otherwise. We propose an upper bound on E max c , and show that the upper bound is achievable for certain scenarios. For the case with ideal PV generation and constant loads, we characterize the exact value of E max c , and also show how the storage size changes as the constant load changes; these results are validated via simulations.

Clouds are the dominant source of PV power output variability and their velocity is a principal input to most short-term forecast models. A new method for deriving cloud speed from data collected at a triplet of sensors at arbitrary positions is presented; cloud speed and the angle of the cloud front are determined from the time delays in two cloud front arrivals at the sensors. Five reference cells at the 48 MW PV plant at Henderson (NV), were used to provide two different triplets of sensors. Over a year of operation cloud speeds from 3 to 35 m s−1 were obtained. Cloud speeds are validated using cross-correlation of power output from 96 inverters at the plant. Overall bias errors were less than 1% and the overall annual RMSE was 20.9%, but results varied with season.

University campuses offer a perfect setting in which to establish a microgrid and maximize its operational benefits. The university setting also offers a unique collection of intellectual resources. In addition to improving operational efficiency, lowering operating costs, and reducing the campus's overall carbon footprint, a university microgrid is an ideal laboratory in which to conduct research to advance modern power system operation and integration of distributed renewable generation for the power delivery industry as a whole. It also provides opportunities for new graduate student research and learning.

Coastal California has enormous potential for rooftop solar photovoltaic (PV) energy production. To reduce grid-integration costs, accurate and certain solar energy forecasts are required. However, frequent marine layer fog and stratus conditions limit the accuracy of numerical weather prediction models, especially during the summer. Thus, irradiance uncertainty is large and probabilistic forecast intervals are generally wide. To produce narrow and meaningful forecast intervals, the correlation of uncertainty to local meteorological conditions describing synoptic-scale atmospheric flow was considered. Specifically, the direction and magnitude of geostrophic flow were used as an indicator of coastal cloud cover probability to produce regime-dependent forecast intervals. The method was tested in summer 2011 for coastal California. The forecast interval was smaller than that provided by previous methods for all except clear conditions and contained 80% of irradiance measurements.

Aggregate ramp rates of 86 distributed photovoltaic (PV) systems installed in Southern California were analyzed and compared to irradiation measured at five ground stations and estimated from satellite. Irradiation data was converted to power output using a PV performance model to evaluate whether widespread on-line metering and telemetry of PV systems is necessary to track output of distributed generation for resource-adequacy applications. The satellite data were able to closely follow the aggregate power output and detect the timing of the ramps while the five weather stations were not as accurate due to smaller number and non-representative geographical distribution with respect to the PV sites. Over one year, the largest hourly aggregate ramp was a 50% increase based on the Performance Test Conditions (PTC) rating but ramps over 30% of PTC occurred only about once per day. The effects of specific meteorological conditions, such as coastal marine layer clouds and frontal system effects, on occurrence of large ramps were investigated over the area using satellite imagery. Evaporation of morning marine layer clouds caused a disproportionally large amount of up-ramps.

In this paper, we study the problem of determining the size of battery storage used in grid-connected photovoltaic (PV) systems. In our setting, electricity is generated from PV and is used to supply the demand from loads. Excess electricity generated from the PV can be stored in a battery to be used later on, and electricity must be purchased from the electric grid if the PV generation and battery discharging cannot meet the demand. Due to the time-of-use electricity pricing, electricity can also be purchased from the grid when the price is low, and be sold back to the grid when the price is high. The objective is to minimize the cost associated with purchasing from (or selling back to) the electric grid and the battery capacity loss while at the same time satisfying the load and reducing the peak electricity purchase from the grid. Essentially, the objective function depends on the chosen battery size. We want to find a unique critical value (denoted as $C_{ref}^c$) of the battery size such that the total cost remains the same if the battery size is larger than or equal to $C_{ref}^c$, and the cost is strictly larger if the battery size is smaller than $C_{ref}^c$. We obtain a criterion for evaluating the economic value of batteries compared to purchasing electricity from the grid, propose lower and upper bounds on $C_{ref}^c$, and introduce an efficient algorithm for calculating its value; these results are validated via simulations., Submitted to IEEE Transactions on Sustainable Energy, June 2011; Jan 2012 (revision)

Spatio-temporal variability of solar radiation is the main cause of fluctuating photovoltaic power feed-in to the grid. Clouds are the dominant source of such variability and their velocity is a principal input to most short-term forecast and variability models. Two methods are presented to estimate cloud speed using radiometric measurements from 8 global horizontal irradiance sensors at the UC San Diego Solar Energy test bed. The first method assigns the wind direction to the direction of the pair of sensors that exhibits the largest cross-correlation in the irradiance timeseries. This method is considered the ground truth. The second method requires only a sensor triplet; cloud speed and the angle of the cloud front are determined from the time delays in two cloud front arrivals at the sensors. Our analysis showed good agreement between both methods and nearby METAR and radiosonde observations. Both methods require high variability in the input radiation as provided only in partly cloudy skies.

Enhancement of solar irradiance (IE) has been observed in many locations under partly cloudy sky conditions. Despite its notoriety, few studies have attempted to systematically examine the underlying mechanism for the event through simulation. As a result, there is no consensus regarding the causes of IE, nor an understanding of the effects of cloud optical depth and/or solar elevation on the event. Using a 2D Monte Carlo radiative transfer model (RTM), we show that IE through a homogenous square cloud is caused by the superposition of a direct irradiance beam with diffuse light scattered through the bottom and out of the edge of a cloud, through Mie and diffusion scattering. Using the RTM, we investigated the effect of optical depth up to 40 and solar zenith angles ranging from 0° to 80° on the IE magnitude and spatial extent. For the overhead zenith case the IE magnitude is maximum between optical depths of 2 and 3, with a value of 1.27 times the clear sky value. IE magnitude increases with increasing solar zenith angle, with the maximum occurring at a higher optical depth. The greatest magnitude overall occurred for a solar zenith angle 80° (our maximum) and optical depth of 20, with a value of 1.46 times the clear sky value. The simulations show that for optically thick clouds and small solar zenith angles forward scattering is the dominate contributor to large IE, but at increased zenith angles outward scattering leads to larger IE’s. Differences between simulated IE maximums and measured values in literature were resolved with a simple two cloud model to show mechanisms behind the production of IE extremes.

We develop a two-part modeling framework to schedule bids for merchant variable renewable energy (VRE) generators participating in the day-ahead wholesale electricity market. The first part is an optimization model that maximizes revenue by optimally selling power into the marketplace. The second is a non-cooperative game-theory model in which the Nash equilibrium is the revenue-maximizing bidding strategy for all VRE market participants. The two models are calibrated using three months of consecutive demand, generation, and market clearing price (MCP) data from the California wholesale market. Analytical results provide three important conclusions for VRE operators, policymakers, and system operators alike: (1) there are periods when VRE operators can increase revenue by curtailing power output; (2) such market outcomes occur with only moderate increases in California's renewables penetration (from present-day 20% to 26%); and (3) VRE operators can increase revenue by forming aggregations, i.e. coupling bids between multiple merchant VRE.

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function., Comment: 6 pages, 3 figures, accepted at The IEEE Conference on Control Applications (CCA)

The question of how energy storage can be used efficiently and effectively in distribution networks is open and ongoing. This work explores optimal allocation of battery energy storage systems (BESS) in distribution networks to maximize their support in integrating high penetration solar photovoltaics (PV). A genetic algorithm (GA)-based multi-layer multi-objective optimization model is developed that minimizes the voltage deviation caused by high PV penetration and decreases energy loss in the distribution system while also accounting for the BESS capital and operational lifetime. The optimization problem considers BESS unit capacities, BESS installation points in the network and the cumulative BESS capacity of the network as decision variables. Siting constraints that would play a practical role in resource allocation, such as construction limitations, environmental and visual impacts are not included in the model. A case study with the IEEE 8500-Node test feeder is carried out to discuss the effectiveness of the proposed method. The results show a clear connection between BESS sizing and siting decisions and voltage deviation reduction benefits in a distribution network.