Optimal Grid Research Articles

Optimal Grid Layouts for Hybrid Offshore Assets in the North Sea Under Different Market Designs

Optimal Grid Layouts for Hybrid Offshore Assets in the North Sea Under Different Market Designs

Optimal grid method for the recovery of the potential from two spectra

Optimal grid method for the recovery of the potential from two spectra

An improved slope-based adaptive control vector parameterization method for dynamic programming

Control vector parameterization method is the most commonly used numerical computation method in solving dynamic programming problems. However, to balance the expected trajectory and the computational cost, this method faces difficulties in dividing the optimal discretization time grid. In this paper, we propose an effective control approach for non-uniform adaptive grid division. By analyzing the slope change trend of the control parameter, time nodes are adaptively refined by merging time grids with gentle slopes to remove unnecessary time nodes and adding time nodes to time grids with steep slopes to improve function approximation accuracy. Eventually, we obtain an adaptive time grid division method under which the trajectory of discretization control parameter is more approximate to the optimal control trajectory. Under the condition of intuitive slope information, the proposed method can achieve better performance with fewer optimization parameters and shorter computation time. Finally, the proposed method is applied to solve a classic optimal control problem and the obtained results are compared with the traditional control vector parameterization method. By comparison through the example, our proposed method can overcome the contradiction between approximation accuracy and computational cost in control vector parameterization method and improve the optimization efficiency.

Impact of real-time pricing and residential load automation on distribution systems

Price-responsive electricity consumption can facilitate the efficient operations of power systems. In this paper, we study the impact of real-time pricing (RTP) and the automation of a major residential load – Heating, Ventilation, and Air Conditioning (HVAC) systems – on residential distribution systems. First, we deploy a simulation-based case study of 437 houses in Austin, Texas, which we calibrate based on real-world data. Second, we study the implications of switching from a fixed retail rate to RTP. We estimate aggregate welfare gains of 39 USD per customer and year. All customers contribute to the welfare gain, but not equally. Moreover, all customers benefit and benefits are higher for customers with electric heating, lower comfort preference, and lower thermal insulation. However, RTP and load automation can critically increase peak system load by more than 30%. Third, we study the introduction of a market-based demand management system under which the local RTP increases if congestion is present. In this case, for reasonable specifications, another 12% of welfare gains can be realized during operations. Moreover, optimal grid investment can be reduced. Our work informs policy makers by illustrating under which conditions load automation under RTP can be particularly beneficial.

Unsupervised domain adaptation methods for photovoltaic power forecasting

The accurate forecasting of photovoltaic (PV) power generation is of great significance in renewable energy systems, as it enables optimal energy management and grid stability. Despite the importance of this issue, substantial limitations still exist in the majority of existing research initiatives, which employ shallow machine learning algorithms. Recently, some studies have proposed employing convolutional and long short-term memory neural networks (LSTMs) in conjunction with transfer learning techniques; however, these approaches require that the production of PV systems is known during training. To overcome these limitations, we present the first study in the task of PV power forecasting utilizing unsupervised domain adaptation methods. Specifically, we employ two unsupervised methods, namely Domain Adversarial Neural Network and Margin Disparity Discrepancy. Both approaches use a source and a target domain during training, where the target labels of the target domain are unknown during training. We use production and weather data from seven PV systems with nominal capacities ranging from 23.52 kW to 271.53 kW, located in different areas. The findings demonstrate that our proposed architectures improve root mean squared error (RMSE), normalized RMSE, and R2 scores over the smart persistence model across all the PV systems used for testing. Furthermore, our approaches improve the performance of the smart persistence model, with a forecast skill index reaching up to 45.35%. Our extensive experiments demonstrate that our introduced approaches offer valuable advantages over state-of-the-art ones, as the target variable of the target domain is unknown during training. We also demonstrate the robustness of our approaches by conducting a series of ablation experiments.

Landscape Ecological Risk Evaluation Study under Multi-Scale Grids—A Case Study of Bailong River Basin in Gansu Province, China

To solve grid-scale problems and evaluation indicator selection in landscape ecological risk index (LERI) evaluation, this paper takes the Bailong River Basin in Gansu Province (BLRB) as an example. The LERI evaluation formulae and optimal grid scales were determined by screening landscape indices and area changes in the LERI at different grid scales. The evaluation indices were finally obtained according to the landscape characteristics and the correlation analysis of the landscape index value. Through the statistical analysis of the area of the LERI at the grid scale of 1–6 km, the optimal grid scale was determined to be 5 km. There was little change in land use patterns, with the most significant increases in artificial surfaces at 3.29% and 3.58%, respectively. Cultivated land was the only land use type to decrease by 184.3 km2. The LERI drops with the reduced cultivated land area; the landscape ecological medium risk area and cultivated land keep the same spatial distribution. Due to the limitation of the topography, cultivated land is generally distributed below 2500 m altitude, so 2500 m becomes the turning point in the spatial distribution of the LERI. The medium risk below 2500 m dominates the LERI type. Reduced cultivated land was the leading cause of reduced ecological risk according to an overlay analysis. The study of LERI evaluations provides a theoretical basis for sustainable and ecological environmental protection in the BLRB.

Impact of Airflow Rectification on Spreading Uniformity for UAV-Based Multichannel Pneumatic Granular Fertilizer Spreader

Unmanned aerial vehicles (UAVs) are an important part of smart farms and have been widely used in granular fertilizer spreading. The multichannel pneumatic granular fertilizer spreader (MPGFS) has the advantages of light weight and precision spreading, and has been applied to UAV variable rate fertilization. Based on the problem that the airflow field disorder of the existing MPGFS reduces the uniformity of spreading, the aim of this study was to further improve the performance of the MPGFS through rectification. The computational fluid dynamics and discrete element method (CFD-DEM) and coupling simulation method were used to study the characteristics of the airflow field and fertilizer particle motion, and a honeycomb rectifier and grid rectifier were developed. The aperture of the honeycomb rectifier and the grid size of the grid rectifier were optimized. Then, the test bench was built to test the consistency of the discharge rate of each channel and the spreading uniformity of the MPGFS. The simulation results of the existing MPGFS showed that the airflow provided by the axial flow fan was rotational, and this caused the particles’ motion to be skewed in the shrinkage section, so the discharge rate of each channel was inconsistent. The airflow field analysis results of the shrinkage section showed that the airflow rotation was reduced after the rectification of the honeycomb rectifier and the grid rectifier. The bench test results showed that the coefficient of variation (CV) of each channel discharge rate of the existing MPGFS was 20.16%, the optimal honeycomb rectifier was 13.07%, and the optimal grid rectifier was 5.27%. The bench test results of spreading uniformity show that the CV of spreading uniformity of the existing MPGFS was 15.32%, the optimal honeycomb rectifier was 15.81%, and the optimal grid rectifier was 8.02%. The grid rectifier spread pattern was more reasonable and the CV of uniformity was better. This study demonstrated that the use of a grid rectifier to rectify the airflow field of MPGFS can effectively improve its spreading uniformity, which was of guiding significance for the design and research of MPGFS.

Optimal mitigation and control over power system dynamics for stochastic grid resilience

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.

Optimal Grid Flexibility Assessment for Integration of Variable Renewable-Based Electricity Generation

This study delves into power system flexibility, with a keen focus on the integration of variable renewable electricity generation into power grids. Two scenarios were analyzed. The base scenario revealed an aging grid, insufficient generation capacity, frequent outages, and little renewable energy generation (1.9%), along with a significant (71.23%) loss of load. In contrast, the investment scenario presented solutions including raising VRE capacity to 44%, adding 1000 MW capacity transmission lines, installing 200 MW capacity grid-scale battery storage, and technological enhancements. These interventions effectively eliminated loss of load, reinforcing energy resilience. Investments in CCGPP and grid-scale batteries proved instrumental in mitigating the variability of renewable energy. Improved transmission promised efficient power exchange and regional collaboration. The elimination of annualized energy spills and the removal of ramping constraints marked significant strides in enhancing power system flexibility. This research underscores the pivotal role of grid flexibility in accommodating VRE sources. By implementing the proposed optimal solutions, Afghanistan can lead the way toward a cleaner, more resilient, and more interconnected energy future. These findings offer a replicable framework for addressing similar challenges in integrating renewable energy sources globally and supporting the transition to sustainable and reliable energy.

Optimal grid size for site‐specific nutrient application

AbstractThis article develops a theoretical framework to determine the economically optimal grid size when sampling to guide precision application of inputs. Our theoretical model shows that a finer grid is optimal with increases in output price. A coarser grid is optimal with increased sampling costs and increased spatial correlation. With an exponential variogram, for example, the optimal grid size increases as the range increases. An applied example of lime application for winter wheat is used to demonstrate the framework. Spatial variograms for pH and Buffer pH were estimated using data from nine farmer fields. At the average spatial variability from these fields and using typical Oklahoma wheat yields of 40 bu/ac, grid sampling was economical when prices were above $5.43/bu. The optimal grid sizes were slightly larger than the 2.5‐acre sizes that are typically used by producers. The empirical example verified the theory in that it found that optimal grid size decreased with higher output prices and crop yields and increased with greater spatial correlation. For example, optimal grid size approximately doubled as the range of the exponential correlation function doubled.

Drag Reduction on Microstructure Surfaces

This study reviews experimental research on friction in bird-feather-like structures, focusing on one modeled using Computational Fluid Dynamics for optimal grid parameters. Shear stresses of 2D models were then explored at Reynolds numbers 110,000-470,000, with insights from prior 3D geometries. Findings were compared to a previous experimental study. Ultimately, surfaces inspired by bird feathers exhibited around 30% drag reduction.

Renewable energy utilizing and fluctuation stabilizing using optimal dynamic grid connection factor strategy and artificial intelligence-based solution method

As a crucial aspect of pollution emissions, the transformation and upgrading of the power industry urgently require attention. Utilizing renewable energy generation techniques is an effective means to promote energy conservation and emission reduction within the power industry. However, the utilization rates of renewable energy generation are hindered by significant randomness and uncertainty associated with renewable energy power. In light of these challenges, this study constructed a hybrid economic emission dispatch (HDEED) model to explore the establishment of effective regulation mechanism under renewable energy grid connection. First, taking into account dynamic constraints, the wind-solar-thermal-storage HDEED model was constructed with operation costs and pollution emissions as objective functions. Second, an optimal dynamic grid connection factor strategy and the GWOH-based solution method were proposed. Finally, the proposed strategy and algorithm were verified using an improved IEEE-39 bus test system. The results revealed that under the same test conditions, the Pareto optimal frontiers obtained by the GWOH algorithm demonstrated the most competitive performance. Furthermore, the system cost achieved by GWOH was 4.52% lower than that without renewable energy access, while emissions were reduced by 11.84% under the optimal dynamic factor grid connection strategy. This study significantly contributes to the improvement of energy management efficiency and the enhancement of renewable energy utilization rates in the power industry.

Multi-GPU-based real-time large-eddy simulations for urban microclimate

This study presents an innovative real-time urban microclimate simulation strategy using a large-eddy simulation (LES) solver deployed on a multi-GPU architecture. The present LES solver is developed using a monolithic projection-based method with staggered time discretization, ensuring efficient computation and a high CFL number. It is hosted on a multi-GPU platform using CUDA Fortran and CUDA-aware MPI, which enhances its performance. To capture the complexity of urban geometries, we utilized a building-resolved, wall-modeled LES augmented by an immersed boundary method. First, we validated the results in an isolated building by comparing them with wind tunnel profiles. Next, we evaluated the developed LES solver using an idealized street array. A set of evaluation metrics, namely FAC2 and hit rate, was employed to determine the optimal grid configuration that produces physically valid results. Moreover, we proposed a real-time indicator that provides insight into the interplay among grid resolution, simulation domain size, and the number of GPUs. This facilitates feasibility assessments for real-time simulations. The performance of the LES solver was further tested using real urban geometry, conducting simulations over an area of 10.49 km2 in Seoul, with a grid resolution of 4 m. The simulation results efficiently highlighted variations in wind patterns with altitude, demonstrating its potential to provide useful wind information for pedestrian-level wind comfort assessment and urban air mobility.

Optimal exclusive perpetual grid exploration by luminous myopic opaque robots with common chirality

We consider swarms of luminous myopic opaque robots that run in synchronous Look-Compute-Move cycles. These robots have no global compass, but agree on a common chirality. In this context, we propose optimal solutions to the perpetual exploration of a finite grid. Precisely, we investigate optimality in terms of visibility range, number of robots, and number of colors. In more detail, under the optimal visibility range one, we give an algorithm which is optimal w.r.t. both the number of robots and colors: it uses two robots and three colors. Under visibility two, we design two algorithms: the first one uses three robots with an optimal number of colors (i.e., one), the second one achieves the best trade-off between the number of robots and colors, i.e., it uses two robots and two colors.

Ultra-short-term forecasting of global horizontal irradiance (GHI) integrating all-sky images and historical sequences

Accurate minute solar forecasts play an increasingly crucial role in achieving optimal intra-day power grid dispatch. However, continuous changes in cloud distribution and coverage pose a challenge to solar forecasting. This study presents a convolutional neural network-long short-term memory (CNN-LSTM) model to predict the future 10-min global horizontal irradiance (GHI) integrating all-sky image (ASI) and GHI sequences as input. The CNN is used to extract the sky features from ASI and a fully connected layer is used to extract historical GHI information. The resulting temporary information outputs are then merged and forwarded to the LSTM for forecasting the GHI values for the next 10 min. Compared to CNN solar radiation forecasting models, incorporating GHI into the forecasting process leads to an improvement of 18% in the accuracy of forecasting GHI values for the next 10 min. This improvement can be attributed to the inclusion of historical GHI sequences and regression via LSTM. The historical GHI contains valuable meteorological information such as aerosol optical thickness. In addition, the sensitivity analysis shows that the 1-lagged input length of the GHI and ASI sequence yields the most accurate forecasts. The advantages of CNN-LSTM facilitate power system stability and economic operation. Codes of the CNN-LSTM model in the public domain are available online on the GitHub repository https://github.com/zoey0919/CNN-LSTM-for-GHI-forecasting.

Economic assessment of integrating fast-charging stations and energy communities in grid planning

Distribution grid companies and distribution system operators (DSOs) still mostly follow a traditional framework for grid planning. Such frameworks have so far served DSOs well in the economic assessment and cost–benefit analysis of passive measures, such as grid reinforcement. However, the development towards active distribution grids requires DSOs to also be able to assess an extended set of active measures. To this aim, this paper extends and implements a general planning framework for active distribution grids that builds upon the well-proven traditional framework. The methodology integrated in the framework includes: (1) decoupled models for (i) operation with active measures and (ii) optimal grid investment, and (2) methods for economic assessment considering active measures from both (i) a DSO cost–benefit analysis perspective and (ii) a willingness-to-pay perspective. In this paper, operational models are integrated for two examples of active measures, namely the use of fast-charging stations (FCS) and local energy communities (LEC). The methodology is demonstrated in a long-term grid planning case study for a realistic Norwegian medium voltage distribution system. For this case, grid planning with FCS as an active measure reduces the present value of grid investment costs by 70% compared with a passive grid planning strategy. The results also demonstrate how the methodology can be used in negotiating the price of active measures between the DSO and distribution system actors such as LEC and FCS operators.

Developing a public EV charging infrastructure in a DSO's perspective: Hosting capacity assessment and grid reinforcements on a real case study

The widespread increase of electric vehicles sales forces Distribution System Operators to evaluate and improve the capability of the distribution system to host distributed charging infrastructures. This paper suggests a procedure to identify grid reinforcements to increase the capability of the system as well as to evaluate the current hosting capacity. The developed procedure is based on a micro-genetic algorithm and its solution identifies the optimal grid reinforcements to be planned on a Medium Voltage network in order to increase the number of charging stations that can be connected. The procedure requires the model of the network, the yearly load profiles of the secondary substations and the algorithm output takes into account an envisioned budget to be spent, avoiding network violations and an iniquitous distribution of the charging stations. The procedure was firstly validated considering a 70 nodes test network. Furthermore, the real case study of the distribution system of the city of Terni was assessed focusing on one of its main subnetwork with 471 nodes; the procedure was exploited to assess the current hosting capacity and to estimate that on average 0.01 M€ has to be spent on grid reinforcements in order to further increase hosting capacity.

Error Analysis of Sound Source Directivity Interpolation Based on Spherical Harmonics

Precise measurement of the sound source directivity not only requires special equipment, but also is time-consuming. Alternatively, one can reduce the number of measurement points and apply spatial interpolation to retrieve a high-resolution approximation of directivity function. This paper discusses the interpolation error for different algorithms with emphasis on the one based on spherical harmonics. The analysis is performed on raw directivity data for two loudspeaker systems. The directivity was measured using sampling schemes of different densities and point distributions (equiangular and equiareal). Then, the results were interpolated and compared with these obtained on the standard 5° regular grid. The application of the spherical harmonic approximation to sparse measurement data yields a mean error of less than 1 dB with the number of measurement points being reduced by 89%. The impact of the sparse grid type on the retrieval error is also discussed. The presented results facilitate optimal sampling grid choice for low-resolution directivity measurements.

On the Unique Solvability of Inverse Problems of Magnetometry and Gravimetry

This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral equations or integral representations. Examples are given of degenerate and nondegenerate systems of different dimensions that arise in the processing of magnetometric and gravimetric data from experimental observations. Conclusions are drawn about the methods for constructing the optimal grid of experimental observation points.

A novel resilience assessment for active distribution networks including a DER voltage regulation scheme considering windstorms

Increasing incidences of extreme weather events pose significant challenges to the electrical grids in terms of the ability to withstand those high-impact eventualities. This paper proposes a resilience assessment framework for net-zero active distribution networks (ADNs) to tackle the impacts of extreme windstorms where only renewable energy resources (RESs) and battery energy storage systems (BESSs) are considered. To accurately capture the influence of windstorms on the grid, a detailed spatiotemporal representation of grid system assets and their exposure to the wind has been implemented. The suggested day-ahead resilience assessment is based on a three-stage approach. The first stage computes the probabilities of failure of each line and determines the most vulnerable ones. The second stage obtains the optimal grid configuration based on the outcomes of the first stage given the available non-dispatchable RESs and commits the available resources in each island to minimize the loss of load during the windstorm. If such a value is still larger than zero after the second stage, a novel voltage regulation scheme is applied in the third stage, taking advantage of the RESs and BESSs in each island. The proposed resilience assessment has been evaluated using the IEEE 33-bus test system with the meteorological data retrieved from an actual windstorm event occurred in the UK on the 20th of February. The outcomes of this paper underscore that a significant reduction in load shedding during such extreme events can be achieved, thus having a notable enhancement to the overall resilience of the system. Finally, the performance of this approach is compared with other resilience-oriented methods for windstorms, where the benefits of using the scheme reported in this paper are highlighted and quantified.