Joint Energy Research Articles

Dual-modification of oxygen vacancies and PEDOT coating on MnO2 nanowires for high-performance zinc ion battery

MnO2 has outstanding potential for application in cathode materials of zinc ion batteries (ZIBs). However, the poor electrical conductivity, poor ion diffusion kinetics, and structural instability greatly limit its rate performance, specific capacity, and cycling stability. Herein, we prepared PEDOT-coated MnO2 cathode material with oxygen vacancy defects, namely Vö-MnO2@PEDOT, by Dual-modification of MnO2 nanowires. The PEDOT coating optimizes the electron transfer capability of the material while inhibiting the dissolution of MnO2. The oxygen vacancies accelerate ion diffusion. Vö-MnO2@PEDOT possesses a joint energy storage mechanism, containing the insertion/extraction of H+/Zn2+ and dissolution/precipitation of MnO2. This joint energy storage mechanism explains the high specific capacity and the increase in capacity. The Vö-MnO2@PEDOT displays a high specific capacity of 400 mAh/g at 0.2 A/g. Besides, at 2 A/g, Vö-MnO2@PEDOT outputs a high capacity of 213 mAh/g after 2000 cycles. This research provides a feasible research idea for the performance optimization of manganese oxide cathode materials.

Energy and Reserve Sharing Considering Uncertainty and Communication Resources

In this paper, we study the joint energy and reserve sharing problem considering renewable generation uncertainty and limited communication resources. We propose a data-driven distributionally robust energy and reserve sharing model among different agents in electricity markets. We put forward data-driven distributionally robust chance constraints (DRCC) to determine the reserve capacity, which cannot be directly solved. The inner approximation is employed to convert the DRCC into tractable linear constraints. Taking into account the agents in the Internet of Things exchange information by a resource-limited communication network, we develop a communication-censored consensus alternating direction method of multipliers (ADMM) to utilize the limited communication resources and solve the sharing problem in a fully decentralized manner. We analyze the convergence of the proposed algorithm, and propose an adaptive penalty parameter method to speed up the convergence. Extensive simulations are conducted to verify the effectiveness of the proposed model and theoretical results.

Effects of low cycle impact fatigue on the residual mode II fracture energy of adhesively bonded joints

Cyclic loading exerts a profound influence on the durability of adhesively bonded joints, particularly under cyclic impact loads. Under normal cyclic loading, adhesive joints typically reach their fatigue limit when subjected to approximately 50% of their maximum static strength. However, the endurance limit is considerably lower for cyclic impact loading, sometimes even falling below 5% of the impact strength. This paper investigates the effects of low-energy cyclic impacts on the fracture energy of an end-notched flexure (ENF) joint bonded with an epoxy-based adhesive. The study includes an analysis of the static fracture energy of the ENF joints prior to subjecting them to repeated impact cycles. Additionally, certain joints were subjected to repeated impact cycles until complete crack propagation occurred. To evaluate the residual critical fracture energy of these joints, certain cyclic impact tests were interrupted, and the joints were subsequently subjected to quasi-static loading conditions. The results reveal the remarkable sensitivity of the fracture energy of adhesive joints to the impact energy level, challenging the assumption of infinite life under cyclic impacts often made in conventional fatigue tests. Stress concentration caused by cyclic impact stress waves leads to a higher density of cracks at the specimen edges. The findings are supported by numerical analysis conducted in this study. These results underscore the importance of comprehensive inspections for bonded structures exposed to low-energy cyclic impacts, as impact fatigue can significantly diminish joint strength. The fracture energy decreases as the number of impact cycles increases, indicating a cumulative effect. The findings contribute to a better understanding of the mode II fracture behavior of adhesively bonded joints under repeated impact loads and provide insights for safe design and inspection practices.

Norm‐based spectrum sensing for cognitive radios under generalised Gaussian noise

AbstractCognitive radio (CR) systems are configured to dynamically assess the spectrum utilisation and contribute towards an improved spectrum efficiency. Hence, accurate detection of the incumbent signal in a given channel, popularly known as spectrum sensing (SS), is essential for CR. Here, in the domain of SS, the authors introduce a new goodness‐of‐fit test (GoFT) founded on p‐norm of the observations at the receiver node. To capture the heavy‐tailed nature of noise distribution in practical communication channels, the authors utilise generalised Gaussian distribution (GGD) as a noise model. A novel p‐norm detector (PND) and a geometric power detector (GPD) is proposed and corresponding probability density function (PDF) under GGD is derived. Via Monte Carlo simulations, the authors show a match of the derived PDFs with the simulation results. Using Neyman‐Pearson framework the performances of PND and GPD are compared with an existing differential entropy detector (DED), the well‐known energy detector (ED) and joint correlation and energy detector (CED) under GGD noise model. Evaluation of proposed PND and GPD utilising Monte Carlo simulations indicate a superior performance. Further, the experiments employing real‐world data establish superiority of the proposed detectors as compared to existing techniques. The authors derive and implement an optimised threshold for PND, providing further improvement in performance.

Contractile Work of the Soleus and Biarticular Mechanisms of the Gastrocnemii Muscles Increase the Net Ankle Mechanical Work at High Walking Speeds.

Increasing walking speed is accompanied by an increase of the mechanical power and work performed at the ankle joint despite the decrease of the intrinsic muscle force potential of the soleus (Sol) and gastrocnemius medialis (GM) muscles. In the present study, we measured Achilles tendon (AT) elongation and, based on an experimentally determined AT force-elongation relationship, quantified AT force at four walking speeds (slow 0.7 m.s-1, preferred 1.4 m.s-1, transition 2.0 m.s-1, and maximum 2.6 ± 0.3 m.s-1). Further, we investigated the mechanical power and work of the AT force at the ankle joint and, separately, the mechanical power and work of the monoarticular Sol at the ankle joint and the biarticular gastrocnemii at the ankle and knee joints. We found a 21% decrease in maximum AT force at the two higher speeds compared to the preferred; however, the net work of the AT force at the ankle joint (ATF work) increased as a function of walking speed. An earlier plantar flexion accompanied by an increased electromyographic activity of the Sol and GM muscles and a knee-to-ankle joint energy transfer via the biarticular gastrocnemii increased the net ATF mechanical work by 1.7 and 2.4-fold in the transition and maximum walking speed, respectively. Our findings provide first-time evidence for a different mechanistic participation of the monoarticular Sol muscle (i.e., increased contractile net work carried out) and the biarticular gastrocnemii (i.e., increased contribution of biarticular mechanisms) to the speed-related increase of net ATF work.

Online Learning for Joint Energy Harvesting and Information Decoding Optimization in IoT-Enabled Smart City

In this study, we first present a framework that jointly optimize energy harvesting and information decoding for Internet of Things (IoT) devices, which are capable of simultaneous wireless information and power reception, in a smarty city. In particular, a generalized power splitting receiver for IoT devices is designed, where each antenna in the receiver has an independent power splitter, unlike the existing works in which only one power splitter is employed regardless of the number of antennas in the receiver. Such a receiver design can provide a great degree of freedom to improve the network performance. Based on the presented framework, for each IoT device, we formulate an optimization problem whose objective is to maximize the harvested energy of each IoT device while satisfying its data rate requirement. To solve this problem, we propose a double-deep deterministic policy gradient based online learning algorithm which enables each IoT device to jointly determine receive beamforming and power splitting ratio vectors in real-time. Further, each IoT device can implement the proposed algorithm in a distributed manner using only its local channel state information. As such, cooperation and information exchange among the base stations and IoT devices are not necessary when performing the proposed algorithm at IoT devices. The extensive simulation results show the validity of the proposed algorithm.

Multi-agent DRL for joint completion delay and energy consumption with queuing theory in MEC-based IIoT

Multi-agent DRL for joint completion delay and energy consumption with queuing theory in MEC-based IIoT

Joint Energy Harvesting and Transmission Optimization for Cell-Free Massive MIMO With Network-Assisted Full Duplexing

This paper investigates the problem of joint energy harvesting (EH) and transmission optimization for cell-free massive MIMO with network-assisted full duplexing (NAFD), where each access point (AP) works in full-duplex mode, half-duplex mode or another flexible mode and is connected to a central processing unit (CPU) via compressed fronthaul links. The high demand on the fronthaul links and series cross-link interference (CLI) are the two main problems in cell-free massive MIMO with NAFD. Therefore, in our scheme, we propose a joint strategy of EH, fronthaul compression, and CLI cancelation to maximize the energy efficiency (EE) of the system under constraints of guaranteed quality-of-service (QoS), EH and compressed fronthaul requirements. A two-stage strategy of EH and transceiver design is proposed to solve the complicated optimization problem. Specifically, in the first stage, we propose an EH/information receiving (IR) antenna selection algorithm to design the operation mode of the antennas for uplink users and receiving APs. In the second stage, with the antennas selected in the first stage, we further attempt to solve the EE maximization problem. Furthermore, to solve the highly nonconvex EE maximization problem, we propose a fractional programming (FP)-based two-tier iterative algorithm in which a series of nonconvex–convex approximation methods, such as FP, iterative convex approximation and equivalent formulation, are used. Simulation results demonstrate that the proposed algorithms yield a higher EE gain than the traditional time-division duplexing (TDD) and co-frequency co-time full duplexing (CCFD) schemes.

Simulated annealing‐based high‐level synthesis methodology for reliable and energy‐aware application specific integrated circuit designs with multiple supply voltages

SummaryIntegrated circuits have become more vulnerable to soft errors due to smaller transistor sizes and lower threshold voltage levels. Energy reduction methods make circuits more error‐prone since even the smallest amounts of environmental radiation can cause a bit flip. Furthermore, redundancy‐based error detection and correction methods induce higher costs and area overhead. Thus, several conflicting parameters may need to be considered during embedded system design (e.g., area, performance, energy, and reliability). High‐level synthesis (HLS) is the most practical design step to consider all these parameters as complexity increases at lower levels. HLS can be viewed as a multi‐objective optimization problem of finding a set of Pareto‐optimal designs, allowing designers to choose the ones that best fit the requirements. Moreover, the number of synthesis options superlinearly affects the search space growth, necessitating efficient optimization methods. In this study, we propose simulated annealing (SA)‐based HLS methods for multi‐Vcc application‐specific integrated circuit design, aiming to optimize energy consumption and reliability under the area and latency constraints. Furthermore, we use duplication to improve design reliability as much as the constraints allow. We compared our methods against genetic algorithm (GA)‐based and integer linear programming (ILP)‐based methods and showed their effectiveness in finding optimum or near‐optimum results in a short running time. SA‐based methods achieved up to 21.20% reliability improvement on average and up to 38% energy reduction on average, while preserving the reliability value against the GA‐based metaheuristic counterpart under joint reliability and energy optimization on four HLS benchmarks.

Experimental study on seismic performance and deformation damage of loose dovetail-tenon joints in ancient timber structures

A looseness is typical damage for mortise-tenon joints in ancient timber structures. The tenon of the loose dovetail-tenon joints is prone to be pulled out, leading to joint failure in the earthquake. Hence, it is necessary to investigate the seismic performance and deformation damage of loose dovetail-tenon joints. This study conducts pseudo-static and acoustic emission (AE) tests on three full-scaled dovetail-tenon joints to determine the four stress stages of each joint, including slight damage, medium damage, severe damage, and nearly failure. It examines the hysteretic and skeleton curve, stiffness and strength degradation, energy dissipation performance, and the variation raw of the amount of tenon pulled out at each stage. The deformation damage mode, damage degree, and damage evolution equation of the joint at each stage are obtained based on the AE characteristic parameters measured at each stage. The results indicate that as the rotation angle increases, each joint's stiffness and energy dissipation capacity decrease, while the joint bending moment rises and then reduces, and the amount of tenon pulled out increases. The greater the degree of looseness, the lower the bearing capacity of each joint, and the more pronounced the degradation of stiffness and strength. At each stage, the maximum decrease of initial stiffness is 85.75%, and the maximum amount of tenon pulled out is 93 mm. The failure modes of joints are mainly tenon pulled out failure, and extrusion deformation greatly influences the tenon pulled out failure. As the degree of looseness grows, joints are more prone to severe deformation damage under large rotation angles. At the slight and medium stages, the joints primarily suffer from tensile damage of material, but at the severe damage and nearly failure stage, they mainly suffer from shear damage of material. The damage value of each joint increases with the relative stress ratio, and looseness significantly impacts the damage degree of the joint.

A data-driven optimization framework for industrial demand-side flexibility

Securing profits while offering industrial demand-side flexibility in both energy and reserve markets is critical to ensure the profitability of energy-intensive industrial plants to make available their flexible assets in the electricity markets and hence accelerating the energy transition. Proposing efficient bidding strategies for simultaneous participation in the energy and reserve market is challenging since it requires the integration of different market mechanisms in a single optimization problem (combining energy and reserve markets), as well as an accurate mathematical model of industrial processes from which to obtain energy flexibility. Often, such mathematical models are either not available or are described through complex simulators, making the design of a computationally efficient bidding strategy a complicated task.This paper introduces a novel framework to support energy-intensive industrial plants to offer energy flexibility in the joint energy and reserve market. We use a neural network to model the complex nonlinear dynamics of the industrial flexible process. Then, to reduce the complexity of the resulting optimization process we convert the neural network into linear constraints, formulating the problem of bidding energy flexibility into the electricity market as a mixed-integer linear program. The uncertainties of the process variables are considered using a scenario-based approach.A realistic simulation considering the case of an evaporative cooling tower used in the chemical industry, participating in the Belgian electricity market is carried out to demonstrate the applicability of the proposed scheme.

JECP: Joint Energy Conservation and Collision Avoidance for Path Construction in Bluetooth Networks

With the growing elderly population of the world population, the number of elderly people who live alone is continuously growing. Providing them with high-quality healthcare has become a major concern nowadays. In order to detect the elderly people’s sudden danger of elderly living alone, this paper proposes a path construction mechanism, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">JECP</i> , which aims to conserve energy and avoid collision for the emergent sensors in Bluetooth mesh networks. In case that the emergent sensors are deployed in the same room, the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">JECP</i> constructs disjoint paths to avoid collisions, which are triggered by the same emergent event at the same time. The other case is that the emergent sensors are deployed in different rooms. The probability that these emergent sensors are triggered by the same event is very small. Hence the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">JECP</i> constructs the best emergent path that shares the general sensors as much as possible to save energy consumption. The experimental results show that the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">JECP</i> outperforms the existing mechanisms in terms of transmission delay and energy consumption for the emergent sensors in Bluetooth Low Energy (BLE) networks.

Joint Data Transmission and Energy Harvesting for MISO Downlink Transmission Coordination in Wireless IoT Networks.

The advent of simultaneous wireless information and power (SWIPT) has been regarded as a promising technique to provide power supplies for an energy sustainable Internet of Things (IoT), which is of paramount importance due to the proliferation of high data communication demands of low-power network devices. In such networks, a multi-antenna base station (BS) in each cell can be utilized to concurrently transmit messages and energies to its intended IoT user equipment (IoT-UE) with a single antenna under a common broadcast frequency band, resulting in a multi-cell multi-input single-output (MISO) interference channel (IC). In this work, we aim to find the trade-off between the spectrum efficiency (SE) and energy harvesting (EH) in SWIPT-enabled networks with MISO ICs. For this, we derive a multi-objective optimization (MOO) formulation to obtain the optimal beamforming pattern (BP) and power splitting ratio (PR), and we propose a fractional programming (FP) model to find the solution. To tackle the nonconvexity of FP, an evolutionary algorithm (EA)-aided quadratic transform technique is proposed, which recasts the nonconvex problem as a sequence of convex problems to be solved iteratively. To further reduce the communication overhead and computational complexity, a distributed multi-agent learning-based approach is proposed that requires only partial observations of the channel state information (CSI). In this approach, each BS is equipped with a double deep Q network (DDQN) to determine the BP and PR for its UE with lower computational complexity based on the observations through a limited information exchange process. Finally, with the simulation experiments, we verify the trade-off between SE and EH, and we demonstrate that, apart from the FP algorithm introduced to provide superior solutions, the proposed DDQN algorithm also shows its performance gain in terms of utility to be up to 1.23-, 1.87-, and 3.45-times larger than the Advantage Actor Critic (A2C), greedy, and random algorithms, respectively, in comparison in the simulated environment.

Joint Speed Control and Energy Replenishment Optimization for UAV-Assisted IoT Data Collection With Deep Reinforcement Transfer Learning

Unmanned-aerial-vehicle (UAV)-assisted data collection has been emerging as a prominent application due to its flexibility, mobility, and low operational cost. However, under the dynamic and uncertainty of Internet of Things data collection and energy replenishment processes, optimizing the performance for UAV collectors is a very challenging task. Thus, this article introduces a novel framework that jointly optimizes the flying speed and energy replenishment for each UAV to significantly improve the overall system performance (e.g., data collection and energy usage efficiency). Specifically, we first develop a Markov decision process to help the UAV automatically and dynamically make optimal decisions under the dynamics and uncertainties of the environment. Although traditional reinforcement learning algorithms, such as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning and deep <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning, can help the UAV to obtain the optimal policy, they often take a long time to converge and require high computational complexity. Therefore, it is impractical to deploy these conventional methods on UAVs with limited computing capacity and energy resource. To that end, we develop advanced transfer learning techniques that allow UAVs to “share” and “transfer” learning knowledge, thereby reducing the learning time as well as significantly improving learning quality. Extensive simulations demonstrate that our proposed solution can improve the average data collection performance of the system up to 200% and reduce the convergence time up to 50% compared with those of conventional methods.

A Comparative Analysis of Separate and Joint Environmental Rights Trading Markets in China

The structuring of effective market-based environmental rights instruments can help to achieve energy efficiency and emission reduction goals while minimizing economic costs. As part of the global drive for sustainable development, pollution rights, carbon emission permits, and white certificates have become widely used as environmental rights trading schemes in many countries. However, interactions between environmental rights can create challenges. For instance, China has established a national carbon market, which it aims to connect with the energy consumption permit trading market. The effectiveness of separate and joint markets in achieving win-win outcomes is an area that requires further research. To address this question, we employed a mixed-integer linear programming model to simulate the potential incremental outputs and energy savings of 16 high-energy-consuming and high-emission industries in China from 2010 to 2019. Our findings indicate that the joint energy consumption permits and the carbon emission permits market yield the greatest economic benefits, but they lack a distinct advantage compared to the separate carbon market. Additionally, industries face less pressure to ensure energy savings in the joint market. The energy saving ratio of the joint market is 0.1% lower than that of the separate carbon market. We also found that the construction of a joint market will incur additional costs for firms and governments. Based on our benefit and cost analysis, we propose that governance subjects of pilot cities prioritize the establishment of the carbon market and not the rapid expansion of the pilot-level scope of energy consumption permits.

Seismic performance of bolted connection between T-shaped section column and I-section beam with L-stubs

Bolted beam-to-column connections can reduce the construction period and are proper for prefabricated structures. Based on the traditional bolted connections, a beam-to-column bolted joint with L-stubs was proposed to connect the I-section beam and T-shaped section column using only bolts on site. Changing the parameters of L-stub end plate thickness, stiffener layouts, friction coefficient, column web thickness and the quantity of the beam flange bolts, experimental and numerical investigations were conducted on the cyclic performances of the proposed joint, and the hysteretic curve, skeleton curve, deformation characteristics, ductility and rotational capacity, as well as the slipping, yield and ultimate resistances, were analyzed. According to the results, the proposed joint can perform as a rigid joint without slipping under small earthquakes, and develop considerable ductility and energy dissipation ability under moderate or large earthquakes by slipping and plastic deformations. Increasing the friction coefficient can improve the slipping moment, and the stiffeners can improve the joints stiffness. The joint energy dissipation capacity could be increased by adding bolts. Based on the analysis, recommended parameter values for the joints were provided, and simplified formulas were proposed to calculate the slipping, yield and ultimate moment resistances, providing satisfactory accuracy when compared to the test and finite element results.

Optimization of the Position and Stiffness of Passive Walking Assistance Devices

Walking is a fundamental movement in daily life; however, many factors affect walking that may reduce the mobility of the people. Walking assistance devices can help with gaining mobility back for people who suffer from walking problems. In the present study, a computational method to determine the location and stiffness of the assistive walking systems was developed. The human walking model was created by using nine rigid bodies and eight revolute joints connecting them in the sagittal plane. The walking assistance system was considered as a tension spring with both ends attached to the human walking model. A coordinate system was defined along the distal–proximal direction of the human body. The position of the walking assistance system was determined by using four design variables, and the optimal position of the assistive walking system to reduce the total positive joint energy was found around the hip joint at a walking speed of 1.3 m/s. Hip joint moment and power were significantly affected by the walking assistance system, and the total positive joint energy was reduced by 8.8%. Because walking speed significantly affects walking kinematics and kinetics, the effect of walking speed on the optimal walking assistance device was investigated. The position of the device was kept the same, and the optimal stiffness and free length of the spring were found at different walking speeds. Two different cases were considered: a speed-specific design in which stiffness characteristics were separately optimized for each speed and a general design in which stiffness characteristics were optimized by considering all walking speeds. It was found that, in both cases, hip joint moment and power significantly reduced, and the speed-specific design produced a slightly larger reduction in total joint energy. The performance of the walking assistance systems in both cases were found to be higher at faster walking speeds.

Stochastic Strategic Participation of Active Distribution Networks With High-Penetration DERs in Wholesale Electricity Markets

With the increasing penetration of distributed energy resources (DERs), traditional distribution networks as load-serving entities in wholesale electricity markets, now evolve towards active distribution networks (ADNs) which can proactively participate in wholesale markets by optimally controlling the DERs in their networks. A stochastic bilevel optimization model is proposed in this paper for the strategic participation of ADNs and DERs to provide energy and grid services in wholesale electricity markets. The bilevel optimization model can capture the interactions between the ADN and the wholesale energy and ancillary service markets, considering the uncertainties of DERs in the ADN. In the upper-level model, the ADN makes optimal decisions on energy and reserve bidding considering the availability, uncertainties, and flexibility of DERs. The joint energy and reserve market-clearing of the independent system operator (ISO) is modeled as the lower-level problem. Using strong duality theory and Karush-Kuhn Tucker (KKT) conditions, the proposed bilevel optimization problem is reformulated as mathematical programming with equilibrium constraints (MPEC) problem and further converted into a computationally-solvable mixed-integer second-order-cone programming (MISOCP) model. The simulation results demonstrate the effectiveness of the model and the interactions between an ADN and wholesale electricity markets.

Joint Energy and Workload Scheduling for Fog-Assisted Multimicrogrid Systems: A Deep Reinforcement Learning Approach

Due to the fluctuation of renewable energy, the uncertainty of electrical loads, and the complexity of networked microgrids, it is challenging to dispatch multiple resources to minimize the operating cost of multi-microgrid system (MMGS). In this article, a fog-assisted operating cost minimization problem of MMGS is investigated with the consideration of source-grid-load-storage-computing coordination. Since there are strong couplings among multiple resources, it is difficult to solve the problem directly. Therefore, the above problem is reformulated as a Markov game. Then, a novel energy management algorithm is proposed to solve Markov game based on multiagent deep reinforcement learning. It is worth mentioning that the proposed energy management algorithm can support local real-time decisions for each microgrid without knowing any prior knowledge of uncertain parameters and private information of other microgrids. Simulation results indicate that the proposed algorithm can reduce the long-term cost of each microgrid by 0.09 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> –8.02 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> compared with baselines.

Flexibility Clearing in Joint Energy and Flexibility Markets Considering TSO-DSO Coordination

Active distribution networks (ADNs) with distributed generators (DGs) can provide flexibility for the upstream grid by participating in energy and flexibility markets. In this paper, a novel market-clearing model is proposed to facilitate energy and flexibility transactions through coordinating the flexibility providers in both transmission and distribution networks. The energy and flexibility market-clearing problem is formulated as a bi-level optimization model. The upper-level models the transmission-level joint energy and flexibility market clearings while the lower-level represents the distribution-level ADN market clearings. In the proposed model, the locational marginal prices (LMP) at the coupling bus will affect the dispatch of DGs and power demands of the ADNs. In turn, the power demands of the ADNs and the offers submitted by DGs will affect energy and flexibility market-clearing results and the LMPs as well. Karush-Kuhn-Tucker (KKT) conditions and the duality theory are used to transform the proposed nonlinear bi-level model to a single-level mathematical program with equilibrium constraints (MPEC) model. Case studies verify the effectiveness of the proposed model.