Distributed Generation Output Research Articles

A Two-Stage Distributionally Robust Optimization Model for Managing Electricity Consumption of Energy-Intensive Enterprises Considering Multiple Uncertainties

Energy-intensive enterprises (EIEs), as vital demand-side flexibility resources, can significantly enhance the power system’s ability to regulate demand by participating in demand response (DR). This helps alleviate supply pressures during tight demand–supply conditions, ensuring the system’s safe and stable operation. However, due to the current level of electricity management in EIEs, their participation in demand response has disrupted the continuity of production to some extent, which may hinder the sustainability of demand-side management mechanisms. To address this issue, this paper proposes a two-stage distributionally robust optimization (DRO) model for managing production electricity in EIEs, considering multiple uncertainties. First, a production electricity load model based on the state task network (STN) is developed, reflecting the characteristics of industrial production lines. Next, a two-stage DRO model for day-ahead and intra-day electricity management is formulated, integrating an uncertainty set for distributed generation output based on the Wasserstein distance and probabilistic constraints for the day-ahead DR capacity. Finally, a cement plant in western China is used as a case study to validate the effectiveness of the proposed model. The results show that the proposed model effectively guides EIE in participating in DR while optimizing electricity costs, enabling cost savings of up to 27.7%.

Two-stage optimization strategy for the active distribution network considering source-load uncertainty

This study aims to advance the development of the active distribution network (ADN) by optimizing resource allocation across different stages to enhance overall system performance and economic benefits. First, an ADN optimization model is constructed based on a two-stage robust optimization approach. The first stage focuses on determining optimal decision variables within the uncertainty set, while the second stage adjusts control variables based on the initial stage decisions. This model effectively addresses source-load uncertainties while preserving the flexibility and adaptability of decision-making solutions. Additionally, this study explores uncertainty models that incorporate correlation factors. The IEEE33-node model is employed to validate the effectiveness and superiority of the proposed optimization strategy through numerical simulations. Simulation results demonstrate that Model 3 comprehensively accounts for photovoltaic and wind turbine generator planning by optimizing their capacity configurations, leading to a 23% increase in distributed generation (DG) penetration. During high-load periods (e.g., 13:00 and 16:00), DG output reaches 47% and 50% of the demand load, underscoring the critical role of DG in supporting the power grid during peak hours. Overall, the proposed two-stage optimization strategy considers source-load uncertainties, significantly reducing economic costs, enhancing DG output, and improving overall system performance. In scenarios with correlated uncertainties, the optimized results exhibit greater accuracy and reliability, providing robust support for the planning and operation of practical distribution networks.

Analysis of steady‐state operation of active distribution network under uncertain conditions

AbstractRecently, distributed generators (DGs) have been widely integrated into distribution network, so that the distribution network is gradually transforming into an active distribution network (ADN). Due to the influence of meteorological conditions, the output of DGs has high uncertainty. At the same time, considering the increasing variety of loads in ADNs, the uncertainty of load demand of user side is also increasing. In order to fully consider the uncertainty of measurement and quantitatively evaluate the operational status, this paper proposes a steady‐state analysis method for ADNs under uncertain conditions. Firstly, this paper proposes a steady‐state analysis method including power flow analysis model and evaluation indicators for the operation status from the perspectives of node and network. Secondly, the uncertainty factors are elaborated from three aspects: sources, impact on evaluation index and impact on scheduling. The evaluation indicators considering uncertain conditions, the impact on system security and scheduling of network are further discussed. Finally, through the simulation analysis of the modified IEEE 33‐node test system, the effectiveness of the proposed method is verified.

Reliability assessment of distribution networks with distributed generation considering different types of user loads

Abstract This paper meticulously evaluates the reliability of distribution networks integrated with distributed generation (DG), considering various user classifications. Initially, we delve into the daily load profiles of residential, commercial, and industrial sectors, establishing a nuanced time-series load model that encapsulates the distinct characteristics of these customer segments. Subsequently, we formulate a model for the harmonious operation of energy storage systems, tailored to the interplay between DG output and load requirements. Utilizing the sequential Monte Carlo simulation algorithm, we compute the reliability metrics for the IEEE RBTSBUS6 feeder system, revealing that DG integration significantly enhances distribution network reliability. Notably, identical DG output yields varied impacts on the reliability of distinct customer sectors, underscoring the need for tailored strategies in DG deployment.

Enhancing reliability assessment in distributed generation networks: Incorporating dynamic correlation of wind-solar power output uncertainty

Amidst escalating environmental concerns and energy scarcity, the integration of distributed generation (DG) within distribution networks (DN) has emerged as a pivotal developmental trend. The uncertainty inherent in renewable energy output often disrupts DG networks. Notably, the dynamic correlation between key renewable sources, such as wind and solar energy, significantly influences the reliability analysis of these networks.To comprehensively assess the impact of wind-solar power output uncertainty and its dynamic correlation on DN reliability, this study leverages copula theory to express the dynamic correlation coefficient between wind and solar power. This coefficient is formulated as the dynamic correlation of wind-solar power through copula dynamic correlation coefficient. Employing an auto-regressive moving average (ARMA) model with constraints solved using maximum likelihood kernel (MLK), we construct the wind-solar joint output (WSJO) model. Subsequently, utilizing sequential Monte Carlo simulation (MCS) with the WSJO model, we analyze DN reliability. In case of DN failure, the WSJO model generates random samples of the wind-solar joint output sequence. Subsequent power restoration to governed islands enables the calculation of DN reliability indices. The WSJO model constructed in this study accounts for wind resource output uncertainty and dynamic correlation, aligning more closely with actual distributed generation output and enhancing the accuracy of reliability assessment. Finally, we simulate the improved IEEE-RBTS-BUS6-F4 system to underscore the crucial role of considering wind-solar energy's dynamic correlation in DN reliability assessment.

Deep Learning-based Intelligent Fault Diagnosis for Power Distribution Networks

Power distribution networks with distributed generation (DG) face challenges in fault diagnosis due to the high uncertainty, randomness, and complexity introduced by DG integration. This study proposes a two-stage approach for fault location and identification in distribution networks with DG. First, an improved bald eagle search algorithm combined with the Dijkstra algorithm (D-IBES) is developed for fault location. Second, a fusion deep residual shrinkage network (FDRSN) is integrated with IBES and support vector machine (SVM) to form the FDRSN-IBS-SVM model for fault identification. Experimental results showed that the D-IBES algorithm achieved a CPU loss rate of 0.54% and an average time consumption of 1.70 seconds in complex scenarios, outperforming the original IBES algorithm. The FDRSN-IBS-SVM model attained high fault identification accuracy (99.05% and 98.54%) under different DG output power levels and maintained robustness (97.89% accuracy and 97.54% recall) under 5% Gaussian white noise. The proposed approach demonstrates superior performance compared to existing methods and provides a promising solution for intelligent fault diagnosis in modern distribution networks.

Enhancing Coordination Efficiency with Fuzzy Monte Carlo Uncertainty Analysis for Dual-Setting Directional Overcurrent Relays Amid Distributed Generation.

In the contemporary context of power network protection, acknowledging uncertainties in safeguarding recent power networks integrated with distributed generation (DG) is imperative to uphold the dependability, security, and efficiency of the grid amid the escalating integration of renewable energy sources and evolving operational conditions. This study delves into the optimization of relay settings within distribution networks, presenting a novel approach aimed at augmenting coordination while accounting for the dynamic presence of DG resources and the uncertainties inherent in their generation outputs and load consumption-factors previously overlooked in existing research. Departing from conventional methodologies, the study proposes a dual-setting characteristic for directional overcurrent relays (DOCRs). Initially, a meticulous modeling of a power network featuring distributed generation is undertaken, integrating Weibull probability functions for each resource to capture their probabilistic behavior. Subsequently, the second stage employs the fuzzy Monte Carlo method to address generation and consumption uncertainties. The optimization conundrum is addressed using the ant lion optimizer (ALO) algorithm in the MATLAB environment. This thorough analysis was conducted on IEEE 14-bus and IEEE 30-bus power distribution systems, showcasing a notable reduction in the total DOCR operating time compared to conventional characteristics. The proposed characteristic not only achieves resilient coordination across a spectrum of uncertainties in both distributed generation outputs and load consumption, but also strengthens the resilience of distribution networks overall.

Active Distribution Network Expansion Planning Based on Wasserstein Distance and Dual Relaxation

In the future, a high proportion of distributed generations (DG) will be integrated into the distribution network. The existing active distribution network (ADN) planning methods have not fully considered multiple uncertainties, differentiated regulation modes or the cost of multiple types of interconnection switches. Meanwhile, it is difficult to solve large-scale problems at small granularity. Therefore, an expansion planning method of ADN considering the selection of multiple types of interconnection switches is proposed. Firstly, a probability distribution ambiguity set of DG output and electrical-load consumption based on the Wasserstein distance is established for dealing with the issue of source-load uncertainty. Secondly, a distributionally robust optimization model for collaborative planning of distribution network lines and multiple types of switches based on the previously mentioned ambiguity set is established. Then, the original model is transformed into a mixed integer second-order cone programming (SOCP) model by using the convex relaxation method, the Lagrangian duality method and the McCormick relaxation method. Finally, the effectiveness of the proposed method is systematically verified using the example of Portugal 54. The results indicate that the proposed method raises the annual net profit by nearly 5% compared with the traditional planning scheme and improves the reliability and low-carbon nature of the planning scheme.

Multi-time-scale voltage control of the distribution network with energy storage equipped soft open points

The integration of distributed generation (DG) units into distribution networks (DNs) has brought about several operational challenges, including voltage issues and increased power loss. Energy storage equipped soft open points (E-SOPs) can accurately and flexibly control active and reactive power flows to address these problems. Additionally, the photovoltaic (PV) inverter and the network reconfiguration (NR) play a significant role in voltage control by adjusting the reactive power and the topology of the DN, respectively. However, due to differences in response times, there is a lack of systematic coordination between NR and the inverters of the E-SOP and PV. This paper proposes a multi-time-scale voltage control model that includes day-ahead NR scheduling, inter-day droop control optimization of the PV and E-SOP, and real-time local droop control. Considering the uncertainties of renewable DG outputs and loads, a robust optimization method is used in the day-ahead stage to obtain a reliable network structure. Then, with more accurate intra-day predictions, a stochastic optimization method is used to obtain the optimal state-of-charge interval, aiming to provide a flexible regulation range for battery energy storage to cope with the power fluctuations during the real-time stage. In addition, to address the intra-day voltage control model with bilinear constraints of the droop control function, a particle swarm optimization method is used. The results are verified on a 33-bus DN system through comparative analyses, showing effective performance.

Optimization of sustainable distributed power generation in distribution networks: a comprehensive analysis of location, capacity, and environmental impact

With the increasing integration of distributed generation (DG) into distribution networks, the impact of its output and configuration on the environment and overall benefits has become more pronounced. To enhance environmental benefits while minimizing costs, an optimization model for DG location and capacity considering environmental benefits (LCEB) is proposed. Initially, a mathematical model for DG location and capacity is established, with optimization objectives including voltage deviation, network loss, and environmental benefit. Subsequently, modified particle swarm optimization (MPSO) with a single-dimension search probability mutation is employed to solve this model, obtaining an optimized DG output and layout scheme. Finally, the feasibility and effectiveness of the proposed model are demonstrated through simulation and analysis by using the IEEE33 node system as an example. The results highlight the model’s capability to improve environmental and economic benefits, enhance voltage levels, and reduce network losses within the distribution network.

Microgrid Formation and Real-Time Scheduling of Active Distribution Networks Considering Source-Load Stochasticity

The post-disruption microgrid (MG) formation and the subsequent scheduling are resilience-enhancing measures for active distribution networks (ADNs) against disastrous events. This paper proposes an integrated MG formation and scheduling solution, considering stochastic loads and distributed generators (DGs). Specifically, a first-stage MG formation model and a sec-ond-stage MG scheduling model are proposed to flexibly identify MG boundaries and restore as many critical loads as possible. The MG formation problem is formulated over multiple time steps to address time-varying generation outputs of intermittent DGs. Moreover, in the MG scheduling problem, the stochasticity of load demands and DG outputs is modeled as joint chance constraints (JCCs) to describe the possibility of security violations in the over-all system. An efficient approximation method is next developed to convexify the JCCs into solvable second-order cones. The interac-tion between the MG formation and scheduling by the model predictive control implementation achieves a responsive solution for enhancing the emergency support capability of ADNs by incor-porating power forecasts and real-time scheduling. The performance of the proposed method is verified in a modified real-world 136-node test feeder under catastrophic failures.

A risk-averse approach for distribution locational marginal price calculation in electrical distribution networks

As distributed generation (DG) systems continue reshaping power networks, optimizing pricing strategies at DG buses using the distribution locational marginal price (DLMP) concept becomes critical for economic efficiency and the optimal operation of the network. This paper proposes a novel approach that combines Information Gap Decision Theory (IGDT) and Particle Swarm Optimization (PSO) to address these challenges. IGDT offers a robust framework for optimizing pricing in the presence of uncertainties and incomplete information in the distribution network. It quantifies and models these uncertainties, enabling the creation of adaptable pricing strategies that respond effectively to changes in DG output and market conditions. To further refine pricing strategies, PSO is integrated into the IGDT framework. PSO's iterative approach allows for the discovery of optimal pricing parameters at DG buses, striking a balance between maximizing DG owner profits and ensuring system optimality. Extensive simulations on two realistic distribution network models validate the effectiveness of the proposed IGDT-PSO approach. It demonstrates that DG owners can reliably achieve their predefined profit targets while also adhering to the objectives of the distribution network.

Stochastic MPC based double-time-scale voltage regulation for unbalanced distribution networks with distributed generators

With the increasing penetration of renewable energy resources, the uncertainty of renewable energy resources output introduces challenges to voltage control in distribution networks (DNs). To solve these problems, this paper proposes a double-time-scale voltage control scheme for unbalanced DNs based on stochastic model predictive control (SMPC) to coordinate multiple voltage control devices. In fast-time-scale control, the active and reactive power outputs of distributed generators (DGs) are optimized to minimize voltage deviation, active power curtailment and reactive power fluctuation. In the slow-time-scale control, optimal tap changes of on-load tap changers (OLTC), step voltage regulators (SVR), and switched capacitor banks (CBs) are calculated to reduce voltage deviation and tap operations. Additionally, in the fast-time-scale control, the SMPC-based scheme adopts a scenario generation approach to represent the uncertainty of DG output. Considering the temporal correlation of the DG output, different prediction scenarios and scenario probabilities are obtained by the empirical cumulative distribution function fitted by the historical measurement data. In this paper, the effectiveness of the proposed double-time-scale voltage control scheme is verified by the unbalanced IEEE123 node system. The case study demonstrates that the proposed voltage scheme can effectively keep the three-phase voltages in unbalanced DN within the secure operation range and achieve better voltage profiles.

Dynamic Reactive Power Compensation Optimization Strategy for Distribution Networks with Distributed Generators and Energy Storage Systems

To balance the output and load dynamic changes of distributed power generators (DG) and energy storage systems (ESS), a demand-side response-based dynamic reactive power optimization (RPO) strategy for distribution networks (DN) is proposed. This strategy adopts a phased optimization method to coordinate and optimize different types of reactive variables within the same period. By adjusting the states of parallel capacitor banks (SCBs) on load voltage transformers (OLTC), DGs, and ESS inverters, the RPO of the DN is carried out. Based on the characteristics of the model, an improved particle swarm optimization algorithm (IPSO) is used to solve different types of variables, and an IPSO based on tent chaotic mapping and levy flight strategy is proposed to improve the efficiency of collaborative solving. The simulation results show that the proposed strategy, considering the change of new energy output and demand side response, can reduce the solution scale while obtaining high satisfaction RPO results.

Weighted Minkowski distance-based differential protection for active distribution networks considering the uncertainty of frequency-domain characteristics

With the increasing use of DGs (distributed generators) in the power system, the distribution network is becoming more and more complicated. The rapid change of DG output power and the diversity of DG location make the computing calculation of relay protection difficult, bringing severe challenges to the current protection based on single-end electrical volume. Therefore, double-end-based protection is a good choice in view of the DG uncertainty and the network complexity. However, the power frequency offset after fault and the uncertainty of DG fault current result in uncertainty in the frequency-domain characteristics, which can also negatively affect the differential protection. In view of this, a new differential protection method based on the weighted Minkowski distance algorithm is proposed in this paper. First, the Minkowski distance algorithm is used to describe the similarity of both currents considering the uncertainty in the frequency-domain characteristics. Second, each current similarity including the phase current, the positive current, and the negative current is calculated separately to increase the protection sensitivity. Through the weighted algorithm distribution, the weight is assigned. Furthermore, a high-performance protection mechanism is designed to improve the protection sensitivity. This method is suitable for the active distribution network with different penetration rates of DGs and different types of DGs. The simulations show that the proposed method has good feasibility and high superiority.

Multi-objective distributed generation hierarchical optimal planning in distribution network: Improved beluga whale optimization algorithm

This study constructs a distributed generation (DG) multi-objective hierarchical optimal planning model. A solution method is proposed based on an improved beluga whale optimization algorithm (IBWO). Reasonable planning of the location and capacity of DG access to the distribution network plays an important role in minimizing actual power losses, reducing grid operating costs, and improving voltage distribution. The output power of DG has uncertainties and the demand response on the load side can also affect the DG planning; however, previous studies have ignored these two critical factors. This study aims to determine the optimal location and capacity of DG access to distribution network considering the demand response and the uncertainty of DG output power to improve the economic benefit, power quality and energy utilization efficiency. This study proposes an IBWO algorithm with better performance, aiming at the multi-objective, multi-constrained and nonlinear DG planning problem and a DG multi-objective hierarchical optimal planning model is established. The results show that proposed method can reduce the annual comprehensive cost, total voltage deviation and power loss of system by 11.66%, 40.55% and 38.61%.

Self-Attention Generative Adversarial Network Enhanced Learning Method for Resilient Defense of Networked Microgrids Against Sequential Events

The resilient responses of networked microgrids (MGs) can greatly improve the survival of critical loads during extreme events. In order to efficiently handle the scarce data issue as well as improve the adaptability of deep reinforcement learning (DRL) methods for complex sequential extreme events (SEEs) such as hurricanes and tornadoes, a new learning-based method is proposed for the survival of critical loads in MGs during SEEs. A generative adversarial network (GAN) is applied to generate a sufficient extreme event-related database in a model-free way. Specifically, a self-attention GAN (SA-GAN) is developed to capture sequential features of the SEE process. Then, the SA-GAN is integrated into a DRL framework, and the corresponding Markov decision process (MDP) and the environment are designed to realize adaptive networked MG reconfiguration for the survival of critical loads. Faced with uncertain distributed generator (DG) output and sequential line damage, the SA-GAN-DRL method provides an adaptive model-free solution to continuously supply critical loads during SEEs. The effectiveness of the proposed method is validated using a 7-bus test system and the IEEE 123-bus system, and the results demonstrate both a strong learning ability with limited practice data, and robustness and adaptability for highly changeable SEE processes.

Evaluation Method of the Incremental Power Supply Capability Brought by Distributed Generation

More and more distributed generation (DG) and energy storage (ES) devices are being connected to the distribution network (DN). They have the potential of maintaining a stable supply load during failure periods when using islanding operations. Therefore, DG and ES have capacity value, i.e., improving the power supply capability of the system. However, there are strong fluctuations in DG outputs, and the operations of ES devices have sequential characteristics. The same capacity of DG has different load-bearing capabilities compared to conventional thermal or hydroelectric units. This paper proposes a method for evaluation of power supply capability improvement in DNs. First, the temporal fluctuation in both power source and load demand during fault periods is considered. A DN island partition model considering the secondary power outage constraint is established. Then, a modified genetic algorithm is designed. The complex island partition model is solved to achieve accurate power supply reliability evaluation. And the incremental power supply capability associated to DG and ES devices is calculated. Finally, a case study is conducted on the PG&E 69-bus system to verify the effectiveness of the proposed method. It is found that with a 20% configuration ratio of ES devices, the power supply capability improvement brought about by 6 MW DG can reach about 773 kW.

A two-layer optimal configuration approach of energy storage systems for resilience enhancement of active distribution networks

Introducing energy storage systems (ESSs) into active distribution networks (ADNs) has attracted increasing attention due to the ability to smooth power fluctuations and improve resilience against fault disturbances. This paper proposes a methodology for simultaneously optimizing the configuration of battery ESSs and the operation of ADNs, and the goal is to increase the resilience of the ADNs withstanding multi-faults. Firstly, based on random sampling and K-means clustering, a generation strategy of typical N-1 and N-2 fault scenarios is designed for the ADNs. Then, a two-layer optimization model is established, where the inner model is to optimize the fault recovery performance from the operational perspective, and the outer model is to obtain the optimal site and size of ESSs from the economic perspective. Further, the second-order cone relaxing (SOCR) method and the hybrid gray wolf optimal and particle swarm optimal (GWO-PSO) algorithm are applied to solve the optimization model. Using MATLAB, the modified IEEE 33-node and 118-node systems are built to check the proposed approach's performance. Different periods are considered to show the multi-faults' development, and by introducing a resilience assessment system with node voltage deviation, fault recovery rate, and network loss rate, the resilience of the ADNs is analyzed. From the comparative results, the proposed approach can optimally configure the battery ESSs, and adjust the network structure as well as the distributed generation outputs. Following the ESS configuration cost reduction of 53.19% and 9.8%, the resilience of the ADNs against the multi-faults will increase by 13.36% and 8.25% for the 33-node and 118-node systems.

A new differential protection method for distribution networks with DGs based on adaptive braking zone

The distribution network with large-scale DGs (distributed generations) brings new challenges to traditional protection schemes, which makes it less adaptable for the single-end based protection. Affected by the large-scale distributed generations, the single-ended based protection of distribution network faces the problem of insufficient adaptability. The uncertainty of DG output and the variety of DG locations make the setting calculation of conventional current protection extremely difficult. As a comparison, the application of differential protection to ADNs (active distribution networks) can reduce the impact of DG uncertainty and network complexity better. However, considering the structure changes and weak communication conditions with larger time delays of ADN, it is difficult to balance the sensitivity of differential protection and its ability to resist synchronization error. In order to solve the problem, the new adaptive differential protection method is proposed, which is based on the traditional standard product brake differential protection criterion, making full use of fault current amplitude and phase characteristics. The braking capability adaptively of the new differential protection changes with the current amplitude ratio, so that the protection has high sensitivity and resistance to synchronization errors. Simulations show the effectiveness of the proposed protection method.