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Robust Capacity Assessment of Distributed Generation in Unbalanced Distribution Networks Incorporating ANM Techniques
Abstract
To settle a large-scale integration of renewable distributed generations (DGs), it requires to assess the maximal DG hosting capacity of active distribution networks (ADNs). For fully exploiting the ability of ADNs to accommodate DG, this paper proposes a robust comprehensive DG capacity assessment method considering three-phase power flow modelling and active network management (ANM) techniques. The two-stage adjustable robust optimization is employed to tackle the uncertainties of load demands and DG outputs. With our method, system planners can obtain the maximum penetration level of DGs with their optimal sizing and sitting decisions. Meanwhile, the robust optimal ANM schemes can be generated for each operation time period, including network reconfiguration, on-load-tap-changers regulation, and reactive power compensation. In addition, a three-step optimization algorithm is proposed to enhance the accuracy of DG capacity assessment results. The optimality and robustness of our method are validated via numerical tests on an unbalanced IEEE 33-bus distribution system.
... Currently, methods for assessing PV consumption capacity can be broadly classified into two categories: software simulation methods [12][13][14] and mathematical optimization algorithms [15][16][17]. Software simulation methods, such as those using MATLAB and other computational software, build systems for simulation, allowing for real-time calculation and evaluation of various parameters. ...
... Software simulation methods, such as those using MATLAB and other computational software, build systems for simulation, allowing for real-time calculation and evaluation of various parameters. Literature [12] employs a two-stage adjustable robust optimization to address the uncertainties in load demands and DG outputs, and proposes a robust comprehensive DG capacity assessment method considering three-phase power flow modeling and active network management (ANM) techniques. Literature [13] discussed the photovoltaic consumption capacity under three different scenarios: concentrated at the feeder source, middle point, and end point, and determined the maximum consumption capacity for each location. ...
... The maximum photovoltaic consumption scheme configuration for the IEEE 33-node system is obtained, as illustrated in Fig. 10. As shown in this figure, the photovoltaic configuration scenarios obtained in reference [15] are nodes 3,6,9,10,12,15,20,22,26,28,29, and 32, with a total photovoltaic capacity of 13.89 MW. Although this is higher than the 12.48 MW result obtained by the method in this paper, the photovoltaic capacity at node 22 reaches 2.8001 MW, exceeding its rooftop area limit of 2.5035 MW, which does not comply with practical constraints. ...
With the large-scale promotion of distributed photovoltaics, new challenges have emerged in the photovoltaic consumption within distribution networks. Traditional photovoltaic consumption schemes have primarily focused on static analysis. However, as the scale of photovoltaic power generation devices grows and the methods of integration diversify, a single consumption scheme is no longer sufficient to meet the actual needs of current distribution networks. Therefore, this paper proposes an optimal evaluation method for photovoltaic consumption schemes based on BASS model predictions of installed capacity, aiming to provide an effective tool for generating and evaluating photovoltaic consumption schemes in distribution networks. First, the BASS diffusion model, combined with existing photovoltaic capacity data and roof area information, is used to predict the trends in photovoltaic installed capacity for each substation area, providing a scientific basis for consumption evaluation. Secondly, an improved random scenario simulation method is proposed for assessing the photovoltaic consumption capacity in distribution networks. This method generates photovoltaic integration schemes based on the diffusion probabilities of different regions and evaluates the consumption capacity of each scheme. Finally, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to comprehensively evaluate the generated schemes, ensuring that the selected scheme not only meets the consumption requirements but also offers high economic benefits and reliability. The effectiveness and feasibility of the proposed method are validated through simulations of the IEEE 33-node system, providing strong support for optimizing photovoltaic consumption schemes in distribution networks.
... RO is a method for optimizing under uncertainty, designed to ensure that system performance is maintained even in the most adverse conditions [15][16][17]. It characterizes uncertainty by constructing an uncertainty set and aims to find solutions that perform effectively across all potential uncertainties. ...
... Equation (15) indicates that (14) holds with a probability of at least 1 − ε. In this equation, the random variable ξ follows a JPDF P, where P is uncertain and belongs to a fuzzy set D. ...
... Based on Equation (15), the confidence interval for PV output can be reformulated as a chance constraint. ...
This paper addresses the challenge of assessing photovoltaic (PV) hosting capacity in distribution networks while accounting for the uncertainty of PV output, a critical step toward achieving sustainable energy transitions. Traditional optimization methods for dealing with uncertainty, including robust optimization (RO) and stochastic optimization (SO), often result in overly conservative or optimistic assessments, hindering the efficient integration of renewable energy. To overcome these limitations, this paper proposes a novel distributionally robust chance-constrained (DRCC) assessment method based on Kullback–Leibler (KL) divergence. First, the time-segment adaptive bandwidth kernel density estimation (KDE) combined with Copula theory is employed to model the conditional probability density of PV forecasting errors, capturing temporal and output-dependent correlations. The KL divergence is then used to construct a fuzzy set for PV output, quantifying its uncertainty within specified confidence levels. Finally, the assessment results are derived by integrating the fuzzy set into the optimization model. Case studies demonstrate its effectiveness of the method. Key findings indicate that higher confidence levels reduce PV hosting capacities due to broader uncertainty ranges, while increased historical sample sizes enhance the accuracy of distribution estimates, thereby increasing assessed capacities. By balancing conservatism and optimism, this method enables safer and more efficient PV integration, directly supporting sustainability goals such as reducing fossil fuel dependence and lowering carbon emissions. The findings provide actionable insights for grid operators to maximize renewable energy utilization while maintaining grid stability, advancing global efforts toward sustainable energy infrastructure.
... Existing research [2][3][4][5][6][7][8][9][10] investigates the impact of unbalanced DESs integration on distribution grid operation through centralized optimization approaches. For instance, a scheme is developed in [2] to schedule the electric vehicles to address the unbalanced operational condition in the grid. ...
... Furthermore, a planning model is proposed in [5] to optimize the integration of single-phase DESs into the grid to mitigate their effects on the unbalanced operational condition of the system. In addition, authors in [6] have developed a planning model utilizing the robust optimization to optimize the siting and sizing of distributed generations (DGs) in unbalanced distribution systems. Moreover, a multi-objective optimization model is developed in [7] in order to minimize the unbalanced condition while optimizing the operation of microgrids. ...
... Furthermore, the re-phasing of PV units is studied in [10] to mitigate the power unbalance in low-voltage systems. However, centralized optimization approaches, utilized in prior research works [2][3][4][5][6][7][8][9][10], may not be ideal for managing unbalances in distributed power systems due to security and scalability issues with growing data and limited adaptability to dynamic changes. Therefore, while centralized optimization has been used in the past, a shift towards distributed optimization approaches for effective power unbalance management may be needed. ...
The emergence of multi‐agent systems and significant integration of distributed energy sources (DESs) are transforming distribution networks. This necessitates a decentralized management strategy for unbalanced operation in multi‐agent distribution systems (MADSs) due to the autonomous nature and potential for unbalanced injection of single‐phase DESs. Accordingly, this paper proposes a novel approach for decentralized management of unbalanced operation in MADSs. The approach leverages a customized alternating direction method of multipliers to facilitate decentralized decision‐making, while incorporating transactive energy signals aligned with the alternating direction method of multiplier framework to enable independent agent operation. In this scheme, independent agents would optimize their operating costs considering the announced transactive signals, which model the power prices and power loss in the grid. The decentralized structure enables agents to apply stochastic and condition value at risk methods to address the uncertainty and associated risk in scheduling resources. Furthermore, without violating the privacy concerns of agents, the developed transactive‐based scheme facilitates minimizing the asymmetrical condition, caused by the unbalanced integration of DESs, in the power request at the connection point of MADSs and transmission networks. Finally, the proposed methodology is simulated on 37‐bus and 123‐bus test‐systems to study its effectiveness in managing the MADSs with unbalanced integration of DESs.
... In this regard, the Optimal Power Flow (OPF) method [18], [19] stands as a foundational mathematical tool for optimizing power system decisions. It has been studied extensively in the literature and widely applied in grid planning, operations, control, and electricity markets [20]- [22]. Existing OPF schemes typically seek optimal power grid decisions to minimize a specific economic cost objective, while satisfying the power flow equations, network constraints, and operational limits of devices. ...
... Based on the ES power model (20), we develop the dynamical carbon footprint model of the ES unit as (22) for t ∈ T : ...
... Model (22) implies that (virtual) carbon emissions are injected into the ES unit when it charges with electricity in the nodal carbon intensity w i,t ; and it releases the stored emissions back to the grid when it discharges with electricity in the ES carbon intensity w es i,t . In particular, (22) models the carbon emission leakage associated with the energy loss during the storage, charging, and discharging processes of the ES unit. ...
To facilitate effective decarbonization of the electric power sector, this paper introduces the generic Carbon-aware Optimal Power Flow (C-OPF) method for power system decision-making that considers demand-side carbon accounting and emission management. Built upon the classic optimal power flow (OPF) model, the C-OPF method incorporates carbon emission flow equations and constraints, as well as carbon-related objectives, to jointly optimize power flow and carbon flow. In particular, this paper establishes the feasibility and solution uniqueness of the carbon emission flow equations, and proposes modeling and linearization techniques to address the issues of undetermined power flow directions and bilinear terms in the C-OPF model. Additionally, two novel carbon emission models, together with the carbon accounting schemes, for energy storage systems are developed and integrated into the C-OPF model. Numerical simulations demonstrate the characteristics and effectiveness of the C-OPF method, in comparison with OPF solutions.
... To identify the HC that minimizes distribution losses or costs while increasing DER integration in [44][45][46] a multi-objective function is established, while in order to maximize the HC a single objective function is defined in [42,[47][48][49][50]. Some of the frequently used approaches to solve the optimization problem are artificial bee colony (ABC) [51] because of its fast convergence, GA [52] because it gives fast results but instead of global optimal solutions with a probability of finding near-optimal solutions, particle swarm optimization (PSO) [45,53] as it is easy to implement and robust optimization [54][55][56] as it takes into account the calculation's uncertainty regarding the DG's output, size, and placement. Ref [57] formulated an optimization problem involving the placement, size, azimuth, and tilt of every panel throughout a residential area in order to maximize PV production over the course of a year while taking into account the power grid voltage and line ampacity limits. ...
... Transformer overloading limits ranges from 100% [77], [78] to 187.5% [79], while more strict cable overloading limits ranges from 85% [77] to 150% [80]. Regarding the lines that go towards the grid connection point in [56] as the primary constraint is used upper of the current ampacity limitations, whose violation indicates backfeeding surplus power for the main grid. In [36] limiting factors such as thermal limits of trans-formers and lines are used as a supplement to voltage fluctuations for a Finnish LV network's HC estimate. ...
... Unlike conventional synchronous generators, inverter-based resources (IBRs) exhibit lower system inertia and faster dynamic behaviors. As a result, renewable generation uncertainties [1], frequent power fluctuations, and fast system dynamics present significant challenges to the classic three-level frequency control architecture [2] in power grids. In particular, traditional secondary and tertiary frequency controls, typically operating on timescales of minutes to hours, become inadequate for promptly restoring frequency and ensuring economic efficiency in IBR-rich systems. ...
The large-scale integration of inverter-interfaced renewable energy sources presents significant challenges to maintaining power balance and nominal frequency in modern power systems.
This paper studies grid-level coordinated control of grid-forming (GFM) and grid-following (GFL) inverter-based resources (IBRs) for scalable and optimal frequency control. We propose a fully distributed optimal frequency control algorithm based on the projected primal-dual gradient method and by leveraging the structure of the underlying physical system dynamics. The proposed algorithm i) restores the nominal system frequency while minimizing total control cost and enforcing IBR power capacity limits and line thermal constraints, and ii) operates in a distributed manner that only needs local measurements and neighbor-to-neighbor communication. In particular, when the line thermal constraints are disregarded, the proposed algorithm admits a fully local implementation that requires no communication, while still ensuring optimality and satisfying IBR power capacity limits. We establish the global asymptotic convergence of the algorithm using Lyapunov stability analysis. The effectiveness and optimality of the proposed algorithms are validated through high-fidelity, 100% inverter-based electromagnetic transient (EMT) simulations on the IEEE 39-bus system.
... The Multi-Objective Advanced Gray Wolf Optimization (MOAGWO) algorithm was used as a solution tool. For fully exploiting the ability of DNs to accommodate PV, ref. [27] proposed a robust comprehensive PVHC assessment method, considering three-phase power flow modelling and AM techniques, including network reconfiguration, on-load-tap-changers regulation (OLTC), and reactive power compensation. Ref. [28] has proposed a two-stage model, in which the dispatching of soft open point (SOP) and management of electric vehicles (EVs) were coordinated together with traditional AM techniques. ...
The access of a high proportion of photovoltaic (PV) will change the energy structure of the distribution network (DN), resulting in a series of safety operation risks. This paper proposes a two-stage PV hosting capacity (PVHC) calculation model to assess the maximum PVHC, considering the uncertainty and active management (AM). Firstly, we employ a robust optimization model to characterize the uncertainty of sources and loads in DN with PV and analyze the worst-case scenarios for PVHC. Subsequently, we construct a PVHC calculation model that takes into account AM, and convert the model into a mixed-integer second-order cone (MISOC) model using linearization techniques. Finally, we apply “heuristic optimization + CPLEX solver” to solve the model and introduce overvoltage and overcurrent indices to analyze the safety of the DN under PV limit access. Case studies are carried out on the IEEE 33-bus system and a practical case. Results show that (1) only the uncertainty that reduces the load or increases the output efficiency will affect PVHC; (2) for DN limited by overvoltage, AM can better improve PVHC; however, for DN limited by maximum transmission power, the effect of AM is low; (3) for most DN, SVC can improve PVHC, but the effect is modest. And network reconfiguration can significantly increase PVHC on the system with poor branch network, even reaching 150% of the original PVHC.
The penetration rate of distributed photovoltaic (PV) in mountainous distribution networks is increasing year by year, and the assessment of distributed PV hosting capacity (PVHC) in distribution networks in mountainous areas is also becoming more and more important. To this end, this paper proposes a robust assessment method for distributed PVHC of flexible distribution networks in mountainous areas. The method utilizes soft open point (SOP) and energy storage to realize the flexible interconnection of distribution networks in mountainous areas, connecting the low-voltage nodes at the end of distribution networks in mountainous areas and improving the overall power quality of distribution networks. Secondly, the output curves of distributed PV output and load demand are analyzed and the distributed PV uncertainty model is drawn, so as to construct a two-layer robust assessment model of distributed PVHC for mountainous flexible distribution networks. Finally, the dual-layer robust assessment model, which cannot be solved directly, is transformed into a solvable mixed-integer linear programming model using the pairwise method, and the effectiveness of this paper’s method is verified by the simulation results of the IEEE 33-node distribution network system.
The strategic energy transition has driven the construction of a new type of power system, and the digital transformation of distribution grids has become particularly urgent. The study focuses on building a transparent grid dynamic monitoring and fault warning system for high-density distributed power access areas. The system integrates artificial intelligence technology and designs key functional modules such as real-time data monitoring, intelligent communication, alarm information, and dispatch data. Multiple fault information is obtained from the grid, and the accuracy of the system’s fault warning and localization is measured. Through practical application, the system is further evaluated for its practical value in grid dynamic monitoring and fault warning. The system’s prediction error for faults in high-density distributed power supply access areas is minimal, and it can acquire fault information with accuracy, boasting a fault localization accuracy rate greater than 95%. In terms of application practice, the system can monitor the current and voltage data of the grid system in real time. For example, the system captures a voltage transient drop with a duration of 5 cycles and a drop of more than 45%. In this paper, the power grid dynamic monitoring and fault early warning system designed using artificial intelligence technology has good application performance.
We present a directed graph-based method for distribution network reconfiguration considering distributed generation. Two reconfiguration situations are considered: operation mode adjustment with the objective of minimizing active power loss (situation I) and service restoration with the objective of maximizing loads restored (situation II). These two situations are modeled as a mixed integer quadratic programming problem and a mixed integer linear programming problem, respectively. The properties of the distribution network with distributed generation considered are reflected as the structure model and the constraints described by directed graph. More specifically, the concepts of “in-degree” and “out-degree” are presented to ensure the radial structure of the distribution network, and the concepts of “virtual node” and “virtual demand” are developed to ensure the connectivity of charged nodes in every independent power supply area. The validity and effectiveness of the proposed method are verified by test results of an IEEE 33-bus system and a 5-feeder system.
With the fact that more distributed generations (DGs) are used in network, the operation uncertainty of active distribution network is becoming significant. Restoration strategies are affected by these uncertainties, especially by the variation of load demand and DG output. In this paper, a robust optimization model using information gap decision theory (IGDT) was proposed for distribution network restoration after failures. With bounded uncertainties, the restoration strategies, as the robust solutions, ensured that restoration results would be better than a given acceptable threshold. Robust restoration decision making software was developed based on the proposed restoration model, whose objective is to maximize the recovery load. In the last part of this paper, numerical tests on a PG&E 69-node system were given to demonstrate the performance of the proposed method.
High penetration of distributed energy resources presents several challenges
and opportunities for voltage regulation in power distribution systems. A local
reactive power (VAR) control framework will be developed that can fast respond
to voltage mismatch and address the robustness issues of (de-)centralized
approaches against communication delays and noises. Using local bus voltage
measurements, the proposed gradient-projection based schemes explicitly account
for the VAR limit of every bus, and are proven convergent to a surrogate
centralized problem with proper parameter choices. This optimality result
quantifies the capability of local VAR control without requiring any real-time
communications. The proposed framework and analysis generalize earlier results
on the droop VAR control design, which may suffer from under-utilization of VAR
resources in order to ensure stability. Numerical tests have demonstrated the
validity of our analytical results and the effectiveness of proposed approaches
implemented on realistic three-phase systems.
Service restoration is important in distribution networks following an outage. During the restoration process, the system operating conditions will fluctuate, including variation of the load demand and the output from distributed generators (DGs). These variations are hard to be predicted and the load demands are roughly estimated because of absence of real-time measurements, which can significantly affect the restoration strategy. In this paper, we report a robust restoration decision-making model based on information gap decision theory, which takes into account the uncertainty in the load and output of the DGs. For a given bounded uncertain set of parameters, the solutions can ensure feasibility and that an objective does not fall below a given threshold. We describe the implementation of a robust optimization algorithm based on a mixed integer quadratic constraint programming restoration model, the objective of which is to restore maximal outage loads. Numerical tests on a modified Pacific Gas and Electric Company (PG&E) 69-node distribution network are discussed to demonstrate the performance of the model.
The branch flow based optimal power flow(OPF) problem in radianlly operated distribution networks can be exactly relazed to a second order cone programming (SOCP) model without considering transformers. However, the introdution of nonlinear transformer models will make the OPF model non-convex. This paper presents an exact linearized transformer's OLTC model to keep the OPF model convex via binary expanstion scheme and big-M method. Validity of the proposed method is verified using IEEE 33-bus test system.
With the rapidly increasing penetration of renewable distributed generation (DG), the maximum hosting capacity (MHC) of a distribution system has become a major concern. To effectively evaluate the ability of a distribution system to accommodate DGs, this paper proposes an MHC evaluation method while considering the robust optimal operation of on load tap changers (OLTCs) and static var compensators (SVCs) in the uncertain context of DG power outputs and load consumptions. The proposed method determines the DG hosting capacities corresponding to different conservative levels. Furthermore, this paper discusses how to find out the most critical technical constraint that may limit the MHC by adjusting parameters of the proposed robust formulation. The effectiveness of the proposed method is demonstrated using a modified IEEE 33-bus distribution system.
In this paper, we propose a method to optimally set the reactive power contributions of distributed energy resources (DERs) present in distribution systems with the goal of regulating bus voltages. For the case when the network is balanced, we use the branch power flow modeling approach for radial power systems to formulate an optimal power flow (OPF) problem. Then, we leverage properties of the system operating conditions to relax certain nonlinear terms of this OPF, which results in a convex quadratic program (QP). To efficiently solve this QP, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM). Furthermore, we include the unbalanced three-phase formulation to extend the ideas introduced for the balanced network case. We present several case studies to demonstrate the method in unbalanced three-phase distribution systems.
Most existing approaches for distribution network reconfiguration assume that the distribution system is (three-phase) balanced and a single-phase equivalent is used. However, distribution feeders are usually unbalanced due to a large number of single-phase loads, nonsymmetrical conductor spacing, and three-phase line topology. This paper builds on our previous work and studies feeder reconfiguration for unbalanced distribution systems with distributed generation (DG). The three-phase bus locations and sizes of DG units are determined using sensitivity analysis and nonlinear programming, respectively, and distribution feeders are reconfigured every hour based on the status of time-varying loads, output power from DG units and faults on the network while minimizing the energy loss costs and DG operating costs. Simulation results show the effectiveness and computational efficiency of the proposed approach.
With the growing use of renewable energy sources, Distributed Generation (DG) systems are rapidly spreading. Embedding DG to the distribution network may be costly due to the grid reinforcements and control adjustments required in order to maintain the electrical network reliability. Deterministic load flow calculations are usually employed to assess the allowed DG penetration in a distribution network in order to ensure that current or voltage limits are not exceeded. However, these calculations may overlook the risk of limit violations due to uncertainties in the operating conditions of the networks. To overcome this limitation, related to both injection and demand profiles, the present paper addresses the problem of DG penetration with a Monte Carlo technique that accounts for the intrinsic variability of electric power consumption. The power absorbed by each load of a medium voltage network is characterized by a load variation curve; a probabilistic load flow is then used for computing the maximum DG power that can be connected to each bus without determining a violation of electric constraints. A distribution network is studied and a comparison is provided between the results of the deterministic load flow and probabilistic load flow analyses.