Network partition and distributed voltage coordination control strategy of active distribution network system considering photovoltaic uncertainty

This article proposes a hierarchical distributed voltage control (HDVC) scheme for active distribution networks (ADNs) with high penetration of photovoltaics based on distributed model predictive control (DMPC) and alternating direction method of multipliers (ADMM). The reactive power outputs of several photovoltaic clusters (PVCs) and photovoltaic (PV) units within each PVC are optimally coordinated to keep PV terminal voltages and the voltages of all critical buses of ADNs within the feasible range and mitigate voltage fluctuations. In the ADN layer, a distributed reactive power control scheme based on DMPC is designed for the PVC, which regulates the voltages of all critical buses to be closed to the rated value and mitigates the reactive power variations. In the PVC layer, the reactive power outputs of PV units are optimized based on ADMM to minimize the voltage deviation of each PV terminal and track the reactive power reference from the PVC control. The proposed HDVC scheme requires communication only between neighboring PVC controller, while each PV controller only communicates with the corresponding PVC controller. This regulates the voltages in a completely decentralized manner and effectively reduces the computation burden of the PVC and PV controllers. A modified Finnish distribution network with 10 PVCs was used to validate the control performance of the proposed HDVC scheme.

Distributed energy resources transform the passive distribution networks into active distribution networks (ADNs). Coordinating the dispatch actions of distributed resources has been studies in the literature, both within an ADN and between an ADN and the transmission system. However, the direct coordination between ADNs interconnected via a physical tie line is a topic boldly under-discussed, despite its practical relevance. In this paper, we consider the problem of coordinating the dispatch actions, including the energy exchange, of two interconnected ADNs, each one integrated with flexible loads (managed by demand response aggregators), energy storage systems, and microturbines (MTs). The bilateral energy trading enables the neighboring ADNs to benefit from the difference in locational marginal prices. The coordination problem is formulated as a robust bi-level program under price uncertainty. At the upper level, the total cost of the ADNs is minimized subject to the uncertainty of electricity market prices and technical constraints of the networks and the resources. At the lower level, the DR aggregators present at each ADN selfishly minimize their own cost. Moreover, the worst case realization of wholesale electricity market prices is considered. The problem is linearized using the Karush–Kuhn–Tucker (KKT) conditions and decomposed using the alternating direction method of multipliers (ADMM). Simulation results verify the convergence behavior of the proposed method and quantify the value of DSO-DSO coordination in the presence of an interconnecting line between the ADNs.

In this dissertation we develop numerical algorithms and software tools to facilitate parallel solutions of nonlinear programming (NLP) problems. In particular, we address large-scale, block-structured problems with an intrinsic decomposable configuration. These problems arise in a great number of engineering applications, including parameter estimation, optimal control, network optimization, and stochastic programming. The structure of these problems can be leveraged by optimization solvers to accelerate solutions and overcome memory limitations, and we propose variants to two classes of optimization algorithms: augmented Lagrangian (AL) schemes and Schur-complement interior-point methods. The convergence properties of augmented Lagrangian decomposition schemes like the alternating direction method of multipliers (ADMM) and progressive hedging (PH) are well established for convex optimization but convergence guarantees in non-convex settings are still poorly understood. In practice, however, ADMM and PH often perform satisfactorily in complex non-convex NLPs. In this work, we study connections between the method of multipliers (MM), ADMM, and PH to derive benchmarking metrics that explain why PH and ADMM work in practice. We illustrate the concepts using challenging dynamic optimization problems. Our exposition seeks to establish more formalism in benchmarking ADMM, PH, and AL schemes and to motivate algorithmic improvements. The effectiveness of nonlinear interior-point solvers for solving large-scale problems relies quite heavily on the solution of the underlying linear algebra systems. The schur-complement decomposition is very effective for parallelizing the solution of linear systems with modest coupling. However, for systems with large number of coupling variables the schur-complement method does not scale favorably. We implement an approach that uses a Krylov solver (GMRES) preconditioned with ADMM to solve block-structured linear systems that arise in the interior-point method. We show that this ADMM-GMRES approach overcomes the well-known scalability issues of Schur decomposition. One important drawback of using decomposition approaches like ADMM and PH is their convergence rate. Unlike Schur-complement interior-point algorithms that have super-linear convergence, augmented Lagrangian approaches typically exhibit linear and sublinear rates. We exploit connections between ADMM and the Schur-complement decomposition to derive an accelerated version of ADMM. Specifically, we study the effectiveness of performing a Newton-Raphson algorithm to compute multiplier estimates for augmented Lagrangian methods. We demonstrate using two-stage stochastic programming problems that our multiplier update achieves convergence in fewer iterations for MM on general nonlinear problems. In the case of ADMM, the newton update significantly reduces the number of subproblem solves for convex quadratic programs (QPs). Moreover, we show that using newton multiplier updates makes the method robust to the selection of the penalty parameter. Traditionally, state-of-the-art optimization solvers are implemented in low-level programming languages. In our experience, the development of decomposition algorithms in these frameworks is challenging. They present a steep learning curve and can slow the development and testing of new numerical algorithms. To mitigate these challenges, we developed PyNumero, a new open source framework implemented in Python and C++. The package seeks to facilitate development of optimization algorithms for large-scale optimization within a high-level programming environment while at the same time minimizing the computational burden of using Python. The efficiency of PyNumero is illustrated by implementing algorithms for problems arising in stochastic programming and optimal control. Timing results are presented for both serial and parallel implementations. Our computational studies demonstrate that with the appropriate balance between compiled code and Python, efficient implementations of optimization algorithms are achievable in these high-level languages.

Australia is a global leader in rooftop solar photovoltaic (PV) installations, which have significantly reshaped power consumption in distribution networks. However, excessive solar generation during low demand periods can cause overvoltage issues, with traditional solutions like capacitor banks and on-load tap changers being effective but costly. This study explores the effectiveness of advanced PV inverter control strategies—Volt-Watt, Volt-Var, and Volt-Watt-Var—as a cost-efficient alternative. Simulations conducted on the IEEE 33-bus distribution system using Python-OpenDSS demonstrate that PV integration substantially reduces active power losses from 2471.37 kW (no PV) to 2212.32 kW. Under Volt-Watt-Var control, losses decrease further with PV penetration up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$80 \%(2202.34 ~\text{kW}$</tex>, 1285.17 kVar) but slightly rise at 100% penetration. These findings highlight the potential of PV control strategies to enhance network performance while maintaining voltage compliance.

This study presents a model predictive control (MPC)‐based centralised control approach for maintaining the voltages of the nodes within permissible limits in the presence of high photovoltaic (PV) penetration. The proposed control scheme coordinates the actions of on‐load tap changer (OLTC) and PV inverters optimally to fulfil the desired objectives. The objectives are minimisation of change in control variables, slack variables, energy loss, and voltage error. These objectives are weighted to form the overall objective function. Three rules are formulated based on the severity of voltage magnitudes. The weights of the objectives are adjusted according to these pre‐defined rules. Simulations are performed in an active distribution network (ADN) integrated with and without microgrids, where both demands and generations vary hourly over the day. As power is injected by the microgrids during most of the time of the day, the excursions of node voltages are slightly higher in the microgrids integrated ADN. Moreover, the incorporation of the proposed rule‐based MPC drastically reduces the energy loss due to active power loss in distribution networks, as is evident from the simulation results obtained by comparing the proposed approach with an existing MPC‐based approach.

Advancements in data-driven voltage control in active distribution networks: A Comprehensive review

This paper proposes a hierarchical look-ahead framework to conduct conservation voltage reduction (CVR) when distributed energy resources such as solar photovoltaic (PV) systems and energy storage systems (ESSs), and demand response programs are integrated into distribution systems. With the increasing deployment of PV systems in distribution systems, their frequently varying power output due to cloud movements could have a detrimental impact on the consumer’s voltage quality, consequently leading to degraded CVR performance. A two-level CVR framework for the coordination of an on-load tap changer (OLTC), capacitor banks (CBs), and the smart inverters of PV systems/ESSs is presented, in which these elements operate to reduce the voltage profile along the distribution feeder at different temporal scales. At the global level, the operations of the OLTC and the CBs are scheduled every hour to achieve the best CVR performance in an optimization problem using mixed-integer linear programming. When voltage violations occur rapidly, the smart inverters of PV systems and ESSs help to maintain a lower voltage profile every second based on the proposed piecewise droop control functions at the local level. A simulation study is carried out in an IEEE 33-bus distribution system with an OLTC, CBs, PV systems, and ESSs, and our results demonstrate the advantages of the proposed approach in terms of voltage level and energy savings. Furthermore, the impact of demand reduction on the proposed approach is quantified, and we verify that a higher demand reduction yields more energy savings in the proposed framework.

China’s rapid renewable energy growth has introduced challenges to the stability and reactive power balance of distribution networks due to the uncertainty of wind and photovoltaic (PV) output and the integration of flexible transportation loads. To address these issues, this paper presents an optimization method for active distribution networks. A Monte Carlo-based scenario simulation and a fast scenario reduction technique are used to manage wind and PV uncertainty. Additionally, an optimization model for reactive power is developed to minimize active power losses and voltage deviations while integrating wind, PV, and transportation loads. The model, solved via an improved second-order cone programming method using the GUROBI solver, optimizes transportation load configuration over time. Simulation results based on the IEEE 33-bus system show that the method enhances voltage quality and reduces network losses, achieving cost and efficiency improvements.

In order to meet the high permeability and the access of large scale distributed generation, at present and in the future, active distribution network becomes the trend of smart grid research. This paper introduces the influence of distribution network voltage distribution and stability of distributed energy access based on active distribution network; The reactive power and voltage optimization control method of active power distribution network is summarized from the aspects of optimal voltage regulation measure, voltage regulation measure of power network equipment, reactive power optimal dispatch of power system, and so on. Analysis of the current status of the research, and summarized the existing active distribution network with a distributed power pickup distribution network reactive power and voltage control of the existence of some problems and the insufficiency still some problems that must be solved in the study of reactive power and voltage optimization control of active distribution network are pointed out.

Source-grid-load-storage has represented an interactive characteristic in the active distribution network (ADN). Moreover, power electronic devices have been widely used for source-grid-load-storage with the rapid development of power electronics technology. In this condition, the large-scale distributed source may cause voltage quality degradation, while the application of large-scale power electronics equipment may also lead to serious harmonic distortion. Power quality has become one of the most important issues in the development of ADN. In this paper, the source-grid-load-storage interactive power quality characteristic of the ADN is analyzed. Firstly, considering the source-grid-load-storage interaction in ADN, the voltage deviation and fluctuation are analyzed and the degrees are further quantified. Then, the source-load-storage harmonic models for the power electronic components are built, which is the basis for harmonic analysis. Moreover, the decoupled harmonic power flow algorithm for ADN is proposed to analyze the system harmonic distributions. Finally, considering the location and capacity of photovoltaic and energy storage, the interaction and power quality are analyzed in the IEEE 33-bus distribution system. With the access of energy storage, more than 20% of the voltage deviation and more than 6% of the voltage fluctuation caused by photovoltaics are effectively suppressed, while the harmonic distortion may be further increased.

As the penetration of intermittent distributed generation (DG) in active distribution network (ADN) growing fast, bus over or under voltage problems in ADN will be more frequently. This paper presents a novel autonomic voltage coordination control in ADN based on model predictive control (MPC). With the optimal coordinated control strategy for solving these voltage problems, this control method takes advantage of on-load tap changer (OLTC) and DG to make voltage stay in reasonable ranges. Based on MPC, autonomic coordination between voltage regulation units is calculated from a multi-step optimization, updated and corrected by real-time measurements optimally. Thus model uncertainties and measure noise are effectively compensated. The proposed autonomic voltage coordination control is tested in a modified IEEE 33-nodes ADN system hosting DG.

With a high proportion of photovoltaic (PV) connected to the active distribution network (ADN), the correlation and uncertainty of the PV output will significantly affect the grid dispatching operation. Therefore, this paper proposes a novel robust ADN dispatching model, which considers the dynamic spatial correlation and power uncertainty of PV. First, the dynamic spatial correlation of PV output is innovatively modeled by dynamic conditional correlation (DCC) generalized autoregressive conditional heteroskedasticity (DCC-GARCH) model. DCC can accurately represent and forecast the spatial correlation of the PV output and reflect its time-varying characteristics. Second, a time-varying ellipsoidal uncertainty set constructed using the DCC, is introduced to bound the uncertainty of the PV outputs. Subsequently, the original mixed integer linear programming (MILP) model is transformed into the mixed integer robust programming (MIRP) model to realize robust optimal ADN dispatching. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

This paper proposes a decentralized adjustable robust operation model achieving the coordinated operation between an active distribution network (ADN) and microgrids (MGs). Thanks to the autonomous characteristic and heterogeneity of the individual agents in ADNs with multi-MGs, we develop a tailored alternating direction method of multipliers (ADMM)based fully decentralized framework. The linear decision rules are utilized to reformulate the microgrid two-stage adjustable robust operation problem as a computationally tractable solution such that the proposed adjustable robust extension of decentralized ADMM is capable of handling renewable energy uncertainties. The numerical results illustrate the effectiveness of the proposed model.

We consider a dynamic time division duplexing wireless network and propose a distributed coordinated beamforming algorithm based on Alternating Direction Method of Multipliers (ADMM) technique assuming the availability of perfect channel state information. Our design objective is to minimize the sum transmit power at the base stations subject to minimum signal-to-interference-plus-noise ratio (SINR) constraints for downlink mobile stations and a maximum interference power threshold for uplink mobile stations. First, we propose a centralized algorithm based on the relaxed Semidefinite Programming (SDP) technique. To obtain the beamforming solution in a distributed way, we further propose a distributed coordinated beamforming algorithm using the ADMM technique. Detailed simulation results are presented to examine the effectiveness of the proposed algorithms. It is shown that the proposed algorithm achieves better performance in terms of the design objective and converges faster than the reference algorithm based on primal decomposition.

Distributed generation (DG), including photovoltaics (PVs), wind turbines (WTs) are becoming vital for Active Distribution Networks (ADN). Therefore, optimal sizing and allocation of these units can improve voltage profiles and reduce active power losses. This study concentrates on optimal allocation and sizing of two kinds of DG units (PVs and WTs) with 1 MW maximum size limits, due to the regulations in Turkey. The Whale optimization algorithm (WOA) and Grey wolf optimization algorithm (GWO) are used as optimization tools to minimize active power losses of 33 and 69 Bus Test Systems. The performance analysis of the methods are performed through simulations and the numerical results are compared in terms of optimal OF values and convergence characteristics.