Unbalanced Three-phase Systems Research Articles

A coordinated restoration method of three-phase AC unbalanced distribution network with DC connections and mobile energy storage systems

In the rapidly changing domain of hybrid AC/DC urban distribution networks, this research unveils a groundbreaking method for the restoration of three-phase unbalanced systems by astutely harnessing the unique potential of DC line interconnections. At the heart of this innovation lies the synthesis of symmetrical Second Order Cone Programming (SOCP) with a sophisticated topology search technique, a union that offers a precise depiction of complex three-phase power flow with network restoration while simultaneously accelerating computational processes. Building upon this foundation, our approach places significant emphasis on the utilization of adaptable DC power control, coupled with the optimal deployment of mobile energy storage systems (MESSs), to ensure a harmonized power balance during critical interruptions. These strategies converge to prioritize the restoration of vital loads, especially those with high weighting factors, thereby significantly augmenting the network’s resilience, particularly in contexts vulnerable to disasters. The corroborative numerical results, as delineated in our study, highlight the distinct advantage and effectiveness of our methodology over prevailing practices in fortifying grid resilience against serious adversities.

A power-based fault direction estimation method for active distribution networks

This paper presents a strategy for estimating fault direction in active distribution networks, focusing on the high penetration of distributed energy resources, changing operating conditions, untransposed lines, and unbalanced loads.The proposed strategy introduces a power-based directional criterion derived from analysing active power within three-phase unbalanced systems known for their inherent unidirectional nature. The method enables rapid direction estimation by measuring the difference between pre-fault average active power and during-fault average active power values, utilising two moving windows. Notably, this difference is positive for forward faults and negative for backward faults, offering clear directionality insights. The strategy is validated using a modified IEEE 34-bus test system, where it demonstrates feasibility under several fault scenarios, including all fault types, varying fault impedance, operating conditions, noise levels, and sampling frequencies. Additionally, the proposed algorithm is compared with contemporary and conventional approaches, highlighting its effectiveness.

Tractable Data Enriched Distributionally Robust Chance-Constrained Conservation Voltage Reduction

This paper proposes a tractable distributionally robust chance-constrained conservation voltage reduction (DRCC-CVR) method with enriched data-based ambiguity set in unbalanced three-phase distribution systems. The increasing penetration of distributed renewable generation not only brings clean power but also challenges the voltage regulation and energy-saving performance of CVR by introducing high uncertainties to distribution systems. In most cases, the conventional robust optimization methods for CVR only provide conservative solutions. To better consider the impacts of load and PV generation uncertainties on CVR implementation in distribution systems and provide less conservative solutions, this paper develops a data-based DRCC-CVR model with tractable reformulation and data enrichment method. Even though the uncertainties of load and photovoltaic (PV) can be captured by data, the availability of smart meters (SMs) and micro-phasor measurement units (PMUs) is restricted by cost budget. The limited data access may hinder the performance of the proposed DRCC-CVR. Thus, we further present a data enrichment method to statistically recover the high-resolution load and PV generation data from low-resolution data with Gaussian Process Regression (GPR) and Markov Chain (MC) models, which can be used to construct a data-based moment ambiguity set of uncertainty distributions for the proposed DRCC-CVR. Finally, the nonlinear power flow and voltage dependant load models and DRCC with moment-based ambiguity set are reformulated to be computationally tractable and tested on a real distribution feeder in Midwest U. S. to validate the effectiveness and robustness of the proposed method.

A linear Distflow model considering line shunts for fast calculation and voltage control of power distribution systems

The line shunts are usually ignored by various linear power flow (PF) models in power distribution system analysis, planning and optimization. However, “charging effects” from line shunts of underground/submarine power cables would cause non-negligible model errors for these commonly used PF models. In this paper, we propose a modified Linear Distflow model (LinDist) with line shunts, i.e., LinDistS. We also further propose its extensions considering the ZIP load, weakly-meshed topology and unbalanced three-phase systems. Moreover, the linearization error of voltage component is theoretically analyzed. Case studies show that compared with other models, the proposed LinDistS achieves the descent calculation accuracy and efficiency. We also show the application scope of LinDistS by a Volt/VAr control (VVC) framework with distributed generators, mainly photovoltaic (PV), and the non-negligible “charging effect”. Simulation exhibits that with LinDistS, the VVC can optimally dispatch the shunt capacitors and also optimize the real-time reactive power output of PV. Moreover, with LinDistS, the VVC shows better solutions’ consistency and higher computing efficiency compared to traditional VVC methods.

Algorithm for passive reactive power compensation of an unbalanced three-phase four-wire system using capacitors ensuring minimum line losses

Currently in three-phase distribution networks, especially low-voltage networks, there are some inefficient powers. These are defined as reactive power, unbalanced power owing to linear loads, power owing to supply unbalanced voltage, and harmonic power. This has given rise to the concept of power quality. To improve power quality, devices called active filters have been developed. These devices eliminate all the inefficient power. However, for most processes, the elimination of reactive power needs to be from a price/performance perspective because the use of active filters is very expensive. Therefore, the use of capacitor banks in any of their versions (single-phase, three-phase, scalable battery, SVC, etc.) is the most economical and sufficient solution. In this study, a calculation algorithm is proposed to obtain compensators for the inductive reactive power of the load, consisting only of single-phase capacitor banks. These capacitors are designed to minimise losses in the supply line, which are lower than those obtained using the minimum loss line (MLL) strategy. The resulting compensator consists of three, two, or one capacitor, depending on the load characteristics.

Spatio-Temporal Graph Convolutional Neural Networks for Physics-Aware Grid Learning Algorithms

This paper proposes novel architectures for spatio-temporal graph convolutional and recurrent neural networks whose structure is inspired by the physics of power systems. The key insight behind our design consists in deriving the so-called graph shift operator (GSO), which is the cornerstone of Graph Convolutional Neural Network (GCN) and Graph Recursive Neural Network (GRN) designs, from the power flow equations. We demonstrate the effectiveness of the proposed architectures in two applications: in forecasting the power grid state and in finding a stochastic policy for foresighted voltage control using deep reinforcement learning. Since our design can be adopted in single-phase as well as three-phase unbalanced systems, we test our architecture in both environments. For state forecasting experiments we consider the single phase IEEE 118-bus case systems; for voltage regulation, we illustrate the performance of deep reinforcement learning policy on the unbalanced three-phase IEEE 123-bus feeder system. In both cases the physics based GCN and GRN learning algorithms we propose outperform the state of the art.

Grid Equivalent Representation of Power Systems With Penetration of Power Electronics

The Thévenin equivalent is considered as the standard grid equivalent for power system analysis. The integration on power electronics components in the power systems introduces non-linear operation characteristics that cannot be captured by Thévenin equivalent. Therefore, an alternative grid equivalent representation is required. This paper presents a steady-state equivalent representation of power systems with penetration of power electronics, which is suitable for both normal operation studies and short-circuit calculations. This equivalent grid representation is developed based on the voltage-current ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U-I</i> ) characteristic of a power system to map the relationship between voltages and currents of a specific network node. Such grid equivalent representation has been presented for single-phase, balanced and unbalanced three-phase power systems in this paper. A methodology is presented to identify operation points when the equivalent system under study is connected to any external system. The proposed equivalent grid representation and the methodology for operation points identification have been tested on the Voltage Source Converter (VSC) based test system and are validated through dynamic simulations.

Low Cost and Precise Frequency Estimation in Unbalanced Three Phase Power Systems

Monitoring the voltage frequency is of great significance in power systems. In this paper we propose two novel frequency estimators, namely the unbalanced HAM-WLS (UHW) estimator and the weighted least squares fusion (WLSF) estimator, to identify the voltage frequency in unbalanced three-phase power systems. The UHW method modifies both the coarse search and the weighted least squares (WLS) post-processing step of our previous HAM-WLS algorithm, and thus removes the spectrum leakage caused by the fluctuant maxima of the signal periodogram in phase unbalanced grids. Meanwhile, a new alternative is used in the WLSF estimator to aggregate the signal information in three difference phases. Compared with the Clarke's transformation that merely maximizes signal to noise ratios (SNRs), the proposed WLSF assigns different weights to the single-phase estimates according to their estimation variances, leading to improved accuracy and higher reliability. Both proposed estimation algorithms employ the Fourier coefficient interpolation and the iterative leakage subtraction in the frequency domain to lower the computation complexity as well as the WLS technique as a post-processing step to enhance the estimation precision. Therefore, both estimators realize accurate estimates with low computational cost. The complexity calculation, simulations and experiments for various scenarios all support the analysis. The results also show that the WLSF estimator exhibits more precise and stable performance than the UHW estimator at the cost of requiring relatively higher computational effort.

Log(v) 3LPF: A Linear Power Flow Formulation for Unbalanced Three-Phase Distribution Systems

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. Log(v) 3LPF uses a logarithmic transform of the voltage phasor to linearize the AC power flow equations around the balanced case. We incorporate the modeling of ZIP loads, transformers, capacitor banks, switches and their corresponding controls and express the network equations in matrix-vector form. With scalability in mind, special attention is given to the computation of the inverse of the system admittance matrix, Ybus. We use the Sherman-Morrison-Woodbury identity for an efficient computation of the inverse of a rank-k corrected matrix and compare the performance of this method with traditional LU decomposition methods using Big- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}$</tex-math></inline-formula> notation. We showcase the solver for a variety of network sizes, ranging from tens to thousands of nodes, and compare the Log(v) 3LPF with commercial-grade software, such as OpenDSS.

Time-domain Dynamic State Estimation for Unbalanced Three-phase Power Systems

In this paper, we present a time-domain dynamic state estimation for unbalanced three-phase power systems. The dynamic nature of the estimator stems from an explicit consideration of the electromagnetic dynamics of the network, i.e., the dynamics of the electrical lines. This enables our approach to release the assumption of the network being in quasi-steady state. Initially, based on the line dynamics, we derive a graph-based dynamic system model. To handle the large number of interacting variables, we propose a port-Hamiltonian modeling approach. Based on the port-Hamiltonian model, we then follow an observer-based approach to develop a dynamic estimator. The estimator uses synchronized sampled value measurements to calculate asymptotic convergent estimates for the unknown bus voltages and currents. The design and implementation of the estimator are illustrated through the IEEE 33-bus system. Numerical simulations verify the estimator to produce asymptotic exact estimates, which are able to detect harmonic distortion and sub-second transients as arising from converter-based resources.

A Hybrid Compensator for Unbalanced AC Distribution System With Renewable Power

A hybrid compensator with a new coordinated control is proposed for mitigating power quality aspects and integration of renewable power in an unbalanced three-phase four-wire distribution system. The proposed compensator comprises of thyristor switched capacitor (TSC) banks, delta connected thyristor controlled reactor (TCR), a 3rd and a 5th harmonic tuned passive LC filter & a low rating three-phase four-wire D-STATCOM. The TSC-TCR operates asymmetrically for the base var compensation and also eliminates negative sequence current during unbalanced loading at the point of common coupling (PCC). The D-STATCOM works in coordination with the TSC-TCR and the passive filters to compensate fundamental var, zero sequence current, voltage flicker & 7th harmonic currents at the PCC. The D-STATCOM thus serves as a supportive var compensator as well as an active filter in selective harmonic compensation mode, thereby improving the var compensation and harmonic current filtering at the PCC. A new coordination control system is proposed to control the operation of the D-STATCOM which is also employed to integrate a PV source & a doubly fed induction generator (DFIG) based wind energy conversion system (WECS) to the PCC. This scheme with grid connected and islanded mode of operation using D-STATCOM exhibits low-voltage ride-through capabilities. Further, the chance of resonance of the passive filters used with source inductance is eliminated in the proposed scheme. Simulation results show that the proposed hybrid system effectively compensates var, negative & zero sequence current, reduces voltage flicker and harmonic currents at PCC.

Temporally-adaptive Robust Data-driven Sparse Voltage Sensitivity Estimation for Large-scale Realistic Distribution Systems with PVs

This letter proposes a new robust data-driven sparse voltage sensitivity estimation approach for large-scale distribution systems with PVs. It has a high statistical efficiency to mitigate the impacts of PV stochasticity and unknown measurement noise under various system operating conditions. A new adaptively-weighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> sparsity-promoting regularization is developed, exploiting the temporal characteristic of time-varying sensitivities for better accuracy. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> regularization is used to mitigate collinearity impacts. The Huber loss function and a concomitant scale estimate are adopted to mitigate the impacts of unknown and non-Gaussian noise. These techniques are implemented in a fast recursive parallel computing framework. The proposed estimator is tested by quasi-static time series simulations of a large three-phase unbalanced system with PVs and various discrete time-delayed control devices. Results validate the superior robustness and efficiency of the proposed estimator over existing alternatives.

Parameter estimation in unbalanced three-phase distribution lines using general regression neural networks with inconsistent data handling capacity

The feeder parameters of a power system play an important role in its operation and analysis. However, in many situations, the values used in the calculations differ from the actual parameters, resulting in large errors. Therefore, in this study, a highly accurate feeder parameter estimation method for a three-phase distribution line was proposed. The proposed method uses the measured node voltages and power quantities from the two ends of the distribution line. A precise electrical model of the three-phase distribution line was used. An improved type of neural network, namely general regression neural networks (GRNN), is used to solve the complex non-linear equation and then estimate the actual parameters. However, the proposed estimation process does not require synchronised phasors or phasor-measurement units installed at the point of measurement. Nonetheless, the estimation process is also capable of handling incorrect data information, noisy datasets, and measurement errors while maintaining accuracy at the desired level. The estimator process is examined and analysed using four different IEEE unbalanced three-phase systems. In addition, the proposed methodology is compared with standard algorithms of radial basis function networks, quasi-Newton, and multi-run optimisation methods on the basis of maximum absolute percentage error and other standard error functions. The hyperparameter-tuned GRNN model was also tested using several statistical significance tests. In all scenarios, the performance and accuracy of the proposed methodology and model exceeded those of the other methods.

Power definitions for three-phase systems in terms of instantaneous symmetrical components

This paper considers power definitions for three-phase power systems with non-sinusoidal and unbalanced voltages and currents. By applying the Lyon transformation to three-phase voltages and currents, instantaneous symmetrical components are obtained and used to define powers. Definitions of instantaneous apparent and reactive powers are derived, as well as definitions of well-known quantities based on rms values, such as apparent and reactive powers. The introduced set of power definitions based on the same mathematical framework could be used for time-instantaneous and time-average compensation types. To provide correct calculation of powers for unbalanced three-phase four-wire systems, all wires and related quantities of the three-phase four-wire system are treated equally. The instantaneous apparent and reactive powers are also expressed in terms of instantaneous symmetrical components derived from the Clarke transformation. The proposed definitions are compared with other power definitions. In the case of a three-phase three-wire system, the proposed definitions give the same values of powers as the most known power definitions. In the case of a three-phase four-wire system, the proposed definitions give the same value of the apparent power as the DIN 40110 Standard and the same value of reactive power as the Currents' Physical Component theory.© 2017 Elsevier Inc. All rights reserved.

Impact of D-STATCOM and OLTC with Integrated Volt/var Control in Distribution System for Power Loss Minimization and Voltage Control

ABSTRACT Voltage control and power loss minimization are some of the crucial issues in distribution system energy management. Finding the best strategy for Voltage control and power loss reduction is a critical task for the distribution network operator (DNO). The main contributions of the proposed work are (i) determination of size and location of the Distribution Static Synchronous Compensator (DSTATCOM) with (OLTC). (ii) to minimize the power loss and Voltage deviation with the Volt/var control strategy. (iii) To obtain the impact of single and multiple D-STATCOM units with and without OLTC. The proposed method is tested on two test systems: (i) IEEE-69 RDS and (ii) IEEE-25 bus three-phase unbalanced system. The benefits of the proposed results are addressed in the reduction of power loss, enhancement of the Voltage profile, and the annual cost of saving for the DNO. The results are tabulated, verified, and compared with other methods. The power loss is reduced to 39.25%, 38.04% for 69 bus and 25 bus test systems. The minimum Voltage profile is enhanced from 0.90918 pu to 0.9619 pu for 69 bus RDS and from 0.922559 pu to 0.9747 pu for 25 bus three-phase system.

Robust estimation of fundamental frequency positive-sequence component for grid-integration applications in energy systems

This article studies the problem of fundamental frequency positive-sequence component separation in unbalanced three-phase systems for grid-integration applications. We propose a-simple-to-implement approach involving a modified delayed signal cancellation method and moving average filtering. A delay-based linear-regression framework is considered to make the sequence component separation frequency-adaptive, providing fast and accurate frequency estimation. Comparative experimental results demonstrate the suitability of the proposed method over conventional approaches.

Optimal Selection of Conductor Sizes in Three-Phase Asymmetric Distribution Networks Considering Optimal Phase-Balancing: An Application of the Salp Swarm Algorithm

This paper presents a new methodology to simultaneously solve the optimal conductor selection and optimal phase-balancing problems in unbalanced three-phase distribution systems. Both problems were represented by means of a mathematical model known as the Mixed-Integer Nonlinear Programming (MINLP) model, and the objective function was the minimization of the total annual operating costs. The latter included the costs associated with energy losses, investment in conductors per network segment, and phase reconfiguration at each node in the system. To solve the problem addressed in this study, a master–slave methodology was implemented. The master stage employs a discrete version of the Salp Swarm Algorithm (SSA) to determine the set of conductors to be installed in each line, as well as the set of connections per phase at each of the nodes that compose the system. Afterward, the slave stage uses the three-phase version of the backward/forward sweep power flow method to determine the value of the fitness function of each individual provided by the master stage. Compared to those of the Hurricane-based Optimization Algorithm (HOA) and the Sine Cosine Algorithm (SCA), the numerical results obtained by the proposed solution methodology in the IEEE 8- and 25-node test systems demonstrate its applicability and effectiveness. All the numerical validations were performed in MATLAB.

Adjustable robust approach to increase DG hosting capacity in active distribution systems

We propose a robust coordinated dynamic hosting capacity (HC) evaluation method considering active network management (ANM) techniques in three-phase distribution systems. Our proposed method extends the literature in two main ways. Firstly, by applying the adjustable robust counterpart methodology, we allow fast-acting devices, such as inverters, to take live recourse actions in response to demand and generation uncertainties while not making the unrealistic assumption that they have real-time communication with a central entity. Secondly, we propose a linear uncertainty model capable of handling the strong spatial correlation between PV outputs. We show that our proposed linear model, compared to the existing linearised ellipsoidal uncertainty model, significantly reduces the computational burden while introducing a minor error. We validate the optimality and robustness of our proposed methods via numerical tests on the IEEE 37-node unbalanced three-phase distribution system.

Three-Phase Unbalance Improvement for Distribution Systems Based on the Particle Swarm Current Injection Algorithm

The aim of this study is to improve the three-phase unbalanced voltage at the secondary side of a distribution transformer. The proposed method involves compensation sources injecting three different single-phase currents into the connected point of a grid. The computations of optimal single-phase currents are performed using the circuit analysis method and particle swarm optimization algorithm. An unbalanced three-phase power distribution system model is constructed, including a transformer Δ–Δ connection, V–V connection, load balance, load unbalance combination, and three single-phase compensation current sources. The results show that the voltage unbalance rate of the electricity user side is improved to less than 1%, and the three-phase total compensation apparent power is approximately 0 VA. In the future, the application of the model as an auxiliary service could be achieved by adding an energy storage system.

Virtual model predictive control of the inverter to achieve unbalance compensation for islanded and grid‐tied operations

Voltage unbalance is a frequent problem in the power system, and using renewable energy power generation devices to achieve unbalance compensation is a promising solution compared to adding additional equipment. Most of the existing unbalance compensation schemes for inverters are implemented based on cascaded linear controllers, which have obvious disadvantages of complex structure and cumbersome parameter adjustment process. In order to develop a simpler unbalance compensation scheme, this paper first derives the equivalent sequence network (ESN) model of the unbalanced three-phase power system, and it reveals the important role of transmission line impedance in the unbalance problem. Inspired by the ESN model, an unbalance compensation scheme based on negative sequence virtual impedance (NSVI) is determined. Then the NSVI is embedded in the inverter mathematical model, and the virtual model predictive control (VMPC) of the inverter to achieve unbalance compensation is proposed. Finally, the proposed VMPC method is validated by experiments, and a comparative analysis is carried out with linear control methods. The development process and validation results show that, compared with the unbalance compensation scheme based on cascaded linear controllers, the VMPC method proposed in this paper has a simpler structure and stable performance.