Unbalanced Three-phase Systems Research Articles

Impact of Coreless Current Transformer Position on Current Measurement

Magnetic sensors have been widely used for current measurements in diverse industries. In order to achieve a large current measurement without an iron core structure, magnetic sensors are often arranged to be a circular array for designing a new electronic current transformer (ECT). However, this ECT with a circular array of magnetic sensors usually suffers from tradeoffs between the number of sensors and the measurement accuracy. This paper visualizes this tradeoff and proposes a 3-D magnetic-field model to analyze the impact of the magnetic sensor circular array position on current measurements. We develop an analytical expression of the current measurement errors to estimate the minimum number of required magnetic sensors and point out the acceptable deviations of the ECT position under various accuracy classes. Based on the estimation results, we design a new circular array with eight magnetic sensors and build a three-phase current measurement system. The test results demonstrate the efficiency and the robustness of the designed class-1.0 ECT, which successfully maintains accuracy class 1.0 under various position deviations in balanced or unbalanced three-phase power delivery systems.

Bayesian Learning-Based Harmonic State Estimation in Distribution Systems With Smart Meter and DPMU Data

This paper studies the problem of locating harmonic sources and estimating the distribution of harmonic voltages in unbalanced three-phase power distribution systems. We develop an approach for harmonic state estimation utilizing two types of measurements from smart meters and distribution-level phasor measurement units (DPMUs). It involves regression analysis for power flow calculation, prediction of demands using recurrent neural networks, and sparse Bayesian learning for state estimation. The proposed approach requires fewer DPMUs than nodes, making it more applicable to existing distribution grids. We show the effectiveness of the proposed estimator through extensive numerical simulations on an IEEE test feeder. We also investigate how the increased penetration of distributed energy resources could affect the performance of our state estimator.

Distributed CVR in Unbalanced Distribution Systems With PV Penetration

In this paper, a distributed multi-objective optimization model is proposed to coordinate the fast-dispatch of photovoltaic (PV) inverters with the slow-dispatch of on-load tap changer and capacitor banks for implementing conservation voltage reduction in unbalanced three-phase distribution systems. In existing studies, PV inverters and voltage regulation devices are generally dispatched by fully centralized control frameworks. However, centralized optimization methods are subject to single point of failure and suffer large computational burden. To tackle these challenges, a distributed dispatch method is developed to coordinate PV inverters and conventional voltage regulation devices in distribution systems. The proposed method is based on a modified alternating direction method of multipliers algorithm to handle non-convex optimization problems without relaxing the original formulation, which could lead to sub-optimality. Numerical results from simulations on modified IEEE 13-bus, 34-bus, and 123-bus unbalanced three-phase systems have been used to verify the proposed method.

Dynamic Frequency and Amplitude Estimation for Three-Phase Unbalanced Power Systems Using the Unscented Kalman Filter

We present a dynamic frequency and amplitude estimation algorithm for unbalanced three-phase power systems with harmonics. To develop the algorithm, we first construct a nonlinear dynamic model of the complex representation of the three-phase voltage with harmonic content and then apply an unscented Kalman filter to estimate magnitudes and frequencies of the fundamental component and its harmonics. Performance evaluation of the algorithm via Monte Carlo simulation shows the accurate tracking and fast convergence time when the frequency and amplitude of the grid voltage waveform change continuously or abruptly. Specifically, we benchmark the proposed algorithm with two types of input amplitudes and two types of frequency changes.

A Unified Method for Online Detection of Phase Variables and Symmetrical Components of Unbalanced Three-Phase Systems with Harmonic Distortion

This paper presents a method for online detection of symmetrical components of arbitrarily distorted and biased three-phase input signals. This method is based on Second-Order Generalized Integrators (SOGIs), for which a new tuning based on a gradient search is presented to achieve the fastest possible estimation. Frequency estimation is achieved by a Frequency Locked Loop (FLL) with Gain Normalization (GN) for which an Output Saturation (OS) is applied; this OS guarantees stability of the overall system. Offset detection is implemented by a combination of High-Pass Filter (HPF) and HPF-Amplitude Phase Correction (APC HPF ); the HPF filters out any offset, where the APC reconstructs the original offset-free signal. An identical method (APC LPF ) can be used for the implemented Low-Pass Filter (LPF) used for noise filtering. The resulting estimates are then used for Harmonic Sequence Detection (HSD) of each harmonic. For the overall system, stability is proven. The estimation performances of the proposed overall system are verified by simulation results. The improvements in tuning and offset detection are compared to standard approaches.

Leveraging Sparsity in Distribution Grids

Power distribution grids are sparse networks. The admittance matrix of a (radial or non-radial) power distribution grid is sparse, safety-critical events are relatively sparse at any given time compared with the number of nodes, and loads that produce significant harmonics at a specific order are also sparse. In this highlight talk, we define different types of sparsity in unbalanced three-phase power distribution systems, and explain how sparsity can be leveraged to address three increasingly important problems:

Dynamic Phasor-Based Analysis of Unbalanced Three-Phase Systems in Presence of Harmonic Distortion

In this paper, a frequency-based analytical approach for dynamic analyzing of unbalanced three-phase systems in the presence of harmonic distortion using sequence domain is put forward. As will be shown, classical symmetrical components proposed by Fortescue is not applicable under nonsinusoidal periodic condition. In such cases, generalized symmetrical components proposed by Tenti et al. can be used to calculate sequences from phase domain values. However, it introduces a new sequence component called residual component, which has a different value for each phase and cannot be directly obtained based on sequence networks. To such aim, using dynamic harmonic domain, an approach that makes it possible to use features of classical symmetrical components and modify the outputs to compute sequences based on the concept of generalized symmetrical components is proposed. Moreover, it is shown that using equivalent circuit for triplen harmonics is essential to find a relation between residual components since if sequences are connected in parallel, it is not possible to modify results of classical symmetrical components and this equivalent circuit should be directly analyzed. Time domain software is used to perform conventional lumped circuit simulation and validate the time domain responses resulted from DHD.

An inclusive methodology for Plug-in electrical vehicle operation with G2V and V2G in smart microgrid environments

Smart initiative concepts as smart grids, cities, and microgrids are redefining the electrical power system. This new scenario enables a completely new perspective of applications that lead to a path of general improvement of grid performance, in which the participation of plug-in electric vehicles has great importance. In this view, this work proposes a comprehensive operation strategy of plug-in electric vehicles for unbalanced smart microgrid environments. The first contribution is the grid-to-vehicle strategy based on buses availability of power whose primary objective is the maintenance of satisfactory operating conditions for the grid while controlling the plug-in electric vehicles charging. The second contribution relates to a holistic vehicle-to-grid coordinated approach, which is triggered in the event of microgrid islanding. The goal, in this case, is to assist the network by using the plug-in electric vehicles available stored energy. At last, the main contribution is obtained by the combination of both methodologies providing a comprehensive operation of plug-in electric vehicles for smart microgrids environments. The proposed method is designed for general three-phase unbalanced distribution systems with a wide range of resources and present versatility in the communication requirements. For validation, simulations are performed in a comprehensive unbalanced three-phase distribution system considering different disruptive scenarios faced by microgrids. The results indicate that the proposed methodology is satisfactory and ensure the operation of the microgrid within acceptable limits in both connected and islanded situations.

Stability Boundary Analysis in Single-Phase Grid-Connected Inverters With PLL by LTP Theory

Stability analysis of power converters in ac networks is complex due to the nonlinear nature of the conversion systems. Whereas interactions of converters in dc networks can be studied by linearizing about the operating point, the extension of the same approach to ac systems poses serious challenges, especially for single-phase or unbalanced three-phase systems. A general method for stability analysis of power converters suitable for single-phase or unbalanced ac networks is presented in this paper, based on linear time periodic theory. A single-phase grid-connected inverter with phase-locked loop (PLL) is considered as case study. It is demonstrated that the stability boundaries can be precisely evaluated by the proposed method, despite the nonlinearity introduced by the PLL. Simulation and experimental results from a 10-kW laboratory prototype are provided to confirm the effectiveness of the proposed analysis.

Optimized Dispatch of Energy Storage Systems in Unbalanced Distribution Networks

This paper presents a method to achieve optimal active and reactive power contributions from each energy storage system in an unbalanced distribution network to minimize power loss, while ensuring network current and voltage constraints are satisfied. By modeling loads as either constant current or constant impedance, the ac optimal power flow is transformed into a noniterative convex optimization problem. The application of capacity constraints, voltage constraints, and energy storage constraints in an unbalanced three-phase four-wire system is considered, addressing specific issues pertaining to unbalanced networks such as voltage unbalance and neutral voltage displacement. The proposed method is then used to demonstrate optimized dispatch of energy storage systems in a suitable four-wire unbalanced distribution test network. The contribution of losses in the neutral wire to the total losses is also determined for a test system under a range of operating conditions and various neutral earthing systems, highlighting the importance of considering this in a typical unbalanced distribution network.

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

Accurate detection of the system parameters in unbalanced three-phase power systems is a prerequisite for the optimal operation and control of future smart grids. However, theoretical and practical performance bounds of various estimators for unbalanced systems are only just being established. To this end, we introduce the appropriate Cramer–Rao lower bounds (CRLBs) for frequency estimation, based on the $\alpha \beta$ -transformed unbalanced voltage contaminated with noise. Next, for rigor, the maximum likelihood estimation (MLE) method for frequency estimation is introduced as a maximizer of an “augmented periodogram.” The underlying augmented complex statistics is shown to cater for all the available second-order information, including the noncircularity associated with unbalanced systems. To find the ML solution, Newton’s iterative method is employed and its initialization is implemented by a discrete Fourier transform-based dichotomous search technique. We show that the MLE of phases and amplitudes of both the positive and negative phase-sequence components within the $\alpha \beta$ -transformed voltage can be generically derived based on the ML frequency estimates. In this way, a unified framework is provided to accurately detect voltage characteristics of the positive and negative phase-sequence components within an unbalanced three-phase power system when its frequency experiences off-nominal conditions. Simulations verify that the proposed MLE approaches theoretical CRLBs for all parameters under consideration.

CONTINUATION POWER FLOW OF AN UNBALANCED THREE-PHASE FOUR-WIRE DISTRIBUTION SYSTEM


 A continuation power flow algorithm for an unbalanced three phase four wire distribution system is presented. The proposed algorithm is used to trace the loci of the voltage of the different phases of an unbalanced three-phase distribution system. The locus of the neutral voltage for a wide range of loading conditions is also obtained. The proposed technique is applied on a typical unbalance three phase radial Iraqi distribution system. The results obtained reveal the effectiveness of the continuation technique for exploring all the possible solutions and the determination of maximum loadability of the distribution feeder.
 

A Novel Fast Voltage Sequence Component Detector of Unbalanced Three-Phase System

The fast and accurate voltage sequence component detection of unbalanced three-phase system is of major importance for the industrial continuous processing. The traditional method is to calculate the voltage in dq synchronous reference frame. This results in low order harmonics and long detection time. A novel fast voltage sequence components detector is proposed in this paper. It is to calculate the sequence component projection on dq rotating reference frame with h times the fundamental angular velocity. Simulation results demonstrate the validity of the algorithm.

Stability Assessment of Power-Converter-Based AC systems by LTP Theory: Eigenvalue Analysis and Harmonic Impedance Estimation

Stability analysis of power-converter-based ac systems poses serious challenges not only because of the nonlinear nature of power converters, but also because linearization is not generally applied around a steady-state operating point, as in the dc case, but around a time-periodic operating trajectory. Typical examples are single-phase and unbalanced three-phase systems. In this paper, two general methods to assess stability of the aforementioned systems are presented. Both are based on the linear time periodic (LTP) systems theory. The first is model-based and relies on the evaluation of the eigenvalues of the linearized model, assuming a complete knowledge of the parameters. By contrast, the second proposes a set of small-signal current injections to measure the harmonic impedances and applies the LTP Nyquist criterion, so that the stability of the system can be assessed with a black-box approach, without relying on the knowledge of the system parameters. The basic LTP systems theory is reviewed in order to provide a mathematical justification for the second method. As case study, a simple network, consisting of a source full-bridge converter in ac voltage-control mode and a load full-bridge converter in ac current-control mode including phase locked loop, is considered. Analytical results based on average modeling and simulations based on both average and switching models are presented, showing good accuracy in the identification of the stability thresholds for both the proposed methods.

Optimally Allocation of Distributed Generators in Three-Phase Unbalanced Distribution Network

Increasing energy demand can be compensated with integration of distributed energy resources in the three-phase distribution system. Load flow analysis of the unbalanced three-phase distribution system requires a tool and algorithm to manage the multiple sources. In this study, Jaya algorithm is applied and interfaced with open source software openDSS to solve the unbalanced three-phase optimal power flow. Further, co-simulation framework is used to obtain the optimal allocation of two types of multiple distributed generators in unbalanced radial distribution system. The effectiveness of the approach is validated on IEEE 123 node distribution system. For a realistic study, mixes of all type of loads and configuration of the actual distribution system are considered. The results are compared with already published results obtained from established particle swarm optimization.

A Comprehensive Analysis and Control Strategy for Nullifying Negative- and Zero-Sequence Currents in an Unbalanced Three-Phase Power System Using Electric Springs

This paper presents a general analysis and a control strategy that enables electric springs (ES) to mitigate the negative-sequence and zero-sequence currents in unbalanced three-phase power systems. The analysis indicates that under certain load conditions, power balance can be restored without the need for active power from the ES. Outside such conditions, the theory can pinpoint the precise operating point at which power balance can be achieved with the minimum active power from the ES. Thus, the optimum use of energy usage and battery size for providing/storing active power can be realized. Simulation and experiment results obtained from a 3-kW hardware setup have verified the new theory and the control method.

Improved Frequency Estimation in Unbalanced Three-Phase Power System Using Coupled Orthogonal Constant Modulus Algorithm

A new iterative method for frequency estimation in the unbalanced three-phase power system is proposed. The proposed solution is based on the transformation of unbalanced three-phase voltage signal into a complex exponential by using the orthogonal constant modulus algorithm. In addition, based on the transformed signal, a simple adaptive algorithm for frequency estimation is proposed. Beside the proposed approach, any frequency estimator designed for a single-tone complex exponential can be used here, which is also the advantage of the proposed method. Simulation results confirm that the proposed algorithm exhibits better performance compared to the considered algorithms.

Distributed Computing Architecture for Optimal Control of Distribution Feeders With Smart Loads

This paper presents a distributed computing architecture for solving a distribution optimal power flow (DOPF) model based on a smart grid communication middleware (SGCM) system. The system is modeled as an unbalanced three-phase distribution system, which includes different kind of loads and various components of distribution systems. In this paper, fixed loads are modeled as constant impedance, current and power loads, and neural network models of controllable smart loads are integrated into the DOPF model. A genetic algorithm is used to determine the optimal solutions for controllable devices, in particular load tap changers, switched capacitors, and smart loads in the context of an energy management system for practical feeders, accounting for the fact that smart loads consumption should not be significantly affected by network constraints. Since the number of control variables in a realistic distribution power system is large, solving the DOPF for real-time applications is computationally expensive. Hence, to reduce computational times, a decentralized system with parallel computing nodes based on an SGCM system is proposed. Using a “MapReduce” model, the SGCM system runs the DOPF model, communicates between master and worker computing nodes, and sends/receives data among different parts of parallel computing system. Compared to a centralized approach, the proposed architecture is shown to yield better optimal solutions in terms of reducing energy losses and/or energy drawn from the substation within adequate practical run-times for a realistic test feeder.

Three-phase Unbalanced Interval Power Flow Calculation of Low-voltage Distribution Network with Distributed PV Power Generation

Low-voltage distribution network is a three-phase unbalanced system due to the integration of single-phase loads and single-phase distributed PV arrays. In this paper, three-phase unbalanced interval power flow calculation model of three-phase four-wire low voltage distribution network with distributed PV power generation is established. In the model, intensity of illumination and battery temperature which influence the power output of distributed PV power generation is described as intervals. Then, through the affine interval algorithm, the interval power flow problem is transformed into a deterministic power flow problem and two linear optimization problems. By solving the above problems, the interval power flow solution can be obtained. Finally, the proposed algorithm is applied to an actual 22-bus low-voltage distribution network, and the solution of the affine interval algorithm is compared to the solution of the Monte Carlo sampling method, which verifies the correctness and effectiveness of the proposed algorithm.

Assessment of unbalance and distortion components in three-phase systems with harmonics and interharmonics

This paper deals with the identification of balance, unbalance and distortion components in unbalanced three-phase systems with distorted waveforms containing harmonics and interharmonics. The analysis starts from the harmonic distortion and unbalance components found through the symmetrical component-based (SCB) approach previously defined by the authors. The SCB approach is extended in this paper by introducing an auxiliary reference frequency and identifying its consistency condition with respect to the fundamental system frequency. After defining the auxiliary reference frequency, the proposed approach directly uses the classical symmetrical component transformation matrix at any harmonic or interharmonic. Various results are presented, for conventional test cases and for measurements gathered from real systems with variable unbalanced and distorted loads. These results show that the extended SCB approach is particularly useful to analyze three-phase systems in unbalanced and distorted conditions with harmonics and interharmonics, because of its simplicity and intuitiveness compared to other approaches.