Showing papers on "Islanding published in 2015"

An Enhanced Islanding Microgrid Reactive Power, Imbalance Power, and Harmonic Power Sharing Scheme

Abstract: To address inaccurate power sharing problems in autonomous islanding microgrids, an enhanced droop control method through online virtual impedance adjustment is proposed. First, a term associated with DG reactive power, imbalance power, or harmonic power is added to the conventional real power-frequency droop control. The transient real power variations caused by this term are captured to realize DG series virtual impedance tuning. With the regulation of DG virtual impedance at fundamental positive sequence, fundamental negative sequence, and harmonic frequencies, an accurate power sharing can be realized at the steady state. In order to activate the compensation scheme in multiple DG units in a synchronized manner, a low-bandwidth communication bus is adopted to send the compensation command from a microgrid central controller to DG unit local controllers, without involving any information from DG unit local controllers. The feasibility of the proposed method is verified by simulated and experimental results from a low-power three-phase microgrid prototype.

An Adaptive Overcurrent Protection Scheme for Distribution Networks

Abstract: Distribution networks are evolving toward the vision of smart grids, with increasing penetration of distributed generation (DG), introduction of active network management (ANM), and potentially islanded modes of operation. These changes affect fault levels and fault current paths and have been demonstrated to compromise the correct operation of the overcurrent protection system. This paper presents an adaptive overcurrent protection system which automatically amends the protection settings of all overcurrent relays in response to the impact of DG, ANM, and islanding operation. The scheme has been developed using commercially available protection devices, employs IEC61850-based communications, and has been demonstrated and tested using a hardware-in-the-loop laboratory facility. A systematic comparison of the performance of the proposed adaptive scheme alongside that of a conventional overcurrent scheme is presented. This comparison quantifies the decrease in false operations and the reduction of mean operating time that the adaptive system offers.

System Operation and Energy Management of a Renewable Energy-Based DC Micro-Grid for High Penetration Depth Application

Abstract: A renewable energy-based dc micro-grid with hybrid energy storage, consisting of battery and ultracapacitor, is investigated. To achieve high penetration depth of renewable sources into the utility grid, a novel system operation strategy and the corresponding energy management method is proposed. In the operation strategy, the ultracapacitor unit works as the sole voltage source of the micro-grid to support the dc link in both connected and islanding mode. The micro-grid is controlled to deliver/absorb predefined amount of power to/from the utility grid during connected mode and zero during islanding mode. This design will certainly simplify the power dispatching algorithm of the power system and increase the possibility of including large quantities of micro-grids into the utility grid. The energy management method is dedicated to conducting the net power of the micro-grid effectively. The net power is separated into high- and low-frequency components. The high-frequency power is suppressed by the ultracapacitor automatically and the low frequency power is shared by the battery and an adjustment unit. A small-scale dc micro-grid structure with a single dc link is considered for investigation. MATLAB/Simulink simulation results are presented to validate the proposed system operation strategy and the energy management method.

Robust Control for Power Sharing in Microgrids With Low-Inertia Wind and PV Generators

Abstract: This paper presents a robust control design scheme for a multidistributed energy resource (DER) microgrid for power sharing in both interconnected and islanded modes. The scheme is proposed for micgrogrids consisting of photovoltaic (PV) units and wind turbine driven doubly fed induction generators (DFIGs). A battery is integrated with each of the wind and solar DER units. The control scheme has two levels: 1)one centralized multi-inputmulti-output robust controller for regulating the set reference active and reactive powers and 2)local real and reactive power droop controllers, one on each DER unit. The robust control scheme utilizes multivariable ${H_\infty}$ control to design controllers that are robust to the changes in the network and system nonlinearities. The effectiveness of the proposed controller is demonstrated through large-disturbance simulations, with complete nonlinear models, on a test microgrid. It is found that the power sharing controllers provide excellent performance against large disturbances and load variations during islanding transients and interconnected operation.

An adaptive neuro-fuzzy inference system for islanding detection in wind turbine as distributed generation

Abstract: This article proposes a new integrated diagnostic system for islanding detection by means of a neuro-fuzzy approach. Islanding detection and prevention is a mandatory requirement for grid-connected distributed generation DG systems. Several methods based on passive and active detection scheme have been proposed. Although passive schemes have a large non-detection zone NDZ, concern has been raised on active method due to its degrading power-quality effect. Reliably detecting this condition is regarded by many as an ongoing challenge as existing methods are not entirely satisfactory. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. In addition, this technique can also overcome the problem of setting the detection thresholds inherent in the existing techniques. In this study, we propose to use a hybrid intelligent system called ANFIS the adaptive neuro-fuzzy inference system for islanding detection. This approach utilizes rate of change of frequency ROCOF at the target DG location and used as the input sets for a neuro-fuzzy inference system for intelligent islanding detection. This approach utilizes the ANFIS as a machine learning technology and fuzzy clustering for processing and analyzing the large data sets provided from network simulations using MATLAB software. To validate the feasibility of this approach, the method has been validated through several conditions and different loading, switching operation, and network conditions. The proposed algorithm is compared with the widely used ROCOF relays and found working effectively in the situations where ROCOF fails. Simulation studies showed that the ANFIS-based algorithm detects islanding situation accurate than other islanding detection algorithms. © 2014 Wiley Periodicals, Inc. Complexity 21: 10-20, 2015

Comparative Study of Advanced Signal Processing Techniques for Islanding Detection in a Hybrid Distributed Generation System

Abstract: In this paper, islanding detection in a hybrid distributed generation (DG) system is analyzed by the use of hyperbolic S-transform (HST), timetime transform, and mathematical morphology methods. The merits of these methods are thoroughly compared against commonly adopted wavelet transform (WT) and S-transform (ST) techniques, as a new contribution to earlier studies. The hybrid DG system consists of photovoltaic and wind energy systems connected to the grid within the IEEE 30-bus system. Negative sequence component of the voltage signal is extracted at the point of common coupling and passed through the above-mentioned techniques. The efficacy of the proposed methods is also compared by an energy-based technique with proper threshold selection to accurately detect the islanding phenomena. Further, to augment the accuracy of the result, the classification is done using support vector machine (SVM) to distinguish islanding from other power quality (PQ) disturbances. The results demonstrate effective performance and feasibility of the proposed techniques for islanding detection under both noise-free and noisy environments, and also in the presence of harmonics.

Single-Phase Microgrid With Seamless Transition Capabilities Between Modes of Operation

Abstract: Microgrids are an effective way to increase the penetration of distributed generation into the grid. They are capable of operating either in grid-connected or in islanded mode, thereby increasing the supply reliability for the end user. This paper focuses on achieving seamless transitions from islanded to grid-connected and vice versa for a single phase microgrid made up from voltage controlled voltage source inverters (VC-VSIs) and current controlled voltage source inverters (CC-VSIs) working together in both modes of operation. The primary control structures for the VC-VSIs and CC-VSIs is considered together with the secondary control loops that are used to synchronize the microgrid as a single unit to the grid. Simulation results are given that show the seamless transitions between the two modes without any disconnection times for the CC-VSIs and VC-VSIs connected to the microgrid.

A Decentralized Multiagent System Approach for Service Restoration Using DG Islanding

Abstract: This paper proposes a decentralized multiagent system (MAS) approach for service restoration using controlled distributed generator (DG) islanding. Furthermore, it investigates the impacts of vehicle-to-grid (V2G) facility of the electric vehicles (EVs) for service restoration. Service restoration is formulated as a multiobjective optimization problem considering maximization of priority load restored and minimization of switching operations as the multiple objectives and solved using the proposed decentralized MAS approach. Extensive case studies are conducted on 38, 69, and 119 bus distribution systems, and the following advantages of the proposed MAS approach are observed: 1) flexibility—to perform under different DG and EV penetration levels; 2) scalability—to restore service for different size test systems, small as well as large; and 3) robustness—ability to perform efficiently for both single as well as multiple-fault situations. The simulation results also highlight the benefits of V2G feature of EVs for service restoration.

Average Absolute Frequency Deviation Value Based Active Islanding Detection Technique

Abstract: An average absolute frequency deviation value based active islanding detection technique is proposed in this paper. The inverter's classical q-axis current controller is modeled with a continuous periodic reference current of a small value. During the loss of mains, the island's frequency deviates with respect to the variation in the reference current; this is detected by making the use of an average absolute frequency deviation value. In case of a stable island formation, there is a small periodic frequency deviation owing to the small value of the periodic reference current, and the frequency deviation is so small that it falls inside the nondetection zone (NDZ) of the frequency relay. The main advantage of the proposed algorithm is that it detects the stable island formation but without forcing the island to lose its stable operation. In case of nonislanding switching events, which may transiently impose a significant deviation in the frequency, the possibility of false detection is eliminated by reconfirming the occurrence of islanding once it is suspected. The reference current is kept to a small value to limit the degradation of the power quality and the power factor. Computer simulation is done with MATLAB.

Universal Integrated Synchronization and Control for Single-Phase DC/AC Converters

Abstract: The universal integrated synchronization and control (UISC) is proposed to operate a single-phase dc/ac converter in both grid-connected (GC) and stand-alone (SA) modes and offer seamless transition between these modes without any reconfiguration of control structure. As a matter of fact, the UISC does not need to use an islanding detection algorithm in the conventional sense. In GC mode, the UISC controls the real and reactive powers independently. In SA mode, it provides voltage and frequency support. The UISC is not based on direct current control or direct output voltage control. It adjusts the internal converter voltage through a nonlinear mechanism that amounts to the control of the current in GC mode and the voltage in SA mode. The UISC does not require a separate synchronization unit such as a phase-locked loop (PLL). In principle, the UISC is analogous to the combined governor and automatic voltage regulator controls in a synchronous machine (SM). In this sense, it may be considered among the converters that mimic the SMs such as the synchronverter. The proposed UISC is arguably the most unified method that can address different modes of operation of a converter within a microgrid environment without control switching actions. This paper presents the derivations, stability analysis, and numerical results to illustrate the performance of the proposed controller in a single phase situation. A mathematical analysis on the analogies and differences between the UISC and some similar methods is also presented.

Current Status and Issues of Concern for the Integration of Distributed Generation Into Electricity Networks

Abstract: As existing distribution networks were designed to deliver unidirectional power to consumers and require minimal control intervention, they result in largely passive infrastructures The installation of distributed generation (DG) units with significant capacity in these passive networks can cause reverse power flows, which will result in some conflicts with the operation of the existing protection system In this context, utilities around the world have started establishing requirements to ensure safe and reliable interconnection of generators in low- and medium-voltage networks The technical grid code requirements and regulations vary considerably from country to country However, any standard should address the critical need to make the DG marketable by providing uniform criteria and requirements relevant to the performance, operation, and safety This paper presents a critical review of the requirements adopted by distribution companies in selected countries, such as the US, the UK, Germany, and Australia, to facilitate the connection of DG The main problems, such as voltage regulation, islanding operation, and dynamic interactions among DG and loads, are discussed to identify a few points where attention is still needed to improve the reliability of distribution systems

Harmony Search Algorithm-Based Controller Parameters Optimization for a Distributed-Generation System

Abstract: This paper presents the utilization of a harmony search algorithm (HSA) to optimally design the proportional-integral (PI) controllers of a grid-side voltage source cascaded converter with two additional loops for smooth transition of islanding and resynchronization operations in a distributed-generation (DG) system. The first loop is the frequency-control loop which is superimposed on the real power setpoint of the cascaded controller of the voltage-source converter to minimize the frequency variation during the transition from the grid mode to islanding mode. The second loop is the resynchronization loop which reduces the phase shift of the ac voltages of the DG with the utility grid ac voltages during islanding operation leading to a successful grid reconnection event. The response surface methodology (RSM) is used to build the mathematical model of the system dynamic responses in terms of PI controllers' parameters. The effectiveness of the proposed PI control scheme optimized by the HSA is then compared with that optimized by both genetic algorithm and conventional generalized reduced gradient techniques. The HSA code is built using the MATLAB software program. The validity of the proposed system is verified by the simulation results which are performed using PSCAD/EMTDC.

Principal Component Analysis of Wide-Area Phasor Measurements for Islanding Detection—A Geometric View

Abstract: This paper presents a new technique for the detection of islanding conditions in electrical power systems. This problem is especially prevalent in systems with significant penetrations of distributed renewable generation. The proposed technique is based on the application of principal component analysis (PCA) to data sets of wide-area frequency measurements, recorded by phasor measurement units. The PCA approach was able to detect islanding accurately and quickly when compared with conventional RoCoF techniques, as well as with the frequency difference and change-of-angle difference methods recently proposed in the literature. The reliability and accuracy of the proposed PCA approach is demonstrated by using a number of test cases, which consider islanding and nonislanding events. The test cases are based on real data, recorded from several phasor measurement units located in the U.K. power system.

Constrained spectral clustering-based methodology for intentional controlled islanding of large-scale power systems

Abstract: Intentional controlled islanding is an effective corrective approach to minimise the impact of cascading outages leading to large-area blackouts. This study proposes a novel methodology, based on `constrained spectral clustering', that is computationally very efficient and determines an islanding solution with minimal power flow disruption, while ensuring that each island contains only coherent generators. The proposed methodology also enables operators to constrain any branch, which must not be disconnected, to be excluded from the islanding solution. The methodology is tested using the dynamic models of the IEEE 39- and IEEE 118-bus test systems. Time-domain simulation results for different contingencies are used to demonstrate the effectiveness of the proposed methodology to minimise the impact of cascading outages leading to large-area blackouts. In addition, a realistically sized system (a reduced model of the Great Britain network with 815 buses) is used to evaluate the efficiency and accuracy of the methodology in large-scale networks. These simulations demonstrate that the author's methodology is more efficient, in a factor of approximately 10, and more accurate than another existing approach for minimal power flow disruption.

Loss-of-mains protection system by application of phasor measurement unit technology with experimentally assessed threshold settings

Abstract: Loss-of-mains protection is an important component of the protection systems of embedded generation. The role of loss-of-mains is to disconnect the embedded generator from the utility grid in the event that connection to utility dispatched generation is lost. This is necessary for a number of reasons, including the safety of personnel during fault restoration and the protection of plant against out-of-synchronism reclosure to the mains supply. The incumbent methods of loss-of-mains protection were designed when the installed capacity of embedded generation was low, and known problems with nuisance tripping of the devices were considered acceptable because of the insignificant consequence to system operation. With the dramatic increase in the installed capacity of embedded generation over the last decade, the limitations of current islanding detection methods are no longer acceptable. This study describes a new method of loss-of-mains protection based on phasor measurement unit (PMU) technology, specifically using a low cost PMU device of the authors' design which has been developed for distribution network applications. The proposed method addresses the limitations of the incumbent methods, providing a solution that is free of nuisance tripping and has a zero non-detection zone. This system has been tested experimentally and is shown to be practical, feasible and effective. Threshold settings for the new method are recommended based on data acquired from both the Great Britain and Ireland power systems.

Analysis and Mitigation of Resonance Propagation in Grid-Connected and Islanding Microgrids

Abstract: The application of underground cables and shunt capacitor banks may introduce power distribution system resonances. In this paper, the impacts of voltage-controlled and current-controlled distributed generation (DG) units to microgrid resonance propagation are compared. It can be seen that a conventional voltage-controlled DG unit with an LC filter has a short-circuit feature at the selected harmonic frequencies, while a current-controlled DG unit presents an open-circuit characteristic. Due to different behaviors at harmonic frequencies, specific harmonic mitigation methods shall be developed for current-controlled and voltage-controlled DG units, respectively. This paper also focuses on developing a voltage-controlled DG unit-based active harmonic damping method for grid-connected and islanding microgrid systems. An improved virtual impedance control method with a virtual damping resistor and a nonlinear virtual capacitor is proposed. The nonlinear virtual capacitor is used to compensate the harmonic voltage drop on the grid-side inductor of a DG unit LCL filter. The virtual resistor is mainly responsible for microgrid resonance damping. The effectiveness of the proposed damping method is examined using both a single DG unit and multiple parallel DG units.

Islanding Detection in Microgrids Using Harmonic Signatures

Abstract: In recent years, there has been a growing interest in incorporating microgrids in electrical power networks. This is due to various advantages they present, particularly the possibility of working in either autonomous mode or grid connected, which makes them highly versatile structures for incorporating intermittent generation and energy storage. However, they pose safety issues in being able to support a local island in case of utility disconnection. Thus, in the event of an unintentional island situation, they should be able to detect the loss of mains and disconnect for self-protection and safety reasons. Most of the anti-islanding schemes are implemented within control of single generation devices, such as dc-ac inverters used with solar electric systems being incompatible with the concept of microgrids due to the variety and multiplicity of sources within the microgrid. In this paper, a passive islanding detection method based on the change of the 5th harmonic voltage magnitude at the point of common coupling between grid-connected and islanded modes of operation is presented. Hardware test results from the application of this approach to a laboratory scale microgrid are shown. The experimental results demonstrate the validity of the proposed method, in meeting the requirements of IEEE 1547 standards.

Synchrophasor-Based Islanding Detection for Distributed Generation Systems Using Systematic Principal Component Analysis Approaches

Abstract: Systematic principal component analysis (PCA) methods are presented in this paper for reliable islanding detection for power systems with significant penetration of distributed generations (DGs), where synchrophasors, recorded by phasor measurement units, are used for system monitoring. Existing islanding detection methods, such as rate-of-change-of-frequency and vector shift are fast for processing local information; however, with the growth in installed capacity of DGs, they suffer from several drawbacks. Incumbent genset islanding detection cannot distinguish a system-wide disturbance from an islanding event, leading to maloperation. The problem is even more significant when the grid does not have sufficient inertia to limit frequency divergences in the system fault/stress due to the high penetration of DGs. To tackle such problems, this paper introduces PCA methods for islanding detection. A simple control chart is established for intuitive visualization of the transients. A recursive PCA scheme is proposed as a reliable extension of the PCA method to reduce the false alarms for time-varying process. To further reduce the computational burden, the approximate linear dependence condition errors are calculated to update the associated PCA model. The proposed PCA and RPCA methods are verified by detecting abnormal transients occurring in the U.K. utility network.

An Analytical Adequacy Evaluation Method for Distribution Networks Considering Protection Strategies and Distributed Generators

Abstract: Reliability evaluation relates to the impact of faults on customer outage frequency and time. Thus, studying the process of fault isolation and supply restoration is critical in reliability evaluation. In distribution systems, distributed generators (DGs), especially renewable DGs, are increasingly integrated into the network. New issues emerge after DG integration: 1) DG reliability model; 2) change of protection strategy and supply restoration process; and 3) islanding operation. In this paper, an analytical method is proposed to assess the distribution system reliability level considering these issues. The reliability model for DG and load are developed using scenarios reduction techniques based on historical data. The correlation between renewable resources and load is also formulated in the model. When a fault occurs in a distribution system, parts of the distribution system can be operated as islands. The reliability indices of the load point in the microgrid vary according to the power adequacy assessment in the island and supply restoration process. To improve calculation efficiency, the analysis of fault isolation and supply restoration process and reliability evaluation is based on segments instead of single components. Then, the overall reliability evaluation framework is proposed. In the end, a detailed case study is presented.

Control of Transient Power During Unintentional Islanding of Microgrids

Abstract: In inverter-based microgrids, the paralleled inverters need to work in grid-connected mode and stand-alone mode and to transfer seamlessly between the two modes. In grid-connected mode, the inverters control the amount of power injected into the grid. In stand-alone mode, however, the inverters control the island voltage while the output power is dictated by the load. This can be achieved using the droop control. Inverters can have different power set points during grid-connected mode, but in stand-alone mode, they all need their power set points to be adjusted according to their power ratings. However, during sudden unintentional islanding (due to loss of mains), transient power can flow from inverters with high power set points to inverters with low power set points, which can raise the dc-link voltage of the inverters causing them to shut down. This paper investigates the transient circulating power between paralleled inverters during unintentional islanding and proposes a controller to limit it. The controller monitors the dc-link voltage and adjusts the power set point in proportion to the rise in the voltage. A small-signal model of an islanded microgrid is developed and used to design the controller. Simulation and experimental results are presented to validate the design.

Hybrid intelligent water drop bundled wavelet neural network to solve the islanding detection by inverter-based DG

Abstract: In this paper, a passive neuro-wavelet based islanding detection technique for grid-connected inverter-based distributed generation was developed. The weight parameters of the neural network were optimized by intelligent water drop (IWD) to improve the capability of the proposed technique in the proposed problem. The proposed method utilizes and combines wavelet analysis and artificial neural network (ANN) to detect islanding. Connecting distributed generator to the distribution network has many benefits such as increasing the capacity of the grid and enhancing the power quality. However, it gives rise to many problems. This is mainly due to the fact that distribution networks are designed without any generation units at that level. Hence, integrating distributed generators into the existing distribution network is not problem-free. Unintentional islanding is one of the encountered problems. Discrete wavelet transform (DWT) is capable of decomposing the signals into different frequency bands. It can be utilized in extracting discriminative features from the acquired voltage signals. In passive schemes with a large non-detection zone (NDZ), concern has been raised on active method due to its degrading power quality effect. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. The simulation results from Matlab/Simulink shows that the proposed method has a small non-detection zone, and is capable of detecting islanding accurately within the minimum standard time.

Analysis and Mitigation of Inverter Output Impedance Impacts for Distributed Energy Resource Interface

Abstract: In order to provide reliable electric power, the interfacing voltage source inverters in distributed generation often rely on autonomous droop control method integrated with virtual impedance and inner voltage and current control loops. In general, the droop-controlled inverters can be modeled as a controllable voltage source in series with output impedance. However, stability, dynamic performance, and load adaptability in islanding mode are sensitive to the inverter output impedance. In this paper, the detailed impacts of the inverter output impedance are investigated in different operation modes. Furthermore, an inverter current feedforward control scheme is proposed to mitigate the effects. With the implementation of the proposed control scheme, system reliability and load adaptability in islanding mode are enhanced without additional control complexity and extra sensors. Moreover, a voltage magnitude control loop is added to improve the control accuracy of reactive power flow in grid-connected mode. Finally, the proposed strategy is validated with simulation and experiments based on a 15-kVA prototype.

Islanding detection method for inverter-based distributed generation with negligible non-detection zone using energy of rate of change of voltage phase angle

Abstract: A simple technique is proposed in this study, aimed at the islanding detection of an inverter-based distributed generation (DG). The main advantage of the proposed technique is its reliance on a simple approach for islanding detection with negligible non-detection zone and keeping the unchanged output power quality. This work attempts to detect islanding conditions through computing the rate of change of voltage phase angle (ROCOVPA) of the point of common coupling by phase-locked loop (PLL) in inverter controllers. Because almost all inverter systems are equipped with the PLL, its implementation for inverter-interfaced DGs is simple and economical. Simulation results show that the durability energy of ROCOVPA is different for islanding and non-islanding conditions. In fact, in non-islanding condition the energy of ROCOVPA reduces to a negligible value after a certain time, but in islanding conditions it has considerable variation. The proposed method is evaluated using the conditions dictated by the IEEE 1547 and UL 1741 standards. The simulation results are presented to highlight the effectiveness of the proposed technique. In addition, the proposed method is compared with several passive and intelligent methods and it is confirmed that the proposed method has better performance and more accuracy.

Monte Carlo Simulation by Using a Systematic Approach to Assess Distribution System Reliability Considering Intentional Islanding

Abstract: This paper describes a method to apply a generalized systematic approach, useful to identify the faults' effect on load points' reliability accounting for intentional islanding, with either random or sequential Monte Carlo simulation (RMCS, SMCS) in order to assess distribution system reliability in smart grids. Moreover, a simple RMCS based on an annual branch fault probability, which correlates with the branch fault frequency, is described as well. A study case is presented to validate the results (in terms of expected reliability indices) of the proposed method in comparison with the analytical one. Further, other useful information, such as the best and worst results as well as the probability distribution of load-point annual outages number and duration is presented too. Finally, the results show that islanding positively affects reliability and then it could became a standard practice provided that the main technical issues are addressed.

Islanding and Scheduling of Power Distribution Systems With Distributed Generation

Abstract: This paper presents a short-term power regulation mechanism for post-segmentation power distribution systems in the presence of severe fault or large disturbance. Firstly, load priority is introduced into system separation and centroids of load clusters are allocated at nodes with distributed sources, respecting power balance and network connectedness. Secondly, fast power flow calculation is performed on the primarily formed islands to resolve load interruption for operational feasibility of partitions from power quality perspective. Then the effect of distributed generation fluctuations on durable operation of subsystems with various optimization objectives is examined. The load response is instructed by the proposed cost-based pricing scheme contemplating consumers' willingness. In addition, the influence of network congestion and load controllability on results of economic scheduling is investigated. Numerical results from the PG&E-69 distribution system are used to show the effectiveness of the developed model in radial structure load clusters. Illustration on the IEEE 118-bus case further proves its robustness and practicability for other distribution systems applications. This property is also useful for transmission switching and micro-grid applications.