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This paper presents a methodology for generating restoration sequences in distribution systems and microgrids with emphasis on deriving optimal switching times for remote control switches. Microgrid architecture considered are assumed to be operating in islanded single master mode. Control methods for handling the unbalance inherent in distribution systems using single-phase controlled PQ inverters were developed and incorporated in the proposed method. The problem of considering simultaneously both energy optimization and dynamic stability of the system, which is lacking in existing methods, was addressed by studying the transient behavior of microgrids based on extended electromagnetic transients program (EMTP) simulations and then approximate and incorporate these behaviors into the optimization formulation for restoration. The approach is based on multi-objective optimization of final restored load and total restoration time. The methodology was studied on a modified IEEE 123 node test feeder. An EMTP simulation in PSCAD of the formed microgrids was used to validate the accuracy of the dynamic and steady-state characteristics of the resulting systems. By considering the transient behavior of distributed generators (DGs) during restoration, a better restoration sequence that does not trigger protection relays could be realized.

The need to restore and keep the grid running or fast restoration during emergencies such as extreme weather conditions is quite apparent given the reliance of other infrastructure on electricity. One promising approach to electricity restoration is the use of locally available energy resources to restore the system to form isolated microgrids. In this paper, we present a black start restoration method that forms islanded microgrids after a blackout. The master DGs in the formed microgrids are coordinated to work together through droop control. Several constraints, including incentive-based demand response (DR) with direct load control (DLC) and distributed generator (DG) operation constraints, were formulated and linearized to realize a mixed-integer linear programming (MILP) restoration model. To improve compactness and to ensure that the model is neither under-sized nor over-sized, a pre-processing graph analysis approach was introduced which helps to characterize the least number of restoration steps needed to optimally restore the microgrid. Studies were performed on a modified IEEE 123 node test feeder to evaluate the effects of demand response, non-dispatchable DGs, and choice of restoration steps on the quality of the restoration solution. When possible, the proposed method yields an interconnected multi-master microgrid with improved redundancy.

The electricity grid faces the possibility of outages due to extreme weather events, cyber-attack, and unexpected events. When these unwanted events occur, it is desired that electricity be restored as soon as possible to meet the power demands of critical loads. The microgrid approach to power restoration holds a lot of promise, since microgrids can operate in island mode. This paper presents a novel sequential restoration methodology for microgrid black start. The microgrid architecture considered is assumed to be operating in multi-master mode. The master distributed generators (DGs) are coordinated to operate together through droop control. Several operational constraints are formulated and linearized to realize a mixed-integer linear programming (MILP) problem. The method is studied on an islanded microgrid based on a modified IEEE 13 node test feeder. Detailed transient simulation in PSCAD was used to verify the accuracy of the restoration methodology. The developed restoration method can maximize the energy restored while ensuring good voltage and frequency regulation, and ensure that power scheduling mismatch is shared in the desired proportion.

Linear power flow formulations enable the integration of power flow constraints to linearly constrained power system optimization problems in transmission and distribution systems. Typical examples include the application of DC power flow and DistFlow to distribution system reconfiguration and restoration. While non-linear power flow equations and its associated optimal power flow have been developed in the literature, there is no existing linear power flow formulation for islanded droop-controlled microgrids to the best of the authors' knowledge. To address this need, this paper presents two linear power flow approximations for three-phase islanded droop-controlled microgrids. The first approximation was derived based on the current injection method and the second approximation was derived from the three-phase DistFlow formulation. The two approximations were verified using detailed time-domain simulations at steady-state in PSCAD with resulting mean errors of the nodal voltages being under 1%. To demonstrate the application of the proposed power flow formulations, the two approximations were expanded for integration in optimal power flow formulations for islanded droop-controlled microgrids to minimize cost. Unlike the existing non-linear models, the linear power flow formulations presented in this paper can be solved easily using non-iterative linear matrix operation and its optimal power flow extensions are linearly constrained.

This paper presents a PSCAD simulation platform for studying reconfiguration methods applied to distribution systems and microgrids. The simulation model allows to manually operate the switches for reconfiguration and service restoration studies. It can also support Python-interfaced automatic switch control. Some performance metrics like unbalance factor and error calculations are introduced. The IEEE 123 node test system was implemented in the simulation platform in order to provide benchmarking results and to demonstrate the process of reconfiguration with dynamic stability considerations. Two case studies are presented. One is on reconfiguration for the purpose of restoration of an isolated section due to a fault and another on dynamic reconfiguration for the restoration of an autonomous microgrid. The PSCAD simulation platform can be extended to verify the control performance and optimization solutions of various distribution and microgrid applications.

For a three-phase islanded microgrid with non-stiff grid-supporting or grid-forming distributed generators (DGs), unbalance power dispatch from these DGs can negatively influence the voltage quality, stability, and lifespan of the DGs. One way to solve such unbalance is to have DGs that can compensate for the load unbalance by being able to dispatch unbalance power. In this work, single-phase controlled PQ inverter interfaced DGs are modeled for this purpose. A detailed control model of the single-phase PQ inverter is derived from which we approximate the power stage of the inverter to a voltage-controlled source. Simulation studies in PSCAD showed that the voltage-controlled model gives an accurate representation of the elaborate switching model of the single-phase PQ inverter. Coordination of unbalanced power dispatch is realized by stacking the single-phase inverter in a manner similar to the three-bridge four wire shunt active filter and dispatch setpoint are sent to the PQ inverters from the secondary and tertiary control level of the microgrid for load compensation purpose. Case studies of balanced, unbalanced and load compensated systems are presented and evaluated with two unbalance indices: phase voltage unbalance rate (PVUR) and true voltage unbalance factor (VUF). The studies showed that in an islanded microgrid with a non-stiff reference source, the primary source of voltage unbalance across three phase nodes is unbalanced loading and that by dispatching unbalanced power to the PQ inverters to compensate for load unbalance, a significant improvement in system balancing could be realized.

Accurate power sharing is essential for the successful operation of an islanded microgrid with droop-controlled inverters particularly at times when the total loads served in the system change significantly like during microgrid black start. In this paper, two paradigms for active power load sharing were derived: 1) load sharing by the proportion of active power limit set by the DC primer mover of DGs and 2) load sharing by the proportion of optimized reference active power. Further, a method was derived for approximate sharing of reactive power by choosing the coupling inductance of the droop-controlled inverters, which though not as precise as active power sharing, could be coordinated by a microgrid central controller to ensure good voltage regulation. The load sharing method was validated by a simulated black start test case with droop-controlled inverters and aggregated loads restored in sequence.

This paper presents a study of the application of a sequential service restoration method to single master operation microgrids with black start capability. Enhancements to a sequential service restoration methodology for frequency response characteristics during sequential load energization for diesel generators with isochronous governors were studied. Results were used to derive safe switching times during sequential service restoration for single master operation microgrid and informed the choice of maximum load step for the master distributed generators. The enhanced method was used to derive restoration sequences for a modified IEEE 123 node test feeder and an EMTP simulation in PSCAD was performed to verify the accuracy of the studies.

Developing a test environment for smart grid forms an indispensable stage to the realization of the next generation of the electricity grid. The coupling of the physical power system and its associated communication network makes modern power grid a typical cyber-physical system. In this paper, a real-time power system was simulated in RTDS and the communication network in NS-3. This test bed includes a wide area control scheme that employs the speed difference of generators in two areas of a simple 11-bus power system to dampen down local and inter-area oscillations. Different network conditions were tested and compared with cases that made use of only local input to dampen oscillations and another case that assumes a perfect communication network. The test bed showed that wide area control implementation with extremely unfavorable network conditions could introduce delays beyond the tolerable limit and lock the power system into a continually unstable mode, while favorable network conditions enhance damping of the local and inter-area oscillations of the power system.

This paper evaluates existing methods to improve state estimation by incorporating substation measurement dependencies. Three main approaches are considered: a traditional weighted least squares scheme, an iterative algorithm using a 2-point estimate to approximate the covariance matrix, and a variant of the algorithm taking just the diagonal of the estimated covariance matrix. These schemes are tested under uniform conditions for systems ranging from 3 to 30 busses, and the results are analyzed to gain intuition about each method. Finally, this intuition is used to recommend a practical weighted least squares state estimation scheme which could potentially be used to improve online state estimation.