A Generalized Index for Static Voltage Stability of Unbalanced Polyphase Power Systems including Th\'evenin Equivalents and Polynomial Models

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., compound hybrid parameters), and the aggregate behavior of the devices in each node by Th\'evenin Equivalents (TEs) and Polynomial Models (PMs), respectively. The proposed VSI is a generalization of the known L-index, which is achieved through the use of compound electrical parameters, and the incorporation of TEs and PMs into its formal definition. Notably, the proposed VSI can handle unbalanced polyphase power systems, explicitly accounts for voltage-dependent behavior (represented by PMs), and is computationally inexpensive. These features are valuable for the operation of both transmission and distribution systems. Specifically, the ability to handle the unbalanced polyphase case is of particular value for distribution systems. In this context, it is proven that the compound hybrid parameters required for the calculation of the VSI do exist under practical conditions (i.e., for lossy grids). The proposed VSI is validated against state-of-the-art methods for voltage stability assessment using a benchmark system which is based on the IEEE 34-node feeder

Using Distributed Energy Resources to Improve Power System Stability and Voltage Unbalance

The increasing penetration of renewables has driven power systems to operate closer to their stability boundaries and makes maintaining power quality more difficult. The goals of this dissertation are to develop methods to control distributed energy resources to improve power system stability and voltage unbalance. Specifically, demand response (DR) is used to realize the former goal, and solar photovoltaic (PV) systems are used to achieve the latter. We present a new DR strategy to change the consumption of flexible loads while keeping the total load constant, improving voltage or small-signal stability without affecting frequency stability. The new loading pattern is only maintained temporarily until the generators can be re-dispatched. Additionally, an energy payback period maintains the total energy consumption of each load at its nominal value. Multiple optimization problems are proposed for determining the optimal loading pattern to improve different voltage or small-signal stability margins. The impact of different system models on the optimal solution is also investigated. To quantify voltage stability, we choose the smallest singular value (SSV) of the power flow Jacobian matrix and the distance to the closest saddle-node bifurcation (SNB) of the power flow as the stability margins. We develop an iterative linear programming (ILP) algorithm using singular value sensitivities to obtain the loading pattern with the maximum SSV. We also compare our algorithm's performance to that of an iterative nonlinear programming algorithm from the literature. Results show that our ILP algorithm is more computationally scalable. We formulate another problem to maximize the distance to the closest SNB, derive the Karush–Kuhn–Tucker conditions, and solve them using the Newton-Raphson method. We also explore the possibility of using DR to improve small-signal stability. The results indicate that DR actions can improve small-signal characteristics and sometimes achieve better performance than generation actions. Renewables can also cause power quality problems in distribution systems. To address this issue, we develop a reactive power compensation strategy that uses distributed PV systems to mitigate voltage unbalance. The proposed strategy takes advantage of Steinmetz design and is implemented via both decentralized and distributed control. We demonstrate the performance of the controllers on the IEEE 13-node feeder and a much larger feeder, considering different connections of loads and PV systems. Simulation results demonstrate the trade-offs between the controllers. It is observed that the distributed controller achieves greater voltage unbalance reduction than the decentralized controller, but requires communication infrastructure. Furthermore, we extend our distributed controller to handle inverter reactive power limits, noisy/erroneous measurements, and delayed inputs. We find that the Steinmetz controller can sometimes have adverse impacts on feeder voltages and unbalance at noncritical nodes. A centralized controller from the literature can explicitly account for these factors, but requires significantly more information from the system and longer computational times. We compare the performance of the Steinmetz controller to that of the centralized controller and propose a new controller that integrates centralized controller results into the Steinmetz controller. Results show that the integrated controller achieves better unbalance improvement compared with that of the centralized controller running infrequently. In summary, this dissertation presents two demand-side strategies to deal with the issues caused by the renewables and contributes to the growing body of literature that shows that distributed energy resources have the potential to play a key role in improving the operation of the future power system.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162969/1/mqyao_1.pd

Investigation of Voltage Stability in Three-Phase Unbalanced Distribution Systems with DGs

Smart grids draw lots of attention and interests and they are fundamentally changing traditional power grids. One of the key aspects of smart grid is that more distributed generators (DGs) are connected in distribution systems. Distribution systems have changed from passive to active. Stability problems become important issues, one of which is voltage stability problems. To analyze voltage stability problems, many methods are proposed for transmission systems. However, because distribution systems are very different from transmission system, the methods for transmission systems cannot be directly applied to distribution systems. Therefore, effective methods of analyzing voltage stability problems for distribution systems are needed. The main focus of this dissertation is on three-phase unbalanced distribution systems with DGs. Firstly, improvements were made to an existing three-phase continuation power flow (CPF) method so that the maximum loading factor of distribution systems can be found accurately. Various distribution system components and DGs in PQ mode and PV mode with reactive power were modeled. Comparisons with Matpower software were made to validate the correctness of the implemented three-phase CPF program. Secondly, to provide more detailed voltage stability analysis and determine the weak buses of distribution systems, a new voltage stability analysis method, the CPF scan method, was proposed. The weak buses found by this method are the buses that have higher impact on the maximum loadability or the maximum total real load power that the system can support. Extensive case studies were performed and the impact of different distribution components were investigated. Lastly, to determine whether a distribution will experience voltage stability problems and to determine the weak buses, a measurement-based three-phase voltage stability index was proposed. This voltage stability index provides not only a system-wide index but also an individual index for each bus/phase. These proposed methods were applied to 8-bus system and a modified IEEE 13-node test feeder with DG to study the performance of the methods and investigate the impact on weak buses of different factors in distribution systems. The case studies showed that the proposed two methods, CPF scan and VSI, can successfully identify the impact of certain distribution system components. For more complicated components, such as untransposed lines and DG in PV mode, more research is needed. Also the CPF scan results shows good applications to distribution system operation and planning. The applications of the new proposed methods are not limited to identifying the weak buses. These methods have a great potential to be extended to voltage stability preventive and corrective control

Operation and restoration of bulk power systems using distributed energy resources and multi-microgrids

The fast-paced and meaningful penetration of distributed energy resources (DERs), such as variable renewable energy sources (RESs), concurrently with the widespread occurrence of natural disasters and man-made threats, has raised several challenges for the modern bulk power systems (BPSs) status quo. Although the DERs are demanding new solutions to ensure adequate stability and security levels, these resources enable significant opportunities to improve multiple BPS perspectives. In this view, seeking to capitalize on these novel features, while aware of the significant changes to BPS outlook, this thesis is focused on developing new methods able to capitalize on modern monitoring infrastructures, DERs and control areas opportunities toward the improvement of BPS operation and stability. Specifically, the thesis focuses on: 1) First, a novel method for the improvement of the static security region (SSR) is proposed based on a new network partitioning algorithm. The proposed algorithm focuses on modern BPS with high penetration of variable RES generation. It divides the BPS into coherence areas according to its criticality mapping, and consequently, areas are adaptively associated with SSRs generators groups. To this end, each bus is assigned a criticality index from the potential energy function, whereas this calculation is based on the data of the wide-area measurement system (WAMS) using phasor measurement unit (PMU); 2) Second, a novel area-based sensitivity index for voltage stability support is proposed, exploring both the network-wide sensitivity and the local characteristics of voltage collapse. The developed index focuses on the determination of the most effective buses for voltage support and their respective capability of increasing the system’s load margin. For this, a novel area-based outlook is developed taking advantage of the new possibilities enabled by BPS distributed controllable resources, such as flexible resources (FRs)

Modeling, Stability Analysis, and Control of Distributed Generation in the Context of Microgrids

One of the consequences of competitive electricity markets and international commitments to green energy is the fast development and increase in the amount of distributed generation (DG) in distribution grids. These DGs are resulting in a change in the nature of distribution systems from being "passive", containing only loads, to "active", including loads and DGs. This will affect the dynamic behavior of both transmission and distribution systems. There are many technical aspects and challenges of DGs that have to be properly understood and addressed. One of them is the need for adequate static and dynamic models for DG units, particularly under unbalanced conditions, to perform proper studies of distribution systems with DGs (e.g., microgrids). The primary objective of this thesis is the development and implementation of dynamic and static models of various DG technologies for stability analysis. These models allow studying systems with DGs both in the long- and short-term; thus, differential and algebraic equations of various DGs are formulated and discussed in order to integrate these models into existing power system analysis software tools. The presented and discussed models are generally based on dynamic models of different DGs for stability studies considering the dynamics of the primary governor, generators, and their interfaces and controls. A new comprehensive investigation is also presented of the effects of system unbalance on the stability of distribution grids with DG units based on synchronous generator (SG) and doubly-fed induction generator (DFIG) at different loading levels. Detailed steady-state and dynamic analyses of the system are performed. Based on voltage and angle stability studies, it is demonstrated that load unbalance can significantly affect the distribution system dynamic performance. Novel, simple, and effective control strategies based on an Unbalanced Voltage Stabilizer (UVS) are also proposed to improve the system control and the stability of unbalanced distribution systems with SG- and DFIG-based DGs

AC system stability analysis and assessment for Shipboard Power Systems

The electric power systems in U.S. Navy ships supply energy to sophisticated systems for weapons, communications, navigation and operation. The reliability and survivability of a Shipboard Power System (SPS) are critical to the mission of a Navy ship, especially under battle conditions. When a weapon hits the ship in the event of battle, it can cause severe damage to the electrical systems on the ship. Researchers in the Power System Automation Laboratory (PSAL) at Texas A&M University have developed methods for performing reconfiguration of SPS before or after a weapon hit to reduce the damage to SPS. Reconfiguration operations change the topology of an SPS. When a system is stressed, these topology changes and induced dynamics of equipment due to reconfiguration might cause voltage instability, such as progressive voltage decreases or voltage oscillations. SPS stability thus should be assessed to ensure the stable operation of a system during reconfiguration. In this dissertation, time frames of SPS dynamics are presented. Stability problems during SPS reconfiguration are classified as long-term stability problems. Since angle stability is strongly maintained in SPS, voltage stability is studied in this dissertation for SPS stability during reconfiguration. A test SPS computer model, whose simulation results were used for stability studies, is presented in this dissertation. The model used a new generalized methodology for modeling and simulating ungrounded stiffly grounded power systems. This dissertation presents two new indices, a static voltage stability index (SVSILji) and a dynamic voltage stability index (DVSI), for assessing the voltage stability in static and dynamic analysis. SVSILji assesses system stability by all lines in SPS. DVSI detects local bifurcations in SPS. SVSILji was found to be a better index in comparison with some indices in the literature for a study on a two-bus power system. Also, results of DVSI were similar to the results of conventional bifurcation analysis software when applied to a small power system. Using SVSILji and DVSI on the test SPS computer model, three of four factors affection voltage stability during SPS reconfiguration were verified. During reconfiguration, SVSILji and DVSI are used together to assess SPS stability

Voltage stability of power systems with renewable-energy inverter-based generators: A review

© 2021 by the authors. The main purpose of developing microgrids (MGs) is to facilitate the integration of renewable energy sources (RESs) into the power grid. RESs are normally connected to the grid via power electronic inverters. As various types of RESs are increasingly being connected to the electrical power grid, power systems of the near future will have more inverter-based generators (IBGs) instead of synchronous machines. Since IBGs have significant differences in their characteristics compared to synchronous generators (SGs), particularly concerning their inertia and capability to provide reactive power, their impacts on the system dynamics are different compared to SGs. In particular, system stability analysis will require new approaches. As such, research is currently being conducted on the stability of power systems with the inclusion of IBGs. This review article is intended to be a preface to the Special Issue on Voltage Stability of Microgrids in Power Systems. It presents a comprehensive review of the literature on voltage stability of power systems with a relatively high percentage of IBGs in the generation mix of the system. As the research is developing rapidly in this field, it is understood that by the time that this article is published, and further in the future, there will be many more new developments in this area. Certainly, other articles in this special issue will highlight some other important aspects of the voltage stability of microgrids

Investigation of the application of UPFC controllers for weak bus systems subjected to fault conditions. An investigation of the behaviour of a UPFC controller: the voltage stability and power transfer capability of the network and the effect of the position of unsymmetrical fault conditions.

In order to identify the weakest bus in a power system so that the Unified Power Flow Controller could be connected, an investigation of static and dynamic voltage stability is presented. Two stability indices, static and dynamic, have been proposed in the thesis. Multi-Input Multi-Output (MIMO) analysis has been used for the dynamic stability analysis. Results based on the Western System Coordinate Council (WSCC) 3-machine, 9-bus test system and IEEE 14 bus Reliability Test System (RTS) shows that these indices detect with the degree of accuracy the weakest bus, the weakest line and the voltage stability margin in the test system before suffering from voltage collapse. Recently, Flexible Alternating Current Transmission systems (FACTs) have become significant due to the need to strengthen existing power systems. The UPFC has been identified in literature as the most comprehensive and complex FACTs equipment that has emerged for the control and optimization of power flow in AC transmission systems. Significant research has been done on the UPFC. However, the extent of UPFC capability, connected to the weakest bus in maintaining the power flows under fault conditions, not only in the line where it is installed, but also in adjacent parallel lines, remains to be studied. In the literature, it has normally been assumed the UPFC is disconnected during a fault period. In this investigation it has been shown that fault conditions can affect the UPFC significantly, even if it occurred on far buses of the power system. This forms the main contribution presented in this thesis. The impact of UPFC in minimizing the disturbances in voltages, currents and power flows under fault conditions are investigated. The WSCC 3-machine, 9-bus test system is used to investigate the effect of an unsymmetrical fault type and position on the operation of UPFC controller in accordance to the G59 protection, stability and regulation. Results show that it is necessary to disconnect the UPFC controller from the power system during unsymmetrical fault conditions.Libyan Governmen

New Analysis and Operational Control Algorithms for Islanded Microgrid Systems

Driven by technical, economic and environmental benefits for different stakeholders in the power industry, the electric distribution system is currently undergoing a major paradigm shift towards having an increasing portion of its growing demand supplied via distributed generation (DG) units. As the number of DG units increase; microgrids can be defined within the electric distribution system as electric regions with enough generation to meet all or most of its local demand. A microgrid should be able to operate in two modes, grid-connected or islanded. The IEEE standard 1547.4 enumerates a list of potential benefits for the islanded microgrid operation. Such benefits include: 1) improving customers’ reliability, 2) relieving electric power system overload problems, 3) resolving power quality issues, and 4) allowing for maintenance of the different power system components without interrupting customers. These benefits motivate the operation of microgrid systems in the islanded mode. However the microgrid isolation from the main grid creates special technical challenges that have to be comprehensively investigated in order to facilitate a successful implementation of the islanded microgrid concept. Motivated by these facts, the target of this thesis is to introduce new analysis and operational control algorithms to tackle some of the challenges associated with the practical implementation of the islanded microgrid concept. In order to accomplish this target, this study is divided into four perspectives: 1) developing an accurate steady-state analysis algorithm for islanded microgrid systems, 2) maximizing the possible utilization of islanded microgrid limited generation resources, 3) allowing for the decentralized operation of islanded microgrid systems and 4) enabling the islanded microgrid operation in distribution systems with high penetration of plug-in electric vehicles (PEVs). First for the steady-state analysis of islanded microgrid systems, a novel and generalized algorithm is proposed to provide accurate power flow analysis of islanded microgrid systems. Conventional power flow tools found in the literature are generally not suitable for the islanded microgrid operating mode. The reason is that none of these tools reflect the islanded microgrid special philosophy of operation in the absence of the utility bus. The proposed algorithm adopts the real characteristics of the islanded microgrid operation; i.e., 1) Some of the DG units are controlled using droop control methods and their generated active and reactive power are dependent on the power flow variables and cannot be pre-specified; 2) The steady-state system frequency is not constant and is considered as one of the power flow variables. The proposed algorithm is generic, where the features of distribution systems i.e. three-phase feeder models, unbalanced loads and load models have been taken in consideration. The effectiveness of the proposed algorithm, in providing accurate steady-state analysis of islanded microgrid systems, is demonstrated through several case studies. Secondly, this thesis proposes the consideration of a system maximum loadability criterion in the optimal power flow (OPF) problem of islanded microgrid systems. Such consideration allows for an increased utilization of the islanded microgrid limited generation resources when in isolation from the utility grid. Three OPF problem formulations for islanded microgrids are proposed; 1) The OPF problem for maximum loadability assessment, 2) The OPF for maximizing the system loadability, and 3) The bi-objective OPF problem for loadability maximization and generation cost minimization. An algorithm to achieve a best compromise solution between system maximum loadability and minimum generation costs is also proposed. A detailed islanded microgrid model is adopted to reflect the islanded microgrid special features and real operational characteristics in the proposed OPF problem formulations. The importance and consequences of considering the system maximum loadability in the operational planning of islanded microgrid systems are demonstrated through comparative numerical studies. Next, a new probabilistic algorithm for enabling the decentralized operation of islanded microgrids, including renewable resources, in the absence of a microgrid central controller (MGCC) is proposed. The proposed algorithm adopts a constraint hierarchy approach to enhance the operation of islanded microgrids by satisfying the system’s operational constraints and expanding its loading margin. The new algorithm takes into consideration the variety of possible islanded microgrid configurations that can be initiated in a distribution network (multi-microgrids), the uncertainty and variability associated with the output power of renewable DG units as well as the variability of the load, and the special operational philosophy associated with islanded microgrid systems. Simulation studies show that the proposed algorithm can facilitate the successful implementation of the islanded microgrid concept by reducing customer interruptions and enhancing the islanded microgrid loadability margins. Finally, this research proposes a new multi-stage control scheme to enable the islanded microgrid operation in the presence of high PEVs penetration. The proposed control scheme optimally coordinates the DG units operation, the shedding of islanded microgrid power demand (during inadequate generation periods) and the PEVs charging/discharging decisions. To this end, a three-stage control scheme is formulated in order to: 1) minimize the load shedding, 2) satisfy the PEVs customers’ requirements and 3) minimize the microgrid cost of operation. The proposed control scheme takes into consideration; the variability associated with the output power of renewable DG units, the random behaviour of PEV charging and the special features of islanded microgrid systems. The simulation studies show that the proposed control scheme can enhance the operation of islanded microgrid systems in the presence of high PEVs penetration and facilitate a successful implementation of the islanded microgrid concept, under the smart grid paradigm

Optimal Sizing and Location of Static and Dynamic Reactive Power Compensation

The key of reactive power planning (RPP), or Var planning, is the optimal allocation of reactive power sources considering location and size. Traditionally, the locations for placing new Var sources were either simply estimated or directly assumed. Recent research works have presented some rigorous optimization-based methods in RPP. Different constraints are the key of various optimization models, identified as Optimal Power Flow (OPF) model, Security Constrained OPF (SCOPF) model, and Voltage Stability Constrained OPF model (VSCOPF). First, this work investigates the economic benefits from local reactive power compensation including reduced losses, shifting reactive power flow to real power flow, and increased transfer capability. Then, the benefits in the three categories are applied to Var planning considering different locations and amounts of Var compensation in an enumeration method, but many OPF runs are needed. Then, the voltage stability constrained OPF (VSCOPF) model with two sets of variables is used to achieve an efficient model. The two sets of variables correspond to the “normal operating point (o)” and “collapse point (*)” respectively. Finally, an interpolation approximation method is adopted to simplify the previous VSCOPF model by approximating the TTC function, therefore, eliminating the set of variables and constraints related to the “collapse point”. In addition, interpolation method is compared with the least square method in the literature to show its advantages. It is also interesting to observe that the test results from a seven-bus system show that it is not always economically efficient if Var compensation increases continuously