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This paper analyzes the robust stability of a mixed source microgrid comprised of a synchronous generator-based distributed energy resource (DER) and an inverter-based DER. Few studies conducted recently indicated that power system stabilizers (PSSs) are advantageous for damping local oscillations of synchronous generator-based DERs. However, stability issues may arise due to interaction of the parameters of PSS and system. This paper proposes a method to determine the stability region for the system when any two parameters are considered uncertain based on robust control theory. A sufficient condition for robust stability is presented using bialternate sum matrix of the system with uncertain parameters. The bialternate sum matrix approach is compared with a branch and bound approach presented in earlier studies. These two methods are shown to yield identical results for a single machine infinite bus system. However, the proposed bialternate sum matrix approach requires far less computational effort. Therefore, it is applied to determine the stability region for the operation of mixed source microgrid in both grid-connected and islanded modes. [ABSTRACT FROM AUTHOR]

This paper proposes a fundamental model for continuous-time scheduling and marginal pricing of energy generation and storage in day-ahead power systems operation. The paper begins with formulating the economic operation problem of power systems with generating units and energy storage (ES) devices as a continuous-time optimal control problem, where the Lagrange multiplier trajectory associated with the continuous-time power balance constraint is proven to be the marginal price of energy generation and storage. The marginal price is calculated in closed-form, which reveals that in addition to the incremental cost rates of generating units, the marginal price embeds the financial ES charging offers and discharging bids that are defined as incremental charging utility and incremental discharging cost rates. This paper shows that the adjoint function associated with the ES state equation establishes a temporal dependence between the marginal prices during the ES charge and discharge states. A function space-based method is developed to solve the proposed model, which converts the continuous-time problem into a mixed-integer linear programming problem with finite dimensional decision space. The features of the proposed scheduling and pricing models are demonstrated using numerical studies conducted on the IEEE Reliability Test System. [ABSTRACT FROM AUTHOR]

For nearly 20 years, the Test Feeder Working Group of the Distribution System Analysis Subcommittee has been developing openly available distribution test feeders for use by researchers. The purpose of these test feeders is to provide models of distribution systems that reflect the wide diversity in design and their various analytic challenges. Because of their utility and accessibility, the test feeders have been used for a wide range of research, some of which has been outside the original scope of intended uses. This paper provides an overview of the existing distribution feeder models and clarifies the specific analytic challenges that they were originally designed to examine. Additionally, this paper will provide guidance on which feeders are best suited for various types of analysis. The purpose of this paper is to provide the original intent of the Working Group and to provide the information necessary so that researchers may make an informed decision on which of the test feeders are most appropriate for their work. [ABSTRACT FROM PUBLISHER]

This paper aims at proposing a mixed-integer linear formulation to incorporate reliability-oriented costs into the expansion planning model of electricity distribution networks. In this respect, revenue lost associated with the undelivered energy caused by network interruptions as well as costs incurred by the widely used reward–penalty regulations is considered as the major reliability-related costs from distribution companies point of view. A set of mixed-integer linear equations is proposed to calculate the most common distribution system reliability indices, i.e., expected energy not served, system average interruption frequency index, and system average interruption duration index. It is found that these equations can also facilitate the formulation of radiality constraint in the presence of distributed generation units. Moreover, application of the proposed method is investigated through various case studies performed on two test distribution networks with 24 and 54 nodes. [ABSTRACT FROM AUTHOR]

Voltage control plays an important role in the operation of electricity distribution networks, especially with high penetration of distributed energy resources. These resources introduce significant and fast varying uncertainties. In this paper, we focus on reactive power compensation to control voltage in the presence of uncertainties. We adopt a chance constraint approach that accounts for arbitrary correlations between renewable resources at each of the buses. We show how the problem can be solved efficiently using historical samples analogously to the stochastic quasi-gradient methods. We also show that this optimization problem is convex for a wide variety of probabilistic distributions. Compared to conventional per-bus chance constraints, our formulation is more robust to uncertainty and more computationally tractable. We illustrate the results using standard IEEE distribution test feeders. [ABSTRACT FROM AUTHOR]

Present-day radial electric power distribution circuit faces multiple challenges due to the increased photovoltaic (PV) generation. This paper aims to examine and design modern distribution circuit topologies for accommodating high PV penetration, while addressing power quality concerns. The central hypothesis of the proposed design approach is that by decreasing the Thevenin impedance at the buses where PVs are connected, the impacts on feeder voltages due to PV generation become less pronounced thereby additional PV capacity can be integrated at the corresponding buses. A novel two-stage optimization framework is proposed. The first stage is a mixed-integer linear programing based formulation to design new optimal configuration for any given distribution circuit. The formulation allows the possibility that the circuit can be operated in either a radial or loop configuration. The second stage, a nonlinear programing based formulation, then finds PV hosting capacity for the identified optimal configuration. The proposed two-stage framework is evaluated for IEEE 123-bus test feeder. It is demonstrated that the PV hosting capacity of the feeder can be increased by 53% by optimally adding two new distribution lines with tie-switches. [ABSTRACT FROM AUTHOR]

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second-order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter semidefinite programming (SDP) relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder. [ABSTRACT FROM AUTHOR]

This paper presents a new method for studying electromechanical transients in power systems using three phase, combined transmission and distribution models (hybrid models). The methodology models individual phases of an electric network and associated unbalance in load and generation. Therefore, the impacts of load unbalance, single phase distributed generation and line impedance unbalance on electromechanical transients can be studied without using electromagnetic transient simulation (EMTP) programs. The implementation of this methodology in software is called the Three Phase Dynamics Analyzer (TPDA). Case studies included in the paper demonstrate the accuracy of TPDA and its ability to simulate electromechanical transients in hybrid models. TPDA has the potential for providing electric utilities and power system planners with more accurate assessment of system stability than traditional dynamic simulation software that assume balanced network topology. [ABSTRACT FROM PUBLISHER]

Realistic representations of contingencies in AC optimal power flow (ACOPF) often challenge traditional bus-branch network models. Derived from nodal analysis, such approaches represent network constraints in terms of the familiar bus admittance matrix, $Y_{\text{bus}}$. A fixed $Y_{\text{bus}}$ is unable to represent common circuit breaker actions such as bus splitting. Work-arounds for $Y_{\text{bus}}$ -based analysis typically rely on topology processing, switching between different $Y_{\text{bus}}$ matrices depending on breaker settings. In this paper, we propose a very general node-breaker approach, employing multi-port element models and using a sparse tableau formulation (STF) for network constraints. Instead of treating breaker action as altering network topology, and hence changing the structure of Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL) equations, this approach represents a breaker's position as impacting only constraints associated with a single component, thereby maintaining fixed structure in the KVL and KCL constraints. While larger numbers of variables are required, STF proves sparser than $Y_{\text{bus}}$ formulations. Numerical case studies herein demonstrate that STF provides computational efficiency comparable to a $Y_{\text{bus}}$ -based ACOPF at the scale of several hundred buses, and lower computational cost in an example of over one thousand buses. [ABSTRACT FROM AUTHOR]

We present a novel distributed Gauss–Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially over a sequence of linear approximations of the SE model, akin to what is done by the Gauss–Newton method. The resulting iterative Gauss–Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed Gauss–Newton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The paper provides extensive numerical study of the GN-BP algorithm, provides details on its convergence behavior, and gives a number of useful insights for its implementation. [ABSTRACT FROM AUTHOR]

Volt/var control (VVC) is one of the primary functions of the distribution management system aiming at optimum operation of power distribution networks while respecting all of their operational and security constraints. However, the recent huge integration of highly stochastic distributed generation (DG) sources with the grid presents a significant challenge to the traditional VVC schemes, which assume the future to be perfectly known. This paper presents a two-stage chance constrained optimization scheme to handle these nodal power uncertainties and guarantees that the operational and security constraints are respected for almost all realizations of the uncertainty. The chance constrained model is solved by collecting enough randomly chosen samples from the probability spaces of the uncertain parameters so that the class of the problem, a mixed integer second-order cone program, is not elevated. The algorithm not only dispatches the optimum schedule for discrete controlling devices like transformers and shunt capacitors but also optimizes the predefined decision rules for reactive power control of DG sources, thus falling in line with the requirement laid down in the revised IEEE 1547 Standard. Numerical simulations on three different test systems show the superiority of the proposed algorithm over the traditional deterministic methods. [ABSTRACT FROM AUTHOR]

The growing adoption of residential photovoltaic (PV) systems around the world is presenting distribution network operators (DNOs) with technical challenges, particularly on low voltage (LV) networks. The need to mitigate these issues with simple yet effective measures in countries with high PV penetrations is likely to drive the adoption of limits on the very exports that affect this infrastructure. Defining the most adequate limit, however, requires understanding the tradeoffs between the technical benefits and the effects on PV owners. This paper proposes two methodologies: an optimal power flow (OPF) based technique to define the export limit that solves technical problems with minimal curtailment, and a Monte Carlo based analysis to investigate the spectrum of such tradeoffs considering different PV penetrations and export limits. A real U.K. residential LV network with 180 customers is analyzed using realistic 1-min resolution daily load and PV generation profiles across seasons. Results demonstrate that, for DNOs, the OPF-based approach is effective in determining the most technically adequate export limit. However, for policy makers, the spectrum of tradeoffs provided by the Monte Carlo approach can help defining export limits that reduce curtailment at the expense of partially mitigating technical issues. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology based on multiobjective optimization techniques to perform an optimized, coordinated, and selective allocation of control and protection devices in distribution networks with distributed generation (DG). The proposed mathematical model consists of two objective functions that consider economic issues and the network continuity index. Physical and operational constraints are taken into account, with emphasis on the set of constraints based on practical rules of distribution companies and international technical standards, which require the specification, coordination, and selectivity of the protection devices installed in the network. The possibility of load transfer from neighboring feeders and islanded DG operation is also considered. The proposed model is a mixed integer nonlinear programming, and we use NSGA-II (Nondominated Sorting Genetic Algorithm) to solve it. The proposed methodology is applied in a real 135-bus system found in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a wide area control (WAC) method to coordinate the local controllers of generators and renewable energy sources (RESs), for robust power oscillation damping. The WAC signals are synthesized by a two-level hierarchical controller, which utilizes wide area measurements from all the installed synchronous generators and RESs for maximizing the performance of their corresponding local controllers. In the resulting WAC scheme, the generators are “aware” of the RES oscillations and vice versa, the RESs are “aware” of the generator oscillations. Further, the WAC signals intended for the RESs are adjusted in order to require only slight modifications on the RES local controllers. This study illustrates that the correct coordination of generators and RESs, through the WAC, improves the damping performance of the entire system even under high penetration of renewables. The performance of the proposed scheme has been tested and validated in the IEEE 9-bus and 39-bus test systems. [ABSTRACT FROM AUTHOR]

This paper proposes a stochastic control strategy, namely the unsynchronized Addictive Increase Multiplicative Decrease (AIMD) algorithm, to manage the power flow of interconnected microgrids (MGs). The proposed control aims at achieving a tradeoff between the individual utility function of each MG while ensuring the stability of the grid. Both centralized and decentralized AIMD approaches are considered and compared. Extensive Monte Carlo simulations are performed on the IEEE 39-bus system, and show that the proposed control strategy is able to provide the sought tradeoff. [ABSTRACT FROM AUTHOR]

In order to support an appropriate level of resource adequacy in the long term and also to achieve a reliable operation in the short term, a new pricing design and mechanism is needed as a key success factor of real-time energy-only market. This paper proposes optimization-based mathematical models to explore operating reserve demand curves (ORDCs) and two price adders in real-time energy-only market, including dispatch correction and extended security-constrained economic dispatch. The Lagrangian multipliers of the dispatch correction problem are used to construct the ORDCs. Then, the derivative of the ORDCs’ social welfare is formulated as real-time online reserve price adders such as the scarcity adder and the price-lift adder. In case studies, we justify the effectiveness of the proposed ORDCs and two price adders by a simple example with two aggregated units and the Electric Reliability Council of Texas data. [ABSTRACT FROM AUTHOR]

This paper proposes a generic steady-state modeling and power-flow analysis approach for droop- and isochronously controlled microgrids. The proposed framework adopts symmetrical sequence component models, rather than phase-coordinate models, of microgrid elements. Such approach immensely reduces the power-flow execution time, as it breaks down the system model into independent equation sets with considerably reduced sizes. To render the proposed approach practical and generic, it integrates different types and control schemes of distributed generation (DG), including synchronous generator-based DG (SGDG) and electronically interfaced DG units. Furthermore, it incorporates unbalanced loads and feeders, transformer connections, different load characteristics, and configurations, as well as microgrid droop features. A novel power-flow algorithm based on a modified Newton–Raphson method is proposed to solve for the microgrid steady-state voltage magnitudes, angles, and frequency. The accuracy of the models and algorithm is verified through comparison with detailed time-domain simulations in MATALB/Simulink. Additionally, the proposed approach is shown to outperform the reported Newton-Trust Region approach in generality, accuracy, and performance. Two case studies, incorporating IEEE 123-node test microgrid, are further performed to examine the effectiveness of the proposed approach in solving complicated droop-controlled microgrids, and to examine the behavior of droop-controlled DGs in isochronous microgrids. [ABSTRACT FROM AUTHOR]

This paper critically evaluates a number of uncertainty importance measures for use in power system stability studies. Sensitivity analysis of uncertain system parameters is vital as new technologies proliferate and the total level of system uncertainty grows. Accurate assessment of the importance of different uncertainties can guide power system operators towards parameters which will require the greatest levels of mitigation or increased monitoring in order to reduce the uncertainty and its subsequent impact. Local and global sensitivity analysis techniques are described and evaluated within this paper, including nonparametric methods, variance-based approaches, and distribution-based techniques. The techniques are illustrated using a large 295-bus realistic network model of a generic distribution system. Numerical experiments on dynamic models are used in order to assess the impact of uncertainties on the mitigation of system frequency excursions using single-site and distributed energy storage devices. [ABSTRACT FROM AUTHOR]

This two-part paper considers the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the bidding and market clearing strategy to motivate self-interested users to realize efficient energy allocation subject to a peak energy constraint. The companion paper (Part I) formulates the problem and proposes a load coordination framework using the mechanism design approach. To address the unknown parameters, Part II of this paper presents a joint state and parameter estimation framework based on the expectation maximization algorithm. The overall framework is then validated using real-world weather data and price data, and is compared with other approaches in terms of aggregated load response. Simulation results indicate that our coordination framework can effectively improve the operational efficiency of the distribution system and reduce power congestion at key times. [ABSTRACT FROM AUTHOR]

This paper deals with the distribution network reconfiguration problem in a multi-objective scope, aiming to determine the optimal radial configuration by means of minimizing the active power losses and a set of commonly used reliability indices formulated with reference to the number of customers. The indices are developed in a way consistent with a mixed-integer linear programming (MILP) approach. A key contribution of the paper is the efficient implementation of the \mmb\varepsilon-constraint method using lexicographic optimization in order to solve the multi-objective optimization problem. After the Pareto efficient solution set is generated, the resulting configurations are evaluated using a backward/forward sweep load-flow algorithm to verify that the solutions obtained are both non-dominated and feasible. Since the \mmb\varepsilon-constraint method generates the Pareto front but does not incorporate decision maker (DM) preferences, a multi-attribute decision making procedure, namely, the technique for order preference by similarity to ideal solution (TOPSIS) method, is used in order to rank the obtained solutions according to the DM preferences, facilitating the final selection. The applicability of the proposed method is assessed on a classical test system and on a practical distribution system. [ABSTRACT FROM AUTHOR]

Recent years have witnessed significant interest in convex relaxations of the power flows, with several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that ac-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-hard for tree networks. [ABSTRACT FROM AUTHOR]

In this paper we address some shortcomings in existing nonlinear dynamic models of power system experiencing symmetrical and unsymmetrical faults in their transmission/distribution networks. The shortcomings relate to: 1) approximations relating to stator dynamics, internal voltage of the positive sequence network and the dynamics of the negative and zero sequence networks, and 2) existing models are time -variant, which may not be suitable for system studies such as stability and fault detection studies that require time invariant model. The approximations outlined in 1) adversely affect the modeling accuracy, especially that of the system response during the period immediately after the occurrence of faults. We present in this paper a full fault-dependent time-invariant dynamical model of power systems experiencing symmetrical and unsymmetrical faults in their transmission/distribution networks and verify it through simulation studies mimicking real life scenarios. IEEE 30 bus power system is considered as the study case. The simulation results are compared to Matlab's “SimPower” and PSCAD/EMTDC software packages. [ABSTRACT FROM AUTHOR]

Power system reliability measures for residential distribution networks have gained a lot of attention in recent years. This is due to the introduction of smart grids, where the quality of the delivered power becomes a crucial issue. In this paper, a new methodology to include cold load pickup (CLPU) events in the reliability assessment of power distribution systems is proposed. The developed methodology presents a platform to include CLPU events in the reliability assessment assuming an optimal systematic procedure is used to restore the affected load points. The methodology is applied on a test system using a state-of-the-art search technique named lightning search algorithm (LSA). The optimal plan takes into account electrical code protection system settings, system operation limits, and stochastic behavior of the load. The reliability indices for a base case without considering CLPU is compared with the case that considers CLPU assuming an optimal restoration. Both cases are compared further under fixed-restoration plans with different time intervals. The results demonstrate the effectiveness of the proposed methodology to improve the distribution network reliability by considering the CLPU events. [ABSTRACT FROM AUTHOR]

Remote-controlled switches (RCSs) play an important role in prompt service restoration of distribution systems (DSs). However, the cost of RCSs and the vast footprint of DSs limit widespread utilization of RCSs. In this paper, we present a new approach to RCS allocation for improving the performance of restoration and optimizing reliability benefits with reasonable RCS cost. Specifically, the optimal number and locations of to-be-upgraded switches can be determined with different objectives: maximizing the reduction of customer interruption cost; maximizing the reduction of system average interruption duration index; or maximizing the amount of loads that can be restored using the upgraded RCSs. We show that these models can actually be formulated as mixed-integer convex programming problems. We further introduce a novel method to equivalently transform and efficiently solve each of them. The global optimum can thus be computed within a reasonable amount of time. The IEEE 33-node and 123-node test systems are used to demonstrate the proposed models and algorithms. [ABSTRACT FROM PUBLISHER]

Quasi-static time-series (QSTS) simulation is used to simulate the behavior of distribution systems over long periods of time (typically hours to years). The technique involves repeatedly solving the load-flow problem for a distribution system model and is useful for distributed energy resource planning. When a QSTS simulation has a small time step and a long duration, the computational burden of the simulation can be a barrier to integration into utility workflows. One way to relieve the computational burden is to simplify the system model. The segment substitution method of simplifying distribution system models introduced in this paper offers model bus reduction of up to 98% with a simplification error as low as 0.2% (0.002 p.u. voltage). In contrast to existing methods of distribution system model simplification, which rely on topological inspection and linearization, the segment substitution method uses black-box segment data and an assumed simplified topology. [ABSTRACT FROM PUBLISHER]

Distribution expansion planning (DEP) is used to determine the best expansion plan of a distribution system. Considering the uncertainties of loads and of power productions of wind distributed energy resources (DERs) and incorporating AC power flow equations make the DEP problem increasingly challenging. In this context, this paper presents a new adaptive robust distribution expansion planning model to identify the timing of feeder reinforcements in addition to the location, capacity, and installation time of dispatchable and wind DERs. The proposed approach characterizes the uncertain nature of loads and power productions of wind DERs through polyhedral uncertainty sets and the robustness of the solution can be controlled by means of a budget of uncertainty. Since AC power flow equations rather than DC ones are considered, the proposed model is a nonlinear and non-convex min–max–min optimization problem, which cannot be solved directly by commercial optimization packages. Hence, a tri-level decomposition algorithm using both primal and dual cutting planes is introduced to solve the problem. Additionally, to attain a smoother optimization problem, the non-convex AC power flow equations are convexified. The working of the proposed model is illustrated using 33-bus and 123-bus distribution networks. [ABSTRACT FROM AUTHOR]

In this paper, a calculation method for quantifying the impact of complex short circuits on active unbalanced distribution systems is proposed. Unlike previous distribution system short-circuit calculations, the proposed method is capable of solving complex short circuits with an arbitrary number of faulted busses and phases, without predefining the boundary (fault) conditions. Different short circuits are defined by simple inspection of these faults. Additionally, all distribution system elements are appropriately modeled and integrated in the proposed method, including electronically coupled distributed energy resources. The method can solve unbalanced systems, including mutually coupled sections, in unsymmetrical prefault states, and it is performed in the sequence domain. This makes the proposed method particularly fast and suitable for online distribution system analysis. The computation results show the advantages of the proposed method relative to previous short-circuit calculation methods, in regards to both the required calculation time and the accuracy. [ABSTRACT FROM PUBLISHER]

Wind power representation is an integral part of stochastic economic dispatch (ED). Compared with the deterministic approach, stochastic ED allocates system reserves more effectively. This improved reserve strategy heavily relies on the wind power distribution boundary area that is not consistent with classical unbounded distribution models. To address this issue, this paper proposes a new probability distribution model named truncated versatile distribution (TVD) for wind power, which is bounded and more accurate than classical models. The fitting effect and mathematical analysis of TVD are thoroughly discussed. Then, we propose a novel look-ahead dynamic ED method with an adjustable confidence interval (ACI) based on TVD, which not only enables system operators to maintain an acceptable predefined level of risk, but also seeks the optimal level of risk to balance the system reserve strategy and risk of power unbalance. With ACI, TVD offers a reliable wind power representation to search for the optimal level of risk in the dispatch model. In addition, the employment of TVD can simplify the wind power uncertainties by its analytical forms. The results show that compared with other classical distribution models, the novel distribution is a more accurate representation of wind power. Moreover, the ED model results in improved economic performances by ACI compared with traditional ones. [ABSTRACT FROM AUTHOR]

This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta constant-power, constant-current, and constant-impedance loads (ZIP loads) has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction over the defined region, and hence converges to the unique solution. [ABSTRACT FROM PUBLISHER]

This paper develops a generalized admittance matrix approach in Fortescue coordinate system to solve unbalanced/unsymmetrical distribution networks including different number of phases. This generalized Fortescue \pi equivalent is defined in this paper for solving the heterogeneous phase, and thus Fortescue, network model. The performance of the approach is demonstrated in different model networks with number of nodes ranging between 168 and 14200. It is found that the current iteration method exploiting the decoupling in admittance matrix in Fortescue coordinate is substantially faster than the typical unbalanced three-phase solution in phase domain. The method has a significant potential for application in real time active power network management. [ABSTRACT FROM PUBLISHER]

This paper proposes a distributed control approach to coordinate multiple energy storage units (ESUs) to avoid violation of voltage and thermal constraints, which are some of the main power quality challenges for future distribution networks. ESUs usually are connected to a network through voltage source converters. In this paper, both ESU converters active and reactive power are used to deal with the above mentioned power quality issues. ESUs' reactive power is proposed to be used for voltage support, while the active power is to be utilized in managing network loading. Two typical distribution networks are used to apply the proposed method, and the simulated results are illustrated in this paper to show the effectiveness of this approach. [ABSTRACT FROM PUBLISHER]

In this paper, an ultra-fast algorithm for the computation of multiphase short-circuit currents at all buses is proposed by addressing the concept of selected inversion. The short circuit summary is achieved through the computation of multiphase Thevenin equivalent at each bus by using the augmented nodal matrix. This typically requires the sequential solution of linear system of equations, i.e., direct inversion which can be demanding in terms of CPU time. In this paper, it is shown that dramatic gains in computational time can be obtained when the selected inversion (SelInv) technique is performed where only a subset of entries of the inverse of augmented nodal matrix is computed. These entries include the phase domain Thevenin impedances seen from network buses which are used in the computation of short-circuit currents with the predefined boundary conditions specific to the fault type. The performance of the method is demonstrated with very large scale and realistic distribution systems. [ABSTRACT FROM PUBLISHER]

This paper proposes an improved analytical model for the study of steady-state performance of droop-controlled VSC-MTDC systems. When power disturbances occur, such as those imposed by normal changes in power settings and converter outages, the powers of the converters with droop control may hit their limits and hence such converters no longer contribute to power sharing, which should be paid special attention when analyzing the impacts of power disturbances on the performance of multi-terminal HVDC (MTDC) systems. Based on the bisection algorithm and superposition principle, the proposed analytical model provides an easy way to estimate the results of power distributions, dc voltage deviations, and power loss variations of the MTDC system taking converter outage and converter overload into account. Simulations of a modified New England 39-bus system incorporating a four-terminal MTDC system are carried out for validating the proposed analytical model. [ABSTRACT FROM AUTHOR]

The number and locations of transmission lines that are likely to get simultaneously congested are useful information for analysis of power market. In this paper, we present a study that demonstrates the number of simultaneously congested transmission lines is very limited, as well as an algorithm for identifying a small set of transmission lines that may become simultaneously congested based on the current states of the system and market. To this end, we first investigate the maximum number of simultaneously congested lines. Then, a novel algorithm is developed to identify a smaller set using two scientific criteria – one is concerned with the absolute impact of generation dispatch decisions, and the other, the relative sensitivities of line flows with respect to the changes of generation outputs. The effectiveness of the proposed algorithm is demonstrated through two simulation studies, one based on IEEE 39-bus for illustration of concepts, and the other based on a large-scale, real-world power system for showing the practical application and significance of results. [ABSTRACT FROM AUTHOR]

This paper proposes a necessary condition for power flow insolvability in power distribution systems with distributed generators (DGs). We show that the proposed necessary condition indicates the impending singularity of the Jacobian matrix and the onset of voltage instability. We consider different operation modes of DG inverters, e.g., constant-power and constant-current operations, in the proposed method. A new index based on the presented necessary condition is developed to indicate the distance between the current operating point and the power flow solvability boundary. Compared to existing methods, the operating condition-dependent critical loading factor provided by the proposed condition is less conservative and is closer to the actual power flow solution space boundary. The proposed method only requires the present snapshots of voltage phasors to monitor the power flow insolvability and voltage stability. Hence, it is computationally efficient and suitable to be applied to a power distribution system with volatile DG outputs. The accuracy of the proposed necessary condition and the index is validated by simulations on a distribution test system with different DG penetration levels. [ABSTRACT FROM AUTHOR]

Power flow analysis is one of the tools that is required in most of the distribution system studies. An important characteristic of distribution systems is the load unbalance in the phases and a three-phase power flow analysis is needed. In this paper, a three-phase linear power flow (3LPF) formulation is derived based on the fact that in a typical distribution system, voltage angles and magnitudes vary within relatively narrow boundaries. The accuracy of the proposed 3LPF is verified using several test cases. Potential applications of the proposed method are in distribution systems state estimation and volt-VAR optimization. [ABSTRACT FROM PUBLISHER]

This paper deals with radial distribution network reconfiguration for loss and switching mitigation. Its main contribution is the presentation of a genetic algorithm (GA) with two network encodings, capable of representing only radial connected solutions without demanding a planar topology or any specific genetic operator. The code was named sequential because the evaluation of the ith gene depends on the information forthcoming from all the previous genes. In addition to a full description of proposed techniques with examples, the paper presents a survey of existing network codifications including their search space and chromosomes for a 33-bus example system. In order to validate the proposed algorithms, these and other two techniques in the state of the art are applied to reconfigure three sample systems which have been broadly published in the technical literature. Performance is assessed by using the results of implemented representations and the reconfiguration literature. [ABSTRACT FROM PUBLISHER]

Increasing penetration of variable loads and renewable generation will cause the conventional operation strategy of the distribution system to become less certain and effective. This paper presents a method of determining the minimum loss network configuration of a distribution system with uncertain load and renewable generation. A robust optimization model is proposed wherein the optimal decisions on network configurations and losses are derived in two subsequent steps. The first step enforces the radiality constraint before knowing the actual system loads and output level of renewable generation. Power flows are computed next to achieve minimum network losses considering the worst operating conditions over the uncertainty sets. A mixed-integer two-stage robust optimization formulation and a decomposition algorithm in a master-slave structure are proposed to solve the problem. Results of an illustrative example and two test systems are presented to demonstrate the proposed method. [ABSTRACT FROM PUBLISHER]

This paper investigates the impact of the overexcitation limiters (OELs) on the stability margin of a power system which is operating under stressed conditions. Several OEL modeling approaches are presented and the effect of their action has been examined in model power systems. It is realized that, more often than not, OEL operating status goes undetected by existing dynamic security assessment tools commonly used in the industry. It is found that the identification and accurate representation of OELs lead to significantly different transient stability margins. Unscented Kalman filtering is used to detect the OEL activation events. In the context of stressed system operation, such quantitative assessment is very useful for system control. This understanding is further reinforced through detailed studies in two model power systems. [ABSTRACT FROM AUTHOR]

In this paper, a new procedure based on a backward/forward sweep (BFS) algorithm for solving power flows in weakly meshed dc traction networks is presented. The proposed technique is able to consider the trains as nonlinear and nonsmooth (nondifferentiable) voltage-dependent loads or generators. This feature permits the inclusion of the trains’ overcurrent protection and the squeeze control. With the use of the mentioned controls, the conventional power flow problem becomes a voltage constrained power flow problem, and the interaction between the trains and the network can be accurately modeled. However, the train control induces a highly nonsmooth voltage-dependent load characteristic, causing convergence problems in most of the derivative-based algorithms. The proposed algorithm is faster, more robust, and more stable than the derivative-based ones. In addition, the authors present all of the formulation in a compact matrix-based form by means of the graph theory application and the node incidence matrix. [ABSTRACT FROM PUBLISHER]

This paper presents a comprehensive mathematical model to solve the restoration problem in balanced radial distribution systems. The restoration problem, originally modeled as mixed integer nonlinear programming, is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound. The proposed mathematical model considers several objectives in a single objective function, using parameters to preserve the hierarchy of the different objectives: 1) maximizing the satisfaction of the demand, 2) minimizing the number of switch operations, 3) prioritizing the automatic switch operation rather than a manual one, and 4) prioritizing especial loads. General and specialized tests were carried out on a 53-node test system, and the results were compared with other previously proposed algorithms. Results show that the mathematical model is robust, efficient, flexible, and presents excellent performance in finding optimal solutions. [ABSTRACT FROM PUBLISHER]

Low-frequency inter-area oscillation is a potentially dangerous phenomenon in power systems involving exchange of power among generators in different areas. In this paper, we study the characteristics of inter-area oscillation by analyzing the distribution of the oscillation energy. First, we introduce equations for the kinetic energy of generators and the potential energy of network branches, derived from the linearization of system dynamic equations. Then, we study the mode composition and the distribution of the generators' kinetic energy during low-frequency oscillations. A modal kinetic energy participation factor is proposed for evaluating the participation of each generator in the oscillation. The relationships among electromagnetic power oscillation distribution, rotor speed deviation, and generator kinetic energy are analyzed and compared to their modal parameter left eigenvectors, right eigenvectors, and linear participation factors, respectively. The bus voltage angle deviation, active power oscillation, and branch potential energy are calculated using the right eigenvector from modal analysis. The distribution characteristics of voltage angle oscillation and branch potential energy in inter-area oscillation is developed. The simulation results for a four-generator two-area system and the New England 10-machine 39-bus system illustrate the feasibility and validity of the proposed theory and method for analysis of inter-area oscillations. [ABSTRACT FROM AUTHOR]

In this paper we present a framework to efficiently characterize the available operational flexibility in a multi-area power system. We focus on the available reserves and the tie-line flows. The proposed approach is an alternative to the current calculation of the available transfer capacity (ATC), as it considers location and availability of reserves, transmission constraints, and interdependencies of tie-line flows between different areas, while it takes into account the N-1 security criterion. The method is based on computational geometry using polytopic projections. It requires only a limited amount of information exchange and does not need central coordination. The method has two versions: a passive approach, and an active approach where neighboring areas can share reserves. In that respect we also introduce the term “exportable flexibility”. Case studies demonstrate the improved tie-line utilization, especially if reserves are shared, and the visualization benefits. [ABSTRACT FROM PUBLISHER]

A model predictive controller (MPC) for load frequency control (LFC) of an interconnected power system is investigated. The MPC is based on a simplified system model of the Nordic power system, and it takes into account limitations on tie-line power flow, generation capacity, and generation rate of change. The participation factors for each generator are optimization variables, and suggestions are made as to how one can ensure tie-line power transfer margins through slack-variables, and pricing information through the objective function. The solution of MPC for LFC is completed by including a Kalman filter for state estimation. The presented MPC is compared against a conventional LFC/AGC scheme with proportional integral (PI) controllers. Simulations show that the MPC gives better frequency response while using cheaper resources. This paper illustrates that MPC could be a realistic solution to some of the LFC problems power systems are facing today. [ABSTRACT FROM AUTHOR]

This paper proposes a computationally efficient technique for estimating the composite load model parameters based on analytical similarity of parameter sensitivity. When the model parameters are updated in the optimization procedure to best fit the actual load dynamics, i.e., measurements, parameters of similar sensitivity representation in the given mathematical model structure are updated in the same manner at every iterative step. This research allows for practically reducing the number of load model parameters to be identified in the estimation process and the overall computational cost while preserving the desired complexity and accuracy of the original model. This approach consequently facilitates the parameter estimation in the optimization process and helps manage increased number of parameters often criticized for adopting the dynamic composite load model via measurement-based approach. Case studies for the real power system demonstrate the computational efficiency and intact accuracy of the proposed method with reference to the existing methods of estimating all the parameters of the given composite load model independently. [ABSTRACT FROM AUTHOR]

Optimal transmission switching (OTS) optimizes simultaneously the generation dispatch and the topology of a power system. It has been shown that taking some transmission lines out of service can significantly reduce the operating cost of the system while respecting the traditional deterministic N-1 security criterion of operational reliability. However, topology modifications could adversely affect probabilistic security metrics. The operational reliability of a power system can be translated into a cost by multiplying the expected energy not served by the value of lost load. This paper therefore explores whether it is possible to maintain a positive economic balance with OTS when considering not only the cost of generation but also the expected socio-economic cost of disruptions in the supply. This is done in two steps: the computation of an N-1 secure OTS and then the calculation of a probabilistic estimate of the operational reliability of the OTS solution. Based on the results obtained with two test systems, it is shown that OTS tends to significantly degrade probabilistic measures of security. It is thus not obvious that OTS can lead to a positive economic balance, even when N-1 security is enforced. Consequently, a probabilistic security analysis should be performed before implementing an OTS solution. [ABSTRACT FROM AUTHOR]

A more realistic management of electric vehicle (EV) charging points requires to cope with stochastic behavior on vehicle staying patterns. This paper presents a stochastic programming model to achieve optimal management taking into account price variation in day-ahead and intraday electricity markets, together with regulating reserve margins. In this model, first-stage decisions determine day-ahead energy purchases and sales and the upward and downward reserve margins committed. Second-stage decisions correspond to intraday markets and deal with reserve requirements and several possible scenarios for vehicle staying pattern. The design of the objective function prioritizes supplying energy to EV batteries while minimizing the net expected energy cost at the EV charging point. A case study describing a parking for 50 EVs is analyzed. The case includes household, commercial and mixed EV staying patterns with several intraday arrival and departure scenarios. Pure and hybrid EVs are included, taking into account their respective energy characteristics. Sensitivity analysis is used to show the potential energy cost savings and the impact of different non-supply penalizations. The case study considers several vehicle staying patterns, energy price profiles and discharge allowances. The model achieves energy cost reductions between 1% and 15% depending on the specific case. A model validation by simulation has been done. [ABSTRACT FROM AUTHOR]

This paper proposes a two-level voltage controller for large-scale power systems. The aim of the controller is to maintain a near-optimal voltage profile in the transmission network by coordinating discrete reactive power (var) control devices in the system. The controller is targeted for implementation in electric power transmission utility companies where most of the voltage controls are coordinated by switching of discrete var devices such as shunt capacitor and reactor banks and transformer banks load tap changers (LTCs). By effectively dividing the controller responsibilities between local substation controls and a central coordinator at control center level, the design is aimed at voltage control of large-scale power systems. At local level, the substation controllers maintain their respective substation bus voltages by local power-flow-like computations using mostly local PMU measurements. The central coordinator computes and provides the voltage set-points to the substation controllers and also coordinates by enabling or disabling the local controllers as needed. The controller is being designed towards prototype implementation in Southern California Edison (SCE), starting with local controllers at specific substations in the first stage. It is tested on real-time dynamic models and large-scale power-flow simulations of SCE transmission network. [ABSTRACT FROM AUTHOR]

The relatively fixed residential day-ahead real-time electricity price reflects insufficient information of the market, so the response of residential energy management system (EMS) to the real-time pricing (RTP) is not complete and therefore retailers are exposed to the risk of price fluctuation in balance market. Direct load control (DLC) in cooperative game is proposed in this paper. A cooperative game union comprised of some users and a retailer is established to minimize the union costs. The union provides an opportunity to access the balance market indirectly for residents and to reduce risks and costs for the retailer. In addition, Shapley value which embodies the fairness is used in union profits allocation. The method that avoids bidding for residential users simplifies the thresholds of residents to participate in market. Furthermore, the DLC union contributes to imbalance self-management for the retailer, which helps him avoid paying for the regulation cost involved in the deviation between the total quantity bought at markets and the actual consumption. The achievement of union’s goal respects the constraints set by users. The method that alleviates the disturbance of DLC to residents meets the dual goals of being both fully responsive and non-disruptive. [ABSTRACT FROM AUTHOR]

The extensive usage of open communication networks in power system control causes inevitable time delays. This paper studies impacts of such delays on the stability of one-area and two-area load frequency control (LFC) systems and proposes an analytical method to determine delay margins, the upper bound on the delay for stability. The proposed method first eliminates transcendental terms in characteristic equation of LFC systems without making any approximation and transforms the transcendental characteristic equation into a regular polynomial. The key result of the elimination process is that real roots of the new polynomial correspond to imaginary roots of the transcendental characteristic equation. With the help of new polynomial, it is also possible to determine the delay-dependency of system stability and root tendency with respect to the time delay. An analytical formula is then developed to compute delay margins in terms of system parameters. For a large set of controller gains, delay margins of LFC systems are computed to investigate the qualitative effect of controller gains on the delay margin. Finally, simulations studies are carried out to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]