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The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real part is defined based on the variation of the voltage magnitude. The latter term is crucial for the correct interpretation and analysis of the variation of the frequency at each bus of the network. The paper also develops a set of differential equations that describe the link between complex powers and complex frequencies at network buses in transient conditions. No simplifications are assumed except for the usual approximations of the models utilized for the transient stability analysis of power systems. A variety of analytical and numerical examples show the applications and potentials of the proposed concept. [ABSTRACT FROM AUTHOR]

DC grid has become an important application in power transmission. However, the exist works only have the method to obtain the droop coefficient in a radial topology. Also, this droop coefficient is for V-I droop control. There is no such like method to obtain the droop coefficient for the P-V droop control. This paper proposed a new method for a complex dc grid to obtain the droop coefficients. Firstly, based on the converter control strategies, the types of converter were classified. It will help to find out which kinds of converter can be participated into the dc-side voltage control. Secondly, a virtual node was defined, and the matrix of the dc grid was reshaped to fit the new added virtual node by using the proposed simplification method. An example was shown how this method worked. After that a new method of calculating the P-V droop coefficient was proposed. Finally, a simulation model was investigated to verify if the proposed method can operate in a real system. The results showed that the simplification method can ensure the mathematical relationships of the dc system. And simulations show good performances of the droop coefficient calculation method. [ABSTRACT FROM AUTHOR]

Accurate load modeling is critical for credible power system stability analysis. Because of the increasing complexity in modern system load, establishing a more comprehensive load model and performing accurate parameter estimation are the two biggest challenges in composite load modeling. In this paper, an induction motor with variable frequency drive (IM-VFD) together with the traditional ZIP+IM model is utilized to describe the dynamic characteristics of the system load. We estimate the time-varying probabilistic distributions of all states and parameters to describe their stochastic characteristics, thereby representing the real-time varying features of an actual load. The Fokker-Planck operator is applied to linearize the updated load model in tensor format. We then use tensor decomposition to reduce the computational and storage costs for calculating load model parameters. A sensitivity indicator is used to analyze the sensitivities of the estimated parameter distributions for subsequent model reduction. Simulations demonstrate that the updated load model has better performance than the traditional ZIP+IM model. [ABSTRACT FROM AUTHOR]

The distributed Volt/Var control solution is a promising one for active distribution networks (ADNs), but a critical issue is how to improve the distributed algorithm's convergence with less communication burden. In this paper, we propose a bi-level consensus alternation direction multiplier method-based fully distributed Volt/Var optimization algorithm (B-FADMM) for ADNs by exploiting inverter-based rapid control devices. In the first level, the Volt/Var optimal solution of subpartitions is obtained in parallel, and the second level completes the variable increment of each partition to correct the search direction of the first level. In the algorithm, firstly, an adaptive matrix $\omega $ initialization strategy is proposed to adapt to the different magnitude of variables, which avoids non-convergence or slow convergence of the algorithm. Secondly, the null-space method is used in the second level of the algorithm to obtain the null-space basis matrix on the active constraint of the subpartition, which reduces the dimensions of the problem and the computational complexity. In addition, the conjugate gradient (CG) algorithm is used to update the dual multiplier of each partition only by exchanging coupling information among partitions, which protects information privacy. Experiments showed the proposed approach attains the same result as the centralized, the computational performance of the proposed method is far superior to some popular other distributed methods in terms of accuracy, computational efficiency, and scalability. [ABSTRACT FROM AUTHOR]

This paper studies the communication time-delay issue in islanded microgrids (MGs) with the distributed secondary control architecture. Firstly, a time-delayed MG small-signal model is developed. Then, a new weight-average-prediction (WAP) controller is proposed to compensate the delayed system states. By introducing a time-delayed differential term in the proposed control law, the traditional time-delayed small-signal model is transformed into a neutral time-delayed mathematic model. Based on the developed model, the stability analysis is conducted considering both fixed time delay and time-varying delay. For the fixed time delay, a novel graphic analytical method is proposed to evaluate the time delay margin, which eliminates the conservatism compared with existing time-domain methods. For the time-varying delay, stability condition is established by a Lyapunov-Krasovskii function and linear matrix inequalities. In addition, some non-linear WAP control methods are discussed to guide the parameter tuning with a higher resolution. Lastly, the proposed method and analytical result are verified in the OPAL-RT real-time test platform. The results demonstrate the effectiveness and high performance of the proposed controller. [ABSTRACT FROM AUTHOR]

The penetration of photovoltaics (PVs) has been increasing in active distribution networks (ADN), which leads to severe voltage violation problems. PV inverters can provide fast and flexible reactive power support and are now allowed to participate in the voltage regulation process. This paper proposes a real-time combined central and local Volt/Var control (VVC) strategy to mitigate voltage violation problems while minimizing the network power loss. Based on the historical PV and load data, the load flow and optimal power flow are performed in the centralized controller (CC) to obtain multiple voltage and optimal power settings for each PV system. The local controller (LC) then generates voltage control curves with these optimal scatters. To improve the voltage control effect, a novel 3-Dimension voltage control curve is proposed considering both the measurements of node voltage and PV generation. Moreover, a data-driven deep convolution neural network is designed and trained to generate optimal local voltage control curves without prior knowledge of specific curve functions. The proposed approach is tested on the IEEE 33-bus distribution system and simulation results verify the effectiveness in voltage control compared with the optimal Q(V) and Q(P) method. [ABSTRACT FROM AUTHOR]

The Virtual Power Plant (VPP) has been proposed to aggregate Distributed Generations (DGs) to act like a single power plant, thus, also has functions on the frequency and voltage support. The previous models of the VPP are static and focus on the energy trading and management. For the system transient response analysis, a dynamic VPP model must be needed. The paper proposes a reduced-order yet accurate aggregated model to represent VPP transients for the stability analysis of power systems. The goal is to provide a model that is adequate for system studies and can serve to the Transmission System Operator (TSO) to evaluate the impact of VPPs on the overall grid. The proposed model can accommodate the transient response of the most relevant controllers included in the distributed generators that compose the VPP. Using a comparison with a real-time detailed Electro-Magnetic Transients (EMT) models of the VPP confirms the validity of the proposed aggregated model. The case studies based on the IEEE 39-bus system verifies the accuracy of the proposed aggregated model on the system stability analysis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a distributed secondary voltage and frequency control scheme for an islanded ac microgrid under event-triggered communication. An integral type event-triggered mechanism is proposed by which each distributed generator (DG) periodically checks its triggering condition and determines whether to update its control inputs and broadcast its states to neighboring DGs. In contrast to existing event-triggered strategies on secondary control of microgrids, the proposed event-triggered mechanism is able to handle the consensus problem in case of asynchronous communication. Under the proposed sampled-data based event-triggered mechanism, DGs do not need to be synchronized to a common clock and each individual DG checks its triggering condition periodically, relying on its own clock. Furthermore, the proposed method efficiently reduces communication rate. We provide sufficient conditions under which microgrid's frequency and a critical bus voltage asymptotically converge to the nominal frequency and voltage, respectively. Finally, effectiveness of our proposed method is verified by testing different scenarios on an islanded ac microgrid benchmark in the MATLAB/Simulink environment as well as a hardware-in-the-loop (HIL) platform, where the physical system is modeled in the Opal-RT and the cyber system is realized in Raspberry Pis. [ABSTRACT FROM AUTHOR]

With increasing penetration of solar PV, some distribution feeders are experiencing highly variable net-load flows and even reverse flows. To optimize distribution systems under such conditions, the scheduling of mechanical devices, such as OLTCs and capacitor banks, needs to take into account forecasted solar PV and actual grid conditions. However, these legacy switching assets are operated on a daily or hourly timescale, due to the wear and tear associated with mechanical switching, which makes them unsuitable for real-time control. Therefore, there is a natural timescale-separation between these slower mechanical assets and the responsive nature of inverter-based resources. In this paper, we present a network admissible convex formulation for holistically scheduling controllable grid assets to position voltage optimally against solar PV. An optimal hourly schedule is presented that utilizes mechanical resources to position the predicted voltages close to nominal values, while minimizing the use of inverter-based resources (i.e., DERs), making them available for control at a faster time-scale (after the uncertainty reveals itself). A convex, inner approximation of the OPF problem is adapted to a mixed-integer linear program that minimizes voltage deviations from nominal (i.e., maximizes voltage margins). The resulting OPF solution respects all the network constraints and is, hence, robust against modeling simplifications.Simulation based analysis on IEEE distribution feeders validates the approach. [ABSTRACT FROM AUTHOR]

For a hybrid ac/dc power system incorporating voltage source converter-based multi-terminal direct current (VSC-MTDC) grids, it is essential to solve the power flow problems efficiently for reliable operation. This paper presents an efficient ac/dc power flow algorithm considering the complementary constraints of VSC's reactive power limit and ac node voltage. It can be distinguished from the existing works in terms of both modeling and algorithm aspects. First, the VSC model is formulated, in which the interactions between the reactive power limit and the ac node voltage of VSC are viewed as complementary relations. The complementary relations are expressed using a smooth Fischer-Burmeister function. Then, power flow models of the ac grid and dc grid with a constant Jacobian matrix are formulated based on the VSC model, respectively. To efficiently solve the power flow of an ac/dc grid, the structure characteristic of the Jacobian matrix of ac/dc power flow computation is analyzed. It shows that the Jacobian matrix can be approximated as a block-upper triangular one. Based on this characteristic, a decoupled ac/dc power flow computation algorithm is provided. Test results on two hybrid ac/dc systems under different scenarios validate the correctness, convergence, and efficiency of the proposed power flow algorithm. [ABSTRACT FROM AUTHOR]

This paper tackles key industry needs in the scope of the AC Security-Constrained Optimal Power Flow (SCOPF) framework, specifically two major challenging requirements regarding generators’ post-contingency behavior: the (droop-based) frequency response and the voltage control mechanism (including PV/PQ switching). To this end, and to obtain a sufficiently accurate solution with a reasonable computational burden, we propose an approximation approach to SCOPF which extends significantly an existing algorithm with novel modelling elements: a continuous formulation to model generators’ post-contingency responses based on successive approximations, a technique to evaluate the viability of contingencies with respect to the base case set-points, and the complexity reduction of all post-contingency states through network compression and power flow piecewise linearization. All new features are validated both separately and in unison, to monitor the improvement of the solution time and the potential degradation of the solution's quality. The proposed approach is successfully applied to three power system network models, the largest of which consists of 2,000 buses and more than 3,000 contingencies. Finally, the trade-off between the limitations in terms of solution quality and the benefits in terms of computational effort are assessed for all proposed approximations. [ABSTRACT FROM AUTHOR]

Load tap changers (LTCs) are commonly used for voltage control in distribution systems. The mechanical relays on LTCs are controlled in discrete steps; hence, distribution optimal power flow (DOPF) formulations require LTCs to be modeled with integer variables. Integer variables are generally ignored or relaxed and rounded off to reduce the computational burden in DOPF models. However, in this paper, we highlight and overcome complex infeasibility issues caused by rounding methods. Moreover, recent advances in convex optimization have improved the computational tractability of the DOPF problem. In this paper, we develop and analyze numerical efficiency of different but exact formulations for incorporating LTCs as integer control assets in a relaxed second-order cone program (SOCP) version of the DOPF model. The resulting formulation becomes a mixed-integer SOCP (MISOCP), which is computationally tractable compared to mixed-integer non-linear program (MINLP). To recover the exact optimal solution in the proposed MISOCP-DOPF model, a McCormick relaxation is employed within a sequential bound-tightening algorithm. We show that solutions obtained from MISOCP-DOPF are always ac feasible. Thus, the MISOCP-DOPF yields optimal and realistic ac solutions, and is validated in large distribution feeders and is compared to MINLP counterpart. [ABSTRACT FROM AUTHOR]

This paper presents a scalable method for improving the solutions of ac optimal power flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The aim of this paper is on providing solutions that are more robust to short-term deviations, and that optimize both the initial operating point and a parametrized response policy for control during fluctuations. We formulate this as a chance-constrained optimization problem. To obtain a tractable representation of the chance constraints, we introduce a number of modeling assumptions and leverage recent theoretical results to reformulate the problem as a convex, second-order cone program, which is efficiently solvable even for large instances. Our experiments demonstrate that the proposed procedure improves the feasibility and cost performance of the OPF solution, while the additional computation time is on the same magnitude as a single deterministic AC OPF calculation. [ABSTRACT FROM AUTHOR]

Different from voltage-source converter (VSC), reactive power absorption of line-commutated converters (LCCs) changes depending on DC voltage level. Therefore, the amount of AC voltage fluctuations at inverter side are different according to I – V droop constants in hybrid multi-terminal high-voltage direct current (MT-HVDC) system. This paper proposes a method for calculating the I – V droop constants in a hybrid MT-HVDC system to suppress these AC voltage fluctuations, based on the sensitivity of AC and DC networks. Simulations performed using PSCAD demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper discusses the implementation of a transient stability model of Compressed Air Energy Storage (CAES) systems in a power system analysis package. A block-diagram based model of a two-machine CAES system is proposed, including specific controls for active power, reactive power, and State of Charge (SoC), which consider limits associated with the cavern pressure. As an application, the model is implemented in Powertech's TSAT software connected to the 9-bus WSCC benchmark power system, which is then used to study the impact of a CAES facility in the transient and frequency stability of the system. Several contingencies are simulated comparing the CAES performance to a gas turbine and a base-case without storage, demonstrating that the CAES system improves the system transient stability due to its charging stage, controls, and additional inertia. Finally, the CAES model is used to study the effects of cavern sizes in the frequency of the system. It is shown that CAES systems have certain special characteristics that make them attractive as a storage technology to provide stability and regulation services, besides their energy arbitrage capabilities. [ABSTRACT FROM AUTHOR]

The existing three-phase imbalanced power flow calculation models for isolated micro-grid do not consider the non-smooth constraints such as voltage control limits and dead zone characteristics, which makes the power flow calculation results cannot meet the actual model constraints. In this paper, a more robust projected Levenberg-Marquardt (PLM) method is used to solve the problem after the non-smooth constraints are converted into smooth functions, which can reduce the model dependence on the initial values and solve the convergence problem caused by non-smooth constraints. The numerical experiments of micro-grid show that considering the non-smooth constraints can effectively improve the accuracy of power flow calculation. In addition, the PLM method has better convergence dealing with non-smooth constraints even poor initial value settings. [ABSTRACT FROM AUTHOR]

Load modelling plays a key role in assessing peak load reduction and has attracted renewed interest recently due to increasing diversity and uncertainty in load characteristic resulted by emergence of new types of loads and more penetrations of distributed renewable generations onto electricity networks. This paper presents a methodology for the development of a static load model based load characteristic profile in medium voltage distribution networks from year-long field measurements. High-resolution load monitoring devices with the 1 s sampling rate installed at 60 primary substations in the U.K. distribution network are used to collect the data for the purpose of load modelling. Load models at these 60 substations comprising domestic, commercial/industrial, and mixed-type load demand are presented in the paper together with relevant model parameters. Field trials (which involve triggering transformer taps to initiate voltage changes) were performed throughout the year on 15 selected substations aimed at load profile validation. The developed load profiles take into account seasonal, weekly, and daily variations of P–V and Q–V characteristics. Representative 24 h (0.5 h) load matrices are developed for all 60 substations and provide an insight into the operational flexibility and network resilience to voltage variations. [ABSTRACT FROM AUTHOR]

This paper examines distribution systems that have a high integration level of distributed energy resources (DERs), and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies wherein the active and reactive power output of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximations of the ac power flow equations and is network-cognizant; that is, the coefficients of the controllers embed information on the location of the DERs and forecasted noncontrollable loads/injections and, consequently, on the effect of DERs power adjustments on the overall voltage profile. A robust approach is pursued to cope with uncertainty in the forecasted noncontrollable loads/power injections. The stability of the proposed local controllers is analytically assessed and numerically corroborated. [ABSTRACT FROM AUTHOR]

Following the vision of future Supergrids, the existing power systems are expected to evolve into AC/DC systems containing voltage source converters with multiterminal configurations. This paper presents a new sequential power flow algorithm for such power systems. The algorithm can be applied to systems with multiple AC and DC grids of any grid topology. Because of its pure AC/DC network decomposition, the simplification of elements within the converter stations is not required, as is the case with other proposals in the literature. The paper also addresses the convergence properties of the proposed algorithm. A convergence factor has been designed that allows controlling the exit criterion within each inner loop of the sequential AC/DC load flow problem. It is shown that by modulating the convergence factor, the number of inner loop iterations needed to achieve a solution can be diminished. [ABSTRACT FROM AUTHOR]

With the increasing use of voltage source converters (VSCs) in power electronics dominated power systems, oscillation phenomena in DC-link voltage control (DVC) timescale (around 10 Hz) among multiple VSCs have occurred. Several studies have tried to analyze these oscillation problems, but all associated with the single VSC situation. To consider the dynamic interactions between VSCs in DVC timescale, especially in the weak grid condition, this paper presents a small-signal model to understand VSC external characteristics based on motion equation concept also featured in synchronous generator (SG). Comparisons of time-domain simulation responses and eigenvalues show that the proposed model can hold the main behaviors of concern. The form of the model is very similar to the rotor motion equation in SG, with which power engineers have been very familiar. In addition, by establishing the relationship between the unbalanced powers and state variables of internal voltage (viz., VSC output voltage), the modeling idea introduced in this paper can be applied to other power electronic devices. [ABSTRACT FROM PUBLISHER]

This paper presents a distributed, robust, finite-time secondary control for both voltage and frequency restoration of an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). The distributed cooperative secondary control is fully distributed (i.e., uses only the information of neighboring DGs that can communicate with one another through a sparse communication network). In contrast to existing distributed methods that require a detailed model of the system (such as line impedances, loads, other DG units parameters, and even the microgrid configuration, which are practically unknown), the proposed protocols are synthesized by considering the unmodeled dynamics, unknown disturbances, and uncertainties in their models. The other novel idea in this paper is that the consensus-based distributed controllers restore the islanded microgrid's voltage magnitudes and frequency to their reference values for all DGs within finite time, irrespective of parametric uncertainties, unmodeled dynamics, and disturbances, while providing accurate real-power sharing. Moreover, the proposed method considers the coupling between the frequency and voltage of the islanded microgrid. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we verify the proposed control strategy's performance using the MATLAB/SimPowerSystems toolbox. [ABSTRACT FROM PUBLISHER]

This paper proposes an efficient dc voltage control scheme in rail transit traction power systems with reversible converters for dc voltage regulation and power sharing. The proposed dc voltage control scheme is executed in a hierarchical structure based on the optimal power flow. Unlike conversional constant dc voltage control applied in traction power systems, this scheme allows the reversible converters operating in both rectifier and inverter regions and considers regenerative braking power sharing among multiple traction substations. The steady-state equivalent models of traction power systems including reversible converters are established, and the ac/dc sequential power flow algorithm based on Newton–Raphson method is presented. Finally, a multi-trains dynamic operation simulation is carried out with Matlab. The simulation results prove the validity of proposed scheme and indicate that the system energy saving effect in traction power systems with reversible converters is obvious with proposed scheme. [ABSTRACT FROM AUTHOR]

Electrical power generation, transmission and distribution systems are often simulated through the single-phase equivalent model by assuming the presence of only the positive sequence in the real system. The well known power flow (pf) analysis is typically used to determine the steady state solution of these single-phase models. After the pf solution was determined, other elements, such as for example synchronous generators and controllers, are initialised. This provides the initial conditions to subsequent transient stability analyses. Nowadays, this simulation approach may be no longer feasible due to the large penetration of unbalanced and/or electronic elements in the power systems. In this paper we present a novel numerical method that allows to freely compute the steady state solution of complex power systems made up of a “mixing” of conventional single-phase models and more complex, detailed three-phase models, for example of some portions of the transmission system and of the distribution ones. This steady state solution can be viewed as a generalization and/or an extension of the conventional pf. [ABSTRACT FROM AUTHOR]

In this paper, we propose a distributed voltage control in power distribution networks through reactive power compensation. The proposed control can operate in a distributed fashion where each bus makes its decision based on local voltage measurements and communication with neighboring buses, always satisfy the reactive power capacity constraint, drive the voltage magnitude into an acceptable range, and minimize an operational cost. We also perform various numerical case studies to demonstrate the effectiveness and robustness of the controller using the nonlinear power flow model. [ABSTRACT FROM AUTHOR]

Constant power loads (CPLs) impose instability issues in DC microgrids due to their negative impedance characteristics. This paper studies the problem of voltage control design of DC microgrids with CPLs. It is assumed that the power of CPLs is uncertain and belongs to a given interval leading to an infinite number of equilibrium points of the system. We develop a polytope model for DC microgrids with uncertain CPLs. Using this model, a robust two-degree-of-freedom feedback-feedforward voltage control framework is then proposed. The voltage controller is obtained by a solution of a set of linear matrix inequalities. The voltage control design strategy for each distributed generation (DG) unit is scalable and independent of the other DGs. The effectiveness of the proposed control approach is evaluated through simulation studies in MATLAB/SimPowerSystems toolbox. [ABSTRACT FROM AUTHOR]

Assembly of power-flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit's behavior. Most power-flow formulations encapsulate network constraints in the bus admittance matrix, $Y_{\text{bus}}$. From a circuit perspective, this admittance representation restricts the network elements to be voltage controlled; resulting drawbacks treating zero-impedance branches in such applications as state estimation have long been recognized. This paper explores the advantages of the alternatives to $Y_{\text{bus}}$ -based formulations in power flow. It proposes a sparse tableau formulation (STF), and it demonstrates its computational efficiency, robustness, and generality in detailed comparison to traditional $Y_{\text{bus}}$ -based solution algorithms. In the examples of power networks ranging from 1888 to 82 000 buses, computational case studies indicate that STF provides comparable computational speed, while allowing simple treatment of zero-impedance branches and more reliably converging to solutions in many cases for which $Y_{\text{bus}}$ -based Newton algorithms diverge. [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]

Due to physical or control-related limitations, some dynamic state variables are constrained, such as the regulated voltage, the exciter reference voltage, etc. In addition, there exists a set of algebraic constraints that exactly confines the evolution of the system states. However, a systematic way to fully consider all inequality and equality constraints is lacking in the existing dynamic state estimation (DSE) literature. This paper proposes a general constrained robust DSE framework that is able to deal with various equality and inequality constraints. The project operator is integrated with the pseudo-measurements formulation in a unique manner to address the inequality and equality constraints, respectively, within the unscented Kalman filter (UKF) framework, which relies on the unscented transformation and is derivative-free. To this end, the derivative-free robust UKF is extended to address all the constraints while maintaining its robustness to measurement noise and bad data. Numerical results on the IEEE 39-bus system show that the proposed method exhibits the following benefits: first, improved accuracy of the state estimates in the presence of measurement noise; second, enhanced convergence speed and ability to address weakly observed dynamic state variables; and third, enhanced capability to deal with bad data and cyber attacks. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed control scheme to compensate for droop-induced frequency deviations in autonomous microgrids. In this scheme, no extra direct frequency control and proportional-integral compensation are employed to remove the frequency deviations; that is, the deviations are compensated instantaneously. To reduce the communication burden, the scheme is then equipped with a need-based (event-triggered) data exchange strategy. An event-triggering mechanism is introduced, which highly reduces the amount of communications in both transient and steady-state stages and ensures that the intervals between consecutive communication instants are positive (i.e., the system is Zeno-free). Stability and equilibrium analyses of the resultant system considering the whole system dynamics are provided, as well. Effectiveness of the proposed controller for different cases is verified by simulating a microgrid in MATLAB/SimPowerSystems software environment. [ABSTRACT FROM AUTHOR]

This paper presents a modeling approach for capturing closed-loop load behavior in distribution networks using bottom-up time-variant load models and incorporating load-flow feedback for thermal loads. Traditional load models are useful for providing insights into instantaneous changes in power, however, they do not capture the time-variant response to changes in voltage due to the effects of appliances with closed-control loops such as those which are thermostatically controlled. This paper proposes a modeling and co-simulation platform to simulate closed-loop load-modeling using state-of-the-art bottom-up load modeling techniques for the residential sector with a feedback model for time series steady-state load-flow. It incorporates time-variant load models and discrete state-space representation of thermostatically controlled appliances. The developed methodology is used in a conservation voltage reduction case study on an urban distribution network, allowing detailed assessment of the voltage response and analysis of changes in active and reactive power and network losses. [ABSTRACT FROM AUTHOR]

Voltage source converter (VSC)-based high-voltage direct current (HVDC) transmission systems have been employed widely in recent years. However, connecting a VSC-HVDC link to a very weak grid (a high-impedance grid) is challenging. A vector-controlled VSC is incapable of injecting/absorbing its maximum theoretical active power in such grids. A simple yet effective control system for a standard vector-controlled VSC in a very weak grid condition has not been reported in the literature. This paper, benefiting from a comprehensive small-signal model, presents a detailed analysis of the VSC dynamics and shows how the assumptions made for designing VSC regulators in strong grids are no longer valid in very weak grids. The paper then proposes and compares two straightforward solutions: retuning the control parameters and using an artificial bus for converter-grid synchronization. Both methods enable the VSC to operate at the maximum theoretical active power at a very weak grid condition (i.e., at unity short-circuit ratio) by minimal modification in the widely accepted vector control method. The advantages and disadvantages of each method are discussed. The analytical results are verified by detailed nonlinear time-domain simulation results. [ABSTRACT FROM AUTHOR]

This paper proposes a novel power flow formulation and solution algorithm for a generalized large-scale interconnected transmission system encompassing multi-frequency HVac and HVdc grids having arbitrary numbers of buses, topologies, and operating frequencies. Back-to-back and ac/dc voltage-source converters are employed to interconnect and control the voltage and power interchange between two power grids operating at different frequencies. The power Flow formulation is based on a steady-state model of back-to-back and ac/dc converters operated in centralized and distributed droop control strategies. Each power grid is represented by a set of nonlinear power balance equations. These equations are solved simultaneously using a unified power flow algorithm, taking into account generator and converter limits. It is shown that the solution convergence is achieved rapidly despite the system size, topology, and converter control strategies. The efficacy and accuracy of the proposed steady-state solution algorithm are demonstrated by comparing the numerical solution to the one obtained by time-domain electromagnetic models of multi-frequency HVac and HVdc transmission systems with fully controllable back-to-back and ac/dc converters. The results obtained by using the proposed algorithm and the time-domain simulation are practically identical. [ABSTRACT FROM AUTHOR]

This paper presents a new model of voltage source converter (VSC) based battery energy storage systems (BESSs) that interface with power grids. A VSC-based BESS is made up of a series connection of a VSC, its connecting transformer, and a BESS. The VSC allows a BESS to generate both active and reactive powers in all four quadrants. The proposed model captures the coupling between active power, reactive power, and the voltage of a BESS. In addition, the proposed model explicitly describes the relationship between the control configuration of pulsewidth modulation (PWM) VSC and the power output of the BESS. Therefore, the proposed model possesses unparalleled control capabilities in the operational parameters of both the ac and dc sides of the converter. By incorporating such a model into the active-reactive optimal power flow (A-R-OPF) formulation, we can not only optimize the active and reactive power output of the BESS in power systems, but also understand how the optimal powers are generated by setting the operational parameters of both the BESS and PWM-VSC. To solve the A-R-OPF problem with the proposed model, we propose a sequence of strong relaxations to transform the problem into a mixed-integer second-order cone programming problem. Such a formulation is amendable for efficient solutions using off-the-shelf solvers. Case studies on the IEEE benchmark systems show that more than 17.73% of power losses in transmission lines and more than 0.961% of interface losses can be reduced by using the proposed model in comparison to the traditional BESS model. [ABSTRACT FROM AUTHOR]

Conservation voltage reduction (CVR) uses Volt-VAR optimization (VVO) methods to reduce customer power demand by controlling feeder's voltage control devices. The objective of this paper is to present a VVO approach that controls system's legacy voltage control devices and coordinates their operation with smart inverter control. An optimal power flow (OPF) formulation is proposed by developing linear and nonlinear power flow approximations for a three-phase unbalanced electric power distribution system. A bi-level VVO approach is proposed, where Level 1 optimizes the control of legacy devices and smart inverters using a linear approximate three-phase power flow. In Level 2, the control parameters for smart inverters are adjusted to obtain an optimal and feasible solution by solving the approximate nonlinear OPF model. Level 1 is modeled as a mixed integer linear program (MILP) while Level 2 as a nonlinear program with linear objective and quadratic constraints. The proposed approach is validated using 13-bus and 123-bus three-phase IEEE test feeders and a 329-bus three-phase PNNL taxonomy feeder. The results demonstrate the applicability of the framework in achieving the CVR objective. It is demonstrated that the proposed coordinated control approach help us to reduce the feeder's power demand by reducing the bus voltages; the proposed approach maintains an average feeder voltage of 0.96 p.u. A higher energy saving is reported during the minimum load conditions. The results and approximation steps are thoroughly validated using OpenDSS. [ABSTRACT FROM AUTHOR]

The ever-increasing utilization of sensitive loads in the industrial, commercial, and residential areas in distribution networks requires enhanced reliability and quality of supply. This can be achieved, thanks to self-healing features of smart grids that already include the control technologies necessary for the restoration strategy in case of a fault. In this paper, an analytical and global optimization model is proposed for the restoration problem. A novel mathematical formulation is presented for the reconfiguration problem reducing the number of required binary variables while covering more practical scenarios compared to the existing models. The considered self-healing actions besides the network reconfiguration are the nodal load-rejection, the tap setting modification of voltage regulation devices (incl. OLTCs, SVR, and CBs), and the active/reactive power dispatch of DGs. The voltage dependency of loads is also considered. Thus, the proposed optimization problem determines the most efficient restoration plan minimizing the number of de-energized nodes with the minimum number of self-healing actions. The problem is formulated as a Mixed-Integer Second Order Cone Programming (MISOCP) and solved using the Gurobi solver via the MATLAB interface YALMIP. A real 83–node distribution network is used to test and verify the presented methodology. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralized control based on static var compensator (SVC) devices to improve the frequency control of high voltage transmission systems. For a realistic structure preserving power system with voltage dependent loads, we propose a sufficient condition based on a strict Lyapunov energy function, which is utilized to design a nonlinear adaptive SVC controller. This controller only requires local bus measures and parameters. Furthermore, we also present an SVC with a conventional frequency droop controller. The performance of the two considered SVC control systems are evaluated on the well known IEEE New England 39-bus 10-machine power system and compared with conventional SVC controllers. [ABSTRACT FROM AUTHOR]

This paper presents a novel and comprehensive method of analyzing transformer taps and phases in power flow (PF) studies. The method is based on constructing a criterion function, which encapsulates physical constraints for the analyzed taps and phases. The root of the criterion function corresponds to the correct solution. To find the root, the Newton method is used. The criterion function is external to the PF routine, and so, the root-finding (and with it, the tap and phase analysis) is done without altering the underlying PF routine. The method is developed for quadrature-boosting-transformers, as well as for regular phase shifting and tap changing transformers. A possibility of accounting for changing impedance is developed and incorporated in the procedure, using real-world phase-impedance relation data of a phase shifting transformer. Generalizing control modes to different types of variables and to non-local variables is illustrated. The method is tested on large benchmark systems: the IEEE118, IEEE300, and Pegase13 659 bus system. Tests show that (since the method is Newtonian) the convergence is normally achieved within 10 iterations. [ABSTRACT FROM AUTHOR]

To solve the coordinated dispatch and time-space coupling problem in the distribution network with distributed generations (DGs), a novel two-stage (Heuristic search and Variable correction) dynamic reactive power dispatch strategy is proposed in this paper. Meanwhile, according to the analysis of Gauss-type and Z-type membership function, a new objective function is put forward to achieve the balance between network loss and voltage deviation. First, the pre-optimization is made in Niche genetic algorithm to coordinate on-load tap changer (OLTC), capacitor banks (CBs), and DGs. Second, the sequential fuzzy c-means (SFCM) based on artificial bee colony (ABC) algorithm is proposed and then the Heuristic search based on this method is used to formulate the day-ahead plans of OLTC and CBs. Finally, the dispatch plans of OLTC and CBs are applied to recalibrate the day-ahead dispatch plans of DGs. Comparing with existing schemes, strategies and optimization approaches based on diverse evaluation indicators, optimization results on IEEE 33-bus, IEEE 14-bus, and PG&E 69-bus test systems verify the practicality and efficiency of the proposed method. In addition, the effects on the optimization results with different adjustment step and action time of the discrete adjust devices are discussed by the IEEE 33-bus test system. [ABSTRACT FROM AUTHOR]

During the last decades, significant advances have been made in the area of power system stability and control. Nevertheless, when this analysis is carried out by means of decentralized conditions in a general network, it has been based on conservative assumptions such as the adoption of lossless networks. In this paper, we present a novel approach for decentralized stability analysis and control of power grids through the transformation of both the network and the bus dynamics into the system reference frame. In particular, the aforementioned transformation allows us to formulate the network model as an input–output system that is shown to be passive even if the network's lossy nature is taken into account. We then introduce a broad class of bus dynamics that are viewed as multivariable input/output systems compatible with the network formulation, and appropriate passivity conditions are imposed on those that guarantee stability of the power network. We discuss the opportunities and advantages offered by this approach while explaining how this allows the inclusion of advanced models for both generation and power flows. Our analysis is verified through applications to the two area Kundur and the IEEE 68-bus test systems with both primary frequency and voltage regulation mechanisms included. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed optimal frequency control of power systems considering a network-preserving model with nonlinear power flows and excitation voltage dynamics. Salient features of the proposed distributed control strategy are fourfold, first, nonlinearity is considered to cope with large disturbances, second, only a part of generators are controllable, third, no load measurement is required, fourth, communication connectivity is required only for the controllable generators. To this end, benefiting from the concept of “virtual load demand,” we first design the distributed controller for the controllable generators by leveraging the primal-dual decomposition technique. We then propose a method to estimate the virtual load demand of each controllable generator based on local frequencies. We derive incremental passivity conditions for the uncontrollable generators. Finally, we prove that the closed-loop system is asymptotically stable and its equilibrium attains the optimal solution to the associated economic dispatch problem. Simulations, including small and large-disturbance scenarios, are carried on the New England system, demonstrating the effectiveness of our design. [ABSTRACT FROM AUTHOR]

A new model of a grid-connected photovoltaic (PV) plant suitable for power flow analysis is proposed in this paper. Unlike existing models, the proposal departs from the equivalent generator representation of the PV plant and is based instead on the operation and control modes of PV panels and voltage source converters. The resulting set of nonlinear equations is assembled together with the network's equations to formulate a generalized power flow problem in a unified frame of reference, which is efficiently solved by using the Newton–Raphson algorithm. The complementarity condition approach is adopted for directly including all operation and control mode constraints of the PV plant in the power flow formulation, which permits the simultaneous and automatic handling of limits of all state variables associated with these constraints during the iterative solution process. The effectiveness of the proposed method is fully demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

The power flow is a nonlinear problem that requires a Newton's method to be solved in dc microgrids with constant power terminals. This paper presents sufficient conditions for the quadratic convergence of the Newton's method in this type of grids. The classic Newton's method as well as an approximated Newton's method are analyzed in both master–slave and island operation with droop controls. Requirements for the convergence as well as for the existence and uniqueness of the solution starting from voltages close to 1 pu are presented. Computational results complement this theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive set of steady-state models to be included in power flow simulation studies of dc railway networks. This simulation framework covers all important aspects and features of each element of modern dc railways. The proposed models are simplified to achieve the maximum simulation speed while keeping the required accuracy. Not only nonreversible, controlled, and uncontrolled reversible substations are considered, but also onboard and offboard accumulation systems. The train model can consider the low network receptivity (overvoltage protection for trains equipped with regenerative braking) and overcurrent protection. It is also possible to include in the simulation dc/dc links between nodes of the railway network at the same or different voltage. To date, there is no other work able to conjugate all the mentioned models in a complex multitrain scenario. [ABSTRACT FROM AUTHOR]

This paper presents an improved corrective security constrained optimal power flow (CSCOPF) for a meshed AC/DC power transmission network with voltage source converter based multi-terminal HVDC (VSC-MTDC) grids. The security constrains of N-1 contingencies for both AC and DC networks are fully considered in the CSCOPF problem. The corrective actions employed in this paper include not only the traditional long-term rescheduling control actions of the AC system, but also the short term post-contingency fast corrective control of multi-terminal VSC-HVDC. A hybrid method is developed to solve the improved CSCOPF problem and the effectiveness of the proposed method is evaluated and demonstrated in this paper by two example meshed AC/DC power systems. [ABSTRACT FROM AUTHOR]

The islanded scenarios of voltage source converter (VSC) high-voltage DC (HVDC) directly supplying power to islanded loads or connecting to wind farm are becoming popular, in which some new issues are required to be further addressed. While several control strategies have been studied, to the authors’ best knowledge, few have investigated the potential capability of VSC HVDC using the typical phase-locked loop (PLL)-synchronized vector control (PLLSynVC) to address islanded operation issues. To explore the potential capability of the typical PLLSynVC in islanded system, this paper proposes a frequency regulation scheme (FRS), including inertia and primary frequency control, for the PLL-synchronized VSC HVDC based on the motion equation concept. By adding the FRS, the VSC HVDC using the PLLSynVC, similar to a synchronous generator from the view of the phase motion equation, not only can self-maintain the frequency stable in an islanded system, but also naturally avoids the transition of control operation modes without changing the basic control structure. Furthermore, based on the developed phase motion equation, the inertia characteristics of VSC HVDC with the FRS is studied, which synthetically considers the impact of different controllers and PLL, and makes VSC HVDC's manifested inertia clear. The effectiveness of FRS and inertia analysis results is verified by time-domain simulations. [ABSTRACT FROM AUTHOR]

Doubly fed induction generator (DFIG)-based wind turbines (WTs) occupy a high penetration in power systems and are being required to emulate inertia response as synchronous generators (SGs). Therefore, it is of value to study the impact of inertia control of DFIG-based WT on electromechanical oscillation damping (EOD) of SG. However, relevant studies that are mainly based on eigenvalue analysis method are not enough and general mechanism study is still lacking. This paper studies the impact rules and mechanism of inertia control parameters (proportional constant and time constant) of WT on EOD of SG with a novel approach. First, linearized model of WT under inertia control is derived based on motion equation concept, which can explicitly describe the external characteristic of WT. From the model, it is clear that the proportional constant determines the inertia characteristic of WT, while time constant has decisive effect on the damping characteristic. Then, by interaction analysis based on motion equation models of both SG and WT, the impact rules and mechanism of inertia control parameters on EOD of SG are explained clearly. Besides, since variable inertia control parameters mean variable inertia and damping coefficients of WT, the impact mechanism can be understood from a general perspective. [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]

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we adopt a chance-constrained AC optimal power flow formulation, which guarantees that generation, power flows, and voltages remain within their bounds with a predefined probability. We then discuss different chance-constraint reformulations and solution approaches for the problem. We first describe an analytical reformulation based on partial linearization, which enables us to obtain a tractable representation of the optimization problem. We then provide an efficient algorithm based on an iterative solution scheme which alternates between solving a deterministic AC optimal power flow problem and assessing the impact of uncertainty. The flexibility of the iterative scheme enables not only scalable implementations, but also alternative chance-constraint reformulations. In particular, we suggest two sample-based reformulations that do not require any approximation or relaxation of the AC power flow equations. In a case study based on four different IEEE systems, we assess the performance of the method, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in- and out-of-sample tests, and that the analytical reformulations outperforms the two alternative, sample-based chance constraint reformulations. [ABSTRACT FROM PUBLISHER]

This paper develops a real-time algorithmic framework for aggregations of distributed energy resources (DERs) in distribution networks to provide regulation services in response to transmission-level requests. Leveraging online primal-dual-type methods for time-varying optimization problems and suitable linearizations of the nonlinear AC power-flow equations, this work establishes a system-theoretic foundation to realize the vision of distribution-level virtual power plants. The optimization framework controls the output powers of dispatchable DERs such that, in aggregate, they respond to automatic generation control and/or regulation-services commands. This is achieved while concurrently regulating voltages within the feeder and maximizing customers’ and utility's performance objectives. Convergence and tracking capabilities are analytically established under suitable modeling assumptions. Simulations are provided to validate the proposed approach. [ABSTRACT FROM AUTHOR]

With the increasing importance of battery energy storage systems (BESS) in microgrids, accurate modeling plays a key role in understanding their behavior. This paper investigates and compares the performance of BESS models with different depths of detail. Specifically, several models are examined: an average model represented by voltage sources; an ideal dc source behind a voltage source converter; a back-to-back buck/boost and bidirectional three-phase converter, with all models sharing the same control system and parameters; and two additional proposed models where the switches are replaced by dependent sources to help analyze the differences observed in the performance of the models. All these models are developed in PSCAD and their performances are simulated and compared considering various issues such as voltage and frequency stability and total harmonic distortion in a benchmark test microgrid. It is shown through simulation results and eigenvalue studies that the proposed models can exhibit a different performance, especially when the system is heavily loaded, highlighting the need for more accurate modeling under certain microgrid conditions. [ABSTRACT FROM AUTHOR]