—Power system model parameter values are becoming increasingly uncertain and time-varying. Therefore, it is important to determine the margin in parameter space between a given set of parameter values for which the system will recover from a particular fault, and the nearest parameter values for which it will not recover from that fault. This work presents an efficient method for computing parameter space recovery margins by exploiting the property that the trajectory becomes infinitely sensitive to small changes in parameter value along the operating point’s region of attraction boundary. Consequently, along this boundary the inverse sensitivity of the trajectory approaches zero. The method proceeds by varying parameter values so as to minimize the inverse sensitivity of the system trajectory. Recent results provide theoretical justification for the approach. The efficacy of the method is demonstrated using a modified IEEE 39-bus New England power system test case.
While coordinated control of a large population of electric loads can provide important services to the electric grid, situations have been observed where control of load ensembles may lead to highly nonlinear behavior such as synchronization, sustained oscillations and bifurcations. Synchronization of thermostatically controlled loads (TCLs) is undesirable since it can lead to increased short-cycling, sudden changes in power demand and network voltage issues. In this paper, we investigate the synchronizing tendency of TCLs under control strategies where updates are broadcast periodically for coordinating TCLs. We study the problem using a hybrid dynamical systems framework to model both the continuous and discrete dynamics of load ensembles. Analysis of eigenmodes of the underlying discrete-time system provide insights into synchronizing tendencies and rate of convergence to the synchronized state. Simulations are provided to illustrate the theory.
This paper investigates the interaction between frequency containment services (FCS) and power oscillation damping (POD) ancillary services installed in a Voltage Source Converter High Voltage DC (VSC-HVDC) line. In VSC-HVDC systems, ancillary services can be installed to maintain appropriate levels of power system stability. Both FCS and POD controllers are typically installed in the active power control loop separately. The modulation signals generated by these two ancillary services both affect the active power injected by the converter. When operating a VSC with FCS and POD ancillary services the resultant combination of the modulation signals in the active power loop may result in reduced performance. The results in this study show that performance of controllers reduces when both ancillary services are activated, particularly in low-inertia systems. Modifications to the control structures of both controllers that improve their performance under various disturbances are proposed.
This paper deals with a centralized tuning of the local controllers parameters in a distribution grid with many Distributed Generators. The optimal controllers settings are obtained by minimizing the confidence level of voltage specification violations. The confidence level optimization problem uses Gaussian uncertainties of short-term forecasting and OLTC errors along with an accurate linear power flow approximation. Considering these assumptions, the optimization problem is shown to be convex and the characteristics of uncertainties are reduced to their means and standard deviations. The proposed method optimizes the full network while keeping the droop-like industrial structure of the controllers and allows to consider feeders which can have low and high voltages. The merits of the method are illustrated via a modified real distribution network showing a decrease of voltage variances and violations.
This paper focuses on online control policies applied to power systems management. In this study, the power system problem is formulated as a stochastic decision process with large constrained action space, high stochasticity and dozens of state variables. Direct Model Predictive Control has previously been proposed to encompass a large class of stochastic decision making problems. It is a hybrid model which merges the properties of two different dynamic optimization methods, Model Predictive Control and Stochastic Dual Dynamic Programming. In this paper, we prove that Direct Model Predictive Control reaches an optimal policy for a wider class of decision processes than those solved by Model Predictive Control (suboptimal by nature), Stochastic Dynamic Programming (which needs a moderate size of state space) or Stochastic Dual Dynamic Programming (which requires convexity of Bellman values and a moderate complexity of the random value state). The algorithm is tested on a multiple-battery management problem and two hydroelectric problems. Direct Model Predictive Control clearly outperforms Model Predictive Control on the tested problems.
This paper presents a practical search algorithm using detailed dynamic simulations to identify plausible harmful N-k contingency sequences. Starting from an initial list of contingencies, progressively more severe contingency sequences are investigated. For that purpose, components, which violated conservative protection limits during a N-k contingency simulation are identified and considered as candidate k+1-th contingencies, since these could be tripped due to a hidden failure. This approach takes into account cascading events, such as over-or under-speed generator tripping, which are considered to be part of the system response. The implementation of the proposed algorithm into a parallel computing environment and its performance are demonstrated on the IEEE Nordic test system.
Transient stability is an important issue in power systems but difficult to quantify analytically. Most of the approaches use a simplified model of the generators, that often reduces to the swing equation. In this work, a more detailed model which includes voltage dynamics and both voltage and frequency regulators is considered to get more realistic results. The proposed analysis framework uses an algebraic reformulation technique that recasts the system's dynamics into a set of polynomial differential algebraic equations in conjunction with a sum of squares method to search for a Lyapunov function and to estimate the region of attraction of the stable operating point. The results are checked against a numerical evaluation of the region of attraction.
Load flow analysis in radial distribution feeders requires probabilistic approaches to cater for random variables such as stochastic load demand and variable renewable generation. Adequate accuracy compared with test solutions and high computational efficiency are vital in the candidate methods. Based on the Herman Beta algorithm initially formulated only for low voltage feeders, a new probabilistic transform suitable for low and medium voltage systems has been developed. The network model simplifications of unity power factor loads and resistive feeders, which were only adequate for LV systems, have been removed. Comparisons with Monte Carlo simulation, including on an IEEE test network, validate the proposed transform for 3-phase 4-wire systems with loads and generation modelled as currents or power.
Regarding hybrid AC-HVDC-systems, an insufficient parameterization of DC voltage control can cause a violation of operational security limits in case of VSC outages. This paper outlines an approach to provide N-1 security for AC-HVDC-systems in these cases. Therefore, the parameters of the VSCs' individual DC voltage control function, which bases on a continuous voltage control characteristic, are optimized preventively considering possible VSC outages. The numerical case study shows that the proposed approach is feasible to provide N-1 security for AC-HVDC-systems in case of VSC outages.
In traditional power systems, the large mechanical inertia of the synchronous generators maintains the system frequency close to 60 Hz. Traditional transient stability programs solve the electrical network at 60 Hz and also use this frequency to convert between power and torque. Currently, however, with the large proliferation of alternative energy sources, larger frequency deviations are often encountered. This paper applies the Shifted Frequency Analysis (SFA) method to transient stability studies. SFA is based on an EMTP discretization of time-varying phasors, which results in the correct electrical frequency for the network admittances. Also, the correct machine velocity is used for the electromechanical equations. Test cases are presented using a classical 3-Bus system and the larger IEEE 39-Bus test system. The results with SFA are very close to the detailed EMTP solution compared to the traditional solution, while using integration steps similar to those of traditional transient stability software.
Primary Control Reserve (PCR), also called Frequency Containment Reserve, is a key component of the safe and stable operation of the electrical power system. The foreseen decrease of synchronous generators, main PCR provider, coupled to the increase of domestic batteries at a household level offer new opportunities. In this frame, this paper investigates the techno-economic feasibility of providing PCR with a coupled storage system: domestic battery and power-to-heat storage (P2HS), typically a resistance in a water tank providing domestic hot water. The presented solution overcomes the main drawbacks for batteries PCR participation: the battery deterioration due to the PCR provision and the decrease of usable energy to ensure the PCR provision, at the expense of other objectives such as self-consumption. Using time simulations performed with historical frequency, representative PV production and thermal demand data over one year, this paper demonstrates the positive coupling effect of battery and power-to-heat storage from a technical and economical point of view.
The soil characterization of an underground cables installation may be poorly known and present a wide variation throughout the year. This represents a challenge when it comes to an accurate evaluation of transient overvoltages/currents and the correct assessment of voltage and current profiles throughout the circuit. This paper presents a discussion based on a sensitivity analysis for the ground return impedance of underground cables systems to soil resistivity, which is typically considered as a deterministic parameter. For the evaluation of the impact of uncertainties we have considered the analysis of the most common configuration in cable systems. A frequency domain analysis was carried out to assess the actual impact of the uncertainties in terminal voltage and currents. Results indicate that the usage of sensitivity might provide a helpful insight in the impact on the overall system performance with respect to soil resistivity uncertainties.
In recent years, microgrids, i.e., disconnected distribution systems, have received increasing interest from power system utilities to support the economic and resiliency posture of their systems. The economics of long distance transmission lines prevent many remote communities from connecting to bulk transmission systems and these communities rely on off-grid microgrid technology. Furthermore, communities that are connected to the bulk transmission system are investigating microgrid technologies that will support their ability to disconnect and operate independently during extreme events. In each of these cases, it is important to develop methodologies that support the capability to design and operate microgrids in the absence of transmission over long periods of time. Unfortunately, such planning problems tend to be computationally difficult to solve and those that are straightforward to solve often lack the modeling fidelity that inspires confidence in the results. To address these issues, we first develop a high fidelity model for design and operations of a microgrid that include component efficiencies, component operating limits, battery modeling, unit commitment, capacity expansion, and power flow physics; the resulting model is a mixed-integer quadratically-constrained quadratic program (MIQCQP). We then develop an iterative algorithm, referred to as the Model Predictive Control (MPC) algorithm, that allows us to solve the resulting MIQCQP. We show, through extensive computational experiments, that the MPC-based method can scale to problems that have a very long planning horizon and provide high quality solutions that lie within 5 % of optimal.
By using the electromagnetic time reversal (EMTR) theory, the paper studies its properties in order to derive a new fault location method to be used in power networks. It is shown that, in the reversed-time stage, the current signal observed at the true fault location can be clearly distinguished since it appears as a time-delayed copy of the back-injected fault-originated transient signal. Then, based on this similarity property, a fault location method is derived. Finally, the method is numerically validated with reference to a reproducible simulated power network composed of an inhomogeneous multi-conductor transmission-line system.
Since the alternating current optimal power flow (ACOPF) problem was introduced in 1962, developing efficient solution algorithms for the problem has been an active field of research. In recent years, there has been increasing interest in convex relaxations-based solution approaches that are often tight in practice. Based on these approaches, we develop tight piecewise convex relaxations with convex-hull representations, an adaptive, multivariate partitioning algorithm with bound tightening that progressively improves these relaxations and, given sufficient time, converges to the globally optimal solution. We illustrate the strengths of our algorithm using benchmark ACOPF test cases from the literature. Computational results show that our novel algorithm reduces the best-known optimality gaps for some hard ACOPF cases.
This paper presents a new method for a detailed modeling of specific fault ride through (FRT) strategies according to the current grid code requirements for renewable energy sources (RES) connected to the low, medium and high voltage level based on an aggregated distribution grid model. By considering the aggregated distribution grid model, the impact of the distribution grid structures is analyzed. It is shown, that the current grid code requirements for the low voltage level cause high active power deficits resulting in high frequency gradients. In addition, progressive voltage sags can be observed, if the droop characteristic is set to k=2 value. Suitable countermeasures are implemented and the impact on power system stability is evaluated. A combination of an increased droop constant and a fast resynchronization of inverter based generation units connected to the LV level is identified as the most effective countermeasure.
Africa has recently engaged in implementing an aggressive renewable energy integration plan. A major challenge in the deployment of renewable power is the management of excess energy. The use of battery storage has been considered as a technically attractive solution. This paper tackles this operational problem using stochastic dual dynamical programming. We present an open-source MATLAB toolbox for multistage stochastic programming which employs stochastic dual dynamic programming. We use the toolbox in order to compare the stochastic solution to a greedy policy which operates batteries without future foresight as a benchmark. We consider a case study of storage management in Burkina Faso. We quantify the benefits of the stochastic solution and test the sensitivity of our results to the optimization horizon of the stochastic program.
In this paper, a novel approach for parameter estimation of static load models based on co-simulation of transmission and distribution dynamic simulators is presented. The advantage of a co-simulation based approach is that the aggregated response of the underlying three-phase unbalanced distribution system can be simulated. In this approach, the combined transmission and distribution dynamics is simulated with information exchanged at the distribution substation buses at each time step. The aggregated response (voltages, active and reactive powers) at the distribution substation bus is then fitted through a constrained linear least squares optimization to obtain the parameters of an equivalent load model. The validity of the proposed load modeling approach is demonstrated to estimate the parameters of a ZIP load model, with results being invariant to, perturbations with different magnitude and location, for multiple operating points, and under single and multiple instances of distribution feeder interfaced to transmission simulator. Furthermore, comparative studies between co-simulation approach and transmission only simulation with equivalenced loads modeled using parameters obtained through proposed approach is provided to illustrate the capability of the presented method in capturing load characteristics of distribution grid.
With growing penetrations of stochastic renewable generation and the need to accurately model the network physics, optimization problems that explicitly consider uncertainty and the AC power flow equations are becoming increasingly important to the operation of electric power systems. This paper describes initial steps towards an AC Optimal Power Flow (AC OPF) algorithm which yields an operating point that is guaranteed to be robust to all realizations of stochastic generation within a specified uncertainty set. Ensuring robust feasibility requires overcoming two challenges: 1) ensuring solvability of the power flow equations for all uncertainty realizations and 2) guaranteeing feasibility of the engineering constraints for all uncertainty realizations. This paper primarily focuses on the latter challenge. Specifically, the robust AC OPF problem is posed as a bi-level program that maximizes (or minimizes) the constraint values over the uncertainty set, where a convex relaxation of the AC power flow constraints is used to ensure conservativeness. The resulting optimization program is solved using an alternating solution algorithm. The algorithm is illustrated via detailed analyses of two small test cases.
Power Park Modules (PPM), such as wind and photovoltaic plants, bring new modelling challenges and they are usually aggregated into equivalent or generic models for stability analysis. However, most of the existing approaches to build these models are suited only for the transient stability and, generally, for a specific kind of PPM like wind farms. Moreover, some of them might not be always appropriate in the case of large-scale systems since they require significant computational effort. In this paper, a new methodology is proposed to construct generic models for PPM based on transfer matrices. It is suited for both transient and small-signal stability analysis, independently on the kind of the PPM and its technology. It has also low computational requirements. Its validation is done in Matlab and Eurostag software's by considering a realistic power system of 23 generators to which a wind farm is connected.
