Synchrophasor data provide unprecedented opportunities for inferring power system dynamics, such as estimating voltage angles, frequencies, and accelerations along with power injection at all buses. ...Aligned to this goal, this work puts forth a novel framework for learning dynamics after small-signal disturbances by leveraging Gaussian processes (GPs). We extend results on learning of a linear time-invariant system using GPs to the multi-input multi-output setup. This is accomplished by decomposing power system dynamics into a set of single-input single-output linear systems with narrow frequency pass bands. The proposed learning technique captures time derivatives in continuous time, accommodates data streams sampled at different rates, and can cope with missing data and heterogeneous levels of accuracy. While Kalman filter-based approaches require knowing all system inputs, the proposed framework handles readings of system inputs, outputs, their derivatives, and combinations thereof collected from an arbitrary subset of buses. Relying on minimal system information, it further provides uncertainty quantification in addition to point estimates of system dynamics. Numerical tests verify that this technique can infer dynamics at non-metered buses, impute and predict synchrophasors, and locate faults under linear and non-linear system models under ambient and fault disturbances.
Uncalibrated instrument transformers present at the inputs of phasor measurement units (PMUs) can significantly degrade their outputs. This also causes problems in downstream applications that use ...PMU data. This paper presents a method for calibrating voltage transformers online using synchrophasor measurements. The proposed approach aims to find the optimal locations where good quality measurements must be added in order to bring the calibration error of all the measurements below a predefined threshold. The IEEE 118-bus system, the IEEE 300-bus system, and a 2383-bus Polish system have been used as the test systems for this analysis. The advantage of the proposed approach is its effectiveness and robustness.
Recent expansion of inverter-based renewable generation (RG) has introduced unprecedented stability issues. One major challenge stems from tripping RGs offline during disturbances based on predefined ...operation thresholds (ride through curves) on voltage magnitudes and frequency at the point of common coupling (PCC). The current practice uses a single set of thresholds for the whole year across all RGs in the system. This could result in loss of these resources during critical times, particularly endangering system voltage security, i.e a significant reduction in the load margin (LM). On the other hand, relaxing these limits could result in them staying online even during islanding scenarios, which is a safety concern to the restoration crew. Thus, an approach to find minimal relaxations to these limits to enhance voltage security is proposed here. This process first constructs an optimization model aiming to minimize adjustments on RG voltage limits to reach anticipated LM increase and then solves it with a multi-stage screening method including base power-voltage (P-V) curve acquisition, critical RGs identification, successive screenings of candidate solutions based on sensitivities, and optimal solutions validation. This largely increases the scalability of the algorithm, which is demonstrated on the IEEE 14-bus, 118-bus systems, and a 500-bus system.
Utilities across the world are seeing increased penetration of inverter-based renewable generation (RG) in their systems. These RGs have ride through curves programmed in them which define operating ...conditions that need to be satisfied during electrical disturbances. If they are violated, the RGs are tripped offline. In systems with large amounts of RGs tightly coupled electrically, there can be disturbances that cause sudden loss of a large number of RGs, which will then considerably exacerbate the stability of the system. Such a phenomenon is not captured by the existing direct methods for TSA. In this paper, by treating RG-rich systems as non-linear switched systems as opposed to the traditional approach of treating this tripping phenomenon as an instability, an approach utilizing multiple low voltage ride through constrained stability regions (CSRs) is proposed for capturing unstable fault clearing times. The CSRs are estimated through Lyapunov functions found using sum of squares programming. The effectiveness of the proposed technique is demonstrated using a three-machine system.
In this paper, a strategy for online detecting and warning of wide area power system islanding disturbances using real time PMU data is introduced and tested. The proposed method is composed of an ...intelligent decision tree algorithm for islanding detection and identification with the aid of an islanding database made of islanding simulations, real world islanding records, and system geographical/topology information. The practical utilization adopting this method in the Dominion Virginia Power system and the functional module design are also introduced.
This article presents a novel data recovery framework for missing synchrophasor measurements. The imputation accuracy for the existing data recovery methods is significantly reduced when there are ...consecutive data losses across multiple data streams. Besides, the recovered data do not necessarily meet the physical constraints of the power grid. To tackle these issues, a regularized low rank tensor completion (LRTC) method is proposed to incorporate the domain knowledge (e.g., Kirchhoff's voltage and current laws, and three phase circuit relationships) as the regularization terms in order to efficiently exploit the data inter-dependencies for a better recovery. We leverage the tensor decomposition and completion as powerful tools to extract the latent structures of phasor measurement unit (PMU) data for the recovery process. Specifically, we first construct the tensor model of the PMU data and then formulate the LRTC problem as a rank minimization by leveraging the low rank property of the PMU measurements and adding the regularization terms into the LRTC problem in order to improve the imputation accuracy. An efficient algorithm based on alternating direction method of multipliers (ADMM) is developed to solve the regularized LRTC problem. The experiments using the real PMU dataset show that the proposed approach exhibits better imputation accuracy, compared with the conventional matrix completion methods.
Modern Smart Grids incorporate physical power grids and cyber systems, creating a cyber-physical system. phasor measurement units (PMUs) transmit time synchronized measurement data from physical grid ...to the cyber system. The System Operator (SO) in the cyber layer analyzes the data in both online and offline format and ensures the reliability and security of the grid by sending necessary command back to the PMUs. However, various physical events such as line to ground faults, frequency events, transformer events as well as cyberattacks can cause deviation in measurements received by the SO, which can be termed as "bad data". These bad data in turn can cause the SO to take a wrong restorative/ mitigating strategy. Therefore accurate detection of bad data and identification of correct bad data type is necessary to ensure grid's safety and optimal performance. In this work we proposed a realtime sequential bad data detection and bad data classification strategy. At first, we have exploited the low rank property of Hankel-matrix to detect the occurrence of bad data in realtime. Secondly, we classify the bad data into two categories: physical events and cyberattacks. The algorithm utilizes the difference in low rank approximation error of multi-channel Hankel-matrix before and after random column permutations during physical events. If the cause of bad data is identified as cyberattack, our proposed algorithm proceeds to identify the cause of cyberattack. We have considered two possible cyberattack types: false data injection attack (FDIA) and GPS-spoofing attack (GSA). The proposed algorithm observes rank-1 approximation error of single-channel Hankel matrix containing unwrapped phase angle data to distinguish FDIA from GSA. Finally, the proposed algorithm is implemented in a realtime cyber-physical testbed containing PMU simulator and openECA. Results from the testbed using IEEE 13 node test feeder show that by choosing optimum parameters of Hankel-matrix, the bad data can be detected as well as the type of bad data can be correctly identified within less than 1 sec. of the occurrence of physical event or cyberattack. The bad data detection shows 100% accuracy for Hankel-matrix data-window greater than 140. Bad data can be classified as either cyberattack or physical event with perfect accuracy for data-window length greater than 73 for the threshold 0.1. A data-window length between 80 to 120 can distinguish GSA from FDIA, while GSA is implemented with varying phase angle shift of 0.1° to 0.5°. The realtime sequential model is also verified with IEEE 118 bus system simulated with SIEMENS PSS/E. Due to more complicated grid structure, IEEE 118 system requires more computational time to identify the bad data type, however that is still less than 2 sec, and can perform detection and classification with data-window length as small as 40.
Phasor measurement units (PMUs) play an important role in the wide-area monitoring and protection of modern power systems. Historically, their deployment was limited by the prohibitive cost of the ...device itself. Therefore, the objective of the conventional optimal PMU placement problem was to find minimum number of devices, which when carefully placed throughout the network, maximised observability subject to different constraints. Due to improvements in relay technology, digital relays can now serve as both relays and PMUs. Under such circumstances, the substation installations consume the largest portion of the deployment cost, and not the devices themselves. Thus, for minimising cost of synchrophasor deployment, number of substation installations must be minimised. This study uses binary particle swarm optimisation to minimise number of substations in which installations must be performed for making all voltage levels observable, while being subject to various practical constraints. Standard IEEE systems have been used to explain the technique. Finally, a large-scale network of Dominion Virginia Power is used as the test bed for implementation.
With the growth of renewable generation (RG) and the development of associated ride through curves serving as operating limits, during disturbances, on violation of these limits, the power system is ...at risk of losing large amounts of generation. In order to identify preventive control measures that avoid such scenarios from manifesting, the power system must be modeled as a constrained dynamical system. For such systems, the interplay of feasibility region (man-made limits) and stability region (natural dynamical system response) results in a positively invariant region in state space known as the constrained stability region (CSR). After the occurrence of a disturbance, as it is desirable for the system trajectory to lie within the CSR, critical clearing time (CCT) must be defined with respect to the CSR instead of the stability region as is done traditionally. The sensitivity of CCT to system parameters of constrained systems then becomes beneficial for planning/revising protection settings (which impact feasible region) and/or operation (which impact dynamics). In this paper, we derive the first order CCT sensitivity of generic constrained power systems using the efficient power system trajectory sensitivity computation, pioneered by Hiskens and Pai in "Trajectory sensitivity analysis of hybrid systems," IEEE Trans. Circuits Syst. Fundam. Theory Appl., vol. 47, no. 2, pp. 204-220, Feb. 2000. The results are illustrated for a single-machine infinite-bus (SMIB) system as well as a multi-machine system in order to gain meaningful insight into the dependence between ability to meet constraints, system stability, and changes occurring in power system parameters, such as, mechanical power input and inertia.
This article proposes a method for identifying potential self-adequate sub-networks in the existing power distribution grid. These sub-networks can be equipped with control and protection schemes to ...form microgrids capable of sustaining local loads during power systems contingencies, thereby mitigating disasters. Towards identifying the best microgrid candidates, this work formulates a chance-constrained optimal distribution network partitioning (ODNP) problem addressing uncertainties in load and distributed energy resources; and presents a solution methodology using the sample average approximation (SAA) technique. Practical constraints like ensuring network radiality and availability of grid-forming generators are considered. Quality of the obtained solution is evaluated by comparison with- a) an upper bound on the probability that the identified microgrids are supply-deficient, and b) a lower bound on the objective value for the true optimization problem. Performance of the ODNP formulation is illustrated through case-studies on a modified IEEE 37-bus feeder. It is shown that the network flexibility is well utilized; the partitioning changes with risk budget; and that the SAA method is able to yield good quality solutions with modest computation cost.
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