On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysi

On the Properties of the Power Systems Nodal Admittance Matrix

This letter provides conditions determining the rank of the nodal admittance matrix, and arbitrary block partitions of it, for connected AC power networks with complex admittances. Furthermore, some implications of these properties concerning Kron Reduction and Hybrid Network Parameters are outlined.Comment: Index Terms: Nodal Admittance Matrix, Rank, Block Form, Network Partition, Kron Reduction, Hybrid Network Parameter

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

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

Real-Time State Estimation and Voltage Stability Assessment of Power Grids: From Theoretical Foundations to Practical Applications

The operators of power distribution systems strive to lower their operational costs and improve the quality of the power service provided to their customers. Furthermore, they are faced with the challenge of accommodating large numbers of Distributed Energy Resources (DERs) into their grids. It is expected that these problems will be tackled with a large-scale deployment of automation technology, which will enable the real-time monitoring and control of power distribution systems (i.e., similar to power transmission systems). For this purpose, real-time situation awareness w.r.t. the state and the stability of the system is needed. In view of the deployment of such automation functions into power distribution grids, there are two binding requirements. Firstly, the system models have to account for the inherent unbalances of power distribution systems (i.e., w.r.t. the components of the grid and the loads). Secondly, the analysis methods have to be real-time capable when deployed into low-cost embedded systems platforms, which are the cornerstones of automation. In other words, the analysis methods need to be computationally efficient. This thesis focuses on the modeling of unbalanced polyphase power systems, as well as the development, validation, and deployment of real-time methods for State Estimation (SE) and Voltage Stability Assessment (VSA) of such systems. More precisely, the following theoretical and practical contributions are made to the field of power system engineering. 1. Fundamental properties of the compound admittance matrix of polyphase power grids are identified. Specifically, theorems w.r.t. the rank of the compound admittance matrix, the feasibility of Kron Reduction (KR), and the existence of compound hybrid matrices are stated and formally proven. These theorems hold for generic polyphase power grids (i.e., which may be unbalanced, and have an arbitrary number of phases). 2. A Voltage Stability Index (VSI) for real-time VSA of polyphase power systems is proposed. The proposed VSI is a generalization of the well-known L-index, which is achieved by integrating more generic models of the power system components. More precisely, the grid is represented by a compound hybrid matrix, slack nodes by Thévenin equivalents, and resource nodes by polynomial load models. In this regard, the theorems mentioned under item 1 substantiate the applicability of the proposed VSI. 3. A Field-Programmable Gate Array (FPGA) implementation for real-time SE of polyphase power systems is presented. This state estimator is based on a Sequential Kalman Filter (SKF), which - in contrast to the standard Kalman Filter (KF) - is suitable for implementation in such dedicated hardware. In this respect, it is formally proven that the SKF and the standard KF are equivalent if the measurement noise variables are uncorrelated. To achieve high computational performance, the grid model is reduced through KR, and the SKF calculations on the FPGA are parallelized and pipelined. 4. The methods stated under items 1-3 are deployed into an industrial real-time controller, which is used to control a real-scale microgrid. This microgrid is equipped with a metering system composed of Phasor Measurement Units (PMUs) coupled with a Phasor Data Concentrator (PDC). The real-time capability of the developed methods is validated experimentally by measuring the latencies of the PDC-SE-VSA processing chain w.r.t. the PMU timestamps

Voltage stability analysis using a complete model of grid-connected voltage-source converters

Due to the increasing popularity of renewable energies, a significant share of the power generation in future microgrids is expected to originate from converter-interfaced Distributed Energy Resources (DERs). Traditionally, idealized device models are used to conduct grid stability studies. For instance, a DER interfaced via a Voltage-Source Converter (VSC) would be modeled as an ideal current or power source (depending on the control schemes), ignoring non-ideal behavior like the response of the converter synchronization. However, such a simplification may lead to misjudging the stability, in particular for weak microgrids. To address this issue, ZIP models of grid-interfaced VSCs, which take into account both the control scheme and the synchronization, are developed in this paper. The influence of the synchronization response on the stability of a weak microgrid system is demonstrated using a benchmark system simulated in MATLAB/Simulink. It is shown that the idealized models normally used for static stability analysis do underestimate the voltage stability issue in the investigated microgrid system

Slack Selection for Unintentional Islanding: Practical Validation in a Benchmark Microgrid

Upon an intentional or emergency disconnection from the main grid, a microgrid is expected to continue working in islanded mode. Thus, (at least) one resource needs to act as slack and compensate for power variations to keep the power balance, and ensure the security of supply. Although several resources might be eligible to become slack, some are more suitable than others (energy storage systems in particular) depending on the state of both the resources and the grid before the islanding transition. In this paper, we validate a recently proposed method to select in real-time the best slack-candidate using an abstract representation of the internal state of the available resources. The same method can be used to actively switch the slack during islanded operation to accommodate the intrinsic stochastic nature of the microgrid’s resources. Our main contribution is the validation of the method in a real-scale microgrid, including a discussion of implementation and deployment aspects. To support our findings, we present extensive experimental results in different operating conditions

Effect of aliskiren on post-discharge outcomes among diabetic and non-diabetic patients hospitalized for heart failure: insights from the ASTRONAUT trial

Aims The objective of the Aliskiren Trial on Acute Heart Failure Outcomes (ASTRONAUT) was to determine whether aliskiren, a direct renin inhibitor, would improve post-discharge outcomes in patients with hospitalization for heart failure (HHF) with reduced ejection fraction. Pre-specified subgroup analyses suggested potential heterogeneity in post-discharge outcomes with aliskiren in patients with and without baseline diabetes mellitus (DM). Methods and results ASTRONAUT included 953 patients without DM (aliskiren 489; placebo 464) and 662 patients with DM (aliskiren 319; placebo 343) (as reported by study investigators). Study endpoints included the first occurrence of cardiovascular death or HHF within 6 and 12 months, all-cause death within 6 and 12 months, and change from baseline in N-terminal pro-B-type natriuretic peptide (NT-proBNP) at 1, 6, and 12 months. Data regarding risk of hyperkalaemia, renal impairment, and hypotension, and changes in additional serum biomarkers were collected. The effect of aliskiren on cardiovascular death or HHF within 6 months (primary endpoint) did not significantly differ by baseline DM status (P = 0.08 for interaction), but reached statistical significance at 12 months (non-DM: HR: 0.80, 95% CI: 0.64-0.99; DM: HR: 1.16, 95% CI: 0.91-1.47; P = 0.03 for interaction). Risk of 12-month all-cause death with aliskiren significantly differed by the presence of baseline DM (non-DM: HR: 0.69, 95% CI: 0.50-0.94; DM: HR: 1.64, 95% CI: 1.15-2.33; P < 0.01 for interaction). Among non-diabetics, aliskiren significantly reduced NT-proBNP through 6 months and plasma troponin I and aldosterone through 12 months, as compared to placebo. Among diabetic patients, aliskiren reduced plasma troponin I and aldosterone relative to placebo through 1 month only. There was a trend towards differing risk of post-baseline potassium ≥6 mmol/L with aliskiren by underlying DM status (non-DM: HR: 1.17, 95% CI: 0.71-1.93; DM: HR: 2.39, 95% CI: 1.30-4.42; P = 0.07 for interaction). Conclusion This pre-specified subgroup analysis from the ASTRONAUT trial generates the hypothesis that the addition of aliskiren to standard HHF therapy in non-diabetic patients is generally well-tolerated and improves post-discharge outcomes and biomarker profiles. In contrast, diabetic patients receiving aliskiren appear to have worse post-discharge outcomes. Future prospective investigations are needed to confirm potential benefits of renin inhibition in a large cohort of HHF patients without D