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Nodal Frequency Performance of Power Networks

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 Added by Huanhai Xin
 Publication date 2021
and research's language is English




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This paper investigates how a disturbance in the power network affects the nodal frequencies of certain network buses. To begin with, we show that the inertia of a single generator is in inverse proportion to the initial rate of change of frequency (RoCoF) under disturbances. Then, we present how the initial RoCoF of the nodal frequencies are related to the inertia constants of multiple generators in a power network, which leads to a performance metric to analyze nodal frequency performance. To be specific, the proposed metric evaluates the impact of disturbances on the nodal frequency performance. The validity and effectiveness of the proposed metric are illustrated via simulations on a multi-machine power system.



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Given the increasing penetration in renewable generation, the UK power system is experiencing a decline in system inertia and an increase in frequency response (FR) requirements. Faster FR products are a mitigating solution that can cost-effectively meet the system balancing requirements. Thus, this paper proposes a mixed integer linear programming (MILP) unit commitment model which can simultaneously schedule inertial response, mandatory FR, as well as a sub-second FR product - enhanced frequency response (EFR). The model quantifies the value of providing faster reacting FR products in comparison with other response times from typical FR products. The performance and value of EFR are determined in a series of future energy scenarios with respect to the UK market and system conditions.
This paper investigates the impact of Kron reduction on the performance of numerical methods applied to the analysis of unbalanced polyphase power systems. Specifically, this paper focuses on power-flow study, state estimation, and voltage stability assessment. For these applications, the standard Newton-Raphson method, linear weighted-least-squares regression, and homotopy continuation method are used, respectively. The performance of the said numerical methods is assessed in a series of simulations, in which the zero-injection nodes of a test system are successively eliminated through Kron reduction.
This paper proposes a control method for allowing aggregates of thermostatically controlled loads to provide synthetic inertia and primary frequency regulation services to the grid. The proposed control framework is fully distributed and basically consists in the modification of the thermostat logic as a function of the grid frequency. Three strategies are considered: in the first one, the load aggregate provides synthetic inertia by varying its active power demand proportionally to the frequency rate of change; in the second one, the load aggregate provides primary frequency regulation by varying its power demand proportionally to frequency; in the third one, the two services are combined. The performances of the proposed control solutions are analyzed in the forecasted scenario of the electric power system of Sardinia in 2030, characterized by a huge installation of wind and photovoltaic generation and no coil and combustible oil power plants. The considered load aggregate is composed by domestic refrigerators and water heaters. Results prove the effectiveness of the proposed approach and show that, in the particular case of refrigerators and water heaters, the contribution to the frequency regulation is more significant in the case of positive frequency variations. Finally, the correlation between the regulation performances and the level of penetration of the load aggregate with respect to the system total load is evaluated.
Stable operation of the electrical power system requires the power grid frequency to stay within strict operational limits. With millions of consumers and thousands of generators connected to a power grid, detailed human-build models can no longer capture the full dynamics of this complex system. Modern machine learning algorithms provide a powerful alternative for system modelling and prediction, but the intrinsic black-box character of many models impedes scientific insights and poses severe security risks. Here, we show how eXplainable AI (XAI) alleviates these problems by revealing critical dependencies and influences on the power grid frequency. We accurately predict frequency stability indicators (such as RoCoF and Nadir) for three major European synchronous areas and identify key features that determine the power grid stability. Load ramps, specific generation ramps but also prices and forecast errors are central to understand and stabilize the power grid.
Frequency fluctuations in power grids, caused by unpredictable renewable energy sources, consumer behavior and trading, need to be balanced to ensure stable grid operation. Standard smart grid solutions to mitigate large frequency excursions are based on centrally collecting data and give rise to security and privacy concerns. Furthermore, control of fluctuations is often tested by employing Gaussian perturbations. Here, we demonstrate that power grid frequency fluctuations are in general non-Gaussian, implying that large excursions are more likely than expected based on Gaussian modeling. We consider real power grid frequency measurements from Continental Europe and compare them to stochastic models and predictions based on Fokker-Planck equations. Furthermore, we review a decentral smart grid control scheme to limit these fluctuations. In particular, we derive a scaling law of how decentralized control actions reduce the magnitude of frequency fluctuations and demonstrate the power of these theoretical predictions using a test grid. Overall, we find that decentral smart grid control may reduce grid frequency excursions due to both Gaussian and non-Gaussian power fluctuations and thus offers an alternative pathway for mitigating fluctuation-induced risks.
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