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This paper discusses linearized models of hydropower plants (HPPs). First, it reviews state-of-the-art models and discusses their non-linearities, then it proposes suitable linearization strategies for the plant head, discharge, and turbine torque. It is shown that neglecting the dependency of the hydroacoustic resistance on the discharge leads to a linear formulation of the hydraulic circuits model. For the turbine, a numerical linearization based on a first-order Taylor expansion is proposed. Model performance is evaluated for a medium- and a low-head HPP with a Francis and Kaplan turbine, respectively. Perspective applications of these linear models are in the context of efficient model predictive control of HPPs based on convex optimization.
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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.
Having sufficient grid-forming sources is one of the necessary conditions to guarantee the stability in a power system hosting a very large share of inverter-based generation. The grid-forming function has been historically fulfilled by synchronous machines. However, with the appropriate control, it can also be provided by voltage source converters (VSC). This work presents a comparison between two technologies with grid-forming capability: the VSC with a grid-forming control coupled with an adequate energy storage system, and the synchronous condensers (SC). Both devices are compared regarding their inertial response, as well as their contribution to the system strength and short-circuit current for an equivalent capacity expressed in terms of apparent power and inertial reserve. Their behaviour following grid disturbances is assessed through time-domain simulations based on detailed electromagnetic transient (EMT) models. The results show that both devices achieve similar performance in the time-scale of seconds. For shorter time-windows, however, they present a different behavior: the SC ensures a better stiffness in the first tens of ms following the disturbance, while the VSC offers a faster resynchronization.
This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polyas relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.
An estimated state-space model can possibly be improved by further iterations with estimation data. This contribution specifically studies if models obtained by subspace estimation can be improved by subsequent re-estimation of the B, C, and D matrices (which involves linear estimation problems). Several tests are performed, which shows that it is generally advisable to do such further re-estimation steps using the maximum likelihood criterion. Stated more succinctly in terms of MATLAB functions, ssest generally outperforms n4sid.
Hydropower plants are one of the most convenient option for power generation, as they generate energy exploiting a renewable source, they have relatively low operating and maintenance costs, and they may be used to provide ancillary services, exploiting the large reservoirs of available water. The recent advances in Information and Communication Technologies (ICT) and in machine learning methodologies are seen as fundamental enablers to upgrade and modernize the current operation of most hydropower plants, in terms of condition monitoring, early diagnostics and eventually predictive maintenance. While very few works, or running technologies, have been documented so far for the hydro case, in this paper we propose a novel Key Performance Indicator (KPI) that we have recently developed and tested on operating hydropower plants. In particular, we show that after more than one year of operation it has been able to identify several faults, and to support the operation and maintenance tasks of plant operators. Also, we show that the proposed KPI outperforms conventional multivariable process control charts, like the Hotelling $t_2$ index.
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