Full- & Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent-Magnet Synchronous Generator

Wind energy is an integral part of nowadays energy supply and one of the fastest growing sources of electricity in the world today. Accurate models for wind energy conversion systems (WECSs) are of key interest for the analysis and control design of present and future energy systems. Existing control-oriented WECSs models are subject to unstructured simplifications, which have not been discussed in literature so far. Thus, this technical note presents are thorough derivation of a physical state-space model for permanent magnet synchronous generator WECSs. The physical model considers all dynamic effects that significantly influence the system's power output, including the switching of the power electronics. Alternatively, the model is formulated in the $(a,b,c)$- and $(d,q)$-reference frame. Secondly, a complete control and operation management system for the wind regimes II and III and the transition between the regimes is presented. The control takes practical effects such as input saturation and integral windup into account. Thirdly, by a structured model reduction procedure, two state-space models of WECS with reduced complexity are derived: a non-switching model and a non-switching reduced-order model. The validity of the models is illustrated and compared through a numerical simulation study.Comment: 23 pages, 11 figure

Distributed Optimization of District Heating Networks Using Optimality Condition Decomposition

The optimal operation of District Heating Networks (DHNs) is a challenging task. Current or future optimal dispatch energy management systems attempt to optimize objectives, such as monetary cost minimization, emission reduction, or social welfare maximization. Typically, this requires highly nonlinear models and has a substantial computational cost, especially for large DHNs. Consequently, it is difficult to solve the resulting nonlinear programming problem in real time. In particular, as typical applications allow for no more than several minutes of computation time. However, a distributed optimization approach may provide real time performance. Thereby, the solution of the central optimization problem is obtained by solving a set of small-scale, coupled optimization problems in parallel. At runtime, information is exchanged between the small-scale problems during the iterative solution procedure. A well-known approach of this class of distributed optimization algorithms is Optimality Condition Decomposition (OCD). Important advantages of this approach are the low amount of information exchange needed between the small-scale problems and that it does not require the tuning of parameters, which can be challenging. However, the DHNs model equation structure brings along many difficulties that hamper the application of the OCD approach. Simulation results demonstrate the applicability range of the presented method

On MPC-based Strategies for Optimal Voltage References in DC Microgrids

Modern power systems are characterized by low inertia and fast voltage dynamics due to the increase of sources connecting via power electronics and the removal of large traditional thermal generators. Power electronics are commonly equipped with fast controllers that are able to reach a desired voltage setpoint within seconds. In this paper, we propose and compare two approaches using Model Predictive Control (MPC) to compute optimal voltage references for the power electronic devices in order to minimize the losses in a DC microgrid: i) a traditional setpoint-tracking MPC which receives a previously computed optimal setpoint; ii) an economic MPC which does not require a priori computed setpoints. We show that the economic MPC outperforms the setpoint-tracking MPC in simulations with the CIGRE benchmark system when multiple load disturbances occur. Some insights and discussions related to the stability of the closed-loop system using its dissipativity properties are highlighted for both approaches

Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator

Full-order state-space models represent the starting point for the development of advanced control methods for wind turbine systems (WTSs). Regarding existing control-oriented WTS models, two research gaps must be noted: (i) There exists no full-order WTS model in form of one overall ordinary differential equation that considers all dynamical effects which significantly influence the electrical power output; (ii) all existing reduced-order WTS models are subject to rather arbitrary simplifications and are not validated against a full-order model. Therefore, in this paper, two full-order nonlinear state-space models (of 11th and 9th-order in the (a, b, c)- and (d, q)-reference frame, resp.) for variable-speed variable-pitch permanent magnet synchronous generator WTSs are derived. The full-order models cover all relevant dynamical effects with significant impact on the system’s power output, including the switching behavior of the power electronic devices. Based on the full-order models, by a step-by-step model reduction procedure, two reduced-order WTS models are deduced: A non-switching (averaging) 7th-order WTS model and a non-switching 3rd-order WTS model. Comparative simulation results reveal that all models capture the dominant system dynamics properly. The full-order models allow for a detailed analysis covering the high frequency oscillations in the instantaneous power output due to the switching in the power converters. The reduced-order models provide a time-averaged instantaneous power output (which still correctly reflects the energy produced by the WTS) and come with a drastically reduced complexity making those models appropriate for large-scale power grid controller design

Distributed Optimization of District Heating Networks Using Optimality Condition Decomposition

The optimal operation of District Heating Networks (DHNs) is a challenging task. Current or future optimal dispatch energy management systems attempt to optimize objectives, such as monetary cost minimization, emission reduction, or social welfare maximization. Typically, this requires highly nonlinear models and has a substantial computational cost, especially for large DHNs. Consequently, it is difficult to solve the resulting nonlinear programming problem in real time. In particular, as typical applications allow for no more than several minutes of computation time. However, a distributed optimization approach may provide real time performance. Thereby, the solution of the central optimization problem is obtained by solving a set of small-scale, coupled optimization problems in parallel. At runtime, information is exchanged between the small-scale problems during the iterative solution procedure. A well-known approach of this class of distributed optimization algorithms is Optimality Condition Decomposition (OCD). Important advantages of this approach are the low amount of information exchange needed between the small-scale problems and that it does not require the tuning of parameters, which can be challenging. However, the DHNs model equation structure brings along many difficulties that hamper the application of the OCD approach. Simulation results demonstrate the applicability range of the presented method