Wind Farm Wake Effect Model — Simulation & Power Modeling

Abstract — Wind Farm Wake Effect Model

Commons. Wind turbines are often placed together in wind farms for economic considerations. This causes wake interactions between turbines, resulting in significant power losses. Models that predict these wake losses are critical for estimating wind farm power output and developing strategies to mitigate the wake effect, such as wind farm control. For these applications, engineering wake models are favoured for their computational efficiency. Hence, the validation and improvement of these models is an ongoing area of research. Currently, consensus on the accuracy of engineering wake models is absent in the literature. Existing studies employ varying validation strategies that impact the perceived model accuracy. Furthermore, proposed model improvements often lack quantitative evaluation, limiting the generalisability of the results. Additionally, the potential benefits of calibrating wake model parameters are recognised, yet research on calibration methods and the impact thereof is limited. This thesis addresses this scientific gap by proposing a holistic framework for the validation and calibration of engineering wake models. The framework combines best practices from literature. First, it accounts for wind direction uncertainty in historical wind farm data. Additionally, it corrects model inputs by including heterogeneous inflow wind speeds.

Analytical & State-Space Control Methodology

Finally, it offers a methodology for parameter calibration to improve the model's accuracy using historical wind farm data. The overarching framework employs both quantitative and qualitative validation methods to mitigate the impact of experiment design and enable a thorough evaluation of model improvements. The effectiveness of this framework is demonstrated through a case study with SCADA data from OWEZ wind farm and four engineering wake models from the popular control-oriented wake modelling tool FLORIS. Results show that wind direction uncertainty in SCADA d|ata must be included when validating wake models for specific wind directions or sectors. Additionally, incorporating heterogeneous inflow wind speeds reduced the absolute turbine error by up to 20%. Furthermore, it is demonstrated that calibrating model parameters significantly improves model accuracy. The resulting error reductions reach up to 92% for individual turbines and 65% at farm-level, i.e., for all turbines collectively. Furthermore, results revealed that while the performance of the different models converges post-calibration, differences persist in various scenarios with numerous wake interactions. In these cases, the CC and TurbOPark models outperform the Jensen and GCH models. Through this holistic framework and the demonstrated potential of model parameter calibration, a path forward is paved for further model improvement in a systematic and quantitative manner.

Simulink Waveforms & Power Quality Findings

Section 1.1: State-Space Averaging, Dynamic Modeling & Small-Signal Derivations for Wind Farm Wake Effect Model. The dynamic behavior of Wind Farm Wake Effect Model is characterized using state-space averaging techniques to capture continuous conduction mode (CCM) and discontinuous conduction mode (DCM) operations. During the on-state interval (DT_s), power semiconductor switches conduct current through energy storage inductors, producing linear flux ramping governed by the state equation: d(i_L)/dt = (V_in - v_sw)/L. During the off-state interval ((1-D)T_s), energy stored within magnetic cores transfers through freewheeling diodes or synchronous active rectifiers into the output filtering capacitance and load network. Small-signal perturbations (x_hat = x + delta_x, d_hat = d + delta_d) yield linearized transfer functions G_vd(s) = v_o_hat(s) / d_hat(s) that quantify control-to-output gain, right-half-plane (RHP) zeros, and resonant peaking frequencies.

Scope & Practical Applications

• High-efficiency DC-DC converters and isolated resonant topologies (LLC / DAB)
• Sinusoidal and Space Vector PWM inverters for grid integration & industrial motor drives
• MOSFET / IGBT gate driver optimization with active Miller-clamp shoot-through protection
• Power quality conditioning with Total Harmonic Distortion (THD) strictly compliant with IEEE 519
• Complete Simscape .SLX model files, parameter calculation scripts, and IEEE dissertation reports