Unrestricted wind farm layout optimization (UWFLO): Investigating key factors influencing the maximum power generation

The creation of wakes, with unique turbulence characteristics, downstream of turbines significantly increases the complexity of the boundary layer flow within a wind farm. In conventional wind farm design, analytical wake models are generally used to compute the wake-induced power losses, with different wake models yielding significantly different estimates. In this context, the wake behavior, and subsequently the farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these factors is paramount to the development of more reliable power generation models; such an understanding is however missing in the current state of the art in wind farm design. In this paper, we quantitatively explore how the farm power generation, estimated using four different analytical wake models, is influenced by the following key factors: (i) incoming wind speed, (ii) land configuration, and (iii) ambient turbulence. The sensitivity of the maximum farm output potential to the input factors, when using different wake models, is also analyzed. The extended Fourier Amplitude Sensitivity Test (eFAST) method is used to perform the sensitivity analysis. The power generation model and the optimization strategy is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. In the case of an array-like turbine arrangement, both the first-order and the total-order sensitivity analysis indices of the power output with respect to the incoming wind speed were found to reach a value of 99%, irrespective of the choice of wake models. However, in the case of maximum power output, significant variation (around 30%) in the indices was observed across different wake models, especially when the incoming wind speed is close to the rated speed of the turbines.

This paper proposes a mixed integer linear programming formulation of the unrestricted wind farm layout optimization problem. The formulation is achieved in part by changing the objective from power generation maximization to the maximization of the smallest penalized downstream distance between any pair of turbines, where downstream distance is defined as the distance between any pair of turbines with overlapping wake cones. The proposed formulation also linearizes other non-linear characteristics of the unrestricted layout optimization problem such as proximity constraints and wake-cone membership. The main advantage of the proposed approach is that an optimal solution to the proposed formulation is guaranteed to be globally optimal. This is in contrast to previous approaches with non-linear formulations that do not come with such guarantees.

Multiple wind farms (WFs) model consists of wind speed model and single WF model. In the multiple WFs integrated power system, the wind speeds at different WFs are correlated to some degree if the distance between WFs is not very large. Hence, a novel MC-Nataf-CD method combining partitions Monte Carlo (MC) sampling, Nataf transformation and Cholesky Decomposition (CD) is proposed to simulate correlated wind speeds with desired cross-correlation coefficients. The wind speeds generated by the proposed wind speed model is closer to both the historical data and the Weibull fitting curve. For the single WF model, wake effects, the forced outage rates (FORs) of wind turbine generators (WTGs) and the reliability of the connected grids inside a WF need to be taken into consideration. Four different single WF models are proposed to reveal the impact of these relevant factors. A statistical method based on state-sampling MC simulation is implemented for the reliability estimation of Roy Billinton Test System (RBTS) with multiple WFs, using both historical and simulated wind speed data. The simulation results and the calculated reliability indices demonstrate that the proposed techniques are effective and accurate in the modeling of correlated multiple WFs.

Wind energy is a rapidly expanding source of renewable energy, but is highly intermittent. The performance of a wind farm, composed of a collection of wind turbines, depends not only on the placement of wind turbines in a farm, but also control actions taken by individual turbines. The wind turbine placement (layout) design problem involves adjusting turbine locations within a given area to improve a performance objective (such as maximizing annualized energy production). This layout problem has been addressed previously considering the effect of constraints such land configuration, installed capacity, and wake model choice on the performance of wind farms. All the studies, however, ignore the effects of the control system, which can have significant impact on performance. A well designed wind farm — without an optimal controller — will not achieve the full system level optimal performance, and vice-versa. In this article, we propose a novel layout co-design approach that includes optimal control considerations to exploit this synergy between farm layout and control. Layout case studies involving 8 and 12 turbines are presented. An annual energy production improvement of up to 17% is observed when accounting for coupling between control and layout design, when compared to layout-only optimization.

Large scale wind power penetration has a significant impact on the reliability of the electric generation systems. A wind farm consists of a large number of wind turbine generators (WTGs). A major difficulty in modeling wind farms is that the WTG not have an independent capacity distribution due to the dependence of the individual turbine output on the same energy source, the wind. In this paper, a model of the wind farm output power considering multi-wake effects is established according to the probability distribution of the wind speed and the characteristic of the wind generator output power: based on the simple Jenson wake effect model, the wake effect with wind speed sheer model and the detail wake effect model with the detail shade areas of the upstream wind turbines are discussed respectively. Compared to the individual wake effect model, this model takes the wind farm as a whole and considers the multi-wakes effect on the same unit. As a result the loss of the velocity inside the wind farm is considered more exactly. Furthermore, considering the features of sequentially and self-correlation of wind speed, an auto-regressive and moving average (ARMA) model for wind speed is built up. Also the reliability model of wind farm is built when the output characteristics of wind power generation units, correlation of wind speeds among different wind farms, outage model of wind power generation units, wake effect of wind farm and air temperature are considered. Simulation results validate the effectiveness of the proposed models. These models can be used to research the reliability of power grid containing wind farms, wind farm capacity credit as well as the interconnection among wind farms

Recently, several literatures reported that sub-synchronous oscillation (SSO) events occurred in wind farms based on direct-driven wind generators (DDWGs). This paper focuses on whether a wind farm consists of only DDWGs would bring an SSO. First, a small-signal model of the DDWG-based wind farm is proposed. Eigen-analysis indicates that there are natural modes with sub-synchronous frequency; however, their damping ratios are significantly large under specific control parameters. Further, the relationships between the sub-synchronous modes and the number of grid-connected DDWGs, the connecting reactance and the circuit topologies of the wind farm are analyzed. Taguchi's orthogonal array testing is also introduced to analyze the impact of the wind farm's stochastic operating conditions on the modes. Results show that if the DDWGs are well-tuned, the dynamics of the wind farm are similar to one DDWG, and the sub-synchronous modes have little correlation with those factors, thus SSO can hardly arise when the model of wind farm only includes DDWGs. Electromagnetic transient simulations are also carried out to prove the accuracy and efficiency of the results.

With increasing installation capacity and wind farms penetration, wind power plays more important role in power systems, and the modeling of wind farms has become an interesting research topic. In this paper, a coherency-based equivalent model has been discussed for the doubly fed induction generator (DFIG). Firstly, the dynamic models of wind turbines, DFIG and the mechanisms are briefly introduced. Some existing dynamic equivalent methods such as equivalent wind model, variable speed wind turbine model, parameter identification method and modal equivalent method to be used in wind farm aggregation are discussed. Then, considering wind power fluctuations, a new equivalent model of a wind farm equipped with doubly-fed induction generators is proposed to represent the interactions of the wind farm and grid. The method proposed is based on aggregating the coherent group wind turbines into an equivalent one. Finally, the effectiveness of the equivalent model is demonstrated by comparison with the wind farm response obtained from the detailed model. The dynamic simulations show that the present model can greatly reduce the computation time and model complexity.

Wind farm layout optimization for levelized cost of energy minimization with combined analytical wake model and hybrid optimization strategy

During recent years, wind energy has moved from an emerging technology to a nearly competitive technology. This fact, coupled with an increasing global focus on environmental concern and a political desire of a certain level of diversification in the energy supply, ensures wind energy an important role in the future electricity market. For this challenge to be met in a cost-efficient way, a substantial part of new wind turbine installations is foreseen to be erected in big onshore or offshore wind farms. This fact makes the production, loading and reliability of turbines operating under such conditions of particular interest.

<strong class="journal-contentHeaderColor">Abstract.</strong> Layout optimisation is essential for improving the overall performance of offshore wind farms. During the past 15 years, the use of yield optimisation algorithms has resulted in a transition from regular to more irregular farm layouts. However, since the layout affects many factors, yield optimisation alone may not maximise the overall performance. In this paper, a comparative case study is presented to quantify the effect of the wind farm layout on the overall performance of offshore wind farms. The case study was performed to investigate two performance indicators: power performance, using yield calculations with WindPRO and wake-induced tower fatigue, using the Frandsen model. It is observed that irregular wind farm layouts have a higher annual energy production compared to regular layouts. Their power production is also more persistent (less sensitive) to wind direction, improving predictability and thus market value of power output. However, one turbine location in the irregular layout has a 24 % higher effective turbulence level, leading to additional tower fatigue. As a result, fatigue-driven tower designs would require increased wall thicknesses, which would result in higher capital costs for all turbine locations. It is demonstrated in this study that layout optimisation using a minimum inter-turbine spacing effectively resolves the induced wake issue while maintaining high-yield performance.

<strong class="journal-contentHeaderColor">Abstract.</strong> Layout optimisation is essential for improving the overall performance of offshore wind farms. During the past 15 years, the use of yield optimisation algorithms has resulted in a transition from regular to more irregular farm layouts. However, since the layout affects many factors, yield optimisation alone may not maximise the overall performance. In this paper, a comparative case study is presented to quantify the effect of the wind farm layout on the overall performance of offshore wind farms. The case study was performed to investigate two performance indicators: power performance, using yield calculations with WindPRO and wake-induced tower fatigue, using the Frandsen model. It is observed that irregular wind farm layouts have a higher annual energy production compared to regular layouts. Their power production is also more persistent (less sensitive) to wind direction, improving predictability and thus market value of power output. However, one turbine location in the irregular layout has a 24 % higher effective turbulence level, leading to additional tower fatigue. As a result, fatigue-driven tower designs would require increased wall thicknesses, which would result in higher capital costs for all turbine locations. It is demonstrated in this study that layout optimisation using a minimum inter-turbine spacing effectively resolves the induced wake issue while maintaining high-yield performance.

<strong class="journal-contentHeaderColor">Abstract.</strong> Layout optimisation is essential for improving the overall performance of offshore wind farms. During the past 15 years, the use of yield optimisation algorithms has resulted in a transition from regular to more irregular farm layouts. However, since the layout affects many factors, yield optimisation alone may not maximise the overall performance. In this paper, a comparative case study is presented to quantify the effect of the wind farm layout on the overall performance of offshore wind farms. The case study was performed to investigate two performance indicators: power performance, using yield calculations with WindPRO and wake-induced tower fatigue, using the Frandsen model. It is observed that irregular wind farm layouts have a higher annual energy production compared to regular layouts. Their power production is also more persistent (less sensitive) to wind direction, improving predictability and thus market value of power output. However, one turbine location in the irregular layout has a 24 % higher effective turbulence level, leading to additional tower fatigue. As a result, fatigue-driven tower designs would require increased wall thicknesses, which would result in higher capital costs for all turbine locations. It is demonstrated in this study that layout optimisation using a minimum inter-turbine spacing effectively resolves the induced wake issue while maintaining high-yield performance.

<strong class="journal-contentHeaderColor">Abstract.</strong> Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses; hence, there is a need for numerical models that can properly simulate wind farm interaction. This work proposes a Reynolds-averaged Navier-Stokes (RANS) method to efficiently simulate the effect of neighboring wind farms on wind farm power and annual energy production. First, a novel steady-state atmospheric inflow is proposed. This inflow model is well suited for RANS simulations of large wind farms because it does not lead to the development of nonphysical wind farm wakes. Second, a RANS-based wind farm parametrization is introduced, the actuator wind farm (AWF) model, which represents the wind farm as a forest canopy and allows to use of coarser grids compared to modeling all wind turbines as actuator disks (ADs). When the horizontal resolution of the RANS-AWF model is increased, the model results approach the results of the RANS-AD model. A double wind farm case is simulated with RANS to show that replacing an upstream wind farm with an AWF model only causes a deviation less than 1 % in terms of wind farm power of the downstream wind farm. Most importantly, a reduction in CPU hours of 74.4 % is achieved, provided that the AWF inputs are known, namely, wind farm thrust and power coefficients. The reduction in CPU hours is further reduced when all wind farms are represented by AWF models; namely 89.3 % and 99.9 %, for the double wind farm case and for a wind farm cluster case consisting of three wind farms, respectively. For the double wind farm case, the RANS models predict different wind speed flow fields compared to output from simulations performed with the mesoscale Weather Research and Forecasting model (WRF), but the models are in agreement with the inflow wind speed of the downstream wind farm. The double wind farm case is also simulated with the TurbOPark engineering wake model. Similar wake shapes are reproduced by TurbOPark but the model predicts a larger wind farm wake magnitude compared to RANS and WRF. TurbOPark predicts much better results when its ground model is switched off and a wake expansion coefficient of 0.06 is used. The RANS-AD-AWF model is also validated with SCADA measurements in terms of wind farm shape; the model captures the trend of the measurements for a wide range of wind directions, although the SCADA measurements indicate more pronounced wind farm wake shapes for certain wind directions.

Performance evaluation of Jepirachi Wind Park

A new Gaussian analytical wake model validated by wind tunnel experiment and LiDAR field measurements under different turbulent flow