Europe’s offshore wind potential is enormous and able to power Europe seven times over. Over 100 GW of offshore wind projects are already in various stages of planning. If realized, these projects would produce 10% of the EU’s electricity whilst avoiding 200 million tonnes of CO
emissions each year. [1
A number of large wind farms in the North Sea is currently in the design stage. The layout and the components of these wind farm are chosen, based on a good estimate of the electricity production costs of different options. To estimate the production costs, the investment costs, the electrical losses and the produced electric power have to be determined. This can be realized by calculating the voltages and currents in all wind farm components.
In this paper, EeFarm-II is used to evaluate thirteen different electrical systems for a 200 MW wind farm with a 100 km connection to shore. The systems are grouped by their way of operation: constant speed, individual variable speed, cluster variable speed and park variable speed. For this evaluation a database with component manufacturer data of 2009 is used. The investment costs for the HVDC converters are from 2007.
2. EeFarm-II Model and Database Description
EeFarm-II calculates the output voltage and current phasor (AC) or voltage and current value (DC) of each wind farm component based on the input voltage and current and the component parameters. This is repeated for each wind speed bin, i.e.
, for the complete range of operation of the wind farm. From the output power for each wind speed bin and the wind speed distribution, the annual energy losses and the annually produced energy are determined. The Levelised Production Costs (LPC), i.e.
, the average production costs over the lifetime of the wind farm, are based on the investment cost, the produced energy and a number of economic parameters. Figure 2
gives an overview of the different steps in the calculation of the Levelised Production Costs.
EeFarm-II is programmed in Matlab-Simulink, which may seem an a bit odd choice because stepping through a wind farm power curve and calculating the output of a wind farm is not a dynamic simulation, the task for which Simulink was designed. On the other hand, Matlab-Simulink has a lot of advantages, also for these kind of steady state calculations:
the graphical user interface and library facility, which makes setting up a new wind farm model from an existing set of component models very easy and transparent;
the Simulink bus signal, which results in simple and error free connection of component models in the wind farm model;
the Matlab data structure, which simplifies the transfer of component parameters to the wind farm model: complete sets of parameters are assigned by a single command.
An advantage of EeFarm-II is that it can handle AC as well as DC components, standard load flow models can only handle AC components. The core of EeFarm-II consists of steady state models of wind farm electrical components. The EeFarm-II component models reside in a Simulink model library, see Figure 1
. A wind farm model is built by copying the model blocs to a Simulink model and connecting the blocks. The electrical model blocs have one input and one output, which is a Simulink bus. The content of a bus for all AC and for all DC blocks is the same, see Table 1
for the AC bus. The component blocks are arranged and connected from the individual wind turbines in the direction of the point of common coupling (PPC: the connection of the wind farm to the HV grid). So, for example, the cable end connected to the turbine generator is input and the cable end connected to the turbine transformer is output. The signal direction also gives the order in which the model blocks are evaluated, starting at the turbines and ending at the HV transformer at the PCC. The voltage at each wind turbine generator is set by the user and is assumed to be constant, all other voltages are calculated by the programme. If two outputs need to be joined, for instance two cables coming from two turbines, a node block is used. Table 2
gives an overview of the components in the library of EeFarm-II.
The AC component models are the well known equivalent circuit diagrams for generators (induction, doubly fed and full converter), cables and transformers. For the PWM converter three different models representing the switching and conduction losses can be chosen. EeFarm-II does not solve the load flow in the classical way because this would make it difficult to include DC components. Instead, it determines an average solution, which is sufficiently accurate to determine the losses and the produced power, due to the small voltage drops and the small voltage angle differences in a wind farm. For a detailed description of EeFarm-II, refer to [2
The independent variable in the EeFarm calculation is the wind speed. The wind turbine power curve specified by the turbine manufacturer is used to determine the turbine electric power. Alternatively, the electric power of each individual wind turbine in the farm, calculated by a wind farm wake program (for instance the ECN program FarmFlow) can be used. The turbine generator and turbine transformer model are only required if the reactive power produced by the turbine has to be determined. The losses in these components are set to zero, since already included in the power curve.
EeFarm model library.
EeFarm model library.
AC bus signals.
|line voltage phasor (RMS) at component output, complex number||(V)|
|current phasor (RMS) at component output, complex number||(A)|
|power at component output||(W)|
|reactive power at component output||(VA)|
|reactive power produced by component||(VA)|
|sum of component losses||(W)|
|sum of component investment costs||(kEuro)|
|power not produced due to component failure||(W)|
|sum of power not produced due to component failure||(W)|
Overview of EeFarm II components.
Overview of EeFarm II components.
|Wind||Wind||wind input block|
| ||GCL wake model||Simulink implementation of GCL wind farm wake model|
|Turbine||Turbine internal curve||single P(V) curve or FyndFarm or FluxFarm input|
| ||Turbine WF eff.||VSP, CSP or CSS turbine, lookup table GCL preprocessor|
| ||VSP turb||single P(V) curve or FyndFarm or FluxFarm input|
|Generator||Generator Generic||type independent simple generator model|
| ||IM stat||directly connected induction machine|
| ||DFIG||doubly fed induction machine|
| ||FCIM||induction machine with full converter|
| ||FCSM||synchronous machine with full converter|
|Transformer||TrafoQ||AC transformer with reactive power calculation|
| ||Trafo Noloss Nofail||AC transformer, only the transformer ratio|
|Cable||CableAC||constant temperature π cable model|
| ||CableDC||constant temperature, earth return DC cable|
| ||CableDCbipolar||constant temperature, bipolar DC cable|
|Node||NodeAC||connects two AC bus signals|
| ||NodeDC||connects two DC bus signals|
| ||SplitterAC||splits an AC bus signal|
| ||SplitterDC||splits a DC bus signal|
|Inductor||InductorQ||fixed size inductor for reactive power compensation|
|Thy||Thy rect||thyristor rectifier|
| ||Thy inv||thyristor inverter|
|PWM||PWM rect Kaz, TUD, Inf||IGBT rectifier Kazmierkovski, TUD, Infineon model|
| ||PWM inv Kaz, TUD, Inf||IGBT inverter Kazmierkovski, TUD, Infineon model|
|Chopper||Step-up chopper||DC-DC transformer|
|Statcom||Statcom TUD||IGBT inverter TU Delft model modified as Statcom|
|Availability||Availability||power reduction due to component failure|
|Control||Qfeedback||sets the reactive power of individual turbines|
EeFarm-II includes a database with electrical parameters (capacitance, inductance, resistance etc.) and costs of the components in wind farms. In the initialization (
in Figure 2
) a wind farm specific m-file reads the component parameters from the database and fills the component parameter structures. The component parameters are passed to the simulation
using a mask. This enables the use of different sets of parameters for different occurences of the same library block. The simulation calculates the voltage, current, power, reactive power, losses, not produced power due to unavailability and maintenance per component and per wind speed bin. This is input for the postprocessor
, which determines the LPC based on the wind speed distribution and the economic parameters.
EeFarm II model overview.
EeFarm II model overview.