Review of Harmonics in Offshore Wind Farms Marco Vinicio Chávez-Báez, Olimpo Anaya-Lara, Kwok L. Lo, Jim McDonald Strathclyde University, UK
[email protected]
AbstractThis paper presents a review of harmonics in offshore wind farm systems. The aim is to gather information of mathematical models for harmonic analysis in wind farms and algorithms to configure offshore network interconnections. A thorough literature review is presented that may help to develop a solution in MatLab or LabView for harmonic analysis in offshore wind farms with multi-technology components. Index Terms— Harmonics models, network configuration, offshore wind farms
I.
INTRODUCTION
The severity of the harmonics injected by wind turbines depends of the technology and control algorithms used; a great challenge is to eliminate them [1, 2]. There are different technologies of wind turbines and each one injects different levels of harmonics, hence the importance of developing efficient mathematical models to study harmonic performance of wind farm and connection. Configuration of a power network involves optimization techniques; a common application is power losses reduction. This paper looks not only on techniques available for this purpose but also pays attention to harmonics minimization (and even a combination of the two), to be applied to offshore wind electricity networks with multiple technologies. There are several investigations looking for new optimization methods to reconfigure the network system to reduce power losses. As the issue is a combinational problem the complexity is high in large electrical systems, reason why this issue is still an unsolved problem [2, 6]. The International Offshore Wind Market to 2020 Report predicts that by the end of 2020, the global offshore wind farm capacity will be around 55GW. This will include offshore wind power clusters in Europe, with all the subsequent connections problems. Figure 1 shows an example of the connection of offshore wind power clusters in the North Sea [8, 12-16]. The extensive cable network associated with offshore wind farms will bring a number of new technical challenges, harmonics associated to wind turbine converters and possible resonance effects being a potential cause of concern. Issues particularly associated with offshore wind farms include the possibility of magnification of low-order harmonic voltages from the main grid due to the large capacitance of long AC cables. Harmonic studies are required to assess the level of harmonic emission from the offshore wind farm at the point of common coupling (PCC). It is important that models used to assess requirements for the mitigation of harmonics are appropriate, and accurate.
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II. MODELS OF MOST COMMON ELEMENTS OF AN OFFSHORE WIND FARM
Elements to consider when modelling wind farms include the wind turbine technology, subsea cables, transformers, and transmission network components (see Figure 2). A. Cables Cables can be modelled as PI equivalents, and usually this representation is sufficient for short cable lengths, but the length of the main HV submarine cable to shore is longer, so it could be solved by subdividing the cable and representing it as a series of PI sections, which provides reasonable accuracy for frequencies up to a few kHz [7]. The cable transmission line acts like a capacitor, so the capacitive reactive power increases with the length of the cable. The reactive power of the cable depends not only on the capacitive component of the cable; also the inductive component has influence.
Fig. 1. Connection of offshore wind power clusters in the North Sea
Fig. 2. Typical offshore wind farm
Thus the reactive power depends on active power output of the wind farm. Adequate compensation could reduce the cable losses at no-load of the wind farm down to about 0.2 % of rated power [17]. Submarine cables can be modelled by “π” equivalent circuits. Some authors have adopted also simplified “π” models for this analysis. Therefore, the submarine cable model should be valid for frequencies further away than the fundamental (50-60Hz). To obtain a valid model based on “π” circuits for transients and different frequency harmonics, it is necessary to model the submarine cable with more than one “π” circuit (see Figure 3). The number of “π” circuits to use is determined by factors such as: -
Fig. 4. Two-winding three-phase transformer
Frequency response required from the model. Length of the submarine cable
A good approximation of the maximum frequency range represented by the “π” circuits line model is given by the following equation [11]: Fmax = Nv /8l B. Transformer Transformers can be represented by a ‘classical’ model; each phase is represented by a single-phase transformer model with no coupling between phases. Frequency dependency is represented by multiplying the series resistance of the transformers by the square root of the harmonic order (see Figure 4) [3]. C. Generators Generators used for wind turbines include fixed-speed induction generator (FSIG), doubly fed induction generator (DFIG) and full power converter (FPC) synchronous or asynchronous generators. A typical configuration of a DFIG wind turbine system is shown schematically in Figure 5. For harmonic analysis, DFIG converters can be considered as two harmonic voltage sources one connected to the rotor and the other connected to the stator. The harmonics produced by each converter depend on the type of switching strategy used. In order to find out the harmonic currents on the stator winding using the induction machine equivalent circuit shown in Figure 6, the following is considered: a) Stator is short circuited for harmonic frequencies b) Slip for harmonics is given by harmonic frequency. c) The stator, rotor and magnetizing reactance are multiplied by a factor of ks [7].
Fig. 3. Submarine cable model with N “π” circuits.
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Fig. 5. Basic configuration of a DFIG wind turbine.
Fig. 6. DFIG equivalent circuit (referred to the rotor side) for harmonic frequencies
Analytical techniques have been proposed to study harmonics in a DFIG connected to the grid. An algorithm based on Hilbert transform for the analysis of harmonics in power systems was developed in [4]. An equivalent circuit is is shown in Figure 7 [10]. D. Compensation equipment: STATCOM In its most basic form, the D-STATCOM configuration consists of a two-level VSC, a dc energy storage device; a coupling transformer connected in shunt with the ac system, and associated control circuits. More sophisticated configurations use multipulse and/or multilevel configurations.
Fig. 7. The equivalent circuit network of connecting and running of the doubly-fed induction wind turbine
Figure 8 shows the schematic representation of a DSTATCOM. The VSC converts the dc voltage across the storage device into a set of three-phase ac output voltages. The VSC connected in shunt with the ac system provides a multifunctional topology which can be used for up to three quite distinct purposes [1]: 1) Voltage regulation and compensation of reactive power; 2) Correction of power factor; 3) Elimination of current harmonics. E. HVDC HVDC systems support the power systems grids with the transmission of energy in weak transmission lines helping to transmit more energy in the same line. With the development of power electronics devices, HVDCs, specially VSC-HVDC, has been used to integrate large-scale renewable energy sources to the grid, specially the large offshore wind farms. The VSC-HVDC is used to interconnect asynchronous networks, as a bulk power transmission, it is also used as back-to-back AC system link [20]. The model of a monopolar VSC-HVDC interconnection, with a dc voltage level of +150kV and converter rating of 300MVA is presented in [9]. Active power can be transmitted in either direction, combined with generation or consumption of reactive power. Active power generated in the wind farm is absorbed by the sending end converter and transmitted across the dc cable. The receiving-end converter reactive power production/absorption can be controlled to meet the terms of the grid code requirements [5]. In [9], a large offshore wind farm is modelled using DIgSILENT PowerFactory simulation package. The wind turbine generator technology used is active stall regulated wind turbines driving fixed speed asynchronous generators. Two different types of interconnections are modelled; VSC-HVDC link and an AC cable interconnection. A simple representation of a wind farm with full converter wind turbines that is connected to the network with possible resonances excitation is presented by Kocewiak as shown in Figure 9 [18].
Fig. 8. Schematic representation of the D-STATCOM as a custom power controller.
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Fig. 9. Simple representation of a wind farm connected to the network with possible resonances excitation
In [19] a HVDC linked with a STATCOM is connected to a weak AC system. The stability problem is solved with the STATCOM that provides a fast recovery from power, harmonic stability and commutation failures. III. ALGORITHMS FOR NETWORK RECONFIGURATION The network configuration with minimum line losses is a problem that has been studied since 1975, when Merlin and Back proposed a non-linear optimization problem that was solved with a branch-and-bound method, a heuristic approach aimed to obtain a global minimum of losses [21]. Later, another heuristic algorithm to improve the one proposed before was presented, opening the switches with the lowest current determined by the optimal flow pattern [22]. After these solutions, various other algorithms have been proposed. In [23], two different algorithms are presented, one resorting to a genetic algorithm and the other solving a conventional mixed-integer linear problem to probe the method. An algorithm based on a heuristic strategy. The solution started with a meshed system obtained by closing all tie switches. Then the switches are opened successively based on minimum power loss increase, determined by a power flow. A branch exchange procedure was applied in the neighbourhoods of the open switches to improve the solution [24]. The optimization problem is a mixed integer nonlinear optimization problem, where the integer variables represent the state of the switches and the current flowing through the branches. In this method the standard Newton method is used to compute the branch currents [25]. A method based on heuristic rules and fuzzy multi-objective approach is presented. Heuristics rules are incorporated to the algorithm for minimizing the number of tie-switch operations [26]. A genetic algorithm, with the searching space reduced when a new codification strategy and accentuated crossover and directed mutation operators, is used, reducing drastically the computational time [27]. An improved search algorithm is presented as an efficient meta-heuristic searching algorithm where a mutation operation is introduced in the algorithm to weaken the dependence of global search ability. Also, the candidate neighborhood is designed to improve local search efficiency saving a large amount of computational time [28].
A fuzzy distribution power flow for weakly meshed balanced and unbalanced distributions systems is presented; a matrix similar to Jacobian inverse is directly evaluated [29]. An optimal power flow-based approach is presented in [30], in which the switch status was represented by continuous functions to reduce the number of power flow runs [24].
distribution systems, the demands are modelled through linear approximations with the benefits of a robust mathematical model, an efficient computational behaviour and convergence guaranteed [44].
A heuristic technique based on the direction of the branch power flows, despite of its simplicity, has a good effectiveness [31]. A two-stage method is presented, its efficiency stems from the use of real power loss sensitivity with respect to the impedances of the candidate branches [32]. A new fuzzy multi-criteria decision making algorithm is proposed for the proper processing of the information sources available at the utilities in the context of distribution network reconfiguration [33]. It is presented an ordinal optimization method that consist in three main phases, that is, namely 1) large search space of potential combinations; 2) objective function is evaluated using a crude but computationally efficient linear programming model; and 3) the top alternatives are simulated via an exact non-linear programming optimal power flow program to find the best distributed generation locations and capacities [34]. To get the precise branch current and system power loss, a power summation-based radiation distribution network load flow method is applied in [35]. A genetic algorithm is used for reconfiguration of radial distribution systems [36]; a forward and backward algorithm is used to calculate load flows in unbalanced distribution systems, simulating the survival of the fittest among the strings, performing crossover and mutation is obtained the optimum string.
A brief review of the main components of an offshore wind farm has been presented. Models must be developed close to reality to design efficient systems, but sometimes it is not possible, as in practice several problems arise and cannot be simulated. A review of existing methods for network configuration to minimize power losses was presented. A solution is to reconfigure the system to maximize the current flow, but keeping constrains like the power flow capacity in the nodes and lines, the voltage magnitude on the nodes, harmonic flow within limits, voltage rise and fluctuations, cost. Because the problem is combinational, and the magnitude of the complexity is very high in large electrical systems, this is the reason why the problem remains unsolved, but there are several papers that try to solve this issue.
A meta-heuristic algorithm to minimize active power loss based on modified honey-bee-mating optimization is presented, where heuristic functions with a higher contribution in solution improvement will be used in the next process, limiting unnecessary objective function evaluation for heuristics functions [37]. An algorithm based on simple heuristic rules where an effective switch status configuration for maximizing the line maximum load ability of the system is identified. Then a profile calculation of the best switching combination is found by load flow solution [38]. A heuristic algorithm based on the branch-and-bound strategy, the search tree is obtained by subdividing the feasible set using the branch exchange technique [39]. A method to obtain an optimal reconfiguration to reduce the total cost of operation and loss reduction is proposed in [40]. A review of techniques of optimization of power distribution systems, that are used to solve problems with different and limited objectives and constraints, is presented in [41]. A genetic algorithm that uses the edge-window-decoder-encoding technique for network representation and building up spanning trees (using efficient operators in order to explore the search space), is introduced in [42]. A method that combines reliability and efficiency to minimize active energy losses using a non-sequential Monte Carlo simulation based on the branch reliability and a genetic algorithm makes the optimization has been discussed in [43]. An algorithm is modelled as a mixed-integer linear programming to solve the problem of reconfiguration of
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IV. CONCLUSIONS
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