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A methodology to design a fuzzy logic based supervision of Hybrid Renewable Energy Systems
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Mathematics and Computers in Simulation 81 (2010) 208–224
A methodology to design a fuzzy logic based supervision of Hybrid Renewable Energy Systems Vincent Courtecuisse a,b , Jonathan Sprooten a,b,∗ , Benoît Robyns a,b , Marc Petit c , Bruno Francois a,d , Jacques Deuse e a
b
Univ. Lille Nord de France, Lille, France Ecole des Hautes Etudes d’Ingénieur (HEI), L2EP, Lille, France c SUPELEC, Plateau de Moulon, Gif-sur-Yvette, France d ECLille, L2EP, Villeneuve d’Ascq, France e Suez-Tractebel, Bruxelles, Belgium
Received 2 October 2008; received in revised form 25 February 2010; accepted 6 March 2010 Available online 1 April 2010
Abstract Hybrid Renewable Energy Systems (HRES) are increasingly used to improve the grid integration of wind power generators. The goal of this work is to propose a methodology to design a fuzzy logic based supervision of this new kind of production unit. A graphical modeling tool is proposed to facilitate the analysis and the determination of fuzzy control algorithms adapted to complex hybrid systems. To explain this methodology, the association of wind generators, decentralized generators and storage systems are considered for the production of electrical power. The methodology is divided in six steps covering the design of a supervisor from the system work specifications to an optimized implementation of the control. The performance of this supervisor is shown with the help of simulations. Finally, the application of this methodology to the supervision of different topologies of HRES is also proposed to bring forward the systematic dimension of the approach. © 2010 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Energy management system; Hybrid power integration; Power management; Renewable energy systems; Fuzzy logic supervision
1. Introduction The electricity market liberalization and the development of the decentralized generation lead to many new scientific and technical problems. The major problem emerging with decentralized energy sources, and particularly renewable energy ones, is their limited abilities to contribute effectively to power system management. Precisely, a large amount of wind energy resources in the energy mix will cause problems for the overall system “stability” [2]. The large scale development of wind power generators work will be facilitated by: • the supply of ancillary services (voltage and frequency control, black starting, etc.), ∗
Corresponding author at: Ecole des Hautes Etudes d’Ingénieur (HEI), Department Energies-Electricity-Automation (EEA), 13, rue de Toul, 59046 Lille, France. Tel.: +33 3 28 38 48 58; fax: +33 3 28 38 48 04. E-mail addresses: [email protected] (V. Courtecuisse), [email protected] (J. Sprooten), [email protected] (B. Robyns), [email protected] (M. Petit), [email protected] (B. Francois), [email protected] (J. Deuse). 0378-4754/$36.00 © 2010 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2010.03.003
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• their association with other foreseeable and controllable sources into a global integrated management, • their association with storage systems. Hybrid Renewable Energy Systems (HRES) are increasingly used to improve the grid integration of wind generators. The goal of this work is to propose a methodology to design the supervision of this new kind of production units. Many publications have been written on HRES [9], but most of these papers (almost 90%) focus on design and economic aspects. However, relatively small changes in the control strategy can significantly affect the performance of the hybrid unit. Three methods are investigated in the literature to supervise hybrid production units: • Power balance analysis [8,14]. This method controls the output power of the HRES but does not integrates energy consideration. However, energy management is critical when a storage system is associated to the hybrid production. • Optimal control strategy [5]. This strategy uses several input signals to reach a multi-objective optimization. However, the algorithms are based on models of the system to be controlled and require much computing time. • Fuzzy logic supervisor [1,4,6,10]. Compared with the first method, this strategy takes into account the energy level of the storage system. Furthermore, this approach is well adapted to represent uncertainties in the inputs or in the behaviour of the HRES by fuzzyfication of uncertain variables and assigning membership functions, which are based on preference and/or experience. However, until now, no dedicated tool for the design of such supervisors is available. The studied HRES is the association of a wind turbine, a foreseeable power source and storage systems. The goal of the supervision is to track a reference power while maximizing the generated wind energy and minimising the use of fossil energy. Furthermore, in case of frequency deviations, the HRES should contribute to the primary frequency control. For this problem, a fuzzy logic based supervision is chosen as it is well adapted to deal with: • the complexity of the system, which has to be controlled and the difficulty to obtain or to use accurate models, and with • the difficulty to predict the behavior of the wind and the variation of the network frequency with load variations. The paper will present a systematic methodology to design a fuzzy supervisor. Currently, to design the control of a complex system in industrial applications, two graphical tools are used; Petri nets [13,16] and grafcets [11]. These tools enable to build graphically and step by step the control system so as the analysis and the implementation of control functions are easier. These tools are well suited for sequential logical systems. However, they are not well adapted for hybrid production units, which include random and continuous variables. The proposed methodology is an extension of this graphical approach to include fuzzy and unknown data. This study shows that the proposed method allows: • • • •
the avoidance of precise and elaborate models of the different sources and storage systems, a systematic determination of the supervisor, smoothed transitions between the different states of the hybrid system, the minimization of the number of fuzzy rules (from 540 to 44 in the considered example) and then the simplification of the real time implementation.
In Section 2, the methodology to design the supervision strategy of the hybrid system is described. In Sections 3 and 4, the performance of the proposed strategy is shown with the help of the modelling (Section 3) and the simulations (Section 4) of the system and its control. In Section 5, the approach is tested on different hybrid systems to illustrate the systematic design of the supervisor. And finally conclusions are drawn on the proposed methodology.
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2. Methodology for supervisor design In order to develop a supervision system, the proposed methodology is based on six steps: 1. the determination of work specifications of the system; the characteristics and the objectives of the system must be clearly identified; 2. the supervisor design; the required inputs and outputs of the supervisor must be determined; 3. the determination of the “functional graphs”; a chart representation of operating modes is proposed based on the knowledge of the system; 4. the membership functions are defined; 5. the determination of the “operational graphs”; a chart representation of fuzzy operating modes is proposed; 6. the fuzzy rules are extracted from the “operational graphs”. This methodology is applied to the proposed HRES system. 2.1. Determination of system work specifications In order to generate a reference power and to ensure a power reserve, the studied HRES system includes a wind turbine generator (WTG), a short-term and a long-term storage system and a foreseeable decentralised generator (FDG). The FDG could be for example a gas turbine. This hybrid generation system is connected at a common coupling point with the network (Fig. 1) and must be considered by the network operator as a classical source. The HRES must provide the reference power, which is imposed by the network operator and maximise the wind power. Furthermore, in order to contribute to the primary control of the frequency [7,15], an energy reserve must be available. In an electrical network, an unbalance between the generated power and the consumed power will be compensated by the kinetic energy of the rotating machines. This will results in a change of the rotating speed and therefore of the grid frequency, which is observed by all generation units in the network. The contribution to the frequency control for production units consists in the increase of its production in case of a frequency drop and in its decrease when the frequency rises. It is classically defined by a linear relation called the droop line as shown in Fig. 2. The characteristics of this relation are its slope and the difference between the reference power Pref and the maximum power Pmax . This difference is called the primary reserve (Preserve ). The size of this reserve is defined by the network operator according to technical and economical criteria.
Fig. 1. System under study.
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Fig. 2. Idealised frequency-power characteristic of a turbo alternator.
In order to avoid the use of wind generators for small grid frequency deviations, a dead band is often introduced by the network operators in the droop characteristic [12]. This feature will be introduced in the proposed supervisor. 2.2. Supervisor design In order to reach the objectives, some required inputs can already be defined; to provide the reference power (Pref ), an input of the supervisor should be the error (P = Pref − Phyb ) where Phyb is the total power generated by the HRES (which is the sum of the power generated by storage units, WTG and FDG). The control of the frequency requires the frequency error (f) between the network normal frequency (f0 ) and the measured frequency (fmeas ). In order to be close to the classical implementation of primary frequency control, the droop characteristic is defined out of the fuzzy supervisor and performed by the storage systems as they represent the energy and power reserve. Therefore, to guarantee the availability of the energy and power reserve for frequency control as well as the regulation of the output power to Pref , the storage levels need to be controlled; the short and long-term storage levels (Levstor sht and Levstor lgt ) are added to the list of the inputs of the supervisor. The outputs of the supervisor should be: • the reference power for the storage systems; Pref stor sht for the short-term storage unit and Pref stor lgt for the long-term storage unit, • the reference power for the FDG (Pref FDG ), and • the pitch angle reference βref , which is used to modify the captured wind energy by changing the blade angle. This action is therefore used to decrease the output power of the WTG. The block diagram of the supervisor is shown in Fig. 3. The supervisor is divided into two parts: • the fuzzy logic supervisor, which manages the FDG (Pref FDG ), the WTG (βref ) and a part of the storage system (Pref stor sht1 , Pref stor lgt1 ), which is used to compensate the wind power variations, • the droop characteristics, which allows to contribute to primary frequency control with the short and long-term storage systems (Pref stor sht2 , Pref stor lgt2 ). The reference power of the storage systems is then the sum of two terms: Pref
stor sht
= Pref
stor sht1
Pref
stor lgt
= Pref
stor lgt1
+ Pref + Pref
stor sht2 stor lgt2
(1) (2)
Furthermore, in extreme situations when the storage levels are very low or very high, the supervisor will use the WTG or the FDG to bring a contribution to the frequency control.
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Fig. 3. Block diagram of the supervisor.
2.3. Determination of the “functional graphs” Based on the knowledge of the system, the strategy of the fuzzy logic supervisor can be defined. This is graphically represented in Fig. 4. The operating modes are represented with rounded rectangles and the states of the system are represented by transitions. As seen in Fig. 4, the fuzzy logic part of the supervisor of Fig. 3 is divided in two main operating modes; N1 and N2. The objective of the first part (N1) is to control the power, which is generated by the HRES. The three operating modes of this part are based on the states of the storage systems: • N1.1: if the storage level is medium the HRES must supply the reference power while maximizing the WTG power. Then the WTG operates in maximal extraction power (MPPT) and the storage unit compensates the difference between the reference power (Pref ) and the hybrid power (Phyb ). • N1.2: if the storage level is high, the HRES must keep storage availability for primary power reserve. In this case the storage unit must be discharged and the WTG power is decreased with the help of the pitch angle (β). When the output power of the WTG is reduced, a power reserve is naturally created by the WTG to take part in primary frequency control. Using this approach, in case of high storage level, the contribution to frequency control is performed not only by the storage system but also by the WTG. • N1.3: if the storage level is low, the HRES must keep storage availability. Then the storage units must be charged and the FDG must ensure the reference power. When the FDG is in operation, it can take part in primary frequency control. Using this approach, in case of very low storage level, the contribution to frequency control is performed not only by the storage system but also by the FDG.
Fig. 4. Chart representation of the fuzzy logic supervisor.
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Fig. 5. Chart representation of different operating modes.
The goal of the second part (N2) is to allow the action of the control of the frequency trough the droop characteristics. Indeed, it is important that the fuzzy logic supervisor modifies it exigencies in HRES power regulation when additional power is required for frequency control. N1.1, N1.2, N1.3 and N2 are the objectives of the supervisor; the transitions (storage level and frequency variation) represent the constraints. Each operating mode (N1.1, N1.2, N1.3 and N2) is associated with a set of fuzzy rules. The transitions between the different operating modes are continuous functions. It is therefore possible to be either fully in one operating mode or partially in several operating modes and therefore to work on several objectives at the same time. This behaviour is obtained by the fuzzy logic supervisor. When several conditions are true, several fuzzy rules impact the same output and the final value of this output is the “center of gravity” of these combined trapezoid functions determined by the fuzzy logic [3]. This approach allows finding a compromise between different operating modes and smoothly moving from one to another. When two storage systems are considered, the three operating modes N1.1, N1.2, N1.3 are duplicated as it will be shown in Sections 4 and 5. N1.11, N1.12, N1.13 are related to the short-term storage and N1.21, N1.22, N1.23 are related to the long-term storage. In Fig. 5, the operating modes of the different subsystems are detailed. 2.4. Determination of the membership functions The next step of the proposed methodology is to define membership functions for the input and outputs variables of the fuzzy logic supervisor. The input membership functions are used as transitions between the different operating modes, they are shown in Fig. 6. The membership functions of the storage levels (Fig. 6a and b) are based on three levels to accommodate the needs of the proposed strategy:
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Fig. 6. Input membership functions of (a) power error; (b) short-term storage level; (c) frequency error and (d) long-term storage level.
• The small and high levels represent the energy reserve, which is required to participate in primary frequency control; in the considered example, in case of over-frequency or under-frequency, a minimum of 0.05 per unit energy reserve in both storage systems is taken. • In the proposed scenario, the medium level is used to compensate the wind power variations around the reference power. At least, 0.6 per unit of the short-term storage and 0.8 per unit of long-term storage are dedicated to this action. Fig. 6c represents the membership functions of the frequency variation f = f0 − fmeas . In the same way, three levels are defined: • When the frequency variation is negative or positive, the primary control of the frequency must be applied. • The trapezoidal form of the membership function Z allows the introduction of the dead band of the droop characteristic. In this case, for −0.1 Hz < f < 0.1 Hz the primary frequency control is not in operation. Fig. 6d represents the membership functions of the power error P = Pref − Phyb . Five levels are considered to perform a compromise between the accuracy of the power control and its complexity [3]. The output membership functions are shown in Fig. 7a–d for respectively, the short-term storage power reference, the long-term storage power reference, the pitch angle and the FDG power reference. The storage power may be positive or negative, then five levels are considered; NB, NM, Z, PM and PB where N stands for Negative, Z for Zero, P for Positive, B for Big and M for Medium. The action of the pitch on the output power being non linear, the membership function the levels Z, M, and B are chosen to linearize this control. The FDG power reference being always positive, three levels are considered to implement a compromise between precision and complexity. However, as the nature of
Fig. 7. Output membership function of (a) short-term reference power, (b) long-term reference power, (c) pitch angle reference and (d) FDG reference power.
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Fig. 8. Operational graph of the supervisor.
the FDG is not taken into consideration, indifferent membership functions are chosen, it this example they correspond to the membership functions of the pitch angle. The fuzzy logic supervisor of the HRES is based on four membership functions to describe the input variables with a total of 14 membership degrees. Therefore a maximum of 135 rules may be considered. Traditionally, to determine the fuzzy rules, all cases are identified with the help of tables [3]. In this case, the table will have four dimensions and contains 540 cases because of the four inputs. The fuzzy inferences are performed using a Mamdani fuzzy model with minimum composition as this model was initially designed to translate human experience into an automatic supervisor. With the proposed methodology, a graphic representation called the “operational graph” will enable to grasp the global performance of the system and extract the pertinent fuzzy rules. 2.5. Determination of the “operational graphs” As shown in Fig. 5, it is possible to decompose the system in many subsystems. This decomposition allows the determination of the fuzzy rules. To achieve this goal the functional graph must be translated with the variables of the membership functions. The transitions between the operation modes are described by the levels of the input membership functions and the actions of the operating modes are described by the levels of the output membership functions. This will lead to the operational graph shows in Fig. 8. The details of this operational graph are given in the case of the operating mode N1.11 for which the operational graph is shown in Fig. 9. The same operation needs to be performed for the other operating modes. 2.6. Extraction of the fuzzy rules From the diagram shown in Fig. 9, the fuzzy rules of the operating mode N1.11 are easily obtained: • IF f is Z AND Levstor sht is M AND P is NB THEN Pref stor sht is NB • IF f is Z AND Levstor sht is M AND P is NM THEN Pref stor sht is Z • IF f is Z AND Levstor sht is M AND P is Z THEN Pref stor sht is Z
Fig. 9. Operational graph of N1.11 operating mode.
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• IF f is Z AND Levstor sht is M AND P is PM THEN Pref stor sht is PM • IF f is Z AND Levstor sht is M AND P is PBTHEN Pref stor sht is PB If this operation is performed for all the operating modes identified in Fig. 5, only 44 fuzzy rules are considered instead of the 540 possible fuzzy rules given by the tables. The list of these rules is given in Appendix A. The proposed methodology not only allows a systematic construction of a fuzzy logic supervisor but also allows a reduction of the number of fuzzy rules (from 540 to 44 in the considered example). This will simplify the real time implementation of the supervisor. 3. Modelling of the system under study In order to illustrate the effectiveness of the supervisor, built using the proposed methodology, several simulations of the electromechanical system and its supervisor will be presented. The models of the different elements of the system will be presented. It is important to note that this modelling effort is not required for the design of the supervisor but allows the simulation of its behaviour. The supervisor structure is therefore independent of the technology used for HRES. However, simulations help to determine some parameters of the supervisor (limits of the membership functions for instance). 3.1. Wind turbine generator (WTG) The considered variable speed wind generator is based on a permanent magnet synchronous generator connected to the network via two back to back AC-DC converters. The turbine is modelled by the classical relation between wind speed and power, which can be extracted: 1 (3) ρAr CP (λ, β)v3 2 where ρ is the air density, Ar is the surface swept by the blades, Cp (λ,β) is the power coefficient, λ = Ωt Rt /v is the speed ratio, Ωt is the turbine speed, Rt is the turbine radius, β is the pitch angle and v is the wind speed. The power coefficient dependence with λ and β(Cp (λ,β)) is classically modelled by considering the analytical expression given in [2]. Pw =
3.2. Foreseeable decentralized generator (FDG) As shown in Fig. 10, the considered FDG is modelled by a simple first order transfer function between the reference power (PFDG ref ) and the output power (PFDG ) [2]. The transfer function is given by (4) where τ FDG is the time constant, which depends on the considered technology: H(s) =
1 τFDG s + 1
(4)
In Fig. 10, PFDG min and PFDG max are respectively the minimum and maximum power of the FDG. 3.3. Storage system In the same way, a simplified model is used to model the short and long-term storage units. Fig. 11 shows the block diagram of this model, where Prefstor is the reference power of the storage system, Wstor is the stored energy and Pstor
Fig. 10. Foreseeable decentralized generator model.
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Fig. 11. Storage unit model.
is the actual power of the storage system. The storage system is not based on a priori defined technology. It is only characterized by a maximum power of charge (Pchmax ), a maximum power of discharge (Pdchmax ), a charging and discharging efficiency (ηch and ηdch ) and a maximum and minimum level of stored energy (Wmin and Wmax ), which defines the value m1 such that if Wstor = Wmax or Wstor = Wmin m1 = 0 and m1 = 1 otherwise. 4. Simulations The most important parameters of the system (presented in Fig. 1) are given in Table 1. In this table, Sconv is the apparent power of the network, Pload1 is the active power of the load 1 and Pload2 is the active power of the load 2. To illustrate a significant contribution of the hybrid generator, the total power of the network is taken relatively small. The simulations are carried out with the help of the Matlab/SimulinkTM software. In the proposed scenario, the reference power of the hybrid generator for 0 h < t < 1 h is set at 600 kW, which is equal to the mean wind power, for 1 h < t < 2 h, a reference power of 400 kW, lower than the mean available wind power, is considered and a reference Table 1 Parameters. Foreseeable source PFDG τ FDG
750 kW 5s
Network Sconv Pload1 Pload2
3 MVA 800 kW 800 kW
Short-term storage Pchmax stor sht Pdchmax stor sht τ ch stor sht τ dch stor sht Wmax stor sht
300 kW −300 kW 0.5 s 0.5 s 4.167 kWh
Long-term storage Pchmax stor lgt Pchmax stor lgt τ ch stor lgt τ dch stor lgt Wmax stor lgt
230 kW −230 kW 5s 5s 416.7 kWh
Wind turbine PWTG
750 kW
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Fig. 12. Hybrid generator performance for three different reference powers: (a) wind and hybrid generator power, (b) network frequency, (c) energy of long-term storage, (d) energy of short-term storage, (e) pitch angle of wind turbine, and (f) power of the FDG unit.
power of 800 kW, above the mean available wind power, is taken for 2 h < t < 3 h. An 800 kW load is connected at t = 0 h20, t = 1 h20 and t = 1 h40 and disconnected at t = 0 h40, t = 1 h40 and t = 2 h40 to create real frequency variations. Fig. 12 shows the simulation results of the WTG power in broken line (Fig. 12a), the total HRES power in full line (Fig. 12a), the grid frequency (Fig. 12b), the storage level of the long-term (Fig. 12c) and short-term storage systems (Fig. 12d), the pitch angle (Fig. 12e) and the FDG power (Fig. 12f). Fig. 12a shows that the power reference is well provided in spite of the wind and load variations. Fig. 12b shows that, when a load is connected, the HRES power increases rapidly, and the inverse phenomenon appears when a load is disconnected in relation with the primary frequency control. Fig. 12d and e illustrate that when the energy of short-term storage is high, the pitch angle is controlled to reduce and smooth the wind power. Fig. 12d and f illustrate that when the energy of the short-term storage is low, the FDG is controlled to compensate the lack of wind power. In addition, the WTG and the FDG take part in frequency control when they are in operation. Finally, Fig. 12c shows that the long-term storage system compensates the low frequency deviations between the wind power and the reference power. 5. Comparison of different HRES topologies In order to illustrate the main advantages of a graphical representation of the fuzzy logic supervisor, the proposed methodology is applied to different topologies of HRES. For each scenario, a chart representation of the supervisor is derived from the one shown in Fig. 5. 5.1. Association of a WTG and a FDG (case a) The considered system is a modification of the system presented in Fig. 1, which only includes a wind turbine generator and a foreseeable source. As previously, the objectives of the supervisor are to generate the reference power and to ensure the primary frequency control. Fig. 13 shows the chart representation of the system, the supervision system is divided in three parts; when the HRES power is lower than the reference power the FDG must provide the difference between the reference power and the WTG power. In the same way, when the HRES power is higher than the reference power, the wind power must be decreased with the help of the pitch angle. For this graph, an operational graph can be obtained and is used to define
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Fig. 13. Chart representation of the different operating modes.
Fig. 14. Hybrid generator power and reference power.
the pertinent fuzzy rules. The 14 rules pertinent rules are the ones of section N1.12 and N1.13 from Appendix A that do not refer to the storage reference power and where the dependence with the storage level is removed. Fig. 14 shows that the reference power is well provided. 5.2. Association of a WTG, a FDG and a short-term storage unit (case b) The considered system is a modification of the system presented in Fig. 1, which only includes the WTG, the FDG and the short-term storage system.
Fig. 15. Chart representation of different operating modes.
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Fig. 16. Comparison of the hybrid generator power and the hybrid reference power.
Fig. 15 shows the chart representation of the supervisor. This supervisor is the part N1.1 and N2 of the supervisor shown in Fig. 5. The 22 pertinent fuzzy rules that can be obtained from this graph are the ones of section N1.1 and N2 from Appendix A that do not refer to the long-term storage reference power. Fig. 16 shows that the reference power is again well provided.
Fig. 17. Chart representation of different operating mode.
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Fig. 18. Hybrid generator power compared to the hybrid reference power.
5.3. Association of a WTG, short and long-term storage units (case c) The considered system is a modification of the system presented in Fig. 1 which only includes a WTG, and short and long-term storage systems. The chart representation of the supervisor presented in Fig. 17 is very similar to the one shown in Fig. 5. The part concerning the FDG of Fig. 5 has been removed. The 30 fuzzy rules that can be obtained from this graph are the ones of the appendix that do not refer to the FDG reference power. Fig. 18 shows that when the reference power is lower than the mean wind power, the storage systems are sufficient to provide the reference power, this is no more the case when the reference power is bigger than the mean available power. 5.4. Association of a WTG and a short-term storage unit (case d) The considered system is a modification of the system presented in Fig. 1, which only includes a WTG and a short-term storage system. Fig. 19 shows the chart representation of the supervisor. The supervision system can be divided in three parts:
Fig. 19. Chart representation of different operating mode.
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Fig. 20. Comparison of the hybrid generator power and the hybrid reference power. Table 2 Comparison between different topologies. Case under study
Grid energy (kWh)
WTG energy (kWh)
FDG energy (kWh)
Average absolute error (kW)
Maximum absolute error (kW)
a b c d e
1800 1800 1783 1635 1800
1563 1636 1823 1635 1823
237 163 0 0 30.9
0.165 0.223 5.4 54.86 0.011
13 38 376 511 18
• When the storage level is medium, the short-term storage controls the reference power. • When the storage is high, the storage unit must be discharged and the WTG power is decreased with the help of the pitch angle. • When the storage level is low, the storage must be charged; in this case the reference power cannot be provided. The 15 fuzzy rules that can be obtained from this graph are the ones of section N1.1 and N2 from Appendix A that do not refer neither to the FDG reference power nor to the long-term storage power reference. In Fig. 20, the curve in broken lines corresponds to the reference power whereas the curve in full line corresponds to the HRES generated power. Only when the reference is smaller than the average wind power, the reference power is provided. When the reference is significantly different than the average wind power, the reference is provided within the limits of the storage system capacity. Five topologies are explored, WTG and FDG based HRES (case a); WTG, FDG and short-term storage unit based HRES (case b); WTG, short-term and long-term storage units based HRES (case c); WTG and short-term storage units based HRES (case d) and the complete system in case e. Table 2 allows us to compare different HRES topologies following different criteria; energy generated on the grid by the HRES, energy generated by the WTG and the FDG as well as average error and maximum error. When a FDG is included (cases a, b and e), a similar energy is provided to the grid. In these cases, the storage system enables to maximize the WTG energy and then to minimize the FDG energy (case b and e). The error between the power reference and the HRES power is rather small. When the HRES does not include the FDG, the reference power cannot be guaranteed when the wind power is lower than the reference power. 6. Conclusion In this paper, a methodology has been proposed to develop a fuzzy logic based supervisor. This method facilitates the analysis and the determination of fuzzy control algorithms adapted for complex hybrid systems. To explain this methodology, the association of a wind turbine based dispersed generators and storage systems have been considered. It avoids precise and elaborate models of the different sources and of the storage systems. Furthermore, this method allows a systematic determination of the supervisor and a minimization of the number of fuzzy rules. The performance of this supervisor has been shown with the help of simulations. Finally, the application of this methodology to the
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supervision of different topologies of HRES and the comparison of the performance of these topologies following 5 energy and power criteria has brought forward the systematic dimension of the approach. Perspectives of this work include optimal design of the input and output membership functions as well as experimental implementation of the proposed supervision on a laboratory test bench. Acknowledgements This work was supported by a funding from the regional Council Nord-Pas de Calais, the European Regional Development Funding, Suez-Tractebel Engineering Company, Supelec and HEI. Appendix A.
N1.11
N1.12 N1.1
N1.13
N1 N1.21
N1.22 N1.2
N1.23
N2
IF Levstor sht is M AND f is Z AND P is NB THEN Pref stor sht1 is NB IF Levstor sht is M AND f is Z AND P is PB THEN Pref stor sht1 is PB IF Levstor sht is M AND f is Z AND P is NM THEN Pref stor sht1 is NM IF Levstor sht is M AND f is Z AND P is PM THEN Pref stor sht1 is PM IF Levstor sht is M AND f is Z AND P is Z THEN Pref stor sht1 is Z IF Levstor sht is B AND f is Z THEN Pref stor sht1 is NM IF Levstor sht is B AND f is Z AND P is Z THEN βref is Z IF Levstor sht is B AND f is Z AND P is NM THEN βref is Z IF Levstor sht is B AND f is Z AND P is NB THEN βref is Z IF Levstor sht is B AND f is Z AND P is PM THEN βref is P IF Levstor sht is B AND f is Z AND P is PB THEN βref is B IF Levstor sht is B AND f is N THEN βref is Z IF Levstor sht is B AND f is P THEN βref is P IF Levstor sht is P AND f is Z THEN Pref stor sht1 is PM IF Levstor sht is P AND f is Z AND P is NB THEN Pref FDG is B IF Levstor sht is P AND f is Z AND P is NM THEN Pref FDG is P IF Levstor sht is P AND f is Z AND P is PB THEN Pref FDG is Z IF Levstor sht is P AND f is Z AND P is PM THEN Pref FDG is Z IF Levstor sht is P AND f is Z AND P is Z THEN Pref FDG is Z IF Levstor sht is P AND f is P THEN Pref FDG is Z IF Levstor sht is P AND f is N THEN Pref FDG is P IF Levstor lgt is M AND f is Z AND P is NB THEN Pref stor lgt1 is NB IF Levstor lgt is M AND f is Z AND P is PB THEN Pref stor lgt1 is PB IF Levstor lgt is M AND f is Z AND P is NM THEN Pref stor lgt1 is NM IF Levstor lgt is M AND f is Z AND P is PM THEN Pref stor lgt1 is PM IF Levstor lgt is M AND f is Z AND P is Z THEN Pref stor lgt1 is Z IF Levstor lgt is B AND f is Z THEN Pref stor lgt1 is NM IF Levstor lgt is B AND f is Z AND P is NB THEN βref is Z IF Levstor lgt is B AND f is Z AND P is Z THEN βref is Z IF Levstor lgt is B AND f is Z AND P is NZ THEN βref is Z IF Levstor lgt is B AND f is Z AND P is PM THEN βref is P IF Levstor lgt is B AND f is Z AND P is PB THEN βref is B IF Levstor lgt is B AND f is N THEN βref is Z IF Levstor lgt is B AND f is P THEN βref is P IF Levstor lgt is P AND f is Z THEN Pref stor lgt1 is PM IF Levstor lgt is P AND f is Z AND P is NB THEN Pref FDG is B IF Levstor lgt is P AND f is Z AND P is NM THEN Pref FDG is P IF Levstor lgt is P AND f is Z AND P is PB THEN Pref FDG is Z IF Levstor lgt is P AND f is Z AND P is PM THEN Pref FDG is Z IF Levstor lgt is P AND f is Z AND P is Z THEN Pref FDG is Z IF Levstor lgt is P AND f is P THEN Pref FDG is Z IF Levstor lgt is P AND f is N THEN Pref FDG is P IF f is P THEN Pref stor sht1 is Z IF f is N THEN Pref stor lgt1 is Z
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References [1] C. Abbey, G. Joos, Energy management strategies for optimization of energy storage in wind power hybrid system, in: Power Electronics Specialists Conference (PESC2005), 2005, pp. 2066–2072. [2] T. Ackerman, Wind Power in Power Systems, Wiley & Sons, Ltd, 2005, ISBN 0-470-85508-8. [3] P. Borne, J. Rozinoer, J.-Y. Dieulot, L. Dubois, Introduction à la commande floue, Technip (1998). [4] G. Boukettaya, L. Krichen, A. Ouali, Fuzzy logic supervisor for power control of an isolated hybrid energy production unit, International Journal of Electrical and Power Engineering (2007) 279–285. [5] R. Caldon, A.R. Patria, R. Turri, Optimal Control of a Distribution System with a Virtual Power Plant, International conference on Bulk Power System Dynamics and Control (2004) 278–284. [6] G. Cimuca, C. Saudemont, B. Robyns, M. Radulescu, Control and performance evaluation of a flywheel energy storage system associated to a variable speed wind generator, IEEE Transactions on Industrial Electronics 53 (2006) 1074–1085. [7] V. Courtecuisse, B. Robyns, B. Francois, M. Petit, J. Deuse, Variable speed wind generators participation in primary frequency control, Wind Engineering 32 (3) (2008) 299–318. [8] Ph. Degobert, S. Kreuawan, X. Guillaud, Micro-grid powered by photovoltaic and micro turbine, International Conference on Renewable Energy and Power Quality (2006) (CD-ROM). [9] M.K. Deshmukh, S.S. Deshmukh, Modeling of hybrid renewable energy systems, Renewable and Sustainable Energy Reviews 12 (2008) 235–249. [10] M.N. Eskander, T.F. El-Shatter, M.T. El-Hagry, Energy flow management of a hybrid Wind/PV/Fuel cell generation system, Energy Conversion and Management 47 (2006) 1264–1280. [11] L. Guillemaud, H. Guegen, Extending grafcet for the specification of control of hybrid systems, IEEE International Conference on Systems, Man, and Cybernetics (1999) 171–175. [12] J.R. Kristoffersen, The horns rev wind farm and the operational experience with the wind farm main controller, Revue E Tijdschrift 2 (2006). [13] D. Lu, H. Fakham, T. Zhou, B. Francois, Application of Petri nets for the energy management of a photovoltaic based power station including storage units, Elsevier Renewable Energy 35 (6) (2010) 1117–1124. [14] J. Morren, S.W.H. de Haan, J.A. Ferreira, Primary power/frequency control with wind turbine and fuel cells, in: IEEE PES General Meeting, 2006. [15] Y.G. Rebours, D.S. Kirschen, M. Trotignon, S. Rossignol, A survey of frequency and voltage control ancillary service—Part I: Technical feature, IEEE Transactions on Power Systems 22 (2007). [16] R. Zurawski, M. Zhou, Petri net and industrial application: a tutorial, IEEE Transactions on Industrial Electronics 41 (1994) 567–583.
Mathematics and Computers in Simulation 81 (2010) 208–224
A methodology to design a fuzzy logic based supervision of Hybrid Renewable Energy Systems Vincent Courtecuisse a,b , Jonathan Sprooten a,b,∗ , Benoît Robyns a,b , Marc Petit c , Bruno Francois a,d , Jacques Deuse e a
b
Univ. Lille Nord de France, Lille, France Ecole des Hautes Etudes d’Ingénieur (HEI), L2EP, Lille, France c SUPELEC, Plateau de Moulon, Gif-sur-Yvette, France d ECLille, L2EP, Villeneuve d’Ascq, France e Suez-Tractebel, Bruxelles, Belgium
Received 2 October 2008; received in revised form 25 February 2010; accepted 6 March 2010 Available online 1 April 2010
Abstract Hybrid Renewable Energy Systems (HRES) are increasingly used to improve the grid integration of wind power generators. The goal of this work is to propose a methodology to design a fuzzy logic based supervision of this new kind of production unit. A graphical modeling tool is proposed to facilitate the analysis and the determination of fuzzy control algorithms adapted to complex hybrid systems. To explain this methodology, the association of wind generators, decentralized generators and storage systems are considered for the production of electrical power. The methodology is divided in six steps covering the design of a supervisor from the system work specifications to an optimized implementation of the control. The performance of this supervisor is shown with the help of simulations. Finally, the application of this methodology to the supervision of different topologies of HRES is also proposed to bring forward the systematic dimension of the approach. © 2010 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Energy management system; Hybrid power integration; Power management; Renewable energy systems; Fuzzy logic supervision
1. Introduction The electricity market liberalization and the development of the decentralized generation lead to many new scientific and technical problems. The major problem emerging with decentralized energy sources, and particularly renewable energy ones, is their limited abilities to contribute effectively to power system management. Precisely, a large amount of wind energy resources in the energy mix will cause problems for the overall system “stability” [2]. The large scale development of wind power generators work will be facilitated by: • the supply of ancillary services (voltage and frequency control, black starting, etc.), ∗
Corresponding author at: Ecole des Hautes Etudes d’Ingénieur (HEI), Department Energies-Electricity-Automation (EEA), 13, rue de Toul, 59046 Lille, France. Tel.: +33 3 28 38 48 58; fax: +33 3 28 38 48 04. E-mail addresses: [email protected] (V. Courtecuisse), [email protected] (J. Sprooten), [email protected] (B. Robyns), [email protected] (M. Petit), [email protected] (B. Francois), [email protected] (J. Deuse). 0378-4754/$36.00 © 2010 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2010.03.003
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• their association with other foreseeable and controllable sources into a global integrated management, • their association with storage systems. Hybrid Renewable Energy Systems (HRES) are increasingly used to improve the grid integration of wind generators. The goal of this work is to propose a methodology to design the supervision of this new kind of production units. Many publications have been written on HRES [9], but most of these papers (almost 90%) focus on design and economic aspects. However, relatively small changes in the control strategy can significantly affect the performance of the hybrid unit. Three methods are investigated in the literature to supervise hybrid production units: • Power balance analysis [8,14]. This method controls the output power of the HRES but does not integrates energy consideration. However, energy management is critical when a storage system is associated to the hybrid production. • Optimal control strategy [5]. This strategy uses several input signals to reach a multi-objective optimization. However, the algorithms are based on models of the system to be controlled and require much computing time. • Fuzzy logic supervisor [1,4,6,10]. Compared with the first method, this strategy takes into account the energy level of the storage system. Furthermore, this approach is well adapted to represent uncertainties in the inputs or in the behaviour of the HRES by fuzzyfication of uncertain variables and assigning membership functions, which are based on preference and/or experience. However, until now, no dedicated tool for the design of such supervisors is available. The studied HRES is the association of a wind turbine, a foreseeable power source and storage systems. The goal of the supervision is to track a reference power while maximizing the generated wind energy and minimising the use of fossil energy. Furthermore, in case of frequency deviations, the HRES should contribute to the primary frequency control. For this problem, a fuzzy logic based supervision is chosen as it is well adapted to deal with: • the complexity of the system, which has to be controlled and the difficulty to obtain or to use accurate models, and with • the difficulty to predict the behavior of the wind and the variation of the network frequency with load variations. The paper will present a systematic methodology to design a fuzzy supervisor. Currently, to design the control of a complex system in industrial applications, two graphical tools are used; Petri nets [13,16] and grafcets [11]. These tools enable to build graphically and step by step the control system so as the analysis and the implementation of control functions are easier. These tools are well suited for sequential logical systems. However, they are not well adapted for hybrid production units, which include random and continuous variables. The proposed methodology is an extension of this graphical approach to include fuzzy and unknown data. This study shows that the proposed method allows: • • • •
the avoidance of precise and elaborate models of the different sources and storage systems, a systematic determination of the supervisor, smoothed transitions between the different states of the hybrid system, the minimization of the number of fuzzy rules (from 540 to 44 in the considered example) and then the simplification of the real time implementation.
In Section 2, the methodology to design the supervision strategy of the hybrid system is described. In Sections 3 and 4, the performance of the proposed strategy is shown with the help of the modelling (Section 3) and the simulations (Section 4) of the system and its control. In Section 5, the approach is tested on different hybrid systems to illustrate the systematic design of the supervisor. And finally conclusions are drawn on the proposed methodology.
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2. Methodology for supervisor design In order to develop a supervision system, the proposed methodology is based on six steps: 1. the determination of work specifications of the system; the characteristics and the objectives of the system must be clearly identified; 2. the supervisor design; the required inputs and outputs of the supervisor must be determined; 3. the determination of the “functional graphs”; a chart representation of operating modes is proposed based on the knowledge of the system; 4. the membership functions are defined; 5. the determination of the “operational graphs”; a chart representation of fuzzy operating modes is proposed; 6. the fuzzy rules are extracted from the “operational graphs”. This methodology is applied to the proposed HRES system. 2.1. Determination of system work specifications In order to generate a reference power and to ensure a power reserve, the studied HRES system includes a wind turbine generator (WTG), a short-term and a long-term storage system and a foreseeable decentralised generator (FDG). The FDG could be for example a gas turbine. This hybrid generation system is connected at a common coupling point with the network (Fig. 1) and must be considered by the network operator as a classical source. The HRES must provide the reference power, which is imposed by the network operator and maximise the wind power. Furthermore, in order to contribute to the primary control of the frequency [7,15], an energy reserve must be available. In an electrical network, an unbalance between the generated power and the consumed power will be compensated by the kinetic energy of the rotating machines. This will results in a change of the rotating speed and therefore of the grid frequency, which is observed by all generation units in the network. The contribution to the frequency control for production units consists in the increase of its production in case of a frequency drop and in its decrease when the frequency rises. It is classically defined by a linear relation called the droop line as shown in Fig. 2. The characteristics of this relation are its slope and the difference between the reference power Pref and the maximum power Pmax . This difference is called the primary reserve (Preserve ). The size of this reserve is defined by the network operator according to technical and economical criteria.
Fig. 1. System under study.
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Fig. 2. Idealised frequency-power characteristic of a turbo alternator.
In order to avoid the use of wind generators for small grid frequency deviations, a dead band is often introduced by the network operators in the droop characteristic [12]. This feature will be introduced in the proposed supervisor. 2.2. Supervisor design In order to reach the objectives, some required inputs can already be defined; to provide the reference power (Pref ), an input of the supervisor should be the error (P = Pref − Phyb ) where Phyb is the total power generated by the HRES (which is the sum of the power generated by storage units, WTG and FDG). The control of the frequency requires the frequency error (f) between the network normal frequency (f0 ) and the measured frequency (fmeas ). In order to be close to the classical implementation of primary frequency control, the droop characteristic is defined out of the fuzzy supervisor and performed by the storage systems as they represent the energy and power reserve. Therefore, to guarantee the availability of the energy and power reserve for frequency control as well as the regulation of the output power to Pref , the storage levels need to be controlled; the short and long-term storage levels (Levstor sht and Levstor lgt ) are added to the list of the inputs of the supervisor. The outputs of the supervisor should be: • the reference power for the storage systems; Pref stor sht for the short-term storage unit and Pref stor lgt for the long-term storage unit, • the reference power for the FDG (Pref FDG ), and • the pitch angle reference βref , which is used to modify the captured wind energy by changing the blade angle. This action is therefore used to decrease the output power of the WTG. The block diagram of the supervisor is shown in Fig. 3. The supervisor is divided into two parts: • the fuzzy logic supervisor, which manages the FDG (Pref FDG ), the WTG (βref ) and a part of the storage system (Pref stor sht1 , Pref stor lgt1 ), which is used to compensate the wind power variations, • the droop characteristics, which allows to contribute to primary frequency control with the short and long-term storage systems (Pref stor sht2 , Pref stor lgt2 ). The reference power of the storage systems is then the sum of two terms: Pref
stor sht
= Pref
stor sht1
Pref
stor lgt
= Pref
stor lgt1
+ Pref + Pref
stor sht2 stor lgt2
(1) (2)
Furthermore, in extreme situations when the storage levels are very low or very high, the supervisor will use the WTG or the FDG to bring a contribution to the frequency control.
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Fig. 3. Block diagram of the supervisor.
2.3. Determination of the “functional graphs” Based on the knowledge of the system, the strategy of the fuzzy logic supervisor can be defined. This is graphically represented in Fig. 4. The operating modes are represented with rounded rectangles and the states of the system are represented by transitions. As seen in Fig. 4, the fuzzy logic part of the supervisor of Fig. 3 is divided in two main operating modes; N1 and N2. The objective of the first part (N1) is to control the power, which is generated by the HRES. The three operating modes of this part are based on the states of the storage systems: • N1.1: if the storage level is medium the HRES must supply the reference power while maximizing the WTG power. Then the WTG operates in maximal extraction power (MPPT) and the storage unit compensates the difference between the reference power (Pref ) and the hybrid power (Phyb ). • N1.2: if the storage level is high, the HRES must keep storage availability for primary power reserve. In this case the storage unit must be discharged and the WTG power is decreased with the help of the pitch angle (β). When the output power of the WTG is reduced, a power reserve is naturally created by the WTG to take part in primary frequency control. Using this approach, in case of high storage level, the contribution to frequency control is performed not only by the storage system but also by the WTG. • N1.3: if the storage level is low, the HRES must keep storage availability. Then the storage units must be charged and the FDG must ensure the reference power. When the FDG is in operation, it can take part in primary frequency control. Using this approach, in case of very low storage level, the contribution to frequency control is performed not only by the storage system but also by the FDG.
Fig. 4. Chart representation of the fuzzy logic supervisor.
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Fig. 5. Chart representation of different operating modes.
The goal of the second part (N2) is to allow the action of the control of the frequency trough the droop characteristics. Indeed, it is important that the fuzzy logic supervisor modifies it exigencies in HRES power regulation when additional power is required for frequency control. N1.1, N1.2, N1.3 and N2 are the objectives of the supervisor; the transitions (storage level and frequency variation) represent the constraints. Each operating mode (N1.1, N1.2, N1.3 and N2) is associated with a set of fuzzy rules. The transitions between the different operating modes are continuous functions. It is therefore possible to be either fully in one operating mode or partially in several operating modes and therefore to work on several objectives at the same time. This behaviour is obtained by the fuzzy logic supervisor. When several conditions are true, several fuzzy rules impact the same output and the final value of this output is the “center of gravity” of these combined trapezoid functions determined by the fuzzy logic [3]. This approach allows finding a compromise between different operating modes and smoothly moving from one to another. When two storage systems are considered, the three operating modes N1.1, N1.2, N1.3 are duplicated as it will be shown in Sections 4 and 5. N1.11, N1.12, N1.13 are related to the short-term storage and N1.21, N1.22, N1.23 are related to the long-term storage. In Fig. 5, the operating modes of the different subsystems are detailed. 2.4. Determination of the membership functions The next step of the proposed methodology is to define membership functions for the input and outputs variables of the fuzzy logic supervisor. The input membership functions are used as transitions between the different operating modes, they are shown in Fig. 6. The membership functions of the storage levels (Fig. 6a and b) are based on three levels to accommodate the needs of the proposed strategy:
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Fig. 6. Input membership functions of (a) power error; (b) short-term storage level; (c) frequency error and (d) long-term storage level.
• The small and high levels represent the energy reserve, which is required to participate in primary frequency control; in the considered example, in case of over-frequency or under-frequency, a minimum of 0.05 per unit energy reserve in both storage systems is taken. • In the proposed scenario, the medium level is used to compensate the wind power variations around the reference power. At least, 0.6 per unit of the short-term storage and 0.8 per unit of long-term storage are dedicated to this action. Fig. 6c represents the membership functions of the frequency variation f = f0 − fmeas . In the same way, three levels are defined: • When the frequency variation is negative or positive, the primary control of the frequency must be applied. • The trapezoidal form of the membership function Z allows the introduction of the dead band of the droop characteristic. In this case, for −0.1 Hz < f < 0.1 Hz the primary frequency control is not in operation. Fig. 6d represents the membership functions of the power error P = Pref − Phyb . Five levels are considered to perform a compromise between the accuracy of the power control and its complexity [3]. The output membership functions are shown in Fig. 7a–d for respectively, the short-term storage power reference, the long-term storage power reference, the pitch angle and the FDG power reference. The storage power may be positive or negative, then five levels are considered; NB, NM, Z, PM and PB where N stands for Negative, Z for Zero, P for Positive, B for Big and M for Medium. The action of the pitch on the output power being non linear, the membership function the levels Z, M, and B are chosen to linearize this control. The FDG power reference being always positive, three levels are considered to implement a compromise between precision and complexity. However, as the nature of
Fig. 7. Output membership function of (a) short-term reference power, (b) long-term reference power, (c) pitch angle reference and (d) FDG reference power.
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Fig. 8. Operational graph of the supervisor.
the FDG is not taken into consideration, indifferent membership functions are chosen, it this example they correspond to the membership functions of the pitch angle. The fuzzy logic supervisor of the HRES is based on four membership functions to describe the input variables with a total of 14 membership degrees. Therefore a maximum of 135 rules may be considered. Traditionally, to determine the fuzzy rules, all cases are identified with the help of tables [3]. In this case, the table will have four dimensions and contains 540 cases because of the four inputs. The fuzzy inferences are performed using a Mamdani fuzzy model with minimum composition as this model was initially designed to translate human experience into an automatic supervisor. With the proposed methodology, a graphic representation called the “operational graph” will enable to grasp the global performance of the system and extract the pertinent fuzzy rules. 2.5. Determination of the “operational graphs” As shown in Fig. 5, it is possible to decompose the system in many subsystems. This decomposition allows the determination of the fuzzy rules. To achieve this goal the functional graph must be translated with the variables of the membership functions. The transitions between the operation modes are described by the levels of the input membership functions and the actions of the operating modes are described by the levels of the output membership functions. This will lead to the operational graph shows in Fig. 8. The details of this operational graph are given in the case of the operating mode N1.11 for which the operational graph is shown in Fig. 9. The same operation needs to be performed for the other operating modes. 2.6. Extraction of the fuzzy rules From the diagram shown in Fig. 9, the fuzzy rules of the operating mode N1.11 are easily obtained: • IF f is Z AND Levstor sht is M AND P is NB THEN Pref stor sht is NB • IF f is Z AND Levstor sht is M AND P is NM THEN Pref stor sht is Z • IF f is Z AND Levstor sht is M AND P is Z THEN Pref stor sht is Z
Fig. 9. Operational graph of N1.11 operating mode.
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• IF f is Z AND Levstor sht is M AND P is PM THEN Pref stor sht is PM • IF f is Z AND Levstor sht is M AND P is PBTHEN Pref stor sht is PB If this operation is performed for all the operating modes identified in Fig. 5, only 44 fuzzy rules are considered instead of the 540 possible fuzzy rules given by the tables. The list of these rules is given in Appendix A. The proposed methodology not only allows a systematic construction of a fuzzy logic supervisor but also allows a reduction of the number of fuzzy rules (from 540 to 44 in the considered example). This will simplify the real time implementation of the supervisor. 3. Modelling of the system under study In order to illustrate the effectiveness of the supervisor, built using the proposed methodology, several simulations of the electromechanical system and its supervisor will be presented. The models of the different elements of the system will be presented. It is important to note that this modelling effort is not required for the design of the supervisor but allows the simulation of its behaviour. The supervisor structure is therefore independent of the technology used for HRES. However, simulations help to determine some parameters of the supervisor (limits of the membership functions for instance). 3.1. Wind turbine generator (WTG) The considered variable speed wind generator is based on a permanent magnet synchronous generator connected to the network via two back to back AC-DC converters. The turbine is modelled by the classical relation between wind speed and power, which can be extracted: 1 (3) ρAr CP (λ, β)v3 2 where ρ is the air density, Ar is the surface swept by the blades, Cp (λ,β) is the power coefficient, λ = Ωt Rt /v is the speed ratio, Ωt is the turbine speed, Rt is the turbine radius, β is the pitch angle and v is the wind speed. The power coefficient dependence with λ and β(Cp (λ,β)) is classically modelled by considering the analytical expression given in [2]. Pw =
3.2. Foreseeable decentralized generator (FDG) As shown in Fig. 10, the considered FDG is modelled by a simple first order transfer function between the reference power (PFDG ref ) and the output power (PFDG ) [2]. The transfer function is given by (4) where τ FDG is the time constant, which depends on the considered technology: H(s) =
1 τFDG s + 1
(4)
In Fig. 10, PFDG min and PFDG max are respectively the minimum and maximum power of the FDG. 3.3. Storage system In the same way, a simplified model is used to model the short and long-term storage units. Fig. 11 shows the block diagram of this model, where Prefstor is the reference power of the storage system, Wstor is the stored energy and Pstor
Fig. 10. Foreseeable decentralized generator model.
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Fig. 11. Storage unit model.
is the actual power of the storage system. The storage system is not based on a priori defined technology. It is only characterized by a maximum power of charge (Pchmax ), a maximum power of discharge (Pdchmax ), a charging and discharging efficiency (ηch and ηdch ) and a maximum and minimum level of stored energy (Wmin and Wmax ), which defines the value m1 such that if Wstor = Wmax or Wstor = Wmin m1 = 0 and m1 = 1 otherwise. 4. Simulations The most important parameters of the system (presented in Fig. 1) are given in Table 1. In this table, Sconv is the apparent power of the network, Pload1 is the active power of the load 1 and Pload2 is the active power of the load 2. To illustrate a significant contribution of the hybrid generator, the total power of the network is taken relatively small. The simulations are carried out with the help of the Matlab/SimulinkTM software. In the proposed scenario, the reference power of the hybrid generator for 0 h < t < 1 h is set at 600 kW, which is equal to the mean wind power, for 1 h < t < 2 h, a reference power of 400 kW, lower than the mean available wind power, is considered and a reference Table 1 Parameters. Foreseeable source PFDG τ FDG
750 kW 5s
Network Sconv Pload1 Pload2
3 MVA 800 kW 800 kW
Short-term storage Pchmax stor sht Pdchmax stor sht τ ch stor sht τ dch stor sht Wmax stor sht
300 kW −300 kW 0.5 s 0.5 s 4.167 kWh
Long-term storage Pchmax stor lgt Pchmax stor lgt τ ch stor lgt τ dch stor lgt Wmax stor lgt
230 kW −230 kW 5s 5s 416.7 kWh
Wind turbine PWTG
750 kW
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Fig. 12. Hybrid generator performance for three different reference powers: (a) wind and hybrid generator power, (b) network frequency, (c) energy of long-term storage, (d) energy of short-term storage, (e) pitch angle of wind turbine, and (f) power of the FDG unit.
power of 800 kW, above the mean available wind power, is taken for 2 h < t < 3 h. An 800 kW load is connected at t = 0 h20, t = 1 h20 and t = 1 h40 and disconnected at t = 0 h40, t = 1 h40 and t = 2 h40 to create real frequency variations. Fig. 12 shows the simulation results of the WTG power in broken line (Fig. 12a), the total HRES power in full line (Fig. 12a), the grid frequency (Fig. 12b), the storage level of the long-term (Fig. 12c) and short-term storage systems (Fig. 12d), the pitch angle (Fig. 12e) and the FDG power (Fig. 12f). Fig. 12a shows that the power reference is well provided in spite of the wind and load variations. Fig. 12b shows that, when a load is connected, the HRES power increases rapidly, and the inverse phenomenon appears when a load is disconnected in relation with the primary frequency control. Fig. 12d and e illustrate that when the energy of short-term storage is high, the pitch angle is controlled to reduce and smooth the wind power. Fig. 12d and f illustrate that when the energy of the short-term storage is low, the FDG is controlled to compensate the lack of wind power. In addition, the WTG and the FDG take part in frequency control when they are in operation. Finally, Fig. 12c shows that the long-term storage system compensates the low frequency deviations between the wind power and the reference power. 5. Comparison of different HRES topologies In order to illustrate the main advantages of a graphical representation of the fuzzy logic supervisor, the proposed methodology is applied to different topologies of HRES. For each scenario, a chart representation of the supervisor is derived from the one shown in Fig. 5. 5.1. Association of a WTG and a FDG (case a) The considered system is a modification of the system presented in Fig. 1, which only includes a wind turbine generator and a foreseeable source. As previously, the objectives of the supervisor are to generate the reference power and to ensure the primary frequency control. Fig. 13 shows the chart representation of the system, the supervision system is divided in three parts; when the HRES power is lower than the reference power the FDG must provide the difference between the reference power and the WTG power. In the same way, when the HRES power is higher than the reference power, the wind power must be decreased with the help of the pitch angle. For this graph, an operational graph can be obtained and is used to define
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Fig. 13. Chart representation of the different operating modes.
Fig. 14. Hybrid generator power and reference power.
the pertinent fuzzy rules. The 14 rules pertinent rules are the ones of section N1.12 and N1.13 from Appendix A that do not refer to the storage reference power and where the dependence with the storage level is removed. Fig. 14 shows that the reference power is well provided. 5.2. Association of a WTG, a FDG and a short-term storage unit (case b) The considered system is a modification of the system presented in Fig. 1, which only includes the WTG, the FDG and the short-term storage system.
Fig. 15. Chart representation of different operating modes.
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Fig. 16. Comparison of the hybrid generator power and the hybrid reference power.
Fig. 15 shows the chart representation of the supervisor. This supervisor is the part N1.1 and N2 of the supervisor shown in Fig. 5. The 22 pertinent fuzzy rules that can be obtained from this graph are the ones of section N1.1 and N2 from Appendix A that do not refer to the long-term storage reference power. Fig. 16 shows that the reference power is again well provided.
Fig. 17. Chart representation of different operating mode.
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Fig. 18. Hybrid generator power compared to the hybrid reference power.
5.3. Association of a WTG, short and long-term storage units (case c) The considered system is a modification of the system presented in Fig. 1 which only includes a WTG, and short and long-term storage systems. The chart representation of the supervisor presented in Fig. 17 is very similar to the one shown in Fig. 5. The part concerning the FDG of Fig. 5 has been removed. The 30 fuzzy rules that can be obtained from this graph are the ones of the appendix that do not refer to the FDG reference power. Fig. 18 shows that when the reference power is lower than the mean wind power, the storage systems are sufficient to provide the reference power, this is no more the case when the reference power is bigger than the mean available power. 5.4. Association of a WTG and a short-term storage unit (case d) The considered system is a modification of the system presented in Fig. 1, which only includes a WTG and a short-term storage system. Fig. 19 shows the chart representation of the supervisor. The supervision system can be divided in three parts:
Fig. 19. Chart representation of different operating mode.
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Fig. 20. Comparison of the hybrid generator power and the hybrid reference power. Table 2 Comparison between different topologies. Case under study
Grid energy (kWh)
WTG energy (kWh)
FDG energy (kWh)
Average absolute error (kW)
Maximum absolute error (kW)
a b c d e
1800 1800 1783 1635 1800
1563 1636 1823 1635 1823
237 163 0 0 30.9
0.165 0.223 5.4 54.86 0.011
13 38 376 511 18
• When the storage level is medium, the short-term storage controls the reference power. • When the storage is high, the storage unit must be discharged and the WTG power is decreased with the help of the pitch angle. • When the storage level is low, the storage must be charged; in this case the reference power cannot be provided. The 15 fuzzy rules that can be obtained from this graph are the ones of section N1.1 and N2 from Appendix A that do not refer neither to the FDG reference power nor to the long-term storage power reference. In Fig. 20, the curve in broken lines corresponds to the reference power whereas the curve in full line corresponds to the HRES generated power. Only when the reference is smaller than the average wind power, the reference power is provided. When the reference is significantly different than the average wind power, the reference is provided within the limits of the storage system capacity. Five topologies are explored, WTG and FDG based HRES (case a); WTG, FDG and short-term storage unit based HRES (case b); WTG, short-term and long-term storage units based HRES (case c); WTG and short-term storage units based HRES (case d) and the complete system in case e. Table 2 allows us to compare different HRES topologies following different criteria; energy generated on the grid by the HRES, energy generated by the WTG and the FDG as well as average error and maximum error. When a FDG is included (cases a, b and e), a similar energy is provided to the grid. In these cases, the storage system enables to maximize the WTG energy and then to minimize the FDG energy (case b and e). The error between the power reference and the HRES power is rather small. When the HRES does not include the FDG, the reference power cannot be guaranteed when the wind power is lower than the reference power. 6. Conclusion In this paper, a methodology has been proposed to develop a fuzzy logic based supervisor. This method facilitates the analysis and the determination of fuzzy control algorithms adapted for complex hybrid systems. To explain this methodology, the association of a wind turbine based dispersed generators and storage systems have been considered. It avoids precise and elaborate models of the different sources and of the storage systems. Furthermore, this method allows a systematic determination of the supervisor and a minimization of the number of fuzzy rules. The performance of this supervisor has been shown with the help of simulations. Finally, the application of this methodology to the
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supervision of different topologies of HRES and the comparison of the performance of these topologies following 5 energy and power criteria has brought forward the systematic dimension of the approach. Perspectives of this work include optimal design of the input and output membership functions as well as experimental implementation of the proposed supervision on a laboratory test bench. Acknowledgements This work was supported by a funding from the regional Council Nord-Pas de Calais, the European Regional Development Funding, Suez-Tractebel Engineering Company, Supelec and HEI. Appendix A.
N1.11
N1.12 N1.1
N1.13
N1 N1.21
N1.22 N1.2
N1.23
N2
IF Levstor sht is M AND f is Z AND P is NB THEN Pref stor sht1 is NB IF Levstor sht is M AND f is Z AND P is PB THEN Pref stor sht1 is PB IF Levstor sht is M AND f is Z AND P is NM THEN Pref stor sht1 is NM IF Levstor sht is M AND f is Z AND P is PM THEN Pref stor sht1 is PM IF Levstor sht is M AND f is Z AND P is Z THEN Pref stor sht1 is Z IF Levstor sht is B AND f is Z THEN Pref stor sht1 is NM IF Levstor sht is B AND f is Z AND P is Z THEN βref is Z IF Levstor sht is B AND f is Z AND P is NM THEN βref is Z IF Levstor sht is B AND f is Z AND P is NB THEN βref is Z IF Levstor sht is B AND f is Z AND P is PM THEN βref is P IF Levstor sht is B AND f is Z AND P is PB THEN βref is B IF Levstor sht is B AND f is N THEN βref is Z IF Levstor sht is B AND f is P THEN βref is P IF Levstor sht is P AND f is Z THEN Pref stor sht1 is PM IF Levstor sht is P AND f is Z AND P is NB THEN Pref FDG is B IF Levstor sht is P AND f is Z AND P is NM THEN Pref FDG is P IF Levstor sht is P AND f is Z AND P is PB THEN Pref FDG is Z IF Levstor sht is P AND f is Z AND P is PM THEN Pref FDG is Z IF Levstor sht is P AND f is Z AND P is Z THEN Pref FDG is Z IF Levstor sht is P AND f is P THEN Pref FDG is Z IF Levstor sht is P AND f is N THEN Pref FDG is P IF Levstor lgt is M AND f is Z AND P is NB THEN Pref stor lgt1 is NB IF Levstor lgt is M AND f is Z AND P is PB THEN Pref stor lgt1 is PB IF Levstor lgt is M AND f is Z AND P is NM THEN Pref stor lgt1 is NM IF Levstor lgt is M AND f is Z AND P is PM THEN Pref stor lgt1 is PM IF Levstor lgt is M AND f is Z AND P is Z THEN Pref stor lgt1 is Z IF Levstor lgt is B AND f is Z THEN Pref stor lgt1 is NM IF Levstor lgt is B AND f is Z AND P is NB THEN βref is Z IF Levstor lgt is B AND f is Z AND P is Z THEN βref is Z IF Levstor lgt is B AND f is Z AND P is NZ THEN βref is Z IF Levstor lgt is B AND f is Z AND P is PM THEN βref is P IF Levstor lgt is B AND f is Z AND P is PB THEN βref is B IF Levstor lgt is B AND f is N THEN βref is Z IF Levstor lgt is B AND f is P THEN βref is P IF Levstor lgt is P AND f is Z THEN Pref stor lgt1 is PM IF Levstor lgt is P AND f is Z AND P is NB THEN Pref FDG is B IF Levstor lgt is P AND f is Z AND P is NM THEN Pref FDG is P IF Levstor lgt is P AND f is Z AND P is PB THEN Pref FDG is Z IF Levstor lgt is P AND f is Z AND P is PM THEN Pref FDG is Z IF Levstor lgt is P AND f is Z AND P is Z THEN Pref FDG is Z IF Levstor lgt is P AND f is P THEN Pref FDG is Z IF Levstor lgt is P AND f is N THEN Pref FDG is P IF f is P THEN Pref stor sht1 is Z IF f is N THEN Pref stor lgt1 is Z
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