A Multi-agent Based Cooperative Voltage and Reactive Power Control

Extended Summary 本文は pp.647–653 A Multi-agent Based Cooperative Voltage and Reactive Power Control Masato Ishida Student Member (Hiroshima Institute...
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Extended Summary

本文は pp.647–653

A Multi-agent Based Cooperative Voltage and Reactive Power Control Masato Ishida Student Member (Hiroshima Institute of Technology, [email protected]) Takeshi Nagata Senior Member (Hiroshima Institute of Technology, [email protected]) Hiroshi Saiki Non-member (NTT Data Sikoku, [email protected]) Ikuhiko Shimada Member (Chubu Electric Power Co. Inc., [email protected]) Ryousuke Hatano Member (Chubu Electric Power Co. Inc., [email protected]) Keywords: multi-agent system, distributed system, voltage control, reactive power control, power system This paper introduced a new concept to improve the traditional control of voltage and reactive power. The proposed system divides the traditional problem of this control into two sub problems, “voltage control” to adjust a substation’s secondary bus voltage and “reactive power control” to adjust a substation’s primary bus voltage. This paper presented the cooperative method of these two controls. As shown in Fig. 1, the proposed method divides voltage control of the whole power system into two types of sub-networks: primary bus voltage control is achieved by the shunt capacitor (SC) that covers the sub-networks denoted by (H1) and (H2) in the figure, and secondary bus voltage control provided by the under-load tap switching transformer (LRT) that is meant for sub-networks (V1) through (V4). Listed below are the features of the proposed method: ( 1 ) The proposed method consists of several SubstationAgents (SS-Agents) and Line-Agents (Line-Agents). ( 2 ) A source SS-Agent adjusts the secondary bus voltage using the “Integrated Operating Voltage Target (IOVT)” which is received from the down stream Line-Agents. On the other hand, leaf SS-Agents adjust the reactive power among the interconnected substations, thus keeping the primary bus voltage within the upper and lower limits and equalizing the voltage distribution. ( 3 ) A Line-Agent calculates IOVT and transmits to the source SS-Agent in order to adjust the whole voltage level. ( 4 ) Before an adjustment is made at a substation, a Line-Agent estimates the change caused by the adjustment in the primary bus voltage at all the upstream substations.

Fig. 2. Result of primary bus voltage

Fig. 3. Total number of controls of each substation

To confirm how our proposed system works, we conducted a computer simulation using the model system illustrated in Fig. 1. The result of control of the primary bus voltage at each substation is shown in Fig. 2 shows. In the figure, the vertical axis denotes voltage and the horizontal axis denotes time (in minutes). Our proposed system successfully achieved its goal of keeping the primary bus voltage between the upper and lower limits permitted. Figure 3 shows the comparion of the total number of controls of each substation with the conventional method (VQC). Although the simulation employed a rather simple model, its showed considerable potential in achieving improved control of voltage and reactive power than conventional VQC.

Fig. 1. Model system

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Extended Summary

本文は pp.654–661

System Identification of Power Network for Coordinated Setting of PSSs Dai Murayama Member (Toshiba Corporation) Kenji Mitsumoto Member (Toshiba Corporation) Yasuo Takagi Member (Toshiba Corporation) Youichi Uemura Member (Toshiba Corporation) Koji Sato Member (Tohoku Electric Power Co., Inc) Takashi Shirasaki Member (Tohoku Electric Power Co., Inc) Kunio Sakamoto Member (Tohoku Electric Power Co., Inc) Keywords: power system, dynamic stability, generator control, system identification, PSS The PSS is the reasonable controller to stabilize the inter-tie and local oscillations of power network. The PSS is usually set with the one-machine infinite-bus system model. But the coordinated setting of the multiple PSSs considering the characteristics of the network is expected to improve the stability. For this purpose, the Modal Performance Measurement method using the power network model is applied for adjusting PSS parameters. The power network model is identified from the waveform of the precise simulator. In this paper, the conditions of identification and the validation of identification are shown. Identified model are validated by comparison of vector diagram, impulse responses etc. In the Modal Performance Measurement, the characteristics of the power network are simulated by identified model that is created by N4SID identification method using the waveform of Y- method. The simple model, shown Fig. 1, is consist of 15 generators and some of them are same characteristics and contains the unstable inter-tie mode. And the precise model is based on simplified model but added the most of equipments located in the power network. The Identification method is applied for both of the power network model. First, the identified model of simplified power network is compared with the S-method result by the vector diagram shown in the Fig. 2. The vector diagram of each generator G2-G6 shows the same tendency, which means the identified model shows good corresponding to the Y-method waveform. Second, the precise model is tested by the impulse responses. The impulse inputs are applied both for the precise method and the identified model. Figure 3 shows the comparison of impulse response of precise model and identified model. The impulses are applied multi generators Ga, Gc, Gd and Ge at the same time, and both waveforms

Fig. 2. Comparison of identified model with S method by vector diagram

Fig. 3. Impulse responses of identified model (dot line) and Y method model (solid line) are in good agreement, which means the behavior of the identified model simulates the power network model. According to these analyses, the identification and the validations of power network that consists of many generators is established. The accuracy of the identified model affects the precision of the coordinated setting of PSS. The design of the coordinated setting of PSS is reported in another paper.

Fig. 1. Power system network

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Y-method and S-method is the program of CRIESPI

Extended Summary

本文は pp.662–669

Capacity Planning and Practicality Evaluation of the Grid-independent Power System based on Supply Reliability Zhuomin Zhou Student Member (University of Tsukuba, [email protected]) Masayoshi Ishida Member (University of Tsukuba) Tetsuhiko Maeda Member (National Institute of Advanced Industrial Science and Technology) Keywords: grid-independent power system, capacity planning, supply reliability As the first step in the capacity planning, mathematical models for characterizing PV, WT, PEFC, and batteries are proposed. The second step is to optimize the capacities of the power sources according to the LPSP and the LCE concepts. The configurations, which meet the required LPSP with the lowest LCE, give the optimal choices. As a case study, a typical household in Kanto area was selected, and surveyed meteorological data and energy demand data of this household were used in the capacity planning. A result of capacity planning for a typical household in Kanto area is shown in Table 1 (PEFC runs following power demand) and Table 2 (PEFC runs following hot water demand). At the condition of that PEFC runs following power demand, the configuration with none of WT, 3 kW of PV, 0.5 kW of PEFC and 20 kWh of battery is able to meet the reliability requirement (LPSP ≤ 0.1) with the minimum LCE (154 yen/kWh). From Table 1 and Table 2 we can see that higher power supply reliability means higher cost. Compared with the condition of that PEFC runs following hot water, at the condition of PEFC runs following power demand, LCE is 2∼5% higher, while EUCO2 is 2∼14% lower.

In recent years, grid-independent power systems, which are utilized as power supply in remote areas or as emergency power systems in cities are actively discussed. This paper presents a methodology to perform the capacity planning of a grid-independent power system, which is mainly composed of PV panels (PV), small wind turbines (WT), proton exchange membrane fuel cell systems (PEFC) and batteries. Figure 1 shows basic configuration of the system. In this system, the power demand is mainly met by the PV, WT and batteries. Batteries are used as short time energy storage here. If any power shortage occurs, the shortage will be compensated by PEFC used as backup power source. Exhaust heat from PEFC is recovered, and stored in hot water tank to supply hot water. A gas boiler is used for backup to supply hot water when shortage occurs from the hot water tank. The methodology aims at finding the optimal capacities of these power sources to meet the required system supply reliability, with the lowest cost and environmental load. However, there is a trade-off relationship between the supply reliability and economy. Therefore, the method to find out the proper system configuration is important. In order to evaluate the supply reliability, economy, and environment load, evaluation indexes are defined respectively as follow: ( 1 ) Loss of power supply reliability (LPSP): LPSP =

Annual power shortage Annual power demand

Table 1. Capacity planning result (PEFC runs following the power demand)

( 2 ) Levelized Cost of Energy (LCE): LCE =

Annual system cost Annual power usage

( 3 ) Emission Unit of CO2 (EUCO2 ): EUCO2 =

Annual CO2 emission Annual power generated

Table 2. Capacity planning result (PEFC runs following the hot water demand)

Fig. 1. Basic Configuration of the system

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Extended Summary

本文は pp.670–676

Issues for Power System Operation for Future Renewable Energy Penetration ——Robust Power System Security—— Naoto Yorino Senior Member (Hiroshima University) Yutaka Sasaki Member (Hiroshima University) Shoki Fujita Student Member (Hiroshima University) Yoshifumi Zoka Senior Member (Hiroshima University) Yoshiharu Okumoto Member (The Chugoku Electric Power Company) Keywords: photovoltaic systems, uncertainties, power supply reliability, robust power system security

( 3 ) Robust reachable region for Time-Ahead security (RTA) When we pay attention to RSS in future (δt-ahead), there

1. Abstract A large amount of PV penetration may introduce uncertainties in the future power system planning and operations. This paper proposes the concept of “Robust Security (RS)” and “RS region” in order to investigate power system security in the presence of a large amount of uncertainties. The RS region is defined as the region of power system operation where the system is secure under uncertainties. It is shown that the region tends to shrink and disappear for a large amount of PV penetrations. Emerging problems are investigated concerned with security in future power systems. 2. New Concept of Robust Security Regions In order to deal with power system security issues against increasing uncertainties in future power system operation, the paper proposes a new concept for power system security. In the future power system operation, controllable generators will be decreased while uncontrollable disturbances and uncertain parameters will be increased. The situation implies that it will become much more difficult to maintain power system security in the future circumstance, where controllable variables are very limited. Then, we pay attention to the controllable variables and their controllable regions to maintain power system security. The outputs of controllable generators are mainly assumed as controllable variables, and power system operation problems are investigated. From this point of view, the following regions of control variables are defined in this paper. ( 1 ) Robust Static Security region (RSS) RSS region is defined as the region where the N-1 security is guaranteed for all pre-specified uncertainties. The term of “robust security,” which is named referring to “robust stability”, implies that the system is secure for any values of uncertain parameters are realized in condition that the domains of the uncertain parameters are pre-specified. The term of “static” implies the snapshot of power system operation for a given loading condition at specific time. ( 2 ) Robust Dynamic Feasible region (RDF) Due to power system dynamic characteristics and various operational constraints, there exists feasible operation region in reality. For example, thermal generators cannot change their outputs exceeding their ramp rate limits. RDF is defined as the feasible region under all static and dynamic constraints.

exist a region of operating point reachable to the future RSS. RTA is defined as the region reachable to δt-ahead RSS in the future. ( 4 ) Robust Dynamic Security region (RDS) RDS is defined as the intersection of RSS and RTA. That is, the power system operation in RDS guarantees that the system is secure at present and can be secure in the future when properly controlled. Figure 1 shows the concept of the proposed robust security regions. When the uncertainty increased, the robust security regions tend to shrink and finally disappear as shown in Fig. 2. Then, the paper investigates future power system operation problems, how to keep system security in planning and operations.

Fig. 1. Concept of robust security regions

Fig. 2. Nonexistence of RSS region

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Extended Summary

本文は pp.677–686

Layout Optimization Method for Magnetic Circuit using Multi-step Utilization of Genetic Algorithm Combined with Design Space Reduction Yoshifumi Okamoto Member (Graduate School of Engineering, Utsunomiya University) Yusuke Tominaga Student Member (Graduate School of Engineering, Utsunomiya University) Shuji Sato Member (Graduate School of Engineering, Utsunomiya University) Keywords: layout optimization, integer programming, multi-step genetic algorithm, reduction of design space, finite element method The layout optimization with the ON-OFF information of magnetic material in finite elements is one of the most attractive tools in initial conceptual and practical design of electrical machinery for engineers. Recently, level-set method based on sensitivity analysis is actively applied to layout optimization (topological optimization) in various fields such as structural analysis, electromagnetic field analysis, and so on. The level-set method is attractive optimization method because the gray scale elements don’t exist at all. However, the utilization of sensitivity based on adjoint variables method restricts the kind of objective function to differentiable. On the other hand, the heuristic algorithms based on the random search, for example, simulated annealing (SA), genetic algorithm (GA), and so on, allow the engineers to define the general-purpose objects, however, there are many iterations of finite element analysis, and it is difficult to realize the practical solution without material island and void distribution by using direct search method. This paper proposes the efficient layout optimization method based on the multi-step GA (MSGA). The framework of MSGA is shown in Fig. 1. Firstly, the solution is largely searched in the coarse finite element mesh. Next, the solution in previous step is assigned to the fine mesh. The assigned solution is set as first chromosome in first generation of next step of GA. Therefore, the number of design variables in next fine mesh will be huge unfavorably. Then, design space is restricted to the adjacent elements with outer contour of magnetic body in previous solution in order to reduce the number of design variables. As a result, the number of design variables nd can be reduced by half against the second design domain. While the final layout is somewhat dependent on the first largely solution, rational magnetic circuit will be derived. The fundamental validation of MSGA is performed in the Cshaped iron core model as shown in Fig. 2. The goal of optimization is maximizing the electromagnetic force imposed on the armature with the constraint condition that the area of iron core is less than the specified value. When the objective function is not improved between 50 generations at all, the solution is considered as the converged value. While the number of unknown design variables in final mesh in the case of conventional GA is set as 1,792, in the case of MSGA design variable number could be reduced to 180. Figure 2(a) shows the layout obtained from conventional GA. There are many air apertures and island distributions of material element, the rational magnetic circuit couldn’t be obtained. On the other hand, the magnetic circuit obtained from MSGA is rational form as shown in Fig. 2(e), in which the protrusion is attached with the edge part of teeth in order to increase the flux on the armature. It is shown that MSGA is effective layout optimization method of the magnetic circuit composed of huge integer design variables from the viewpoint of potential of making clear the rational layout with new idea.

Fig. 1. Digest of multi-step genetic algorithm with the reduction procedure of design space

(a) Conventional

(d) 3rd solution

(b) 1st solution

(c) 2nd solution

(e) 4th solution

Fig. 2. Optimized layouts of 2-D C-shaped iron core, (a): conventional GA, (b)–(e): MSGA

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Extended Summary

本文は pp.687–692

Development of Partial Discharge Sensing Device for Epoxy Resin Bushing Tatsuya Mutakamihigashi Member (Kaden Engineering Co., Inc.) Makoto Kawasaki Non-member (Kaden Engineering Co., Inc.) Yasuhito Hashiba Member (Kansai Electric Power Co., Inc.) Keywords: partial discharge, electro-magnetic wave, sensing device, epoxy bushing

1. Introduction For the electric power equipment and the cables, prevention of accident is very important. And in substations, a lot of solid insulations using epoxy resin are introduced into cubicle-type switchgears because of its high insulation reliability and down-sizing ability. We know a phenomenon that partial discharge occur when electric installation have degraded. When void or crack exist in the polymer insulating materials or interface of conductor, partial discharge is caused and finally results in breakdown. In recent years, the feature is seen in the partial discharge generated in the epoxy resin before and after the progress of electric tree by our research. From such a background, we developed the partial discharge sensing device intended for the epoxy resin bushing in 22∼33 kV cubicle. This device can continuously observe the insulation of cubicle by sensing specific frequency. And in this paper, we report on the result of evaluating the performance of the device. 2. Outline of the Device By our research, it was proved that electro-magnetic wave spectra radiated from partial discharge have specific frequency region from 200 MHz to 450 MHz. Then, we developed the sensing device that can detect the electric discharge by receiving the signal by mobile antenna. Schematic representation of sensing device is shown in Fig. 1. The sensing device is composed of the antennas, the antenna switcher, and the main body of the detection device. The antennas receive electro-magnetic wave radiated from partial discharge in epoxy resin. And the antennas are switched after the arbitrary measurement time automatically. The main body of device calculates charge level of the partial discharge by analyzing frequency and level of the radiated electro-magnetic wave.

Fig. 2. Example of measurement result in 22 kV cubicle from November 1st to November 17th (348 MHz)

Fig. 3. Partial discharge level of removed bushing

3. Evaluation of Device Performance We proved the performance of this equipment in operating substations; As a result, partial discharge in epoxy resin was detected by electro-magnetic wave. Figure 2 shows one example of the measurement result by the sensing device. This figure is a measurement result of 348 MHz that the aspect of the electrical discharge was remarkable. And, this figure shows the detection of the pulse for every three minutes. According to this figure, though 25∼50 pC discharging had been detected, the pulse of the partial discharge is not detected at all after November 11. As a result of the investigation, it was confirmed that the circuit breaker was opened in this feeder on November 11. It is guessed that the voltage had not been applied to load side epoxy resin bushing by opening the circuit breaker, and the partial discharge had not been generated in the epoxy resin. And then, we removed epoxy resin bushing from the cubicle and measured partial discharge by discharging current. Figure 3 shows the result. As a result, we confirmed that presumed level is correct.

Fig. 1. Schematic representation of sensing device

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Extended Summary

本文は pp.693–700

Proposal on Modeling of Pressure-rise and Propagation due to Short-circuit Fault Arc on a CVT Cable Installed in a Protective Pipe Tomo Tadokoro Member (CRIEPI, [email protected]) Toshiya Ohtaka Member (CRIEPI) Tadashi Amakawa Member (CRIEPI) Keywords: underground distribution, arc, computational fluid dynamics, pressure-rise, CVT cable In underground distribution systems, a CVT (Cross-Linked Polyethylene Insulated PVC Sheathed Triplex) cable is installed in a protective pipe. When a fault arc occurs on the CVT cable, instantly the pressure increases due to the high temperature of the arc and it propagates in the pipe. The pressure-rise and the propagation may seriously damage the pipe and connected power equipment. There are many different sizes of pipes and cables depending on the installation situations, and fault arc occurs under various conditions. Therefore, the simulation technique is effective for examining such pressure-rise and propagation in addition to short-circuit tests. The objective of this paper is to present a CFD (Computational Fluid Dynamics) modeling that can be used to evaluate the characteristics of the pressure-rise and propagation by the fault arc in the protective pipe. To evaluate the characteristics, the CFD modeling was considered on the basis of the short-circuit test results (1) . Figure 1 shows a simplified schematic of the short-circuit test. Here, a pipe 130 mm in diameter (d) was used, as well as cables with conductor areas per cable (S c ) of 100, 250 and 500 mm2 . The pressure-rises in the pipe were measured under the condition of arc current ranging from 4 to 13 kA and arc duration of 0.4 s. Figure 2(a) shows the measurement waveforms of the pressure-rise obtained at P2 and P5 shown in Fig. 1 as an example of the test results. Firstly, the CFD modeling was performed as follows to obtain simulation waveforms of the pressure-rise which correlate well to the experimental waveforms as in Fig. 2(a). The cross-sectional area and perimeter were calculated based on the sizes of the pipe and cable, and the structure was simplified to a double cylinder configuration. This simplified structure can be easily rebuilt in case the sizes of the pipe and CVT cable change. Additionally, half the arc power, which is calculated from three-phase current and arc voltage, is set into the volumetric source term of the conservation of energy as a heat source. The roughness height on the double cylinder surface, which affects the propagation, was decided based on the radius of the CV cable. The ablation of the pipe and cable due to the fault arc was simulated by air injection into the heat source area from the boundary, assuming an increasing mass of air in the heat source area. In particular, the increasing mass of air was adjusted to the maximum pressure-rise at P2 as shown in Fig. 2(a). Figure 2(b) shows the simulation results, which were considered to correlate well to the experimental equivalents. Secondly, the CFD model was applied to other test conditions.

Fig. 2. Waveforms of pressure-rise (d: 130 mm, S c : 250 mm2 , Irms : 8.7 kA)

Fig. 3. Comparison of maximum pressure-rise between experimental formulas and simulation results (d: 130 mm const.) When the size of the cable changed, the double cylinder and roughness height were modified. When changing the arc current, the arc power was adjusted, and the increasing mass of air was determined as directly proportional to the current based on 8.7 kA. Figure 3 shows the relationship between the maximum pressure-rise at P2 and the arc current. In Fig. 3, the lines show approximate correlations which are obtained by the experimental results (1) , while the plots show simulation results. Consequently, the dependences of the maximum pressure-rise on the sizes of the CVT cable and arc current were simulated well. In conclusion, the CFD model can be applied to extensive study for various pressure-rise and propagation phenomena due to shortcircuit faults arc in the protective pipe.

References (1)

Fig. 1. Simplified schematic of short-circuit test –7–

T. Chino: “Aspects of Short-Circuit Faults in CVT Cables for Underground Distribution Lines”, CRIEPI Report, 686001 (1986)

Extended Summary

本文は pp.701–707

Experimental Study on DBD Plasma Actuator with Combination of AC and Nanosecond Pulse Voltage Taichi Kimura Non-member (Tokyo Institute of Technology) Keisuke Udagawa (Takashima) Non-member (The Ohio State University) Hiroyuki Yamasaki Non-member (Tokyo Institute of Technology) Keywords: dielectric barrier discharge (DBD) plasma actuator, nanosecond pulse discharge, combination of AC and nanosecond pulse voltage In the last several years, a Dielectric Barrier Discharge (DBD) plasma actuator driven with combination voltage of AC and nanosecond pulse has been studied. The combined-voltage-driven plasma actuator increased the body force effect, which induces wall jet and flow suction, by overlapping nanosecond pulse voltage. DBD plasma actuator driven by nanosecond pulses is a flow control actuator generating compression waves due to pulse heating, which allows us to do active flow control in high speed flow reported up to Mach number 0.7, though AC-DBD actuator can control the low speed flow. In this study, DBD plasma actuator driven by combination voltage of sinusoidal AC and nanosecond pulse has been experimentally studied with an experimental apparatus shown in Fig. 1. 1.5 kHz, 18 kVpk−pk AC sinusoidal voltage and −15 kV peak 100 ns (FWHM) pulse voltage were used. Both high voltages are applied to single DBD actuator through high pass filter and low pass filter to isolate the power supplies. Time-averaged actuator net thrust and cycle-averaged power consumption were characterized by electrical weight balance and electric charge-voltage cycle of DBD plasma actuator, respectively. Low-passed charge -voltage characteristics with 1.5 kHz AC and 3 kHz NS pulses at AC phases of 90 and 180 degree are shown in Fig. 2. At 90 and 180 degree when the AC voltage is on the peak and pulse voltage is superimposed to the DBD actuator, the electric charge on the DBD actuator was drastically increased or decreased. Although the pulse voltage polarity is negative, charging polarity depends on AC voltage polarity when the pulse voltage was imposed to the DBD actuator. Because the phase of voltage and this drastic charge motion is matched, cycle-averaged power consumption is ten times or higher than the case with just AC voltage. This indicates that AC DBD actuator can be switched to flow heating operation which may allow controlling the flow with repetitive heating. The actuator net thrust was increased by applying the pulse voltages and increasing the pulse repetition rate. Figure 3 shows dependencies of the DBD plasma actuator thrust. Figure 3 also shows that cycle-averaged power consumption measured by V-Q Lissajous plot on AC cycle phase at which nanosecond pulse is superimposed. The influence of the nanosecond-pulse-imposed phase on the thrust

is significantly less than that on the power consumption. The thrust is varied about 10% by the pulse voltage phase. On the other hand, power consumption was increased more than a factor of 10. This phase and pulse repetition rate dependency indicates ability to control the ratio of thrust to power consumption and feasibility of flow control by body force and heating effects with single DBD plasma actuator.

Fig. 2. Low-passed voltage and actuator charge waveforms, with 3.0 kHz nanosecond pulses at 90 and 270 degrees (solid line), without nanosecond pulse (broken line)

Fig. 3. Dependencies of DBD plasma actuator thrust in quiescent Air and measured power consumption on AC cycle phase when nanosecond pulse is superimposed

Fig. 1. AC+NS-DBD system schematic –8–

Extended Summary

本文は pp.708–714

FIS/ANFIS Based Optimal Control for Maximum Power Extraction in Variable-speed Wind Energy Conversion System Ahmad Nadhir Student Member (Department of Computer Sci. and Electrical Eng., Kumamoto University) Agus Naba Non-member (Department of Physics Brawijaya University) Takashi Hiyama Member (Department of Computer Sci. and Electrical Eng., Kumamoto University) Keywords: optimal control, wind energy, maximum power point tracking, wind power curve Control of variable-speed fixed-pitch wind energy conversion system (WECS) in the partial load regime generally aims at regulating the power harvested from wind by modifying the electrical generator speed; in particular, the control goal can be to capture the maximum power available from the wind. The goal can be achieved by indirectly manipulating the turbine rotor speed Ωl through driving the rotor speed Ωh of SCIG as close to the reference rotor speed Ω∗h as possible. The proposed approach for extracting maximum energy from the wind in the variable-speed SCIG-based WECS at partial load region can be illustrated in Fig. 1. There are two approach to get a maximum power extraction from wind in this case: ( 1 ) MPPTFC: fuzzy inference system (FIS) based maximum power point tracking controller; ( 2 ) LWSFC: adaptive neuro fuzzy inference system (ANFIS) based linear feedback controller; The maximum power efficiency (MPE) curve can be used to know

Fig. 2. Power line comparison

about the effectifenes performane of optimal control in WECS. Figure 2 shows the plot of the turbine power vs the turbine rotor speed resulting from applying MPPTFC and LWSFC. The maximum turbine power is almost achieved in the LWSFC. The turbine power line deviates from the ideal MPE line reference This deviation is due to the imperfectness of LWSFC as it was derived from the fuzzy model not modelling completely the behavior of the true power curve. Identifying the fuzzy model using more data, well chosen training data, and well designed fuzzy model structure should lead better fuzzy model capable of better estimating the true power curve, and therefore, better LWSFC. Nevertheless, despite such a defect of the obtained LWSFC, the deviation can be considered quite small and does not deteriorate the WECS efficiency significantly. In general, power of turbine generator can be improved by using LWSFC, also the operation range of turbine rotor is more wide. The performance of the proposed optimal control, verified by a power coefficient C p kept on its near maximum almost all the time.

Fig. 1. Proposed control approach

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