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Saturday, 30 January 2021

Modelling and Simulation of Standalone PV Systems with Battery supercapacitor Hybrid Energy Storage System for a Rural Household

 ABSTRACT

This paper presents the comparison between the standalone photovoltaic (PV) system with battery-supercapacitor hybrid energy storage system (BS-HESS) and the conventional standalone PV system with battery-only storage system for a rural household. Standalone PV system with passive BS-HESS and semi-active BS-HESS are presented in this study. Two control strategies, Rule Based Controller (RBC) and Filtration Based Controller (FBC), are developed for the standalone PV system with semi-active BS-HESS with the aim to reduce the battery stress and to extend the battery lifespan. The simulation results show that the system with semi-active BS-HESS prolongs the battery lifespan by significantly reducing the battery peak current up to 8.607% and improving the average SOC of the battery up to 0.34% as compared to the system with battery-only system.

KEYWORDS

1.      Renewable energy

2.      PV

3.      Hybrid energy storage system

4.      Supercapacitor

5.      Battery

6.      Control strategy

SOFTWARE: MATLAB/SIMULINK

CONCLUSION

The BS-HESS shows the positive impact to the battery and the overall system. The passive BS-HESS is easy to be implemented, but the improvement is not significant as it cannot be controlled. Therefore, semi-active BS-HESS is a better configuration that improves the battery lifespan and maximizes the level of utilization of the supercapacitor. The system with semi-active BS-HESS (moving average filter) has significantly smoothened the battery current. The system with semi-active BS-HESS (RBC) shows a great capability in battery peak current reduction and the prevention of battery deep discharge by reducing the peak power demand by 8.607% and improving the average SOC of the battery by 0.34% as compared to the system with battery-only system.

REFERENCES

[1] Kan SY, Verwaal M, and Broekhuizen H, The use of battery-capacitor combinations in photovoltaic powered products, J. Power Sources 2006, 162: 971–974.

[2] Chong LW, Wong YW, Rajkumar RK, Rajkumar RK, and Isa D, Hybrid energy storage systems and control strategies for stand-alone renewable energy power systems, Renew. Sustain. Energy Rev. 2016, 66, pp: 174–189.

[3] Kuperman A and Aharon I, Battery-ultracapacitor hybrids for pulsed current loads: A review, Renew. Sustain. Energy Rev. 2011, 15: 981– 992.

[4] Dougal RA, Liu S, and White RE, Power and life extension of battery-ultracapacitor hybrids, IEEE Trans. Components Packag. Technol 2002., 25: 120–131.

[5] Kuperman A, Aharon I, Malki S, and Kara A, Design of a semiactive battery-ultracapacitor hybrid energy source, IEEE Trans. Power Electron.2013, 28: 806–815.

Modeling, Implementation and Performance Analysis of a Grid-Connected Photovoltaic/Wind Hybrid Power System

ABSTRACT

This paper investigates dynamic modeling, design and control strategy of a grid-connected photovoltaic (PV)/wind hybrid power system. The hybrid power system consists of PV station and wind farm that are integrated through main AC-bus to enhance the system performance. The Maximum Power Point Tracking (MPPT) technique is applied to both PV station and wind farm to extract the maximum power from hybrid power system during variation of the environmental conditions. The modeling and simulation of hybrid power system have been implemented using Matlab/Simulink software. The effectiveness of the MPPT technique and control strategy for the hybrid power system is evaluated during different environmental conditions such as the variations of solar irradiance and wind speed. The simulation results prove the effectiveness of the MPPT technique in extraction the maximum power from hybrid power system during variation of the environmental conditions. Moreover, the hybrid power system operates at unity power factor since the injected current to the electrical grid is in phase with the grid voltage. In addition, the control strategy successfully maintains the grid voltage constant irrespective of the variations of environmental conditions and the injected power from the hybrid power system.

KEYWORDS

1.      PV

2.      Wind

3.      Hybrid system

4.      Wind turbine

5.      DFIG

6.      MPPT control

SOFTWARE: MATLAB/SIMULINK

CONCLUSION

In this paper, a detailed dynamic modeling, design and control strategy of a grid-connected PV/wind hybrid power system has been successfully investigated. The hybrid power system consists of PV station of 1MW rating and a wind farm of 9 MW rating that are integrated through main AC-bus to inject the generated power and enhance the system performance. The incremental conductance MPPT technique is applied for the PV station to extract the maximum power during variation of the solar irradiance. On the other hand, modified MPPT technique based on mechanical power measurement is implemented to capture the maximum power from wind farm during variation of the wind speed. The  effectiveness of the MPPT techniques and control strategy for the hybrid power system is evaluated during different environmental conditions such as the variations of solar irradiance and wind speed. The simulation results have proven the validity of the MPPT techniques in extraction the maximum power from hybrid power system during variation of the environmental conditions. Moreover, the hybrid power system successfully operates at unity power factor since the injected reactive power from hybrid power system is equal to zero. Furthermore, the control strategy successfully maintains the grid voltage constant regardless of the variations of environmental conditions and the injected power from the hybrid power system.

REFERENCES

[1] H. Laabidi and A. Mami, "Grid connected Wind-Photovoltaic hybrid system," in 2015 5th International Youth Conference on Energy (IYCE), pp. 1-8,2015.

[2] A. B. Oskouei, M. R. Banaei, and M. Sabahi, "Hybrid PV/wind system with quinary asymmetric inverter without increasing DC-link number," Ain Shams Engineering Journal, vol. 7, pp. 579-592, 2016.

[3] R. Benadli and A. Sellami, "Sliding mode control of a photovoltaic-wind hybrid system," in 2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), pp. 1-8, 2014.

[4] A. Parida and D. Chatterjee, "Cogeneration topology for wind energy conversion system using doubly-fed induction generator," IET Power Electronics, vol. 9, pp. 1406-1415, 2016.

[5] B. Singh, S. K. Aggarwal, and T. C. Kandpal, "Performance of wind energy conversion system using a doubly fed induction generator for maximum power point tracking," in Industry Applications Society Annual Meeting (IAS), 2010 IEEE, 2010, pp. 1-7.

 

Power Quality Assessment of Voltage PositiveFeedback Based Islanding Detection Algorithm

ABSTRACT

Islanding refers to a condition where distributed generators (DGs) inject power solely to the local load after electrical separation from power grid. Several islanding detection methods (IDMs) categorized into remote, active, and passive groups have been reported to detect this undesirable state. In active techniques, a disturbance is injected into the DGs controller to drift a local yardstick out of the permissible range. Although this disturbance leads to more effective detections even in well-balanced island, it raises the total harmonic distortion (THD) of the output current under the normal operation conditions. This paper analyzes the power quality aspect of the modified sliding mode controller as a new active IDM for grid-connected photovoltaic system (GCPVS) with a string inverter. Its performance is compared with the voltage positive feedback (VPF) method, a well-known active IDM. This evaluation is carried out for a 1 kWp GCPVS in MATLAB/Simulink platform by measuring the output current harmonics and THD as well as the efficiency under various penetration and disturbance levels. The output results demonstrate that since the proposed disturbance changes the amplitude of the output current, it does not generate harmonics/subharmonics. Thereby, it has a negligible adverse effect on power quality. It is finally concluded that the performance of the sliding mode-based IDM is reliable from the standpoints of islanding detection and power quality.

KEYWORDS

1.      Islanding detection method (IDM)

2.      Power quality

3.      Sliding mode controller

4.      Total harmonic distortion (THD)

5.      Voltage positive feedback (VPF)

SOFTWARE: MATLAB/SIMULINK

CONCLUSION

In this paper, the influence of the classic VPF and modified sliding-mode IDM on the GCPVS’s power quality and efficiency has been evaluated. The study has been done for a 1 kWp PV system with string inverter. The simulation results show that, while the THD of output current in the proposed IDM is smaller than the simple VPF, both methods render acceptable power quality in a wide range of system operation. This proper performance has been achieved due to the variation of the current magnitude rather than the angle or frequency. This magnitude variation is realized in VPF and the proposed method in the current and voltage control loops (MPPT), respectively. The simulations also confirm that the acceptable THDI and harmonics are guaranteed in multi-GCPVSs connection situation even at low power generation levels as the worst scenario. Since the new technique tries to deviate the system from its MPP condition, the effect of embedded disturbance on the efficiency is also performed. In this regard, the simulations are carried out and a negligible reduction in MPPT and inverter efficiencies (less than 0.04%) has been demonstrated in the proposed method. This occurs since MPP can be gained at a small bound around ref. It has been finally concluded that the modified sliding mode controller has the advantages of the conventional VPF scheme in islanding detection as well as a higher power quality in the production of energy.

REFERENCES

[1] H. Laabidi and A. Mami, "Grid connected Wind-Photovoltaic hybrid system," in 2015 5th International Youth Conference on Energy (IYCE), pp. 1-8,2015.

[2] A. B. Oskouei, M. R. Banaei, and M. Sabahi, "Hybrid PV/wind system with quinary asymmetric inverter without increasing DC-link number," Ain Shams Engineering Journal, vol. 7, pp. 579-592, 2016.

[3] R. Benadli and A. Sellami, "Sliding mode control of a photovoltaic-wind hybrid system," in 2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), pp. 1-8, 2014.

[4] A. Parida and D. Chatterjee, "Cogeneration topology for wind energy conversion system using doubly-fed induction generator," IET Power Electronics, vol. 9, pp. 1406-1415, 2016.

[5] B. Singh, S. K. Aggarwal, and T. C. Kandpal, "Performance of wind energy conversion system using a doubly fed induction generator for maximum power point tracking," in Industry Applications Society Annual Meeting (IAS), 2010 IEEE, 2010, pp. 1-7.

Five-Level Reduced-Switch-Count Boost PFC Rectifier with Multicarrier PWM

 ABSTRACT

A multilevel boost PFC (Power Factor Correction) rectifier is presented in this paper controlled by cascaded controller and multicarrier pulse width modulation technique. The presented topology has less active semiconductor switches compared to similar ones reducing switching losses as well as the number of required gate drives that would shrink manufactured box significantly. A simple controller has been implemented on the studied converter to generate a constant voltage at the output while generating a five-level voltage waveform at the input without connecting the load to the neutral point of the DC bus capacitors. Multicarrier PWM technique has been used to produce switching pulses from control signal. Multi-level voltage waveform harmonics has been analyzed comprehensively which affects the size of input current and required filters directly. Full simulation and experimental results confirm the good dynamic performance of the proposed five-level PFC boost rectifier in delivering power from AC grid to the DC loads while correcting the power factor at the AC side as well as reducing the current harmonics remarkably.

KEYWORDS

1.      Multilevel Converter

2.      Active Rectifier

3.      Multicarrier PWM

4.       Cascaded Control

5.      Power Quality

SOFTWARE: MATLAB/SIMULINK

CONCLUSION

In this paper a reduced switch count 5-level boost PFC rectifier has been presented. A cascaded PI controller has been designed to regulate the output DC voltage and to ensure the unity power factor mode of the input AC voltage and current. Moreover, low harmonic AC current waveform has been achieved by the implemented controller and employing a small inductive filter at the input line. One of the main issues of switching rectifiers is the high switching frequency that has been reduced in this work using PWM technique through adopting multicarrier modulation scheme. Moreover, DC capacitors middle point has not been connected to the load that had required splitting the load to provide a neutral point. Using a single load with no neutral point makes this topology practical in realistic applications. Comprehensive simulations cases including change in the load, AC voltage fluctuation and generating different DC voltage values have been analysed and performed to ensure the good dynamic performance of the rectifier, adopted controller and switching technique.

REFERENCES

[1] B. Singh, B. N. Singh, A. Chandra, K. Al-Haddad, A. Pandey, and D. P. Kothari, "A review of single-phase improved power quality ACDC converters," Industrial Electronics, IEEE Transactions on, vol. 50, pp. 962-981, 2003.

[2] B. Singh, B. N. Singh, A. Chandra, K. Al-Haddad, A. Pandey, and D. P. Kothari, "A review of three-phase improved power quality AC-DC converters," Industrial Electronics, IEEE Transactions on, vol. 51, pp. 641-660, 2004.

[3] H. Abu-Rub, J. Holtz, J. Rodriguez, and G. Baoming, "Mediumvoltage multilevel converters—State of the art, challenges, and requirements in industrial applications," IEEE Trans. Ind. Electron., vol. 57, pp. 2581-2596, 2010.

[4] H. Abu-Rub, M. Malinowski, and K. Al-Haddad, Power electronics for renewable energy systems, transportation and industrial applications: John Wiley & Sons, 2014.

[5] L. Yacoubi, K. Al-Haddad, L.-A. Dessaint, and F. Fnaiech, "A DSPbased implementation of a nonlinear model reference adaptive control for a three-phase three-level NPC boost rectifier prototype," Power Electronics, IEEE Transactions on, vol. 20, pp. 1084-1092,

2005.

Tuesday, 26 January 2021

Modeling and Simulation of a Distribution STATCOM using Sirnulink’s Power System Blockset

ABSTRACT

This paper presents a study on the modeling of a STAT-COM (Static Synchronous Compensator) used for reactive power compensation on a distribution network. The power circuits of the D-STATCOM and the distribution network are modeled by specific blocks from the Power System Blockset while the control system is modeled by Simulink blocks. Static and dynamic performance of a E3 Mvar D-STATCOM on a 25-kV network is evaluated. An “average modeling” approach is proposed to simplify the PWM inverter operation and to accelerate the simulation for control parameters adjusting purpose. Simulation performance obtained with both modeling approaches are presented and compared.

 SOFTWARE: MATLAB/SIMULINK

CONCLUSION

A detailed model of a D-STATCOM has been developed foruse in Simulink environment with the Power System Blockset.Models of both power circuit and control system have beenimplemented in the same Simulink diagram allowing smooth simulation. Two modeling approaches (device and average modeling) have been presented and applied to the case of a +3Mvar D-STATCOM connected to a 25-kV distribution network. The obtained simulation results have demonstrated the validity of the developed models. Average modeling allows a faster simulation which is well suited to controller tuning purposes.

REFERENCES

[1] K.K. Sen, “STATCOM: Theory, Modeling, Applications,”in IEEE PES 1999 Winter Meeting Proceedings, pp. 11 77- 1183.

[2] Flexible AC Transmission Systems (FACTS), edited by Y.H. Song and A.T. Johns, The Institution of Electrical Engineers, London, UK, 1999.

[3] K.V. Patil, et al., “Application of STATCOM for Damping Torsional Oscillations in Series Compensated AC Systems,” IEEE Trans. on Energy Conversion, Vol. 13, No. 3,Sept. 1998, pp.237-243.

[4] C.D. Schauder, H. Mehta, “Vector Analysis and Control of Advanced Static VAR Compensators,” IEE Proceedings-[SI Power System BlocksetFor Use with Sirnulink, User’s Guide, The MathWorks Inc., 2000. C, Vol. 140, NO. 4, July 1993, pp. 299-306.

Design and Performance Analysis of Three-Phase Solar PV Integrated UPQC

 ABSTRACT:

 

This paper deals with the design and performance analysis of a three-phase single stage solar photovoltaic integrated unified power quality conditioner (PV-UPQC). The PV-UPQC consists of a shunt and series connected voltage compensators connected back to back with common DC-link.The shunt compensator performs the dual function of extracting power from PV array apart from compensating for load current harmonics. An improved synchronous reference frame control based on moving average filter is used for extraction of load active current component for improved performance of the PVUPQC. The series compensator compensates for the grid side power quality problems such as grid voltage sags/swells. The compensator injects voltage in-phase/out of phase with point of common coupling (PCC) voltage during sag and swell conditions respectively. The proposed system combines both the benefits of clean energy generation along with improving power quality. The steady state and dynamic performance of the system are evaluated by simulating in Matlab-Simulink under a nonlinear load. The system performance is then verified using a scaled down laboratory prototype under a number of disturbances such as load unbalancing, PCC voltage sags/swells and irradiation variation.

KEYWORDS:

1.      Power Quality

2.      Shunt compensator

3.       Series compensator

4.      UPQC

5.      Solar PV

6.      MPPT

 

SOFTWARE: MATLAB/SIMULINK


CONCLUSION:

The design and dynamic performance of three-phase PVUPQC have been analyzed under conditions of variable irradiation and grid voltage sags/swells. The performance of the system has been validated through experimentation on scaled down laboratory prototype. It is observed that PVUPQC mitigates the harmonics caused by nonlinear load and maintains the THD of grid current under limits of IEEE-519 standard. The system is found to be stable under variation of irradiation, voltage sags/swell and load unbalance. The performance of d-q control particularly in load unbalanced condition has been improved through the use of moving average filter. It can be seen that PV-UPQC is a good solution for modern distribution system by integrating distributed generation with power quality improvement.

REFERENCES:

[1] B. Mountain and P. Szuster, “Solar, solar everywhere: Opportunities and challenges for australia’s rooftop pv systems,” IEEE Power and Energy Magazine, vol. 13, no. 4, pp. 53–60, July 2015.

[2] A. R. Malekpour, A. Pahwa, A. Malekpour, and B. Natarajan, “Hierarchical architecture for integration of rooftop pv in smart distribution systems,” IEEE Transactions on Smart Grid, vol. PP, no. 99, pp. 1–1, 2017.

[3] Y. Yang, P. Enjeti, F. Blaabjerg, and H. Wang, “Wide-scale adoption of photovoltaic energy: Grid code modifications are explored in the distribution grid,” IEEE Ind. Appl. Mag., vol. 21, no. 5, pp. 21–31, Sept 2015.

[4] M. J. E. Alam, K. M. Muttaqi, and D. Sutanto, “An approach for online assessment of rooftop solar pv impacts on low-voltage distribution networks,” IEEE Transactions on Sustainable Energy, vol. 5, no. 2, pp.663–672, April 2014.

[5] J. Jayachandran and R. M. Sachithanandam, “Neural network-based control algorithm for DSTATCOM under nonideal source voltage and varying load conditions,” Canadian Journal of Electrical and Computer Engineering, vol. 38, no. 4, pp. 307–317, Fall 2015.

A Switched-Capacitor Inverter Using Series/Parallel Conversion with Inductive Load

 ABSTRACT

A novel switched-capacitor inverter is proposed. The proposed inverter outputs larger voltage than the input voltage by switching the capacitors in series and in parallel. The maximum output voltage is determined by the number of the capacitors. The proposed inverter, which does not need any inductors, can be smaller than a conventional two-stage unit which consists of a boost converter and an inverter bridge. Its output harmonics are reduced compared to a conventional voltage source single phase full bridge inverter. In this paper, the circuit configuration, the theoretical operation, the simulation results with MATLAB/ SIMULINK, and the experimental results are shown. The experimental results accorded with the theoretical calculation and the simulation results.

 

KEYWORDS

1.      Charge pump

2.       Multicarrier PWM

3.       Multilevel Inverter

4.       Switched capacitor (SC)

 

SOFTWARE: MATLAB/SIMULINK

CONCLUSION

 In this paper, a novel boost switched-capacitor inverter was proposed. The circuit topology was introduced. The modulation method, the determination method of the capacitance, and the loss calculation of the proposed inverter were shown. The circuit operation of the proposed inverter was confirmed by the simulation results and the experimental results with a resistive load and an inductive load. The proposed inverter outputs a larger voltage than the input voltage by switching the capacitors in series and in parallel. The inverter can operate with an inductive load. The structure of the inverter is simpler than the conventional switched-capacitor inverters. THD of the output waveform of the inverter is reduced compared to the conventional single phase full bridge inverter as the conventional multilevel inverter.

 REFERENCES

 [1] H. Liu, L. M. Tolbert, S. Khomfoi, B. Ozpineci, and Z. Du, “Hybrid cascaded multilevel inverter with PWM control method,” in Proc. IEEE Power Electron. Spec. Conf., Jun. 2008, pp. 162–166.

[2] A. Emadi, S. S. Williamson, and A. Khaligh, “Power electronics intensive solutions for advanced electric, hybrid electric, and fuel cell vehicular power systems,” IEEE Trans. Power Electron., vol. 21, no. 3, pp. 567–577, May 2006.

[3] L. G. Franquelo, J. Rodriguez, J. I. Leon, S. Kouro, R. Portillo, and M. A. M. Prats, “The age of multilevel converters arrives,” IEEE Ind. Electron. Mag., vol. 2, no. 2, pp. 28–39, Jun. 2008.

[4] Y. Hinago and H. Koizumi, “A single phase multilevel inverter using switched series/parallel DC voltage sources,” IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2643–2650, Aug. 2010.

[5] S. Chandrasekaran and L. U. Gokdere, “Integrated magnetics for interleaved DC–DC boost converter for fuel cell powered vehicles,” in Proc. IEEE Power Electron. Spec. Conf., Jun. 2004, pp. 356–361.

[6] Y. Hinago and H. Koizumi, “A switched-capacitor inverter using series/ parallel conversion,” in Proc. IEEE Int. Symp. Circuits Syst., May/Jun. 2010, pp. 3188–3191.

[7] J. A. Starzyk, Y. Jan, and F. Qiu, “A dc–dc charge pump design based on voltage doublers,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 3, pp. 350–359, Mar. 2001.

[8] M. R. Hoque, T. Ahmad, T. R. McNutt, H. A. Mantooth, and M. M. Mojarradi, “A technique to increase the efficiency of high-voltage charge pumps,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 5, pp. 364–368, May 2006.

[9] O. C.Mak and A. Ioinovici, “Switched-capacitor inverter with high power density and enhanced regulation capability,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 4, pp. 336–347, Apr. 1998.

[10] B. Axelrod, Y. Berkovich, and A. Ioinovici, “A cascade boost-switchedcapacitor- converter-two level inverter with an optimized multilevel output waveform,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 12, pp. 2763–2770, Dec. 2005.

[11] J. I. Rodriguez and S. B. Leeb, “A multilevel inverter topology for inductively coupled power transfer,” IEEE Trans. Power Electron., vol. 21, no. 6, pp. 1607–1617, Nov. 2006.

[12] X. Kou, K. A. Corzine, and Y. L. Familiant, “A unique fault-tolerant design for flying capacitor multilevel inverter,” IEEE Trans. Power Electron., vol. 19, no. 4, pp. 979–987, Jul. 2004.

[13] S. Lu, K. A. Corzine, andM. Ferdowsi, “A unique ultracapacitor direct integration scheme in multilevel motor drives for large vehicle propulsion,” IEEE Trans. Veh. Technol., vol. 56, no. 4, pp. 1506–1515, Jul. 2007.

[14] J. I. Leon, S. Vazquez, A. J. Watson, L. G. Franquelo, P. W. Wheeler, and J. M. Carrasco, “Feed-forward space vector modulation for single-phase multilevel cascaded converters with any dc voltage ratio,” IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 315–325, Feb. 2009.

[15] B. P. McGrath and D. G. Holmes, “Multicarrier PWM strategies for multilevel inverters,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 858–867, Aug. 2002.

[16] R. Gupta, A. Ghosh, and A. Joshi, “Switching characterization of cascaded multilevel-inverter-controlled systems,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 1047–1058, Mar. 2008.

[17] J. Zhang, Y. Zou, X. Zhang, and K. Ding, “Study on a modified multilevel cascade inverter with hybrid modulation,” in Proc. IEEE Power Electron. Drive Syst., Oct. 2001, pp. 379–383.

[18] V. G. Agelidis, A. I. Balouktsis, and C. Cossar, “On attaining the multiple solutions of selective harmonic elimination PWM three-level waveforms through function minimization,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 996–1004, Mar. 2008.

[19] J. A. Pontt, J. R. Rodriguez, A. Liendo, P. Newman, J. Holtz, and J. M. San Martin, “Network-friendly low-switching-frequency multipulse high-power three-level PWM rectifier,” IEEE Trans. Ind. Electron., vol. 56, no. 4, pp. 1254–1262, Apr. 2009.

[20] M. K. Kazimierczuk, “Switching losses with linear MOSFET output capacitance,” in Pulse-Width Modulated DC–DC Power Converters, 1st ed. West Sussex, U.K.: Wiley, 2008, ch. 2, pp. 37–38, sec. 2.