Instantaneous Reactive Power Theory And Its Applications
Instantaneous Reactive Power Theory and its Applications to Active Power Filtering<br />Arun Jayendran<br />B060110EE<br />
Conventional Power Theory<br />Traditional power theory for 1 phase, sinusoidal systems is well established<br />But these concepts fail to explain power components under non linear load conditions<br />These theories assumes reactive power arises due to oscillation of power between source and load <br />Relationship between v, i and p in a capacitor<br />Courtesy : www.wikipedia.org<br />
Power under non-sinusoidal conditions <br />Power definitions by Budeanu  (in frequency domain) can be applied only for steady state analysis, limited to periodic waveforms of voltage and current<br />Power definitions by Fryze  (in time domain) is based on rms values of voltages and currents too not valid under transient phenomena<br />
Need for a new power theory<br />Developments in the field of semiconductor technology have led to an explosion in electronic and power electronic devices in use today<br />Power electronic converters behave as a non linear load and represent a significant amount of power compared with other traditional linear loads.<br />The speed response of these converters and the way they introduce harmonic components demands the evolution of time domain techniques to analyze energy flow in non linear circuit at instantaneous levels <br />
About P-Q Theory…<br />In 1983 Hirofumi Akagiintroduced p-q theory through his paper “The Generalized theory of Instantaneous Reactive Power in Three Phase Circuits” <br />Most widely used for Non Linear load compensation for APF.<br />Introduction of instantaneous imaginary power makes p-q formulation a formal theory of electrical power in three phase system.<br />Compensates harmonic power optimally in balanced/unbalanced and sinusoidal supply voltage systems, but not so good with non sinusoidal voltages.<br />
Basis of P-Q Theory<br />Based on instantaneous powers defined in time domain.<br />Can be applied to 3 phase systems with or with out neutral.<br />It is valid not only in the steady state, but also in the transient state.<br />P-Q theory considers 3 phase system as a unit , not as a superposition or sum of three single phase circuits<br />Clarke transformation of voltages and current from the abc to 𝛼𝛽0 coordinates.<br />Defines instantaneous power on 𝛼𝛽0 coordinates<br /> <br />
Clarke Transformation<br />Transforms voltages, currents from a-b-c coordinates to mutually perpendicular set of α-β-0 axis<br />0<br />ω = 0<br />β<br />α<br />a<br />900<br />c<br />1200<br />b<br /><ul><li>α-β-0 is a stationary frame </li></li></ul><li>Inverse Clarke Transformation<br />(2.a)<br />vo , vα , vβ are zero sequence voltage, α axis ,β axis voltages respectively<br /> <br />(2.b)<br />io , iα , iβ are zero sequence current, α axis ,β axis currents respectively<br /> <br />
The Instantaneous Powers of the P-Q Theory<br />p= vα.iα + vβiβ<br /> p is the instantaneous real power<br />q =vα⋅ iβ − vβ⋅ iα <br /> q is the instantaneous imaginary power<br />p0= v0⋅ i0 <br />p0is the instantaneous zero-sequence power<br />(3)<br />(4)<br />(5)<br />
The P-Q Theory in 3Phase, 3 Wire Systems<br />In αβ axis, <br /> voltage vector, e= vα +jvβ (6)<br /> current vector, i= iα + jiβ (7) <br />Complex power, <br /> (8)<br /> The same can be expressed in matrix form as follows:<br />(9) <br /> <br />
Physical meaning of p and q<br />Definition of p (unit: Watt)<br />For a three phase system with or with out neutral conductor in steady state or during transients, the three phase instantaneous active powerp3ϕtdescribes the total instantaneous energy flow per second between two subsystems <br /> <br />Definition of q (unit: Volt Ampere Imaginary)<br />The imaginary power q is proportional to the quantity of energy that is being exchanged between the phases of the system. It does not contribute to energy transfer* between source and load at any time<br />
Physical meaning of p and q<br />p<br />vc<br />vb<br />va<br />a<br />q<br />b<br />c<br />p: instantaneous total energy flow per time unit<br />q: energy exchanged between phases without transferring energy<br />
Note on Instantaneous imaginary power q<br />Conventional power theory defined reactive power as a component of the instantaneous (active ) power, which has an average value equal to zero.<br />The imaginary power means a sum of products of instantaneous three phase voltage and current portions that does not contribute to energy transfer between two subsystems at any time <br />Eqn. (10) is similar to that implemented in some instruments for measuring reactive power. But instead of phasors, here instantaneous values are used <br />(10)<br />
Components of p , q and p0<br />Courtesy: <br />
p , p<br /> <br />p - Mean value of the instantaneous real power. <br />transferredfrom the power source to the load, in a balanced way through the a-b-c coordinates <br />only desired power component to be supplied by the power source<br />due to fundamental active current<br /> <br /><ul><li>p - Alternating value of the instantaneous real power.
exchanged between the power source and the load, through the a-b-c coordinates.
since p does not involve any energy transference from the power source to load, it must be compensated.
q , q<br /> <br />q - Mean value of the instantaneous imaginary power. <br />exchangedbetween system phases and does not imply transfer of energy between power source and load<br />choice of compensation of q depends on reactive power compensation <br />due to fundamental reactive current<br /> <br /><ul><li>q -Alternating value of the instantaneous imaginary power.
exchangedbetween system phases and does not imply transfer of energy between power source and load
since q is not necessary, it must be compensated.
FFT of Load and Source currents<br />THD= 33.09%<br />V1 = 22.16<br />V5= 32(% of V1)<br />V7= 2 (% of V1)<br />V11= 7 (% of V1)<br />THD= 1.61%<br />V1 = 22.16<br />V5= 1.5(% of V1)<br />V7= 0.2 (% of V1)<br />V11= 0.1 (% of V1)<br />
Developments in power theory<br />Original definitions of PQ theory were applicable only for balanced 3 phase systems with or with out neutral wire<br />Later on P-Q theory for single phase and N Phase systems were developed.<br />Some researchers argue that P-Q theory is not a complete power theory and it doesn’t assign correct physical meaning to its power terms<br /> Research is still going for developing unified power theory electrical engineering applicable under any generic voltage and current conditions.<br />Some of these theories are : P-Q-r theory, CPC theory, Cross vector theory, Hilbert space based power theory etc.<br />
Conclusions<br />Instantaneous reactive power theory (P-Q theory) is one among the modern power theories which is used in instantaneous evaluation of real and imaginary powers.<br />It was introduced at first as a compensation theory, but later on formal definitions were given.<br />It introduces the term instantaneous imaginary power q <br />Widely used in power conditioners for harmonic/reactive power compensation.<br />Optimal for balanced/unbalanced,sinusoidal 3 Phase systems.<br />Latest reformulation of P-Q theory is P-Q-r theory.<br />
References<br /> Mr. Suresh Kumar K.S &Dr. S. Ashok, “FACTS Controllers and Applications”,Nalanda Digital Library at National Institute of Technology Calicut.,2003<br /> ZainalSalam, Tan Perng Cheng and AwangJusoh,“Harmonics Mitigation Using Active Power Filter: A Technological Review”, ELEKTRIKA, VOL. 8, NO.2, 2006, 17‐26.<br /> A. M. Massoud, S. J. Finney, and B. W. Williams, “Review of Harmonic Current Extraction Techniques for an Active Power Filter”, 2004 11th International Conference on Harmonics and Quality of Power.<br /> Hirofumi Akagi, Mauricio Aredes, E.H. Watanabe, “Instantaneous Power Theory and Applications in Power Conditioning”, page no.53-220.<br /> JoãoAfonso, Carlos Couto, Júlio Martins, “Active Filters with Control Based on the p-q Theory”, IEEE Industrial Electronics Society Newsletter vol. 47, no 3, Sept. 2000, ISSN: 0746-1240, pp. 5-10.<br /> Arun Jayendran, Sreeram V, Subin V Sivadas “Comparative Simulation Study of Harmonic Extraction Schemes in Active Power Filtering Applications”, published by Academy Publishers, Finland, in IJRTE( International Journal for Recent Trends in Engineering)<br />