ELECTRIC POWER QUALITY Hanoch Lev-Ari Northeastern University, Boston, MA and ...

94 Pages·2012·1 MB·English

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ELECTRIC POWER QUALITY
Hanoch Lev-Ari
Northeastern University, Boston, MA
and
Aleksandar M. Stankovi´c
Tufts University, Medford, MA
Sept 9, 2015
CURENT & NUCEER Centers, Northeastern University
& %
' $
POWER QUALITY METRICS
Frequency
•
Voltage level
•
Transients
•
Harmonic distortion
•
Power factor
•
Inactive/reactive power
•
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& %
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HISTORICAL EVOLUTION
Power factor (a.k.a cosφ) introduced in the 1920s for sinusoidal single-phase
•
waveforms.
Continuing evolution of the concept of inactive power:
•
è
Budeanu (1927) ï “reactive power” (via phasors) for multi-harmonic waveforms
è Fryze (1931) ï universal power factor (in waveform space)
è Shepherd & Zakikhani (1972), Sharon(1973) and others ï multi-component
decomposition of apparent power
è
Czarnecki (1980s) ï 5-component decomposition
è Lev-Ari and Stankovi´c (2005) ï 7-component decomposition
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Agreement on Reactive Power
Standard definitions [Buchholz, Schallenberger, Stanley]:
2 ⊤ 2 ⊤
V =< v v > , I =< i i > , S = V I
0 0
k k k k k kk k
P
⊤ 2 2 2
P =< i v > , Q = S P , k =
0 PF
− S
EnergyProcessingLaboratory–p.4/38
Agreement on Reactive Power
Standard definitions [Buchholz, Schallenberger, Stanley]:
2 ⊤ 2 ⊤
V =< v v > , I =< i i > , S = V I
0 0
k k k k k kk k
P
⊤ 2 2 2
P =< i v > , Q = S P , k =
0 PF
− S
For single frequency and single phase/ balanced polyphase in
steady state:
P = V I cos φ , Q = V I sin φ = Q
1 1 B1
k kk k k kk k
△
k = cos φ , S = P + Q
PF 1 c
EnergyProcessingLaboratory–p.4/38
Agreement on Reactive Power
Standard definitions [Buchholz, Schallenberger, Stanley]:
2 ⊤ 2 ⊤
V =< v v > , I =< i i > , S = V I
0 0
k k k k k kk k
P
⊤ 2 2 2
P =< i v > , Q = S P , k =
0 PF
− S
For single frequency and single phase/ balanced polyphase in
steady state:
P = V I cos φ , Q = V I sin φ = Q
1 1 B1
k kk k k kk k
△
k = cos φ , S = P + Q
PF 1 c
In multi-frequency k = cos φ , [Steinmetz 1898]; similarly for
PF 1
6
unbalanced.
EnergyProcessingLaboratory–p.4/38
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OUTLINE
è
SINGLE-PHASE SINUSOIDAL WAVEFORMS
Single-phase non-sinusoidal waveforms
•
Euclidean waveform spaces
•
Inactive power components
•
Polyphase waveforms
•
Dynamic power components
•
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GENESIS: SINGLE-PHASE SINUSOIDAL WAVEFORMS
Waveforms (via rms phasors):
1/2
T
1
v(t) = √2 V eωt ï V d=ef v2(t) dt = V
rms
< T | |
(cid:20) Z0 (cid:21)
(cid:8) (cid:9)
i(t) = √2 I eωt ï I = I
rms
< | |
(cid:8) (cid:9)
Instantaneous power:
def 2ωt
p(t) = v(t)i(t) = V I + V I e (more to come)
∗
<{ } <{ }
Average (“real”) power:
T
1
def
P = p(t) dt = V I
∗
T <{ }
0
Z
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& %
1
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SINGLE-PHASE SINUSOIDAL WAVEFORMS (2)
Power factor:
P V I
def ∗
PF = = <{ } = cosφ 1 (direct manipulation)
V I V I ≤
rms rms
| | | |
def
where φ = arg (V/I)
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& %
2
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SINGLE-PHASE SINUSOIDAL WAVEFORMS (2)
Power factor:
P V I
def ∗
PF = = <{ } = cosφ 1 (direct manipulation)
V I V I ≤
rms rms
| | | |
def
where φ = arg (V/I)
Euclidean space of phasors: V I is the inner product on this space
∗
<{ }
(cid:17)3
(cid:17)
(cid:17)
(cid:17)
(cid:17)
(cid:17)
V (cid:17)
(cid:17)
(cid:17)
(cid:17)
(cid:17)
(cid:17)
(cid:17)
(cid:17)
(cid:17)φ
(cid:17)
(cid:17) -
I
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2