The Implementation of Correct Reactive Power Measurement is Long Overdue Tan Zhang, SIEEE, Stephen Cialdea, MIEEE, Alexander E. Emanuel, LFIEEE, John A. Orr, LFIEEE Department of Electrical & Computer Engineering Worcester Polytechnic Institute Worcester, MA USA
This paper is dedicated to Mr. Rejean Arseneau for his pioneering work on the study of power meter performance.
If not enough reactive power is supplied by sources located in the distribution network, then the reactive power will be supplied by the power plant generators causing an increase in the transmission line power loss as well as an increase in the voltage drop across the impedance of transmission and distribution lines. Modern distributed generators are ideal reactive power sources that can supply inexpensive reactive power to local customers and help reduce power losses in transmission and distribution systems. Customers must be supplied with the needed reactive power. A cost must be allocated for the kvar hours [2], and customers must be charged for the amount of reactive power “sunk” in their equipment. If the demand for reactive power exceeds a critical limit that cannot be supported by the voltage supplied at the observed load’s terminals, then a voltage collapse condition may lead to the much feared outage situation.
• Abstract—The scope of this study is two fold: first, it advocates the recognition of the 60/50 Hz, positive-sequence reactive power as the significant reactive power component of apparent power. This nonactive component must be monitored in the same way that the 60/50 Hz active power is monitored under nonsinusoidal conditions. Secondly, this paper documents the fact that instrumentation used today for reactive power measurement is marred by a significant difference between the indicated reactive power and the correct 60/50 Hz reactive power. Regrettably, such instrumentation is still favored by many utilities, instrumentation manufacturers and supervisors of energy markets. This paper documents a wide spectrum of situations that shed light on the discrepancies between the correct value of the reactive power and the measured value.
•
•
Index Terms—Power definitions, Reactive Power Metering, Cost of Reactive Power.
I. INTRODUCTION Presently power systems engineers are embarked on a major challenge; this is the re-engineering of the power systems. Their task is to improve the efficiency of transmission and distribution systems. Among many requirements for achieving such a goal the optimization of the reactive power flow holds a key role. There are many reasons that justify the need for accurate reactive power monitoring; following are a few significant issues [1,2]: • The reactive power must be generated by sources connected near the customers that need it. This condition reduces power losses caused by the reactive power flow. • The load voltage profile and quality is strongly dependent on the reactive power flow. Carefully planned power flow of reactive power helps to keep the voltage level between regulated limits. • The thermal stress on substation equipment depends also on the amount of reactive power supplied to the end users.
•
II. DEFINING REACTIVE POWER CORRECTLY The problem of correct measurement of power in systems operating under nonsinusoidal conditions has been of concern to engineers for many years. The performance of watt and watt-hour meters was published with due professional care [3]; however reactive power meters’ performance still requires consideration and dissemination. This paper is intended to increase awareness of problems with common measurement techniques and stimulate the proliferation of a new generation of instruments dedicated to monitoring reactive power. Assuming a load supplied with the nonsinusoidal voltage and current given by the expressions:
v = ∑ Vˆh cos(hω t + α h ) i = ∑ Iˆ cos(hω t + β )
(2)
V = ∑ Vh2 = V12 + ∑ Vh2
(3)
h
All four authors are with Worcester Polytechnic Institute (WPI), Department of Electrical and Computer Engineering, Worcester, MA 01609, USA. For correspondence e-mail:
[email protected]. 978-1-4673-6487-4/14/$31.00 ©2014 IEEE
467
with the rms values
h
h ≠1
(1)
I = ∑ I h2 = I12 + ∑ I h2
(4)
h ≠1
one will obtain five terms for the apparent power squared [4]:
2 S 2 = P12 + Q12 + DI2 + DV2 + S H where P1 = V1I1 cos (ϑ1 )
(5) (6)
is the 60/50 Hz active power (W), Q1 = V1I1 sin (ϑ1 ) ; with ϑ1 = α1 − β1 is the 60/50 Hz reactive power (var), DI = V1I H = S1 THDI
(7) (8)
is the current distortion power (var), THDI is the total harmonic distortion of the current and S1 is the 60/50 Hz apparent power, (9)
DV = VH I1 = S1 THDV is the voltage distortion power (var) and THDV is the total harmonic distortion of the voltage.
S H = VH I H = S1 THDV THDI =
PH2
2 + DH
(10)
∑ Vh I h cos(ϑh ) is the total
h ≠1
the accurate measurement of the meaningful Q1 . III. SURVEY OF VAR METER PERFORMANCE.
is the total harmonic apparent power, DH is the harmonic distortion power and PH =
avoiding the injection and proliferation of such powers in the electric networks. The magnetic fields associated with the above three nonactive powers are detrimental to the performance of motors and transformers. They cause parasitic torques, skin effect losses, mechanical vibrations, excessive leakage flux, unwanted resonance and electromagnetic interference. The literature dealing with the definition and quantification of reactive power reveals two schools of thought [6,7]; one aggregates totally or partially the nonactive powers. The other declares the 60/50 Hz Q1 as the meaningful reactive power. For three-phase systems the appropriate choice for reactive power is the 60/50Hz positive sequence reactive power. The authors concur with the engineering school that advocates the theory that Q1 is a key quantity at par with P1 and S1 . Thus, the industry needs the right tools that allow
harmonic active power. The apparent power S contains four nonactive terms, (5) and (10). The 60/50 Hz, Q1 , is the true, the only correct reactive power. The reason for this claim stems from the fact that loads such as transformers and motors, whose operation depends on energy stored in electromagnetic fields are generating or sinking reactive power in the form of electromagnetic energy that oscillates between the respective motors or transformers and one or more supply sources, or even between capacitive and inductive loads. These oscillations have a nil mean value and take place at 120/100 Hz. Loads and equipment that depend on a given magnetic flux cannot perform without being supplied with the right amount of 60/50 Hz reactive power. The operation of equipment that contains any type of inductors has magnetizing currents 90 0 out of phase with the supplied voltage, currents sustained by the reactive power that correlates with the magnetic flux. In a transformer the primary and the secondary windings are linked by the magnetic flux quantified by magnetizing currents that together with the supplied voltage define the instantaneous 60/50 Hz reactive power. In a synchronous or induction machine the existence of the rotating magnetic field is due to the three-phase magnetizing currents that are “supported” by the well-defined reactive power whose physical mechanism has its roots on the Poynting Vector theory [5]. In such rotating machines it is the positive sequence rotating field that is supported by the 60/50 Hz reactive power that sustains the dominant (useful) torque. The distortion powers, D I , DV and DH are also supporting nonactive instantaneous powers that have zero net energy transfer and also cause power loss; however, these powers are sheer electromagnetic pollution [4]. They are the byproduct of energy conversion and good engineering practice requires
The results of seven simulations and one field measurement are presented. Each set of results corresponds to six reactive power metering methods [6], meant to help determine the normalized differences between the measured reactive power Q and the correct reactive power Q1 . The names of the six methods are listed in TABLE I. The mathematical background for the computation of ΔQ / Q1 is presented in the Appendix. Results for each measurement method were calculated numerically for waveforms resulting from eight representative circuit situations: 1. Single-phase rectifier 2. Thyristorized phase controlled load 3. Three-phase, six-pulse rectifier, 1 MVA 4. Adjustable speed drive, 2.0 kW 5. Three-phase, six-pulse rectifier, 1.8 MVA 6. A 7.2 kVA nonlinear load with adjustable power factor 7. Results calculated as a function of second harmonic content 8. Actual measurements obtained with a 2.5 kW adjustable speed drive induction motor TABLE I Reactive Power Measurement Methods SYMBOL METHOD NAME A VECTOR B QUARTER - CYCLE VOLTAGE DELAY C QUARTER- CYCLE CURRENT DELAY D DIFFERENTIAL PHASE SHIFT E BUDEANU F INTEGRAL PHASE SHIFT
Figure 1 gives the curves ΔQ / Q1 versus the time constant 2 ≤ L / R ≤ 30 ms for a large single-phase rectifier rated 100 kVA, 1600 V, 50 Hz supplying a dc load R = 10 Ω in series with an inductance L. It is observed that the methods A, B and C yield unacceptable differences where 100 ΔQ / Q1 > 1%.
One will also notice that the difference ΔQ can be positive or negative. At the transformer’s load terminals the voltage and
468
current had reasonably low values, 2.68 < THDV < 2.82% and
10
18.32 < THDI < 36.89% . 10
A
2
10
10
A
1
0
D 10 10 10
Δ Q/Q1 (%)
Δ Q/Q 1 (%)
10
2
B&C
-1
E
10
10
1
D E
B&C
0
F -1
-2
F 10
-3
-2
1
2
3
4
5
6
Delay Time (ms) 10
Figure 2. Normalized Differences ΔQ / Q1 % vs. the Delay Time for a Thyristorized Single-Phase Load, 60 kVA, 1600 V, 60 Hz. Load Resistance R = 20 Ω in series with L = 10 mH. .
-4
0
5
10
15
20
25
30
Time Constant (ms) Figure 1. Normalized Differences
ΔQ / Q1 % vs. the Load Time-Constant
Solid Trace
τ = L / R for a Single-Phase Full Rectifier, 100 kW, 1600 V, 50 Hz. Load Resistance R = 10 Ω , Load Inductance L is Varied. Solid Trace
10
In Figure 2 are presented the difference curves for a thyristorized phase-controlled load, 1600 V, 60 kVA, 60 Hz, with R = 20 Ω in series with L = 10 mH. This yields 0.98 < THDV < 3.65%
and
3.65 < THDI < 93.33% .
The
curves give ΔQ / Q1 % vs. the firing time (delay time). It is
Δ Q/Q (%) 1
ΔQ > 0 and Dashed Trace ΔQ < 0
learned from these results that for firing time larger than 1.0 ms, ΔQ / Q1 is excessively high with the exception of method F (Integral Phase Shift). The third measurement, Figure 3, was carried for a threephase six-pulse rectifier rated 1 MVA, 13.8kV, 60 Hz. The load consists of a 100 Ω resistance in parallel with a 17 mF capacitance. Measurements were carried out using the line-toground (L-G) and the line-to-line (L-L) voltage. The voltage and current distortion was characterized by THDVL − L = 4.95% and THDVL − G = 4.96% and
10
2
L-G L-G L-L L-L 1
10
an exceptionally large error, 100ΔQV / Q1 = 237% , a result that totally disqualifies the Vector Method.
-20.95
27.83
-2.36
0
-2.36
5.71
-7.42
-1.34 -0.71
-0.83
-0.83 -0.25
10
-1
A
B
C
D
E
Method Figure 3. Normalized Differences ΔQ / Q1 %
Solid Trace 10
10
F
for a Three-Phase Six-Pulse
Rectifier, 1 MVA, 13.8 kV, 60 Hz. Load Resistance
Δ Q/Q (%) 1
environment with THDV = 2.63% and THDI = 72.78% . The measurements were implemented at the input terminals of the rectifier transformer. With the exception of Vector Method all the differences ΔQ are negative. The Vector Method presents
Positive Negative Positive Negative
-3.77
THDI = 23.64% . It is found that measurements using the
line-to-ground voltage yield larger differences ΔQ . The largest differences were caused by the Vector method (27.83%) and the Differential Phase Shift method (-20.95%). The fourth measurement, Figure 4, summarizes the results obtained from the simulation of an adjustable speed drive rated 2.0 kW, 208 V, 60 Hz, with an equivalent dc load R = 16.5 Ω in parallel with C = 500 μF , operating in an
ΔQ > 0 and Dashed trace ΔQ < 0
R = 20 Ω in series
with L = 10 mH. ΔQ > 0 and Dashed trace ΔQ < 0
3
Positive Negative 2
237.86
10
10
1
0
-4.24
-4.24
-6.42
-1.78 -0.43
10
-1
A
B
Figure 4. Normalized Difference
C
D
E
Induction Motor, Rated 2.0 kW, 208 V, 60 Hz. Solid Trace ΔQ > 0 and Dashed trace ΔQ < 0
469
F
Method ΔQ / Q1 % for an Adjustable Speed Drive
The fifth results, Figure 5, were obtained from the simulation of a six-pulse rectifier rated 1.8 MVA, 20 kV, 60 Hz, with an equivalent dc load R = 200 Ω in series with L = 1.0 H and supplied with a mildly distorted voltage and current THDVL − L = THDVL − G = 4.62% and THDI = 22.76% .
Comparing the differences ΔQ obtained using the line-to-line voltage versus the line-to-ground one discovers some advantage in favor of the line-to-line approach, nevertheless, the differences are still too large to promote the acceptance of these results.
Δ Q/Q 1 (%)
L-G L-G L-L L-L
-30.98
1
-8.37
6.15
10
100 ΔQ / Q1 = 1.0% and at PF1 = 0.98 , 100 ΔQ / Q1 = 4% (note the logarithmic scale). 10
10
Positive Negative Positive Negative
A
-0.58
-0.58
-0.16
-0.16
B
C
D
E
E
fundamental
current
higher harmonic phasors are listed in TABLE II. TABLE II Higher Harmonic Phasors for the study of
-1
F 0.50
0.60
0.70
0.80
0.90
1.00
ΔQ / Q1 % vs. the Load’s Fundamental Power Factor. Resistance R = 10 Ω , Load Inductance L is Varied. Solid Trace ΔQ > 0 and Dashed Trace ΔQ < 0
I1 = I1 / ϑ 1 is adjusted over the range 0.40 ≤ PF1. ≤ 0.98 . The
PF1 Effect
Vh
Ih
ϑh
Ph
Qh
(V)
(A)
5
4.0 / 60 0
12 / − 130.00
(deg) 190
(W) -141.8
(var) -25
7
7.5 / 89 0
8.0 / − 72 0
161
-170.2
58.6
11
1.0 / 119 0
1.0 / − 28.50
147.5
-2.5
1.6
h
0
Figure 6. Normalized Differences
F
The measurements presented above indicate that an inductive load with low power factor, PF1 = P1 / S1 = cos (ϑ1 ) , yields a lower difference ΔQ and the reverse effect takes place when the power factor nears unity. To get a better grasp on this issue a nonlinear inductive load supplied with a constant S1 = 7200 VA is considered. The supplied voltage is distorted, but kept unchanged. The fundamental voltage The
D B&C
Power Factor
-0.22
ΔQ / Q1 % for a Large Three-Phase Rectifier 1.8 MVA, 20 kV, 60 Hz. Solid Trace ΔQ > 0 and Dashed trace ΔQ < 0
V1 = 120 / 00 V.
1
10 0.40
Figure 5. Normalized Differences
is
A
2
-2
-0.82
Method
phasor
10
10
0
-1
10
3
-4.86
-1.31
10
the B and C cases (the quarter-cycle methods), at PF1 = 0.40 ,
2
49.76
10
significant influence on the value of ΔQ . For example, note
Δ Q/Q 1 (%)
10
In Figure 6 are plotted the normalized percent differences as a function of the 60/50 Hz power factor PF1 . The curves correspond to the six methods of measurement. The obtained results show that the 60/50 Hz power factor PF1 has a
The seventh simulation is focused on the situations where even harmonics are present. It is known that the 2nd harmonic causes one half-cycle to extend or to shrink from the canonic value of half period [8]. The consequence of this condition is generation of direct current, I 0 and direct voltage V0 . A full
bridge rectifier supplying a 140 V battery in series with a 2 Ω resistor was selected for the study of the effect of the second harmonic. The supplying voltage is 120 V, 60 Hz in series with an adjustable 120 Hz source. The feeder connecting the sources with the rectifier has a resistance of 8.0 mΩ and an inductance L = 0.3 mH. The rectifier has an input transformer with a short-circuit impedance 2.4+j30 Ω (at 60 Hz). The results presenting ΔQ / Q1 versus the normalized second harmonic V2 /V1 are summarized in Figure 7. In all the previous cases it was found that due to the lack of even harmonics both Quarter-Cycle Delay methods, B and C, caused the same differences ΔQ / Q1 . When even harmonics are present dc components are produced and the methods B and C provide different ΔQ curves.
470
10
10
3
10
Positive Negative
A
2
1
B 10
10
10
Δ Q/Q 1 (%)
Δ Q/Q 1 (%)
10 10
3
E
C F
0
D
411.15
10
1
-27.86
10
-1
2
0
3.12
3.12
-3.16 -0.38
-2
2
4
6
8
10
10
12
V 2 /V 1 (%) ΔQ / Q1 % vs. the Normalized Second Voltage Harmonic. Solid Trace ΔQ > 0 and Dashed Trace ΔQ < 0
Vh /V1
1
0
100 / 0
0.04 / 187
5
0.13 / 172 0
0
I h / I1
D
E
F
83.2 / 1750 72.8 / − 3
11
0.84 / 530
47.9 / 172 0
The most reliable method for reactive power measurement in three phase systems is by using three varmeters, one measuring the vars flowing through each line according to the particular measurement method implemented. The three varmeters measure the total reactive power (11) Q = Q A + Q B + QC = Q1 + ΔQ
Q A , QB and QC are the reactive powers measured on
the phases A, B, and C, respectively and Q1 = Q A1 + Q B1 + QC1 are the 60/50 Hz reactive power. The difference ΔQ = Q − Q1
9.1 / 91
0.83 / − 141
IV. THREE-PHASE SYSTEMS
where
0
7
0
C
ΔQ / Q1 % for an Actual Adjustable Speed Drive System rated 2.5 kW, 120 V, 60 Hz. Solid Trace ΔQ > 0 and Dashed trace ΔQ < 0
100/-140
3
B
Figure 8. Normalized Difference
Lastly the paper reports the results of measurements implemented with an actual adjustable speed drive rated 2.5 kW, 120 V, 60 Hz. The normalized harmonics are summarized in TABLE III and the normalized differences are given in Figure 8. With the exception of the integral phase shift method the reported differences are not acceptable.
h
A
Method
Figure 7. Normalized Differences
Table III Normalized Harmonics
-1
0
The results presented in Figure 8 are quite similar to the results shown in Figure 4. Since no even harmonics are present methods B and C yield identical results. It is confirmed that method A, the Vector method, is characterized by an unusually large difference, 100 ΔQ / Q1 = 411% and method F causes an acceptable difference.
(12) (13)
The difference ΔQ will be even larger if the 60/50 Hz positive sequence is recognized as the useful reactive power, in which case (14) Q1+ = 3V1+ I1+ sin(θ1+ ) and (15) ΔQ = Q − Q1+
Evidently the observations provided for the single-phase measurements apply unchanged for the Three-Varmeters method. A second widely used var metering method is the ThreeWattmeters method. This method was proposed for perfectly balanced three-phase systems with sinusoidal waveforms. In this method the wattmeter that is supplied by the current transformer of phase A has the voltage terminals supplied by the voltage transformer connected between the phases B and C. In the same way the wattmeter of phase B has the voltage terminals supplied by the voltage transformer connected to phase C A, and phase C wattmeter is supplied from phase A B. The Three-Wattmeters method is also affected by the voltage and current distortion as well as the load unbalance. The reactive power measured is
471
Q= where
1 3
( PBC + PCA + PAB ) = Q1+ + Q1− + PH
−
−
−
The measured reactive power is obtained from the expression [5,6]
(16)
QQCV =
−
Q1 = 3V1 I1 sin(ϑ1 ) is the 60/50 Hz negative reactive power and PH = PBCH + PCAH + PABH is the higher harmonics contribution to the difference
ΔQ = Q − Q1+ = Q1− + PH
(17)
1 kT
kT +τ
⎛
T⎞
∫τ i(t ) v⎜⎝ t − 4 ⎟⎠ dt
(4.A)
Substitution of (2.A) and (3.A) in (4.A) gives
(18)
QQCV = V0 I 0 + ∑Vh I h cos(α h − β h − πh / 2) h
(19)
= Q1 + ΔQQCV where ΔQQCV = P0 − P2 − Q3 + P4 + Q5 − P6 − Q7 + P8 + Q9 − P10 − Q11 + "
V. CONCLUSIONS The results obtained from this study point to the fact that varmeters based on the described design concepts, when operating under nonsinusoidal conditions, do not provide the expected accuracies, and should be declared obsolete and replaced with varmeters that measure the correct reactive power Q1 . The 60/50 Hz reactive power can be conveniently
C. QUARTER-CYCLE CURRENT DELAY Now the current harmonic phasors I h are rotated with −hπ / 2 rad and the key signals are v" = V + ∑Vˆ cos (hω t + α ) (6.A) 0
obtained using modern signal acquisition and processing technologies incorporating high-speed data acquisition, analog to digital conversion, and Fast Fourier Transform methods to isolate fundamental and harmonic frequencies. The ability to accurately measure the magnitude and phase of each harmonic frequency component of voltage and current, and hence to enable precise calculation of apparent, active, and reactive powers, is a powerful tool for determining and understanding the performance of modern power systems.
h
h
h
hπ ⎞ ⎛ i " = I 0 + ∑ I h cos ⎜ hω t + β h − ⎟ 2 ⎠ ⎝ h
(7.A)
kT +τ
T ⎞ −1 ⎛ i " ⎜ (t − ) ⎟ v" (t ) dt kT ∫τ 4 ⎠ ⎝ substitution of (6.A) and (7.A) in (8.A) gives
QQCI =
(8.A)
QQCI = −V0 I 0 + ∑Vh I h cos(α h − β h + πh / 2) h
VI. APPENDIX
= Q1 + ΔQQCI
where
The six basic methods [6] lead to different expressions for ΔQ. Following are the computations that yield the
ΔQQCI = − P0 + P2 − Q3 − P4 + Q5 + P6 − Q7 − P8 + Q9 + P10 − Q11 + "
difference expressions for ΔQ = Q − Q1 :
(9.A)
D. DIFERENTIAL PHASE SHIFT
A. VECTOR:
The Differential Phase Shift uses the expression
The computation is straight forward, the measured QV = S 2 − P 2
QD =
Q1 = V1 I1 sin(ϑ1 )
⎡⎛ Q ΔQ and % V = 100 ⎢⎜⎜ V Q1 ⎣⎢⎝ Q1
(5.A)
⎞ ⎤ ⎟⎟ − 1⎥ ⎠ ⎦⎥
kω T
−1 ⎛ d [v(t )] ⎞ i (t ) ⎜ ⎟ dt ∫ kωT 0 ⎝ dt ⎠
(10.A)
Substitution of (1) and (2) in (10.A) gives QD = Q1 + ΔQD where ΔQD = ∑ h Qh
(1.A)
h ≠1
B. QUARTER-CYCLE VOLTAGE DELAY The harmonic voltage phasors Vh are rotated with −hπ / 2 rad. If one also includes eventual dc traces V0 and I 0 then the expressions (1) and (2) become hπ ⎞ ⎛ v ' = V0 + ∑ Vˆh cos ⎜ hω t + α h − ⎟ 2 ⎠ ⎝ h
(2.A)
i ' = I 0 + ∑ Iˆh cos (hω t + β h )
(3.A)
(11.A)
E. BUDEANU The measured reactive power has the well-known expression QB = ∑ Vh I h sin(ϑh ) = Q1 + ΔQB ; thus
h
472
h
ΔQ B =
∑Vh I h sin(ϑh )
h ≠1
ϑh = α h − β h
(12.A) (13.A)
VIII. BIOGRAPHIES
F. INTEGRAL PHASE SHIFT This method is based on the voltage integral QI =
ω kT
kω T
∫ i(t ) [∫ v(t )]dt
(14.A)
0
Substitution of (1) and (2) in (14.A) gives QI = Q1 + ΔQI where
ΔQI = kπP0 + ∑ Qh / h
(15.A)
h ≠1
Due to the presence of dc caused by even harmonics, the method can lead to huge differences. The presented results assumed k=1. VII. REFERENCES [1] [2] [3]
[4]
[5] [6] [7] [8]
A. Saxena and M. D. Ilic, "A Value Based Approach to Voltage/Reactive Power Control," Energy Laboratory Publications # MIT EL 00-004 WP, May 2000. Federal Energy Regulation Commission, “Principles for Efficient and Reliable Reactive Power Supply and Consumption,” Staff Report, Docket No AD05-1-000, Feb. 2005. R. Arseneau and P. S. Filipski "Application of a Three-Phase Nonsinusoidal Calibration System for Testing Energy and Demand Meters Under Simulated Field Conditions," IEEE Transactions on Power Dlivery, Vol. PWD-3, July 1988, pp.874-79. IEEE Standard 1459-2010, IEEE Power Engineering Society, Power Systems Instrumentation and Measurements Committee: “IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions,” IEEE February 2010. A. E. Emanuel, Power Definitions and the Physical Mechanism of Power Flow, Wiley, 2010. NEMA C12.24 TR-2011, “Definitions for Calculations of VA, VAh, and varh for Poly-Phase Electricity Meters,”ANSI, May 2011. IEC, Technical Committee No. 25/WG 7: “Quantities and Units, and their Letter Symbols. Reactive Power in Non-Sinusoidal Situations,” 25(SecretariatI113, Dec. 1979. J. A. Orr and A. E. Emanuel, "On the Need for Strict Second Harmonic Limits," IEEE Trans. Power Delivery, vol. 15, No.3, July 2000, pp. 96771.
Tan Zhang (S’13), was born in Beijing, China, in 1989. He earned his BS degree from Beijing Jiaotong University and his MS degree from WPI, Worcester Polytechnic Institute, both in Electrical Engineering, in 2011 and 2013, respectively. He received outstanding teaching assistant and community service awards from the WPI Electrical & Computer Engineering department. His engineering career experience in the power & energy area spans power system simulation, transformer and power supply design. His research interests include power electronics, power system analysis, energy conversion and energy storage systems. Stephen Cialdea (M’12), received his BS in Electrical and Computer Engineering from Worcester Polytechnic Institute in Worcester, MA in 2012 with an expected MS in 2014. His engineering career experience in power and energy focus in large capacity battery energy storage, renewable energy, system modeling, equipment testing and maintenance, and protection systems. His research interests are in power system modeling and analysis, large capacity battery energy storage, distributed generation, system stability in microgrids, and electric vehicle penetration. Alexander Eigeles Emanuel (SM’71-F’97-LF’2005), was born in Bucuresti, Rumania, in 1937. He studied Electrical Engineering at the Technion, Haifa, Israel where he earned the B.Sc, M.Sc and D.Sc in 1962, 1965 and 1969, respectively. In 1969 he joined High Voltage Engineering where he worked as Research and Development Engineer till 1974 when he joined WPI, Worcester Polytechnic Institute, where he conducts research and is teaching. His favorite topics are power electronics, energy quality, energy conversion, electromagnetic fields and high voltage technology. John Andrew Orr (S’68-M’77-SM’90-F’03-LF’14) received the BS and PhD degrees in Electrical Engineering from the University of Illinois, UrbanaChampaign, and the MS degree in Electrical Engineering from Stanford University. He began his engineering career at Bell Telephone Laboratories, and joined WPI in 1977. He is currently Professor of Electrical and Computer Engineering. Dr. Orr's research interests span several aspects of digital signal processing as applied in electric power systems and in navigation systems. His other professional interest is in the area of engineering education.
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