AbstractâThe increase in the number of power electronic applications has led to harmonic pollution of the power grid. Harmonic resonance that can result in ...
Controlling harmonics in electrical power systems for satisfying total and individual harmonic distortion constraints Camila S. Gehrke, Antonio M.N. Lima, Alexandre C. Oliveira Graduate Program in Electrical Engineering - PPgEE Department of Electrical Engineering - DEE Universidade Federal de Campina Grande - UFCG Rua Apr´ıgio Veloso, 882, 58429-900 Bairro Universit´ario, Campina Grande, Para´ıba, Brazil Email: {camila.gehrke}@ee.ufcg.edu.br, {amnlima,aco}@dee.ufcg.edu.br
Abstract—The increase in the number of power electronic applications has led to harmonic pollution of the power grid. Harmonic resonance that can result in severe voltage distortion is a well documented problem. Several suppression techniques have been proposed to solve this problem. This paper proposes a technique to cooperatively operate multiple Active Power Line Conditioner (APLC) installed in the same Electric Power System (EPS) for minimizing the effect of harmonic pollution. The APLC operates as a tunable conductance for specific harmonic frequencies based on to the maximum desired harmonic voltage distortion. The proposed control is based on the reference Total Harmonic Distortion (T HD) and Individual Harmonic Distortion (IHD) values specified by the IEEE Std 519-1992 recommendations. The damping conductance for each harmonic frequency can be adjusted separately and autonomously without any communication between the points of common coupling. Simulation and experimental results are used to demonstrate the correctness of the proposed approach as well as its feasibility. Index Terms—Power Quality, Active Power Line Conditioner (APLC), Harmonics, optimization
N OMENCLATURE b h H i∗harm Idc i∗dc if i∗f IHD ihd∗ kgT kgI T HD v Vdc ∗ Vdc ω
droop coefficient harmonic order maximum harmonic order reference of the harmonic current DC bus current amplitude DC bus current reference measured current APLC current reference Individual Harmonic Distortion new Individual Harmonic Distortion T HD minimization factor IHD minimization factor Total Harmonic Distortion measured voltage DC bus voltage DC bus voltage reference grid frequency
978-1-4799-2325-0/14/$31.00 ©2014 IEEE
I. I NTRODUCTION
The widespread use of electro-electronics equipments connected to the grid result in harmonic pollution, interferences and voltage regulation problems. Those problems degrade the power quality, which may cause malfunction and damaging equipment. To improve power quality, Active Power Line Conditioner (APLC) can be installed, which can present more versatility than the traditional compensators, as passive filters and capacitor banks. Conventional control is based on load compensation, in which the currents are calculated individually for each APLC using the load current. However, when many APLCs are installed in the same Electric Power System (EPS), one unit operation influence the others, so, the compensation control should be cooperative. Different from the load compensation, the compensation current in cooperative compensation is based on the voltage distortion observed at the Point of Common Coupling (PCC), which when multiplied by a proper gain yields the EPS conductance [1]. Several authors have investigated how to control such gain. In [2] an automatic gain control to split equally the power between two compensators based on the data provided by a communication system, has been proposed. In [3] EPS droop control has been used to share the power between units without any communicating channel. In these two case the Total Harmonic Distortion (T HD) was used as a reference for controlling the gain and no control action for Individual Harmonic Distortion (IHD) was implemented. In [4] a control based on IHD control without communication was implemented, but it just ensure constrained T HD level if only two harmonics are presented in the EPS. Note that, no work impose both IEEE Std 519 constrains. In this work a method that does not require any data communication between the APLCs allows to use both T HD and IHD indexes, to control the gain. For this purpose, an analogy to the standard droop control has been conceived.
3342
II. O PERATION P RINCIPLE
From Fig. 2 it is possible to reach the equations:
To share the power between units without communication, the APLC control strategy must operate in analogy to the standard droop control used with the synchronous generators in the EPS. The block diagram of an EPS governor is shown in Fig. 1, where, TT is the ”charging time” time constant, TV is a time constant, M is the angular momentum of the machine, G represents the ration between the load and frequency variation (system dynamics), ∆PL is the load variation and ω is grid frequency. The ∆P ∗ is the load reference, which can change the power output of the generator, [5], [6]. ∆P ∆ω
/R
(Ms+G) Rotating mass & load ∆PL Fig. 1. [6].
ω 0 = ω0 + (1/R1 )(P1 − P10 ), 0
ω = ω0 + (1/R2 )(P2 −
−1
∆ω(s) = ∆PL (s)
1+
1 R
∆ω steady state
Governor
∆Pmech
for various generators : ∆Pvalve
1 1+sTG
Ms+G
1 1+sTT
1 M s+G
lims→0 [s∆ω] −∆PL = 1 R +G −∆PL = 1 1 + + ··· + R1 R2
(3)
=
(4) 1 RN
+G
Knowing that, it is possible to extract from the block diagram of the governor, each generator droop control, which is represented by Fig. 3. Note, that the load variation in the EPS impedance result a frequency variation, as the load and the system impedance are not measured, the control is based on the frequency variation given by the error between ω-ω ∗ .
(+sTT) Prime mover
Block diagram of governor, prime mover and rotating mass , [5],
∆P
Besides the machine plants described to reach the system dynamic, note, a gain 1/R. This gain is added because, each asynchronous generator operates with an unique frequency, so when two or more generators are in the same area, it will lead to an unstable operation, as each unit would impose its own frequency. To operate in cooperation, there is an adjust in generator power by droop inclination, shown in Fig. 2, which allows two or more generators share the same load. In usual asynchronous operation, when the load rises, the generator frequency reduces, so the generator increases the output to meet again the fundamental frequency. In droop operation, when the load increases, unit 1 increases the output P1 to P10 , unit 2 increases the output P2 to P20 , which represents ∆PL = P10 − P1 + P20 − P2 . Although, the final frequency can be a bit different from the fundamental, being a new common operating frequency, ω’. This new frequency will provide the stability operation to both units. To constrain the frequency under regulations levels, the R value should be calculated by the allowed frequency variation and generator power.
ω
∆ω
*
Governor
∆Pvalve (+sTV)
/R
ω* Fig. 3.
Block diagram of droop control.
The EPS control analysis was used as a stability tool, because it applies linear system methods, providing important information about the system dynamics due to the load variation, which is the base to the APLC in EPS. So, for APLC compensation, instead of frequency and power, voltage and current are analyzed. The load variation can be detected by voltage frequency variation, so, instead of control valves, turbine and generator power, it is possible to calculate the harmonic compensation current for an APLC, represented by F . An analog representation of the block diagram with APLC is shown in Fig. 4. Note that R was called gain. Voltage change in function of load current variation was approximated by the impedance plant GE (s). ∆v
Frequency
Frequency
gain F(s)
ω ω’
∆if
GE (s)
P P ’ Power of unit 1
P Power of unit 2
∆iL
P ’
Fig. 4. Fig. 2.
(2)
The load power sharing between the generator, when these operate cooperatively, can be proved applying the steady state rule to (3) obtained from Fig. 1, which results in (4).
*
(+sTV)
(1)
P20 ).
Variation of the generator power output due to the load change.
3343
Analog block diagram to APLC.
A. APLC control The proposed APLC control is based on voltage detection with gain control. It should regulate harmonic distortion, T HD < 5% and IHD < 3%, so the gain is controlled by both those indexes. The proposed control is illustrated in Fig. 6. The control acquire the voltage v and decompose in A block, the output is the normalized harmonic voltages, v(h) , h= [2, · · · ,H]. v(h) is the input of B block resulting in the minimization gain kgI (h) based on IHD reference and droop inclination. The gain is multiplied by voltage input to calculate the harmonic current reference, as i∗(h) = (kgI(h) )v(h) . This is the droop to the APLC control. Although, to also ensure T HD reference, an additional loop is used in cascade with the droop control. The sum of the quadratic v(h) is the C block input, the output, kgT , modifies the reference value of B block depending on the T HD level. The discrete harmonic current, i∗(h) , are summed to obtain PH continuous harmonic current: i∗harm = h i∗h . The i∗dc is the current to maintain the DC voltage, Vdc , that is regulated to ∗ Vdc by Rv block. Finally, the APLC current compensation can be given by: i∗f = i∗dc + i∗harm . The reference current is compared to the actual APLC current, if , to determine the switch voltage reference and generates the gating pulses based on Pulse Width Modulation (PWM). 1) A Block: A sliding Discrete Fourier Transform (DFT) was implemented to obtain the decomposed harmonic voltage using a rectangular window. Using this technique it is possible to tune the controller for each frequency increasing accuracy of the results. To select the harmonic order a filter bank was used, so for each chosen frequency sine and cosine are calculated, based on (5). Where, xn is the signal value at√the discrete instant n, N is the discrete signal period, j = −1 is the complex unity, and Xk is the complex DFT representation of the h-eth harmonic. Xh =
N −1 X
xn exp
n=0
−2jπ hn N
(5)
Direct determination of Xh for every new input signal sample would require considerable computational effort, which is undesired on real-time systems with limited CPUs. An alternate approach is to determine how Xh changes in response to changes of xn , and then updating Xh from previous estimates. Since both xn and the complex exponential are considered periodic after N samples, it is also possible to determine the DFT representation by using N samples starting at instant l instead of 0. This offset represented as Xhl , and is given by (6). Xhm =
N −1 X n=0
xn+l exp
−2jπ k(n + l) N
This equation is used for each harmonic.
(6)
2) B Block: Gain control is implemented in B block. The gain is used to minimize the harmonic distortion calculating the current reference based on the acquired voltage. The gain is controlled using droop control changing gain and IHD reference as (7), Fig. 7. The droop control allows the APLC to equal share power between the units without communication increasing the reliability of the proposed control. Note, that ihd∗ is the new IHD reference after the subtraction, so it is 0.03 or lower, to ensure T HD under 5%, as explained before. kgI(h) = 0 + b(ihd∗ − v(h) )
v (h)
B(h) Fig. 7.
∆IHD
b
(7)
k gI(h)
IHD*-k gT Control system block diagram - IHD.
The droop coefficient b can be calculated similar to EPS droop control, [5], in which it is used the maximum and minimum frequency and generator power. For the implemented droop, the coefficient value is based on minimum and maximum IHD reference and the maximum APLC conductance. When few APLCs with different capacities are operating in frequency droop control, each unit may have a unique value for the droop coefficient; b. Different droop coefficients allow sharing the total load power requirement among the APLCs according to a predefined ratio. 3) C Block: Considering h = [2, · · · , H] with H = 25 T HD control is also necessary, because if the EPS present more than two harmonic above IHD reference, T HD reference value is not satisfied, (32 + 32 + 32 ) > 5. So to control the T HD value, a cascade control was added to the droop control. The additional loop control varies the maximum IHD reference based on one kgT factor, which is calculated as Fig. 8. C block consist of a PI controller to regulate T HD reference, the output signal reduces IHD reference when more than two harmonic are above 3%, in other words, T HD > 5%. Note that the output is constrained between zero and IHD reference. P
C
v (h)
∆THD
PI
k gT
THD* Fig. 8.
T HD based control.
The T HD controller was considered a PI controller based on the EPS parameters. As the line segments are represented by π segments, which consist in RLC parameters, the usual
3344
IHD* (THD*)2
ihd*
k gT
PI
∆il
C
∆if
k gI(h)
b
B() B(H) | |
| v ()|2
| v (H)|
| v ()|
( )2
2
| v (H)|
( )2 Fig. 5.
|
|
v ()
|
|
v (H)
| cos(hwt+φ) | cos(hwt+φ) A() A(H)
An APLC unit controlled by the proposed method.
APLC
z(,k,h)
v
GS(s)
APLC
z(k,k+,h)
z(k+,k+,h)
z(N,N,h) +
| v (h)|
2
∗ ω()
A()
v
∗ ω()
A()
∗ ω(H)
A(H)
v ()
Vdc
C
-
k gT
Vdc∗
k gI() B() | | | |cos(hwt+φ) k gT
v ()
∗ iharm
k gI()
B() | | | |cos(hwt+φ)
Rv ∗ idc if∗
q if
Ri
v∗
PWM
k gT v(H)
k gI(H) B(H) | | | |cos(hwt+φ) Fig. 6.
APLC
An APLC unit controlled by the proposed method.
controller would lead to a PID controller, although, the capacitance for each segment is very small considering the resistance and inductance used. So an approximation to RL segment can be used. Like this, PI controller can be used. 4) DC Link Control: The DC link control is based on the voltage error, that is regulated by a PI controller (Rv ) to obtain zero error and generates the DC current compensation, Idc . To ensure grid synchronization, Idc is multiply by a sine using θ of the Phase-Locked Loop (PLL) signal, so: i∗dc = Idc sin θ
5) Current Control: The last controller is proposed to close the governor loop. The current regulator (Ri ) controls the APLC current, if , which circulates in the coupling inductors. As the current has sinusoidal waveform, a resonant control is implemented. To generate zero error for all frequencies, one resonant controller is tuned for each selected harmonic, beginning in the fundamental frequency ω until the maximum harmonic order H. III. APLC R ESULTS The circuit implemented to obtain results are illustrated in Fig. 9, see [7]. Used parameters values are also showed in [7].
3345
APLC
51
50
1
8 2
3
4
5
6
7
20 9 22 26
21 24 23
25
APLC Fig. 9.
18-bus IEEE distributed system.
To compare compensation strategies, each technique result is presented in Table II. Note the highest reduction should be presented using load current detection, although, as mentioned in the literature this strategy is not stable in EPS, besides, the current compensation is also high. The automatic gain control with communication result the lowest current, but it is needed a communication which do not represent high reliability in EPS. Droop control based on power and conductance line inclination (S→G) regulate the T HD level to 4.5%, the reference changed because of the behavior of the droop control. Note that those strategies, presented by [9] and [8], do not satisfied the IHD level, IHD=3.5% and IHD=3.6%. The proposed method result in T HD < 5% and also satisfying the IHD constrain of 3%. The current is a little bit higher than droop control, this is explained because in some harmonics the compensation need to be higher.
A. Control Analysis To analyze the proposed control, it was implemented two others voltage detection strategies: with automatic gain, [2] and gain based on droop, [8], besides the proposed method. The nonlinear load considered has 3, 5, 7, 9, 11, 13, 17, 19, 23 and 25 harmonic orders. The published control based on voltage detection strategies are presented in Fig. 10(a) and Fig. 10(b). Observing the PCC voltage, it is noted that the waveform is nonsinusoidal, presenting high harmonic distortion in PCC voltage, caused by the load current in the EPS impedance. After the compensation, the harmonic distortion reduces at PCC voltage, although, it is not eliminated as conventional control, which represents a current minimization. The strategy proposed by [9] has compensation current if = 3.6A. Under droop control, Fig. 10(b), the waveform is also nonsinusoidal, but the compensation current is lower, just if = 4.4A. Analyzing the waveform presented in Figs. 10(a) and 10(b), it is possible to calculate the T HD value, which are presented in Figs. 10(d) and 10(e). For the automatic gain control the T HD reduction is lower than the droop control. This difference is due to the method to adjust the gain, the first used increment and decrement, while droop used PI controller. Both satisfy the constrains, T HD = 5% for automatic gain and T HD = 4.5% for droop. The results obtained with the proposed control strategy are presented in Figs. 10(c) and 10(f). The results are similar to the previous strategies, satisfying the T HD constraint. It is important to note that the proposed control ensures not only the T HD level, but also the IHD, satisfying both requirements stipulated in the IEEE Std 519 recommendation. IHD levels of the manly harmonics are presented in Tab. I. Note that hte IHD is under 3%, as regulates IEEE Std. 519.
TABLE II C OMPARATIVE AMONG TESTED CONTROL .
Automatic gain Droop (S→G) Proposed method
T HDv 5.0% 4.5% 5.0%
T HDig 13% 10% 11%
IHDig (max) 3.5% 3.6% 3.0%
if (rms) 3.8 A 4.2 A 4.4 A
B. Control analysis under fault In [9], the author presented an cooperative control to avoid the fault situation when the system is readjusted and two APLCs previously far, start to operate close. In this situation one unit operates with high current and the other still almost without power. For verifying the cooperative control proposed, the published works are tested and compared. The fault was imposed in branch 2 between PCCs k = 23 and k = 24, after the fault, the system is readjusted and k = 24 is fed by branch 1, as illustrates Fig. 11. At fault moment, in red, the switch between PCC 8 and 24 is closed, in blue, readjusting the circuit, keeping all PCCs fed. The APLCs are reallocated, being positioned basically in the same point. 51
50
1
8 2
3
4
5
6
7
20 9 22 26
25
21
APLC 23
24
APLC Fig. 11.
Simplified representation under fault PCCs k = 23 and k = 24.
TABLE I IHD VALUES OPERATING WITH PROPOSED CONTROL . Ordem harmˆonica 3 5 7
IHDv 3% 2.5% 2.0%
The automatic gain without communication is shown in Fig, 12(a). The fault starts in t = 1.2 s, before the fault the APLCs are operating in k = 7 e k = 24. Before fault, the currents are not equal, because the APLCs are far, athough, T HD < 5%. At fault moment, the system is
3346
(a)
(b)
(d)
(c)
(e)
(f)
Fig. 10. Results of PCC voltage T HD (blue), EPS current (red), and reference (green) with and without APLC compensation: a - Automatic gain control with communication [9]. b - Droop control [3] and c - Proposed control.
THD (%)
10
THD 7 THD 24
5
0
1
RMS Current (A)
15
1.4
I
rms7
Irms24
10 5 0
(a)
1.2 Time(s)
1
1.2 Time(s)
1.4
(b)
(c)
(d)
Fig. 12. Results before (t1.2 s) the fault: a- Automatic gain control without communication [9]. b - Automatic gain control with communication [9]. c - Droop control [3] and d - Proposed control.
3347
automatic readjusted, so both APLCs should operate with the same current. However, when the automatic gain [9] operates without communication, the APLC in k = 24 provides almost all the current, irms = 10A. To solve this problem, it was implemented a communication, so the APLCs operate in cooperation, as shown in Fig. 12(b). At fault moment, both PCCs preset T HD < 5% and different currents. After the fault, the currents are equal. However, this strategy is limited, because it needs a communication between the APLCs. One alternative solution was present by [3]. A cooperative control based on droop without communication was implemented, Fig. 12. After the fault, the APLC current at k = 24 reduces and k = 7 rises, reaching the same current, Irms = 8.5A. The proposed control under fault is illustrated in Fig. 12(d). The control also operates without communication and achieve the same current after t = 1.2 s. Different from the others strategies, it operates to satisfy not only T HD level, but also IHD. The compensation current is lower than the droop control and a little higher than the automatic gain.
[4] T.-L. Lee, J.-C. Li, and P.-T. Cheng, “Discrete frequency tuning active filter for power system harmonics,” Power Electronics, IEEE Transactions on, vol. 24, pp. 1209 –1217, may 2009. [5] A. R. Bergen, Power System Analysis. Upper Saddle River: Prentice-Hall, 1989. [6] A. J. Wood and B. F. Wollenberg, Power Generation Operation and Control. New York, NY: John Wiley and Sons, 1996. [7] W. Grady, M. Samotyj, and A. Noyola, “Minimizing network harmonic voltage distortion with an active power line conditioner,” Power Delivery, IEEE Transactions on, vol. 6, pp. 1690 –1697, oct 1991. [8] T.-L. Lee and P.-T. Cheng, “Design of a new cooperative harmonic filtering strategy for distributed generation interface converters in an islanding network,” Power Electronics, IEEE Transactions on, vol. 22, pp. 1919 –1927, sept. 2007. [9] P. Jintakosonwit, H. Akagi, H. Fujita, and S. Ogasawara, “Implementation and performance of automatic gain adjustment in a shunt-active filter for harmonic damping throughout a power distribution system,” Power Electronics, IEEE Transactions on, vol. 17, pp. 438 –447, may 2002.
IV. C ONCLUSION Most of the APLC control strategies are implemented to act on a load and reduce the harmonics to zero. To hold this local data voltage and current of the load. This strategy works well in the local neighborhood, considering that the source of harmonics is the load itself. However, due to the amplification effect of harmonics, this strategy can maximize harmonics in distant locations. The major advantage of the voltage detection strategy is the resistive behavior of power converters, which minimizes all harmonics without instability problems. A disadvantage is that the overall compensation of harmonics is hardly obtained. However, when standards such as IEEE-519, are applied, the control does not need to compensate integrally all harmonics, it is necessary satisfy the maximum levels defined in the standards, so the overall compensation is not a problem. The proposed control to minimize harmonics showed versatility as it showed no problems with stability in any of the scenarios tested. It was able to follow the imposed references and satisfy both IEEE-519 constrains, T HD and IHD level. In fault situations, which result in the proximity between the APLCs, the control is capable of dividing the power without the need for a physical communication, which increases the reliability of the structure in which the control is implemented. This structure can be used in distribution networks as described in the paper or in large industrial plants. R EFERENCES [1] H. Akagi, “Control strategy and site selection of a shunt active filter for damping of harmonic propagation in power distribution systems,” Power Delivery, IEEE Transactions on, vol. 12, pp. 354 –363, jan 1997. [2] P. Jintakosonwit, H. Fujita, H. Akagi, and S. Ogasawara, “Implementation and performance of cooperative control of shunt active filters for harmonic damping throughout a power distribution system,” Industry Applications, IEEE Transactions on, vol. 39, pp. 556 – 564, mar/apr 2003. [3] T.-L. Lee, P.-T. Cheng, H. Akagi, and H. Fujita, “A dynamic tuning method for distributed active filter systems,” Industry Applications, IEEE Transactions on, vol. 44, pp. 612 –623, march-april 2008.
3348
