New Resolution of the Unbalance Power According to Std. 1459

Salvador Orts-Grau, Member, IEEE, José Carlos Alfonso-Gil, Francisco J. Gimeno-Sales, and

Salvador Segui-Chilet, Member, IEEE

Abstract—Harmonic distortion and load unbalances have been an important issue in the last few years, motivating a large number of studies in active power compensators used for the power network quality improvement. Following an approach similar to the one used in IEEE Std. 1459 for the non-fundamental effective apparent power, a new resolution of the unbalance power is presented in this paper. The proposed power magnitudes allow explanation of the results obtained when shunt active power compensators are used in customer installations to improve the power quality. Related to the new unbalance power resolution, new merit factors are introduced in this paper to provide a measure of the quality level in the installation. Simulated and experimental results are analyzed in the paper by using the proposed resolution.

Index Terms—Active power filters, electrical power-quality indexes, IEEE Std. 1459, revenue power quantities, unbalance power resolution.

I. Introduction

IN a highly industrialized and technological society, the increase in energy demand is a worrying issue for government and energy utility companies [1]-[4]. The increase in the electrical energy demand all around the world is producing an increase in the prices of fossil fuels and a big interest in the production of electricity from renewable power sources such as wind or photovoltaic [1], [2]. Simultaneously, electrical power-quality problems are a very important issue for engineers who try to attain the maximum efficiency of the electrical system [5]-[13].

Electrical power-quality problems are analyzed from different points of view. Some recent topics under development are the following: electrical power definitions [5], [6], [14], [15], definition of electric power-quality indexes [14], [16], [17], evaluation of electric energy quality [18]-[21], electrical energy billing [22]-[24], identification and location of non-efficient loads [21], and active compensators [5]-[9], among others.

IEEE Standard 1459 [16] includes new definitions for the measurement of electric power quantities under sinusoidal, non-

Manuscript received May 06, 2009. First published December 11, 2009; current version published December 23, 2009. This work was supported in part by the Generalitat Valenciana under grant GVPRE/2008/343. Paper no. TPWRD-00295-2008.

S. Orts-Grau, F. Gimeno-Sales, and S. Segui-Chilet are with the Departamento de Ingeniería Electrónica, Universidad Politécnica de Valencia, Valencia 46022, Spain (e-mail: sorts@eln.upv.es; fjgimeno@eln.upv.es; ssegui}@eln. upv.es).

J. C. Alfonso-Gil is with the Departamento de Ingeniería de Sistemas Industriales y Diseño, Universidad Jaume I de Castellón, Castelló de la Plana 12071, Spain (e-mail: jalfonso@esid.uji.es).

Digital Object Identifier 10.1109/TPWRD.2009.2033964

sinusoidal, balanced, or unbalanced conditions. IEEE Std. 1459 is intended to evaluate the performance of modern equipment or to design and build the new generation of instrumentation for energy and power quantification [16], [25]. Some studies and explanations about definitions included in IEEE Std. 1459 are developed in [25]-[27] while in [14] some IEEE Std. 1459 terms are formulated following an instantaneous power approach.

Examples of instrumentation compatible with IEEE Std. 1459-2000 are developed in [28]-[30]. The core of all these instruments is a Digital Signal Processor (DSP) that carries out advanced algorithms over the three-phase load currents and the line to neutral voltages [30]. IEEE Std. 1459 states that the new definitions were developed to give guidance with respect to the quantities that should be measured or monitored for revenue purposes [22]-[24], engineering economic decisions, and determination of major harmonic polluters [19]-[21], [31], [32].

The charge for the different power magnitudes depends on the governmental regulations in some countries and the electrical utility tariffs [22], [24]. In [21] it is suggested that for a correct electrical energy billing, it is necessary to determine the responsibility for the existence of some power quantities between end customers or electrical utilities. It is also asserted that new indices are needed "for the evaluation of harmonic distortion levels at the metering section and for the determination of loads and supply polluting contributions". The purpose of the "Toll Road" model described in [20] and [31] is to attribute and allocate the cost and expenses of the circuits needed to maintain the power network with the minimum available harmonic pollution.

The presence of loads demanding fundamental positive-sequence reactive power (Qf), unbalance power (Su i), and nonfundamental effective apparent power (5ejv) produce quality problems to the electric power systems [9], [10]. Reactive power is traditionally compensated by means of capacitor banks [5], [19]. Unbalance power and harmonic distortion are mitigated by means of the use of passive and active compensators or hybrid arrangements [5], [33], [34]. Shunt active compensators are preferred in low-voltage distribution networks, near the end non-linear load that demand harmonic currents [5], [9], [33].

Shunt active power compensators (SAPCs) are connected to the customer installation at the point of common coupling (PCC) between power network and customer installation. The addition of an SAPC to the customer electric installation improves the power quality of its installations and has effects in the electric bill. The SAPC presented in [6] operates supplying the load current components that are responsible for the existence of the power quantities different from the fundamental positive-sequence active power (Pi ). The results included in

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the paper show that with the use of the SAPC, it is impossible to cancel completely some power terms related with Sejv and (Sui). This motivated a further analysis of the power quantities described in the IEEE Std. 1459 in relation with the unbalance and harmonic phenomena. The results of the analysis are exposed in this paper.

The organization of the paper is as follows. In Section II, the power magnitudes defined in IEEE Std. 1459 are summarized, especially the power terms included in SeN. In Section III, (Sui) is decomposed into new magnitudes following an approach similar to the one used by IEEE Std. 1459 with Sejy. In Section IV, a balanced resistive load is fed by a power supply that includes fundamental voltage asymmetries. The system is simulated and analyzed before and after the operation of an SAPC. Section V analyses the experimental results of an installation that includes an SAPC connected to a power network with high-voltage asymmetries at the PCC and a load that demands all kinds of useless powers. The last section includes the conclusions of the performed study.

II. IEEE Std 1459 Quantities

The important electrical quantities recognized by IEEE Std. 1459 for three-phase electrical systems are as follows.

• The fundamental powers, which are quantified all together by means of the fundamental effective apparent power (^ei). -Sei includes P¿, and Sui-

• The non-fundamental powers, quantified by means of 5ejv • SeN quantifies the whole load apparent power produced by the flow of the harmonic components of the load current and the PCC voltage harmonic components.

• The effective apparent power (Se) obtained from the effective voltage (Ve) and current (Ie), such as is defined in the standard.

Only P^ is considered a useful power quantity while the rest (Qi, Sui, and Sei\) are recognized as useless powers because they are not associated with the transfer of useful energy from generators to loads [6], [16], [25], [28]. The term "useless powers" is preferred with respect to the most common "non-active powers" because active fundamental negative-sequence power (Pi) and active fundamental zero-sequence power (Pf) are included in Sui, and harmonic active power (Ph) is included in SeJ\>.

Attending to the IEEE Std. 1459 resolution of the PCC voltages and load currents, Sc,n is resolved as it appears in (1) while Sui resolution is not performed in IEEE Std. 1459

SÎn —

Del — 3IeH Vcl-

and the harmonic effective voltage (Ven)- Dev quantifies the part of SCl\ produced by the voltage distortion

DrV = 3Ir,Vr

el VcH-

The harmonic apparent power (SeH)■ It is calculated in (4) from the product of the effective harmonic current (Ich) and the effective harmonic voltage (Ven)■ SeH quantifies the part of Sen produced by the product of voltage and current harmonic components

SeH = SleHVeH-

SeH is resolved into Ph and the residual harmonic distortion

power i

), being defined as follows:

c2 _ p2 , 7~)2 eH ~-rH+ e.

PH=3j2vhIh COS 6h = P - Pi, h^l

DeH=JslH-Pl

where Vh is the PCC rms harmonic voltage, is the load rms harmonic current, and Oh is the phase shift between the current and the voltage of the same harmonic order h.

Sel\ quantifies the whole load effective harmonic power demanded to the power network at the PCC. This magnitude is used to evaluate the level of the power network pollution due to harmonic components and also to define the apparent power rating of the active compensator that can reduce Se^ upstream the PCC [28].

Some ratios are defined in relation to the presence of harmonic components in the installation: the equivalent total harmonic distortion of the effective current (THDei) and the equivalent total harmonic distortion of the effective voltage (THDeV). Their definitions and relations with DcI and DcV are shown as follows:

THDei =

DeJ = Sel

cl y^ el el ( cl )

(8) (9)

The power magnitudes that appear in (1) are as follows.

• The current distortion power (DeI). It is calculated from the product of the fundamental effective voltage (Vei) and the harmonic effective current (Ieii), as it appears in (2). Dei quantifies the part of SeN produced by the current distortion. This is usually the dominant component of SCl\

The voltage distortion power (DeV). It is calculated in (3) from the product of the fundamental effective current (Iei)

The power demand of small industries and commercial and residential customers is significantly smaller than the power capability of the electric distribution network to which they are connected. Under this operating condition, the phase to neutral voltages are forced by the power network and SeN quantifies some power magnitudes that are not caused by customers. Reference [24] states that it is necessary to distinguish between customers who are harmonic sources and harmonic sinks. It is also necessary to distinguish between the part of useless powers produced by the customer and the part that is imposed by the power network at the PCC.

If a consumer connected at the very end of the feeder uses an SAPC in its installations, the use of DeI for the measurements of the customer pollution looks like the most correct option, as it is demonstrated in the performed tests. The other two quantities (SeH and Dcy) are directly influenced by the PCC harmonic voltages, which are imposed by the power network. For

Fig. 1. Power magnitudes under ideal supply conditions.

the same reason, THDej is preferred as a ratio for the evaluation of the pollution produced by customers that includes an SAPC to compensate or reduce useless powers. With the unbalance power resolution proposed in the next section, some of the new quantities are imposed by the power network while others must be charged to customers.

III. Unbalance Power Decomposition

The unbalance power quantifies the effect of the load fundamental current unbalances jointed with the PCC fundamental voltage asymmetries. Su 1 is a fundamental power that is calculated from the resolution of 5ei. Sei can be expressed as a function of Vei and 7ei or as the quadratic sum of all the fundamental power quantities as follows:

?el)2 =

The value of Sui is calculated from (10) as follows:

with voltage asymmetries and harmonic voltage distortion in the PCC, an SAPC cannot cancel completely the useless powers. If is directly used in this case for penalty purposes, the customer is paying for something that is caused by the power network.

Something similar happens with Sui- With the SAPC connected, the remaining Sui is caused by the power network fundamental voltages asymmetries at the PCC. This residual power magnitude is not defined in the IEEE Std. 1459 and is really important for customers because they cannot cancel or reduce this term, so they must not be charged for it. A further decomposition of the unbalance power is necessary if utilities desire to bill adequate for customers that add an SAPC to their installation.

The paper proposes a decomposition of Sui similar to the one done by IEEE Std. 1459 for SeN. For the calculation of the new power terms, Vei is resolved using the fundamental positive-sequence (Vi+), and the fundamental unbalance (Vui) voltages, while Iei is resolved in the fundamental positive-sequence (7+) and the fundamental unbalance (Iui) currents. Using the definitions included in [16], the resolution of Vei and Ie\ is as follows

III = (It)' + (IT? + 4 (I°i)2 = (It? + Ik, d2)

^l0)2 / T /

Vx ) +

+ (13)

S± is calculated by using and resulting in the following expression of Sui'

Replacing the values of 7+ and V* from (12) and (13), Sui is written as follows:

where is the fundamental positive-sequence effective apparent power. The calculation of Sui using the fundamental symmetrical components of the PCC voltages and line currents is performed in [14]. If PCC fundamental voltages present asymmetries, an ideal balanced resistive load will demand a set of unbalanced currents. The main goal of an SAPC that follows IEEE Std. 1459 is to convert the customer load in its equivalent balanced resistive load that only consumes [6], [16], [25], [28], as is indicated in Fig. 1. If PCC fundamental voltages present asymmetries, it is impossible to reach that goal because all the unbalance power is not caused by the customer. With fundamental voltage asymmetries at the PCC, the SAPC can only minimize certain powers.

This fact was first detected during the analysis of the simulated and experimental results presented in [6]. The SAPC used in [6] delivers the load current components related with the existence of <2+, Sui, and Scn. The SAPC can achieve a balanced set of supply fundamental currents, with a small content of high frequency harmonics caused by the self-switched operation of the VSI inverter. The customer is demanding only the active part of the fundamental positive-sequence current (7^a), the only one related with the presence of P+. With the normal operation of the SAPC, some power terms related with Scn and Sui keep in the supply lines. The SAPC cancels correctly Ich, so Dej and SeH are nil but it is not possible to cancel Dey. Therefore,

&U1 — ^el ~~ ^ (Vei — Vui) ' {lei ~ ^Ul) '

Resolving Sei as a function of Vei and 7ei and simplifying terms Sui is calculated as follows:

S2V1 = (3 • VelIui)2 + (3 • Vuileif - (3 • Vuiluif . (16)

The first term in (16) represents the unbalance produced by the fundamental currents demanded by the customer unbalanced load. The second term in (16) represents the unbalance produced by the PCC fundamental voltage asymmetries. The third term in (16) is produced by the load fundamental unbalances and the fundamental voltage asymmetries. Sui decomposition includes the following power quantities.

• The current unbalance power (Sun) - It is calculated from the product of the fundamental effective voltage (Vei) and the fundamental unbalance current (7[/i), as it appears in (17). Sun quantifies the part of Sui due to customer fundamental current unbalance

Sun — SVeilui-

The voltage unbalance power (Sj/iy ). It is calculated from the product of the fundamental effective current (7ei) and the fundamental unbalance voltage (Vui), as it appears in

Fig. 2. Resolution of Se including the new resolution of Sui •

(18). Suiv quantifies the part of Sui due to the PCC fundamental voltage asymmetries

Su IV — 3V[/i/el.

The unbalance apparent power (Suiu)- It is calculated from the product of Iui and Vui, as it appears in (19). Suiu quantifies the part of Sui produced by the fundamental voltage and current unbalanced components

Suiu = SVuiIui-

With the use of these new power quantities, Sui is calculated as follows:

Q 2 _ Q 2 I Q 2 Q 2

ÖU1 — ÖU1I ' DUIV ~ Duiu-

ÖU1U —

+ PÏ)'

+ ^Ule

where Px and Pf are defined in IEEE Std. 1459 and Suie is calculated using the previous definitions as follows:

— S2

quality of the installation from the point of view of the fundamental unbalances and asymmetries: • The total current unbalance factor (TUt):

1 I el

The total voltage unbalance factor

TUy and TUj provide a global ratio of the voltage asymmetry and the current unbalance, respectively. With these new factors, (17) -(19) can be written as follows:

Sun — Sei SuiU = Sei

(26) (27)

Suiu includes the negative-sequence apparent power (S^), and the zero-sequence apparent power (SJ), between other power terms, as defined in [16]. The resolution of Suiu proposed in this paper distinguishes the following three power terms: the negative-sequence active power (Pf), the zero-sequence active power (Pj3), and a residual unbalance power designated as Suie- Suie includes between others, the negative-sequence reactive power (Qi), and the zero-sequence reactive power (Q?), as defined in [16]. The following relationship is verified:

Using [25, Fig. 6], the resolution of the effective apparent power (Se) according to the IEEE Std 1459 and the proposed resolution of Sui are shown in Fig. 2

With these power magnitudes, the different terms of Sui are measured individually, with separate identification of the unbalance power due to fundamental current unbalances or due to fundamental voltage asymmetries. With the use of an SAPC in the customer installation, the supply currents contain mainly and Iui is nil, so Sun and Suiu are canceled from the supply lines. These power terms quantify the unbalance level of the load current. Using the previous definitions, new merit factors are added to IEEE Std 1459 to measure the electric power

These power magnitudes and their related factors are useful for revenue purposes, for engineering economic decisions, for the determination of the pollution source, and for the SAPC sizing. Two different examples are analyzed in the next two sections. The first one corresponds to an ideal three-phase balanced resistive load that is connected to a power network that presents fundamental voltage asymmetries. The circuit is analyzed by means of simulation using Matlab/Simulink and demonstrates how an ideal load demands non-efficient power owing to power network disturbances. An experimental example is performed in the second case. It consists of an unbalanced linear load in parallel with a three-phase balanced non-linear load. The load is connected to the power network by means of a three-phase transformer to force a high-voltage asymmetry during the experimental test. The proposed power terms and factors are calculated from the samples acquired from the PCC voltages and load currents. The power terms and factors obtained when the SAPC is connected demonstrate the validity of the proposed resolution.

IV. Simulated Results

Some simulated results are shown here to validate the proposed Sui decomposition (Sun, Suiv, Suiu, and Suie) and the new merit factors (TE/j and TUy). The values used in the averaged model of the circuit of Fig. 3 are La = LB = Lc = 6 mH; Rla = Rlb = Rlc = 0.5 ÍÍ. In [35], the selection of the ac output inductances is presented. A further description of the model used during the simulations, and the control algorithm used in the SAPC control are described in [6]. During the simulation, the PCC line to neutral voltages (vr — vs - vT) represented in Fig. 4 include fundamental voltage asymmetries, with the following rms voltages: VR = 220 V, Vs = 230 V, and Vt = 205 V. The fundamental frequency is 50 Hz. The load used in the simulation is implemented by using a balanced linear load with the following values: Rr — Rs — RT = 10 ÍÍ.

Fig. 5 shows the load currents (top plot) and the neutral current (bottom plot). The load currents (iR ioad - is load ~ iT load) are unbalanced due to the PCC voltage asymmetry, with an rms neutral current (In load) equal to 2.18 A. Tables I and II show

Fig. 3. SAPC connection to the power network.

Fig. 4. Phase-to-neutral voltages used in the simulations.

Fig. 6. Phase (top) and neutral (bottom) supply currents after SAPC operation.

TABLE I

Load Voltage, Current, and Power Magnitudes During the Simulation

VR = 220 V VS = 230V VT = 205 V

Ve = 218.51 V =218.51 V veH= 0 V

V\ = 218.33 V Vf = 7.25 V Vi° = 7.27 V

VeU= 8.89 V V\!V\ = 3.32 % V\!V\ = 3.33 %

hs =22 A /,,=23 A ITs =20.5 A INs = 2.18 A

Ie = 21.87 A Iei = 21.87 A IeH= OA

I\+= 21.81 A If = 0.72 A = 0.72 A

IeU = 1.62 A Ifllx+ = 3.32 % I\°/I\+ = 3.33 %

Se = 14337.86 VA Sel = 14337.86 VA OVA

SS = 14286.40 VA Px+= 14286.40 W Ô!+ = 0 var

Pi= 14318.10 W P= 14318.10 W Su 1 = 1212.56 VA

^=^1=4830.53 W Ps=Psi=52&7.26 W Pf=Pn=4200.31 W

PF = PFl = 0.9986 PFI+ = 1

Suiv= 583.31 VA Suu= 1063.91 VA 5,(/iC/= 43.28 VA

Pf = 15.77 W Px°= 15.83 W St/ig = 29.58 VA

TUV = 4.01% 777/= 7.42%

Fig. 5. Phase (top) and neutral (bottom) currents for a pure resistive three-phase balanced load.

the main magnitudes of the circuit. Table I includes the voltages, currents, power magnitudes, and merit factors of the three-phase balanced linear load.

The values included in the tables are grouped according to the magnitudes represented: • Voltages Ve, Vei, Vgh, and Veu are calculated from the rms line to neutral voltages (Vr — Vs — Vt).

• Currents 7e, 7ei, 7+, 7e#, and Ieu are calculated from the rms line supply currents (Irs — Iss — Its) and the rms current through the neutral wire (Ins)-

• Power magnitudes and related ratios are calculated following IEEE Std. 1459 and the new definitions proposed in the paper. All of the values are calculated using the voltages and currents detailed previously. The effective power factor (Pf& — P/S&) > the fundamental power factor (Pfi = Pi/Si), and the fundamental positive-sequence power factor (P^ = P^ /are defined in the IEEE Std. 1459.

For the operating conditions of the simulation, only Px+ and exist because no harmonic currents are demanded by the load and the PCC voltage contains only fundamental components. The value of the active power (P) verifies in any kind of electrical system the following relationship:

P = p+ + P" + po + PH,

TABLE II

Supply Voltage, Current, and Power Magnitudes After SAPC Operation (Simulated Results)

/Ä, =21.85 A =21.86 A ITs =21.86 A INs = 0.02 A

/, = 21.86 A le 1 = 21.86 A ieh = 0 A

/i+= 21.86 A /f = 0.01 A /i° = 0.00 A

IeU= 0.04 A /f//i+ = 0.06 % /i°//i+ = 0.02 %

Se = 14330.25 VA Se\ = 14330.25 VA SeN=0VA

Si+ = 14318.32 VA Pi+ = 14318.32 W Qi = 0 var

Px = 14318.36 W P= 14318.36 W Sui = 583.10 VA

PR=PRi=4804.62 W iV=P51=5030.26 W Pf=Pn=4483.47 W

Pp = Pp\ = 0.99917 Pfi+= 1

Smv= 583.00 VA $uu= 10.47 VA Smu = 0.43 VA

Pf = -0.02 W Px° = 0.00 W Sule = 0.43 VA

TUV= 4.01% TUj= 0.07%

tios Ii —

Fig. 7. SAPC output currents.

Despite that, the system unbalance is produced only by the fundamental voltage asymmetries at the PCC, the main part of

Sui is caused by Sun, followed by Suiv•

After the SAPC is connected at t — 0.24 s, the line and neutral supply currents change to the waveforms shown in Fig. 6, which only contains a. The small value of the ratios /f //+,

demonstrates that no current unbalance exists from

the point of view of the power network. The SAPC output currents represented in Fig. 7 are a set of unbalanced currents. With these currents, the SAPC eliminates or reduces significantly all useless powers different from P+, as is demonstrated with the power magnitudes shown in Table II. Voltages not shown in Table II remain equal to the values detailed in Table I. After SAPC operation, the useless power term that still remains in a similar value is Suiv, because the fundamental PCC voltage asymmetries cannot be corrected by the use of an SAPC. A hybrid (series-shunt) active power compensator could cancel all useless powers, but its use is not so common in low distribution power networks owing to the high currents flowing through the series circuit of the hybrid compensator. The values of TUy and the ratios Vi — and V[} /V\ before and after the SAPC is connected are the same due to the fact that PCC voltages are forced by the power network. The values of TUi and the ra-

drop to a value near zero with the

SAPC operation, not being exactly equal to zero due to the small steady-state error of the SAPC current controller used in the simulation model. The proposed powers before and after SAPC operation are compared in Fig. 8.

The simulated results demonstrate that the proposed resolution of Su i allows distinguishing between the different apparent powers included in Sui- The new power terms and factors can be used, in combination with other magnitudes, to determine the origin of the pollutions in the power network. As is demonstrated in the simulations, a perfect balanced resistive load connected to a power network, which includes fundamental voltage asymmetries, present a non-efficient behavior even when an SAPC is connected to cancel load non-active currents because some useless power terms are not cancelled. If IEEE Std. 1459 is used for penalty purposes in this case, the

Fig. 8. Experimental phase (top) and neutral (bottom) load currents.

part of the expenses corresponding to Sui is not the customer responsibility.

V. Experimental Results

To verify the validity of the proposed power quantities and factors, some experimental results are obtained with the small-scale prototype described in [6]. The experimental test reproduces different supply conditions and load values than in the simulations, to increase the effect of the load unbalances and voltage asymmetries. SeN, Dej, Dey, Sen, and P# exist in the experimental test. The SAPC operates reducing all the exiting useless load powers as is described in [6].

The load used in the test is implemented using an unbalanced linear load in parallel with a balanced three-phase non-linear load. Fig. 8 shows the load current waveforms, and the rms values of the load currents are detailed on the right of the scope. The waveforms are captured with a Yokogawa DL7100 oscilloscope. The scale used in all oscilloscope current waveforms is 100 mV = 1 A . The per-phase non-linear load is built using a

VR = 124.24 V Vs= 123.82 V VT= 78.71 V

Ve = 110.50 V Vei = 110.48 V VeH=2.lO\

Vi+= 108.89 V Vf= 15.52 V Vi°= 14.68 V

VeU= 18.68 V Vf!Vi= 14.26% VilVi = 13.48 %

1rs = 6.02 A ISs = 4.59 A Zu, = 1.75 A INs = 5.80 A

Ie = 5.60 A Iei = 4.83 A IeH= 2.82 A

/i+= 3.78 A If = 1.24 A Ii = 1.37 A

IeU= 3.01 A If/I\~ = 32.85 % Ii°/Ii+ = 36.30 %

THDj r=29.43 % THDi s=41.23 % THDi t=85.36 %

Se = 1854.70 VA Se\ = 1601.17 VA SeN = 936.04 VA

Si+ = 1234.15 VA Pi+= 1205.09 W Qi = 266.24 var

Pi = 1315.01 W P= 1324.13 W Sm = 1020.10 VA

PR = 701.56 W Ps = 521.55 W PT= 101.02 W

PRi = 698.90 W PSi = 516.81 W PTi = 99.30 W

PF= 0.7139 PFi = 0.8213 /V = 0.9764

Smv= 270.68 VA Suu= 997.90 VA Suiu= 168.70 VA

Pf = 50.20 W Pi = 59.72 W Sme = 111.91 VA

TUV= 16.91% 71//= 62.32%

THDeV= 1.90% THDeI = 58.42%

DeV= 30.42 VA DeI= 935.38 VA Seh= 17.77 VA

DeH= 15.25 VA PH= 9.12 W

Fig. 9. Experimental phase-to-neutral supply voltage waveforms.

Fig. 10. Main power magnitudes when the SAPC is connected.

single-phase uncontrolled rectifier with an LC filter and a resistive load (L = 5.4 mH, C = 2.2 mF, R = 100 ft). The unbalanced linear load is connected from phase terminals to neutral wire and has the following values:

* Zt load = Rt load = OO ft.

The supply current total harmonic distortion (THD^) for the three phases is included in Table III. Despite the non-linear loads demanding the same harmonic currents in the three phases, the values of the THD^ are different due to the load fundamental currents being unbalanced.

During the tests, the rms PCC line to neutral fundamental voltages are approximately Vrsi = Vs31 = 125 V and Vrsi = 80 V. The voltage asymmetry is obtained by means of a three-phase Y-Y transformer, in which a different secondary terminal is used for phase c. The primary of the transformer is connected to the power network, so some voltage distortion at the PCC is included in the experimental tests due to power network normal conditions (THDev = 1.9%). The values of TUV and the ratios Vf and V{]/Vi are quite similar before and after the SAPC is connected. Fig. 9 shows the line-to-neutral voltage waveforms used during the tests. The SAPC control is implemented in a TMS320F2812 DSP, which executes all algorithms needed for the SAPC control: SVPWM with a switching frequency equal to 19.2 kHz, dc bus voltage control, analog-to-digital conversion, current control, etc. [6].

As in the previous section, Tables III and IV show the main magnitudes of the circuit. Table III includes the voltages, currents, power magnitudes, and merit factor of the supply with the SAPC disconnected. Table IV shows the same values when the

SAPC is connected. Fig. 10 shows the main power magnitudes supplied by the power network and the SAPC. With the use of the SAPC:

• SeN is reduced but not completely canceled from the power network. Dej and Sen are reduced significantly while Dey keeps in a similar value. Dei and Sen are mainly supplied by the SAPC although Dey remains in the power network.

• In a similar way, Sjj i is reduced but not completely canceled. The most important reduction appears in Sun and in Sum , which are delivered by the SAPC. Only Suiv re_ mains equal because the SAPC cannot correct the voltage asymmetries of the PCC. The modification of the new Sui power terms with the SAPC operation is similar to their equivalent terms in Sejy.

• Pf, P®, and Ph are reduced to values near to zero. P is almost equal to Px+, demonstrating that the installation is near to its ideal conditions. The small increase in is produced by the self-supporting dc bus. The dc voltage controller establishes the increase of the active power needed to compensate the power losses in the SAPC [36]-[38].

• The values of the different power factors are improved, demonstrating that the power quality of the installation is increased.

Fig. 11 shows the SAPC output currents for the compensation of all load useless powers. Fig. 12 shows the supply currents when SAPC is connected. These currents are almost balanced and mainly contains , with a small harmonic component due to SAPC operation, as can be seen by the value of Ieu

IRs = 4.59 A ISs = 4

Ie = 4.73 A

Ix+= 4.72 A

7e[/= 0.28 A

THD; T>=4.93 %

TABLE IV

of the ratios L

Fig. 12. Experimental phase (top) and neutral (bottom) supply currents after SAPC operation.

Fig. 11. Experimental SAPC output current: a-b-c phases and neutral (from top to bottom, respectively).

in Table IV. A comparison between new power terms before and after SAPC operation is presented in Fig. 13. Before SAPC operation, the main part of Sui corresponds to Sun- After the SAPC is connected, Sun is reduced around 90% of its initial value, with a TUi that varies from 58.4% to 5.9%. The values

are reduced to a value smaller

than 3% with the SAPC operation, demonstrating the capability of the SAPC to minimize the unbalance of the fundamental current components.

The SAPC operation does not modify Suiv as is demonstrated by the value of TUy, which remains in the same value during the test.

The experimental results confirm that the proposed resolution of Sjji allows the calculation of the different power terms included in Sui • With the use of these power terms, the residuals Sjji and SeN after SAPC operation are completely identified and quantified. The new power terms allow calculation of the

Fig. 13. Comparison between new power terms before (left) and after (right) SAPC operation.

reduction of Sui after SAPC operation if the PCC voltage conditions are imposed by the power network. After the analysis is realized using the new resolution, a customer who connects an SAPC to improve the power quality of its installation must not be charged with the part of Sui corresponding to Suiv and with the part of Sejy corresponding to Dey because it is impossible to cancel it by means of an SAPC.

VI. Conclusion

IEEE Std. 1459 provides definitions for the electric power quantities that can exist in any situation of the electric power network. A new generation of instrumentation for energy and power quantification following IEEE Std. 1459 is now under development. Simulated and experimental results obtained for unbalanced loads that use an SAPC to compensate all useless powers motivated a further analysis about Sui- Following an approach similar to the one used in IEEE Std. 1459 for SeN, a new resolution of Sui is presented in the paper. The new power magnitudes and factors introduced in the paper are used in the simulations and in the experimental tests performed in the paper. The results obtained demonstrate that the proposed resolution of Sui allows distinguishing between the different apparent powers included in Sui - The proposed power magnitudes allow explaining the results obtained when SAPC are used

in customer installations to improve the power quality. The new power terms and factors can be used for proper electrical energy billing and, in combination with other magnitudes, to determine the origin of the pollutions in unbalanced power networks.

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Salvador Orts-Grau (M'06) was born in Valencia, Spain, in 1972. He received the M.E. and Ph.D. degrees in electronics engineering from the Universidad Politécnica de Valencia (UPVLC), Valencia, Spain, in 2000 and 2008, respectively.

He is an Assistant Professor in the Electronics Engineering Department in the UPVLC (EED-UPVLC), where he has been since 2001. His research work is focused on the improvement of the electrical power network quality by means of digitally controlled shunt active power compensators.

José Carlos Alfonso-Gil was born in La Cañiza, Spain, in 1974. He received the M.E. degree in automation and industrial electronics engineering from the Universidad Politécnica de Valencia (UPVLC), Valencia, Spain, where he is currently pursuing the Ph.D. degree in electronic engineering.

From 2005 to 2007, he was a Researcher at the UPVLC and since 2007, he has been a Visiting Teacher in the Department of Industrial Systems Engineering and Design, Universitat Jaume I (Castellón), Castelló de la Plana, Spain. His research work is focused on digital signal processors applied to the control of power converters and to the design of instrumentation that measures electric quantities.

Salvador Seguí-Chilet (M'01) was born in Valencia, Spain, 1962. He received the B.E. degree in industrial electronics, the M.E. degree in electronic engineering, and the Ph.D. degree in electronics engineering from the Universidad Politécnica de Valencia (UPVLC), Valencia, Spain, in 1986, 1999, and 2004, respectively.

Since 1990, he has been lecturing in the Electronics Engineering Department, UPVLC. His major fields of interest are power electronics, renewable energy systems, and active power compensators.

Francisco J. Gimeno-Sales was born in Valencia, Spain, in 1958. He received the Ph.D. degree in electronics engineering from the Universidad Politécnica de Valencia (UPVLC) in 2004.

From 1986 to 1993, he worked in several R&D departments, developing industrial products (hardware and software). Since 1993, he has been teaching power electronics and applied to power converter control in the Electronics Engineering Department, Universidad Politécnica de Valencia, Valencia, Spain. His research field of interest is the control of power-electronics converters and grid quality.