# Deterministic Algorithm for Selective Shunt Active Power Compensators According to IEEE Std. 1459

^{1}

^{2}

^{*}

## Abstract

**:**

_{1}

^{+}, S

_{U}

_{1}, S

_{eN}). The non-efficient powers can be reduced in six possible sequences according to the priority of compensation. When SAPC maximum output current capacity is exceeded, the proposed algorithm limits the SAPC output compensating currents and the non-efficient currents can only be partially reduced in the power network. The reduction of the non-efficient powers depends on the selected compensation sequence. Experimental results for several compensation sequences demonstrate the appropriate operation of the selective SAPC using the proposed scaling algorithm.

## 1. Introduction

## 2. SAPC Output Currents for Selective Compensation According to IEEE Std. 1459 under Overloading Conditions

_{z_SAPC}) are calculated from the measurement of the load currents (i

_{zload}) and the supply voltages (v

_{zs}) at the pcc (z = a, b, c). Global compensation is used when the SAPC has enough capacity to compensate all non-efficient powers detailed in [23]: positive-sequence reactive power (Q

_{1}

^{+}), unbalance power (S

_{U}

_{1}), and non-fundamental effective apparent power (S

_{eN}). As indicated in [24], the SAPC output currents for global compensation (i

_{z_SAPC_G}) are calculated as follows:

_{1}

^{+}), the unique power term considered efficient [23,25]. The main drawback of a SAPC under overloading condition and using global compensation algorithms is that the SAPC can supply new harmonic components into the power networks, affecting other loads connected in the same distribution system and reducing the power quality indicators.

_{1}

^{+}, S

_{U}

_{1}, and S

_{eN}can only be partially reduced or some are cancelled while others are still present without modification. The approach used to obtain the reference currents of a selective SAPC based on the non-effective power magnitudes defined in IEEE Std. 1459–2010 was presented in [19]. The approach relates each non-efficient power magnitude with some current terms, allowing the selective compensation of the load non-efficient powers. The SAPC output currents that cancel Q

_{1}

^{+}and keep P

_{1}

^{+}, S

_{U}

_{1}, and S

_{eN}unchanged in the supply lines are as follows:

_{z}

_{1}

^{+}. The fundamental positive-sequence active voltage in phase a (v

_{a}

_{1}

^{+}) is the origin of all phase angles. The SAPC output currents that cancel only S

_{U}

_{1}are calculated as follows:

_{eN}are obtained as follows:

_{z1load}are the instantaneous load fundamental currents while i

_{zH_SAPC}only contains the instantaneous non-fundamental currents demanded by non-linear loads. The SAPC output currents that cancel all load non-efficient currents (global compensation mode) can be obtained if Equations (2)–(4) are added up as follows:

_{SAPC_max}), scaling factors K

_{Q}, K

_{U}, and K

_{H}are multiplying in Equation (6) their corresponding current terms. The scaled SAPC output currents (i

_{z_SAPC_K}) are calculated as follows:

_{z_SAPC}) must not exceed, at any instant, the maximum SAPC output current (I

_{SAPC_max}) to avoid SAPC overloading (I

_{SAPC_max}≥ i

_{z_SAPC_K}). The subscript “K” is used to indicate that the SAPC selective mode is used. The algorithm to assign the values of K

_{Q}, K

_{U}, and K

_{H}according to the power compensation sequences and SAPC current capacity is explained in the next section.

## 3. Calculation of the Scaling Factors in a Selective SAPC

_{SAPC_max}≥ I

_{z_SAPC_G_max}), therefore K

_{Q}= K

_{U}= K

_{H}= 1. When the output current limit in the SAPC is reached, the SAPC can only partially reduce the non-efficient powers demanded by the load. The values of K

_{Q}, K

_{U}, and K

_{H}depend on the selected power compensation sequence, the value of I

_{SAPC_max}and the load characteristics. Scaling factors K

_{Q}, K

_{U}, and K

_{H}can vary between “0” (no compensation) and “1” (full compensation). The SAPC output effective power, when operating in the selective mode, is calculated as follows:

_{1}

^{+}, S

_{U}

_{1}, and S

_{eN}) recognized in [23]. The priority in the compensation order can be assigned on the basis of importance of power quality defects, power losses in lines and transformers, engineering economic decisions, and, moreover, considering the interests of consumers and utilities. Table 1 shows the six CS, where i

_{z_comp_}

_{1}correspond to the compensating current terms with the highest priority, i

_{z_comp_}

_{2}are the second current terms to be compensated, and i

_{z_comp_}

_{3}correspond to the current terms with the lowest priority. i

_{z_comp_}

_{1}, i

_{z_comp_}

_{2}, and i

_{z_comp_}

_{3}are defined to denote the phase compensating currents without establishing a particular sequence of power compensation between Q

_{1}

^{+}, S

_{U}

_{1}, and S

_{eN}. The corresponding scaling factors are denoted as K

_{1}, K

_{2}, and K

_{3}, respectively. Scaling factors K

_{1}, K

_{2}, and K

_{3}are defined to allow partial compensation of i

_{z_comp_}

_{1}, i

_{z_comp_}

_{2}, and i

_{z_comp_}

_{3}respectively. For example, CS1 indicates that the first power term to compensate is S

_{eN}, followed by S

_{U}

_{1}and Q

_{1}

^{+}, Q

_{1}

^{+}being the last one to be compensated.

_{z_comp_}

_{1}, i

_{z_comp_}

_{2}, and i

_{z_comp_}

_{3}are completely compensated and K

_{1}= K

_{2}= K

_{3}= 1. If a selective compensation mode is needed, three situations arise. These three cases are included as software functions in the flowchart of the main algorithm shown in Figure 2, being denoted as selective compensation modes SCM

_{1}, SCM

_{1+2}, and SCM

_{1+2+3}, as appears in the first column in Table 2.

_{SAPC_max}, as it is represented in Figure 3. Subroutine “Global Compensation” returns the values K

_{1}= K

_{2}= K

_{3}= 1 to the algorithm.

_{SAPC_max}< I

_{z_SAPC_G_max}and more comparisons must be done to determine the correct scaling factors. Then, attending to the selected CS, the current terms calculated in Equations (2)–(4) are assigned to the corresponding phase compensating currents (i

_{z_comp_*}, where * = 1, 2, 3). The SCM

_{1}subroutine is executed when the maximum value of i

_{z_comp_}

_{1}is greater than or equal to I

_{SAPC_max}in a complete period of the fundamental current wave. In this case, the full or partial compensation of i

_{zComp_}

_{1}must be applied (0 < K

_{1}≤ 1), while i

_{zComp_}

_{2}and i

_{zComp_}

_{3}are not compensated (K

_{2}= K

_{3}= 0). SCM

_{1}returns the correct value of K

_{1}that permits the partial compensation of the non-efficient current with the highest priority considering the CS selected. The subroutine starts calculating the factors K

_{z}

_{1}as follows:

_{a}

_{1}, K

_{b}

_{1}, and K

_{c}

_{1}is assigned to K

_{1}, as appears in the following expression.

_{1+2}is selected if the SAPC has enough capacity for the complete compensation of i

_{z_comp_}

_{1}(K

_{1}= 1), and also has surplus capacity for the partial or complete compensation of i

_{z_comp_}

_{2}(0 < K

_{2}≤ 1). For this situation, i

_{z_comp_}

_{3}are not compensated (K

_{3}= 0), as it is showed in Figure 4. SCM

_{1+2}starts calculating the time instant (t

_{1+2_max}) when the sum of i

_{z_comp}

_{_1}and i

_{z_comp}

_{_2}is maximum (I

_{comp_}

_{1+2_max}) and determines which of the three phases is limiting the SAPC operation. For the limiting phase, denoted as # (# = {a, b, c}), the values of the currents i

_{#_comp}

_{_1}and i

_{#_comp}

_{_2}are calculated at t

_{1+2_max}. The following relationships are verified:

_{2}is calculated as follows:

_{1+2+3}is executed if the SAPC has enough capacity for the full compensation of i

_{z_comp_}

_{1}and i

_{z_comp_}

_{2}(K

_{1}= K

_{2}= 1), but the remaining SAPC capacity only permits the partial compensation of i

_{z_comp_}

_{3}(0 < K

_{3}< 1). In this case I

_{comp_}

_{1+2_max}< I

_{SAPC_max}< I

_{comp_}

_{1+2+3_max}, where I

_{comp_}

_{1+2+3_max}coincides with the maximum of the global compensation current I

_{SAPC_G_max}. The subroutine calculates the time instant (t

_{G_max}) where i

_{z_SAPC_G}is maximum (I

_{SAPC_G_max}) and determines which of the three phases is limiting the SAPC operation. The values of the currents i

_{#_comp}

_{_1+2}and i

_{#_comp}

_{_3}are calculated for the phase # that limits the SAPC output current at the instant t

_{G_max}, verifying the following expression:

_{#_comp}

_{_3}is calculated as I

_{SAPC_max}minus i

_{#_comp}

_{_1+2}(t

_{G_max}), so the value of the factor K

_{3}for the three phases is calculated as follows:

## 4. Experimental Results

_{a}

_{1}, V

_{b}

_{1}, and V

_{c}

_{1}) were balanced and approximately equal to 125 V. Table 3 shows the main pcc voltage magnitudes (RMS values) calculated applying IEEE Std. 1459. The supply voltages showed, for all performed tests, a distortion lower than 3% and a slight imbalance.

- Z
_{a load}= R_{a load}= 65.9 Ω//L_{a load}= 67.2 mH. - Z
_{b load}= L_{b load}= 67.2 mH (R_{b load}= ∞ Ω). - Z
_{c load}= L_{c load}= 69.7 mH (R_{c load}= ∞ Ω).

_{SAPC_max}) to 3750 VA. The DC bus has a capacitance equal to 7050 μF and was designed to handle up to 800 V. Voltage and current sensors used in the experimental SAPC are LEM LV 25-P and LEM LAH 50-P, respectively. Figure 6 shows the implementation of the prototype.

_{SAPC_max}was limited by the DSP controller to 1125 VA, so the maximum SAPC output compensating current (I

_{SAPC_max}) is equal to 4.24 A (equivalent to 3 A

_{rms}). For the load used in the tests the maximum currents obtained with Equations (2)–(5) are the following: I

_{zQ}

_{1_SAPC_max}= 3.08 A, I

_{zU}

_{1_SAPC_max}= 1.34 A, I

_{zH_SAPC_max}= 3.21 A, and I

_{z_SAPC_G_max}= 5.56 A. With these values, SAPC current capacity is reached and the algorithm needs to be executed for adjusting the reference currents.

_{1}

^{+}is increased approximately in 250 W during SAPC operation because SAPC losses are compensated by means of three balanced fundamental positive-sequence active currents supplied by the power network [19]. The non-efficient currents are full, partial, or not compensated according to the scaling factors determined for each CS. Effective apparent power (S

_{e}) is calculated as follows:

_{e}at the pcc. CS4 has the following scaling factors: K

_{Q}= 1, K

_{U}= 0, and K

_{H}= 0.67. The application of this scaling factors results in a Q

_{1}

^{+}that is almost reduced to zero (18.88 VA), a S

_{U}

_{1}that is not compensated, and a S

_{eN}that is partially reduced from 1183.41 VA to 371.71 VA. The reduction in S

_{eN}is equal to 68.5%, slightly greater than the corresponding scaling factor. This small difference is explained due to minor variations in the pcc characteristics during the measurements that were taken in different moments. The same reason explains the small increase that appears in S

_{U}

_{1}when CS4 is applied or in other cases in which the power term is not compensated (K = 0) but the power term presents some variation. Information provided in Table 5 proves that the inclusion of the proposed algorithm in the control of a SAPC permits the selective compensation of the non-efficient currents and reduces the non-efficient powers according to the selected compensation sequence.

_{z_SAPC_max}) and the apparent power supplied by the SAPC (S

_{SAPC}) for the six CS. Maximum values are used in Table 6 due to the fact that the scaling factor algorithm uses the maximum values of the corresponding signals. It could be considered that the proposed algorithm works appropriately limiting the SAPC currents to the restricted current (4.24 A) in each phase. I

_{SAPC_max}is slightly overcome in some cases (I

_{z_SAPC_pk}> 4.24 A), due to the current ripple in the SAPC output current waveforms (on the order of 0.1 A) and the characteristics of the current regulator [22]. The values of S

_{SAPC}for the six CS oscillate around 1125 VA. The small deviation around the maximum value established for S

_{SAPC}capacity is related with the SAPC control, which works with the non-efficient currents instead of the non-efficient power terms.

_{zH_SAPC}). The load current term ${i}_{z1load}^{+r}$ is completely supplied by the SAPC since K

_{Q}= 1, producing the reduction of ${I}_{z1load}^{+r}$ from 2.18 A to 0.23 A (a reduction of 89.4%). The current i

_{zH_SAPC}is partially injected to the pcc since K

_{H}= 0.67, producing the decrease of I

_{eH}from 1.68 A to 0.53 A (a reduction of 68.4%). The current i

_{zU}

_{1_SAPC}is not compensated since K

_{U}= 0, as it can be seen in the values of I

_{1}

^{−}and I

_{1}° that keep similar values as in Table 4 (before compensation) and Table 7 (with CS4 compensation). After compensation, the effective current I

_{e}is reduced from 4 A to 3.6 A. The reduction in the fundamental effective current I

_{e}

_{1}due to the cancelation of ${i}_{z1load}^{+r}$ is small (from 3.64 A to 3.57 A) since the other fundamental current terms are still present in the load current (${i}_{z1load}^{+a}$, ${i}_{z1load}^{-}$, and ${i}_{z1load}^{0}$). The neutral current (I

_{n}) is also reduced from 4.8 A to 2.2 A (a reduction of 54%) due to the reduction of some zero-sequence harmonic currents that can be seen in bottom plot in Figure 5 (load) and Figure 8 (upstream pcc). The harmonic neutral current (I

_{nH}) decreases by 68.8%, varying from 4.5 A to 1.4 A due to K

_{H}= 0.67 for CS4 case. The effect of the SAPC operation is also seen in the THD

_{i}values. Minimum load THD

_{i}is around 37% while with the CS4 selective SAPC operation and they change to values between 10.9% and 19.2%. If a higher decrease in the values of THD

_{i}is desired, CS1 or CS2 must be selected, since both prioritize the cancelation of the harmonic current terms while, in CS4, the SAPC only partially reduces these currents. For the sake of shortness, only values of THD

_{i}are given for CS1: THD

_{Ia}= 1.99%, THD

_{Ib}= 1.99%, THD

_{Ic}= 2.28%, and THD

_{eI}= 1.99%. These values demonstrate how the selective SAPC can be used to reduce the load THD

_{i}to high power quality levels.

## 5. Conclusions

_{1}

^{+}, S

_{U}

_{1}, and S

_{eN}. Three scaling factors (K

_{Q}, K

_{U}, and K

_{H}) are used to reduce the current terms related with Q

_{1}

^{+}, S

_{U}

_{1}, and S

_{eN}. The proposed algorithm permits to obtain the scaling factors that limit the SAPC output currents for the six sequences of current compensation (CS1 to CS6). Each CS gives different priorities to the non-efficient current terms. The values of the scaling factors can vary between 0 and 1. The final value of the scaling factors is determined considering the selected power compensation sequence, the maximum SAPC output current and the load characteristics.

_{i}upstream the pcc. CS4 is selected for being the CS that most reduces the effective power in the power network (S

_{e}is reduced to 1462.04 VA for CS4). Waveforms and magnitudes of the SAPC output and the power network currents are included, demonstrating the correct behavior of the current controller during the operation of the SAPC in the selective mode. The reduction in the non-efficient currents that are flowing in the power networks during the selective SAPC operation agrees with the priorities established in CS4 and the values calculated for the scaling factors. Selecting the corresponding CS, other quality indices can be improved, as it is demonstrated with the small THD

_{i}values (around 2%) obtained when CS1 is selected.

_{Q}= 1, K

_{U}= 0, and K

_{H}= 0.67; this yields to the reduction of Q

_{1}

^{+}almost to zero, S

_{U}

_{1}is not compensated, and S

_{eN}is partially reduced from 1183.41 VA to 371.71 VA). The inclusion of the deterministic algorithm permits the selective SAPC operation at its maximum capabilities, CS4 most reduces the apparent power in the network and at the same time use adequately the apparent power available (S

_{SAPC}= 1149.22 VA). The proposed algorithm can also be used for other current decompositions: individual harmonics, negative-sequence currents, zero-sequence currents, etc.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Compensating Current Priority | CS1 | CS2 | CS3 | CS4 | CS5 | CS6 |
---|---|---|---|---|---|---|

i_{z_comp_}_{1} | S_{eN} | S_{eN} | S_{U}_{1} | Q_{1}^{+} | S_{U}_{1} | Q_{1}^{+} |

i_{z_comp_}_{2} | S_{U}_{1} | Q_{1}^{+} | S_{eN} | S_{eN} | Q_{1}^{+} | S_{U}_{1} |

i_{z_comp_}_{3} | Q_{1}^{+} | S_{U}_{1} | Q_{1}^{+} | S_{U}_{1} | S_{eN} | S_{eN} |

Operating Mode | i_{z_comp_}_{1} | i_{z_comp_}_{2} | i_{z_comp_}_{3} |
---|---|---|---|

Global Comp. | K_{1} = 1 | K_{2} = 1 | K_{3} = 1 |

SCM_{1} | 0 < K_{1} ≤ 1 | K_{2} = 0 | K_{3} = 0 |

SCM_{1+2} | K_{1} = 1 | 0 < K_{2} ≤ 1 | K_{3} = 0 |

SCM_{1+2+3} | K_{1} = 1 | K_{2} = 1 | 0 < K_{3} ≤ 1 |

V_{a} = 125.46 | V_{b} = 126.82 | V_{c} = 129.26 | |
---|---|---|---|

$\overrightarrow{{V}_{a1}}=125.44\angle 0\xb0$ | $\overrightarrow{{V}_{b1}}=126.78\angle -120.35\xb0$ | $\overrightarrow{{V}_{c1}}=129.23\angle -239.74\xb0$ | |

$\overrightarrow{{V}_{1}^{+}}=127.15\angle -0.03\xb0$ | $\overrightarrow{{V}_{1}^{-}}=0.82\angle -124.38\xb0$ | $\overrightarrow{{V}_{1}^{0}}=1.45\angle 149.23\xb0$ | |

V_{aH} = 2.45 | V_{bH} = 3.24 | V_{cH} = 3 | |

V_{e} = 127.19 | V_{e}_{1} = 127.16 | V_{eH} = 2.92 | |

THD_{Va} = 1.95% | THD_{Vb} = 2.55% | THD_{Vc} = 2.36% | THD_{eV} = 2.30% |

I_{a} = 4.83 | I_{b} = 3.54 | I_{c} = 3.52 | I_{n} = 4.8 | |||
---|---|---|---|---|---|---|

$\overrightarrow{{I}_{a1}}=4.52\angle -28.62\xb0$ | $\overrightarrow{{I}_{b1}}=3.14\angle -166.18\xb0$ | $\overrightarrow{{I}_{c1}}=3.08\angle -283.65\xb0$ | $\overrightarrow{{I}_{n1}}=1.65\angle -2.59\xb0$ | |||

$\overrightarrow{{I}_{1}^{+}}=3.54\angle -38.07\xb0$ | $\overrightarrow{{I}_{1}^{-}}=0.63\angle -0.45\xb0$ | $\overrightarrow{{I}_{1}^{0}}=0.55\angle 2.59\xb0$ | ||||

$\overrightarrow{{I}_{z1load}^{+a}}=2.79\angle 0\xb0$ | $\overrightarrow{{I}_{z1load}^{+r}}=2.18\angle -90\xb0$ | |||||

I_{aH} = 1.7 | I_{bH} = 1.64 | I_{cH} = 1.71 | I_{nH} = 4.51 | |||

I_{e} = 4.01 | I_{e}_{1} = 3.64 | I_{eH} = 1.68 | ||||

THD_{Ia} = 37.6% | THD_{Ib} = 52.2% | THD_{Ic} = 55.5% | THD_{eI} = 46.1% |

P_{1}^{+} (W) | Q_{1}^{+} (var) | S_{U}_{1} (VA) | S_{eN} (VA) | S_{e} (VA) | |
---|---|---|---|---|---|

Load | 1063.49 | 832.09 | 483.76 | 1183.41 | 1859.53 |

CS1 (0; 0.55; 1) | 1340.86 | 812.38 | 206.06 | 59.22 | 1582.35 |

CS2 (0.4; 0; 1) | 1348.73 | 453.11 | 512.29 | 67.42 | 1513.72 |

CS3 (0; 1; 0.81) | 1314.93 | 818.16 | 56.27 | 198.88 | 1562.41 |

CS4 (1; 0; 0.67) | 1319.68 | 18.88 | 507.42 | 371.71 | 1462.04 |

CS5 (1; 1; 0.29) | 1304.56 | 1.14 | 33.57 | 848.36 | 1556.51 |

CS6 (1; 1; 0.29) | 1304.56 | 1.14 | 33.57 | 848.36 | 1556.51 |

Compensation Sequences | I_{a_max} (A) | I_{b_max} (A) | I_{c_max} (A) | S_{SAPC} (VA) |
---|---|---|---|---|

CS1 | 4.22 | 4.22 | 4.37 | 1158.14 |

CS2 | 4.22 | 4.37 | 4.22 | 1178.92 |

CS3 | 4.37 | 4.06 | 4.06 | 1073.42 |

CS4 | 4.38 | 4.37 | 4.22 | 1149.22 |

CS5 | 4.22 | 4.39 | 4.37 | 1002.69 |

CS6 | 4.22 | 4.39 | 4.37 | 1002.69 |

I_{as} = 4.72 | I_{bs} = 2.92 | I_{cs} = 2.87 | I_{ns} = 2.24 | ||
---|---|---|---|---|---|

$\overrightarrow{{I}_{a1s}}=4.69\angle 3.69\xb0$ | $\overrightarrow{{I}_{b1s}}=2.87\angle -117.22\xb0$ | $\overrightarrow{{I}_{c1s}}=2.82\angle -234.81\xb0$ | $\overrightarrow{{I}_{n1s}}=1.74\angle 1.72\xb0$ | ||

$\overrightarrow{{I}_{1s}^{+}}=3.46\angle 3.85\xb0$ | $\overrightarrow{{I}_{1s}^{-}}=0.65\angle 4.62\xb0$ | $\overrightarrow{{I}_{1s}^{0}}=0.58\angle 1.72\xb0$ | |||

$\overrightarrow{{I}_{z1s}^{+a}}=3.45\angle 0\xb0$ | $\overrightarrow{{I}_{z1s}^{+r}}=0.23\angle 90\xb0$ | ||||

I_{aHs} = 0.51 | I_{bHs} = 0.54 | I_{cHs} = 0.54 | I_{nHs} = 1.41 | ||

I_{es} = 3.61 | I_{e}_{1s} = 3.57 | I_{eHs} = 0.53 | |||

THD_{Ias} = 10.9% | THD_{Ibs} = 18.8% | THD_{Ics} = 19.2% | THD_{eIs} = 14.8% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Muñoz-Galeano, N.; Orts-Grau, S.; Seguí-Chilet, S.; Gimeno-Sales, F.J.; López-Lezama, J.M.
Deterministic Algorithm for Selective Shunt Active Power Compensators According to IEEE Std. 1459. *Energies* **2017**, *10*, 1791.
https://doi.org/10.3390/en10111791

**AMA Style**

Muñoz-Galeano N, Orts-Grau S, Seguí-Chilet S, Gimeno-Sales FJ, López-Lezama JM.
Deterministic Algorithm for Selective Shunt Active Power Compensators According to IEEE Std. 1459. *Energies*. 2017; 10(11):1791.
https://doi.org/10.3390/en10111791

**Chicago/Turabian Style**

Muñoz-Galeano, Nicolás, Salvador Orts-Grau, Salvador Seguí-Chilet, Francisco J. Gimeno-Sales, and Jesús M. López-Lezama.
2017. "Deterministic Algorithm for Selective Shunt Active Power Compensators According to IEEE Std. 1459" *Energies* 10, no. 11: 1791.
https://doi.org/10.3390/en10111791