# Effectiveness of Distributed vs. Concentrated Volt/Var Local Control Strategies in Low-Voltage Grids

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Behavior of Distributed versus Concentrated Volt/var Local Control Strategy

#### 2.1. Definitions

#### 2.2. Theoretical Background

_{1}—active power of the prosumer; Q

_{1}—reactive power of the prosumer.

_{R}—real part of the voltage drop; ΔU

_{X}—imaginary part of the voltage drop.

_{R}) modifies the voltage amplitude, and the other one in phase quadrature (ΔV

_{X}) rotates the voltage vector. The latter has no significant impact on the amplitude of the voltage drop; therefore, ΔV

_{X}is neglected. Under these assumptions, the amplitude of voltage drop is expressed as:

#### 2.3. Distributed Var-Sinks

_{Total}—total voltage drop of a feeder; n—number of feeder segments; ΔU

_{Σ}—voltage drop over the whole feeder; ΔU

_{i}—voltage drop in the feeder segment i.

_{fhb}—voltage at the feeder–head–bus bar; U

_{feb}—voltage at the feeder–end–bus bar.

_{d}(n), is function of n as long as the X, Q, and U

_{1}= U

_{feb}are constant. It is derived from Equations (6) and (8), and is defined by the following recursive formula:

#### 2.4. Concentrated Var-Sink

_{c}(n), is a function of n as long as X and U

_{1}= U

_{feb}are constant. f

_{c}(n) is derived from Equations (6) and (7), and is defined by:

#### 2.5. Distributed versus Concentrated Var-Sinks

_{c}, at bus one is set so that the voltage drop over the feeder is equal to that of the distributed case, as in:

- the reactive power exchange, Q
_{ex}, - the voltage drop behavior, and
- the voltage profile.

#### 2.5.1. Reactive Power Exchange

^{ex}as a function of the bus number, n, for the distributed and concentrated var-sink cases. Q

^{ex}for the distributed var-sinks case is calculated as in:

_{ex,}to achieve the same total voltage drop is smaller in the case of a concentrated var-sink than in the case of the distributed var-sinks. Q

_{ex}is the same for both strategies only when the feeder has one bus, n = 1. With increasing n, the difference between ${Q}_{d}^{ex}$ and ${Q}_{c}^{ex}$ increases monotonically.

#### 2.5.2. Voltage Drop Behavior

#### 2.5.3. Voltage Profile

_{d}(i)—voltage at node i in the case of distributed var-sinks, ${U}_{imp}^{c}\left(i\right)$—the impact of concentrated var-sinks on node i for the distributed and concentrated control strategies, respectively.

## 3. Comparison of Different Control Strategies in a Test Feeder

_{load}= Q

_{load}= 0). The largest possible PV penetration is simulated by installing a 5.0-kWp PV facility on each house roof. The Q(U) control is applied on each PV inverter, or only the L(U) control is applied at the end of the feeder.

_{inv}= 5 kW into the grid. The active power flow at the feeder beginning is defined by the number of PV facilities, their production P

_{inv}, and feeder loss, ΔP

_{d}. The latter modifies the active power flows at the feeder beginning. Each inverter consumes reactive power; Q

_{inv}conforms with its Q(U) characteristic, as shown in Figure 11b. They are over-dimensioned by a factor of 1:0.9 to enable reactive power support with cos(φ) = 0.9 also during peak active power production. The main goal of using Q(U) local control is the elimination of violations of upper voltage limit. Normally, the dead band of the characteristic and the slope gradient are defined to cause minimal losses and reactive flow by avoiding oscillations [21]. Since in our case the simulated feeder is about two kilometers long, the dead band of the characteristic is set as narrow to eliminate all of the voltage violations [25]. The reactive power flow at the beginning of the feeder—i.e., Q

^{ex}—is defined by the number of PV facilities, their individual Q(i) production, and the feeder loss ΔQ

_{d}.

_{set-point}is exceeded. Both active and reactive feeder loss, ΔP

_{c}and ΔQ

_{c}, respectively, increase the power flows at the beginning of the feeder. The reactive power consumption of the sink (coil) is set at the feeder end, and the feeder loss ΔQ

_{c}defines the reactive power flow at the feeder beginning.

_{inv}provokes the violation of the upper voltage limit. The voltage violation begins at node 15 (0.6 km from the feeder head bus) and reaches 8.85% at the feeder–end–bus (node 1, U(1) = 271.06 V). The use of the Q(U) or L(U) control strategy eliminates all of the voltage violations and stabilizes the voltage at the feeder–end–bus at 1.08 p.u. In both cases, the voltage profile shows a concave behavior, but the concavity caused by the Q(U) control is weaker than the one caused by the L(U) control strategy. As well as the theoretical results, Q(U) achieves lower voltage profile values than the L(U) control. This is because the control strategy Q(U) causes higher reactive power consumption than L(U). This behavior is discussed in detail below.

_{inv}, distributed Q(U), and concentrated L(U) control strategies. The |ΔU| caused by P

_{inv}reaches the maximal value at the feeder beginning, fs20. The |ΔU| caused by the distributed Q(U) shapes as in the theoretical case discussed above. In both cases, |ΔU| steadily decreases to reach the minimum value at the feeder–end–bus, fs1. Whereas, the |ΔU| caused by the concentrated L(U) shapes differently from the theoretical case shown in Figure 7. The |ΔU| is not equal in all of the feeder segments. It is slightly increased at the beginning of the feeder, then begins to diminish up to the middle and further remains almost constant. The reason of the increase is the reactive loss, ΔQ

_{c}= 15.29 kvar (see Table 1), which is neglected in the theoretical case. ΔQ

_{c}is about 42% of ${Q}_{c}^{ex}$.

^{ex}for different control strategies. Meanwhile, Figure 16 presents a graphical overview of the consumed reactive power flows and Q

^{ex}for the distributed Q(U) and concentrated L(U) control strategies. All of the inverters together consume more reactive power than the concentrated coil: 34.52 kvar and 22.77 kvar, respectively. Also, reactive power loss is higher for the distributed Q(U) local control strategy, 16.55 kvar, than for the concentrated L(U) local control strategy, 15.29 kvar. For the distributed control strategy, Q

^{ex}is calculated by:

_{inv}(i)—reactive power consumption of the inverter I; n—number of inverters; ΔQ

_{d}—feeder reactive power losses with the distributed Q(U) control strategy, and for the concentrated one by:

_{c}—coil reactive power consumption; ΔQ

_{c}—feeder reactive power losses with the concentrated L(U) control strategy.

^{ex}to reach the same voltage target at feeder end is by L(U) always smaller than by Q(U). The longer the feeder, the greater the advantages of L(U) versus Q(U).

## 4. Behavior of Distributed versus Concentrated Local Control Strategy in Different Real Grids

#### 4.1. Description of the Real Grids

_{0}·(1.2 − 1.17·U + 0.96·U

^{2})

_{0}·(4.88 − 10.16·U + 6.28·U

^{2}),

_{0}and Q

_{0}are the active and reactive power of the load at nominal conditions.

_{inv-nom}= 5.0 ⁄ 0.9 kVA. Inverters are associated with a local control strategy as follows.

#### 4.2. Local Control Strategies

#### 4.2.1. Distributed

- cosφ(P)—it is assumed that all of the prosumers have the same weather conditions. That means that all of the prosumers inject the maximal real power with a cos(φ) = 0.9 as given from the inverter characteristic shown in Figure 19a.

#### 4.2.2. Concentrated

_{set−point}.

#### 4.3. Behavior of Concentrated versus Distributed Control Strategy

^{ex}and the distribution transformer loading for different control strategies. The results show that in both grids, the Q

^{e}

^{x}is higher for the distributed control strategies than for the concentrated one. Transformer loading follows the same trend as Q

^{e}

^{x}, thus being higher for the distributed cosφ(P) or Q(U) than for the concentrated L(U) local control strategy.

## 5. Impact of the Control Strategies in the Reciprocal Behavior between MVG and LVGs

#### 5.1. Combined Medium and Low-Voltage Grid Modeling

#### 5.2. Impact of Different Control Strategies on the Behavior of MVG

^{ex}and their influence on the voltage profile of MV feeders is analyzed for the different control strategies.

#### 5.2.1. Influence of the DTR Connection Point on Q^{ex}

^{ex}. Figure 23 shows the daily Q

^{ex}for different control strategies and various LVGs connected to the MV feeder. To understand the influence of the DTR connection point on the Q

^{ex}, two connection points are selected: the first at the feeder beginning, and the second at the feeder end, as shown in Figure 23e. Due to the feedback active power supply from low to medium and then to the high-voltage grid, the voltage at the end is higher than at the beginning of the MV feeder. Thus, the voltage at the beginning of the feeder is assumed as 1.01 p.u., while at the end, it is assumed as 1.06 p.u. Power flow simulations are performed on both LVGs as described in Section 4.1 by sequentially setting the two different voltages on the slack bus—i.e., the 20-kV bus of the DTRs. Figure 23a,b correspond to the daily Q

^{ex}for the urban LVG connected at the beginning and end of the feeder, respectively, and when distributed cosφ(P), distributed Q(U), or concentrated L(U) local control strategy is exercised. Simulation results for the rural grid are shown in Figure 23c,d. Q

^{ex}consists of the reactive power of load and loss as well as the additional reactive power produced by different voltage control strategies. The reactive power of load and loss depends on the voltage, but this dependence is barely visible in the figures due to the large Q

^{ex}scale. The dependence of the additional reactive power on voltage is determined by the control strategy used. The reactive power produced in case of the cosφ(P) control, ${Q}_{inv}^{cos\phi \left(P\right)}$, is independent of the voltage. ${Q}_{inv}^{cos\phi \left(P\right)}$ is present at the same period 08:50–15:30 in all of the cases, as shown in Figure 23a–d. The distributed cosφ(P) control is active in accordance with its characteristic, as shown in Figure 19a. Unlike this case, the additional reactive power flow provoked by exercising the distributed Q(U) control strategy, ${Q}_{inv}^{Q\left(U\right)}$, strongly depends on voltage at the DTR’s connection point. The Q(U) control may be active even in periods without solar irradiation as long as its local voltage in LVG is outside the dead band of the control characteristic, as shown in Figure 19b. This case is clearly visible in periods 00:00–07:30 and 17:00–24:00 in Figure 23b; 00:00–07:30 in Figure 23c; and 00:00–07:30 and 17:00–24:00 in Figure 23d, where Q

^{ex}is larger than in the cosφ(P) case. In all of the cases, the maximum provoked Q

^{ex}is reached at the critical time, t

_{crit}. Around this time, the cosφ(P) control provokes a much larger Q

^{ex}than the Q(U) control for the urban and rural LVG when the DTRs are connected at the feeder beginning, as shown in Figure 23a,c. When the DTRs are connected at the feeder end, the difference of Q

^{ex}is smaller in the urban LVG case, as shown in Figure 23b, and it becomes almost zero in the rural LVG case, as seen in Figure 23d. As shown in Figure 23a–d, the concentrated L(U) local control strategy causes the smallest Q

^{ex}in all of the cases. Q

^{ex}depends on voltage at the DTR’s connection point, because the L(U) control is active as long as its local voltage in LVG exceeds the U

_{set-point}. In summary, regardless of the connection point of the DTRs at the MV feeder and the daily load consumption and PV production profiles, the use of a concentrated local control strategy in LVGs causes less Q

^{ex}than the distributed strategies.

^{ex}provoked by the various control strategies on the voltage profile of the MV feeder is analyzed below.

#### 5.2.2. Influence of the Concentrated versus Distributed Control Strategy on the Voltage Profile in MVG

_{crit}. The STR’s high-voltage bus is selected as a slack bus with a voltage of 1.01 p.u. Figure 24 depicts the voltage profiles of the MV feeder and of the second and 32

^{nd}LVGs for different control strategies at t

_{crit}= 12:12. Figure 24a–c show the voltage profiles for the distributed cosφ(P) and Q(U) controls, and concentrated L(U), respectively. As expected, the concentrated L(U) control strategy provokes the smallest reactive power exchange through the STR, ${Q}_{STR}^{ex}$, as shown in Table 3. Therefore, the corresponding voltage profiles are less suppressed than in the both cases of the distributed control strategy, where the voltage profiles are pushed down more than is needed. In the DTR level, the global effect (GE) provoked by Q

^{ex}is present in all of the cases. GE is the voltage displacement on the transformer buses provoked by the reactive power injection in radial structures [26]. The ${Q}_{STR}^{ex}$, OLTC position change, and the GE for different control strategies used in real LVGs are summarized in Table 3. In the case of the concentrated strategy, GE is smaller than in the distributed control strategies. The distributed cosφ(P) has the worst performance. It provokes not only the largest ${Q}_{STR}^{ex}$ and GEs, but it also causes an OLTC position change from 13 to 15.

## 6. Conclusions

^{ex}to reach the same voltage target at the feeder end, and the distribution transformer loading are always smaller than by use of Q(U). The longer the feeder, the greater the advantages of a concentrated versus distributed control strategy. Even in rural grids with the longest feeders, where the distributed Volt/var local control strategies do not eliminate all of the violations of upper voltage limit, the concentrated Volt/var local control strategy successfully eliminates all of the voltage violations. Therefore, the latter increases the PV hosting capacities of the feeders, regardless of their length. Simulations in a combined medium and low-voltage grid model have shown that the effects of the concentrated local control strategy in MVG behavior are more favorable than those of the distributed strategies. However, a practical implementation of the concentrated Volt/var local control strategy in the context of smart grids with a high DG share would validate the relevance of these outcomes.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 3.**Overview of a feeder segment with back-up active power supply: (

**a**) Equivalent circuit; (

**b**) Phasor diagram.

**Figure 6.**The theoretical exchanged reactive power as a function of the bus number for the distributed and concentrated var-sink cases.

**Figure 7.**The theoretical voltage drop amplitude in every feeder segment as a function of the bus number for the distributed and concentrated var-sink cases.

**Figure 10.**Equivalent circuit of an LV feeder where the distributed Q(U) or concentrated L(U) local control strategies can be applied.

**Figure 11.**Schematic presentation of the power flows when Q(U) is applied: (

**a**) the active and reactive power flows supplied by the PV inverters; (

**b**) Q(U) characteristic set by all of the inverters.

**Figure 13.**Voltage profiles for different control strategies: No control (inverters inject with cos(φ) = 1), distributed Q(U) and concentrated L(U) control.

**Figure 14.**The particular impact of the injected active power, the absorbed reactive power caused by the different control strategies, and the impact of their combination on the shape of the voltage profile.

**Figure 15.**The amplitude of voltage drop in every feeder segment caused by distributed active power, an injection of PV facilities, P

_{inv}, distributed Q(U), and concentrated L(U) control strategies.

**Figure 16.**The consumed reactive power and the Q

^{ex}flows for the Q(U) and L(U) control strategies.

**Figure 17.**Exchanged reactive power as a function of the bus number or feeder length for the Q(U) and L(U) control strategies.

**Figure 18.**Schematic presentation of different real low-voltage grids (LVGs): (

**a**) urban and (

**b**) rural.

**Figure 20.**Overview of voltage profiles of two typical real grids, urban and rural, when no-control, distributed cosφ(P), distributed Q(U), and concentrated L(U) local control strategies are exercised.

**Figure 21.**Schematic representation of a medium-voltage grid (MVG) combined with the respective LVGs.

**Figure 23.**Daily Q

^{e}

^{x}for different control strategies and various LVGs connected at the MV feeder: (

**a**) urban, connected at the feeder beginning; (

**b**) urban, connected at the feeder end; (

**c**) rural, connected at the beginning; (

**d**) rural connected at the end; (

**e**) overview of the MVG.

**Figure 24.**Voltage profiles of the MV feeder and of the second and 32

^{nd}LVGs for different control strategies at t

_{crit}= 12:12: (

**a**) cosφ(P); (

**b**) Q(U); and (

**c**) L(U).

**Table 1.**Reactive power consumption, loss, and exchange for different control strategies in the LV test grid.

ΣQ_{inv} or Q_{c} (kvar) | Q-Loss (kvar) | Q^{ex} (kvar) | |
---|---|---|---|

distributed Q(U) | 34.52 | 16.55 | 51.07 |

concentrated L(U) | 22.77 | 15.29 | 38.06 |

**Table 2.**Reactive power consumption, loss, and exchange for different control strategies in real LVGs.

Distributed | Concentrated | |||||
---|---|---|---|---|---|---|

cosφ(P) | Q(U) | L(U) | ||||

Q^{ex} (kvar) | Tr^{L} (%) | Q^{ex} (kvar) | Tr^{L} (%) | Q^{ex} (kvar) | Tr^{L} (%) | |

Urban | 491.68 | 130.00 | 436.03 | 125.11 | 305.02 | 114.52 |

Rural | 176.44 | 181.65 | 176.44 | 181.65 | 115.15 | 158.38 |

**Table 3.**Reactive power exchange through supplying transformer (STR), on-load tap changer (OLTC) position change, and the global effect in distribution transformers (DTR) level for different control strategies in real low-voltage grids (LVGs).

${\mathit{Q}}_{\mathit{S}\mathit{T}\mathit{R}}^{\mathit{e}\mathit{x}}\left(\mathbf{Mvar}\right)$ | OLTC Position Change | GE (p.u) | |||
---|---|---|---|---|---|

DTR_{2} | DTR_{32} | ||||

distributed | cosφ(P) | 11.493 | 13→15 | −0.0318 | −0.0305 |

Q(U) | 8.118 | none | −0.0113 | −0.0267 | |

concentrated | L(U) | 5.452 | none | +0.0014 | −0.0151 |

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## Share and Cite

**MDPI and ACS Style**

Ilo, A.; Schultis, D.-L.; Schirmer, C.
Effectiveness of Distributed vs. Concentrated Volt/Var Local Control Strategies in Low-Voltage Grids. *Appl. Sci.* **2018**, *8*, 1382.
https://doi.org/10.3390/app8081382

**AMA Style**

Ilo A, Schultis D-L, Schirmer C.
Effectiveness of Distributed vs. Concentrated Volt/Var Local Control Strategies in Low-Voltage Grids. *Applied Sciences*. 2018; 8(8):1382.
https://doi.org/10.3390/app8081382

**Chicago/Turabian Style**

Ilo, Albana, Daniel-Leon Schultis, and Christian Schirmer.
2018. "Effectiveness of Distributed vs. Concentrated Volt/Var Local Control Strategies in Low-Voltage Grids" *Applied Sciences* 8, no. 8: 1382.
https://doi.org/10.3390/app8081382