# Reactive Power Management Considering Stochastic Optimization under the Portuguese Reactive Power Policy Applied to DER in Distribution Networks

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## Abstract

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## 1. Introduction

- To design a two-stage stochastic reactive power management model considering a full AC-OPF. It has the purpose of aiding the decision-making of the DSO under the uncertain and variable behavior of RES connected in the distribution network;
- To propose a reactive power service provided by the DSO to the TSO in advance of the operating hour. This service can be used by the TSO in the transmission system management, defining a reactive power operation in the TSO/DSO boundary substations. This can help the TSO in different services like the voltage control and congestion management in the transmission system;
- Take into account the Portuguese reactive power policy on distribution grids, assessing the behavior and applicability of the proposed model.

## 2. Reactive Power Policies

#### 2.1. Portuguese Reactive Power Policy

#### 2.2. Proactive Reactive Power Management

## 3. Mathematical Formulation

#### 3.1. Objective Function

^{DA}) comprises the here-and-now decisions and the second-stage (F

^{RT}) the wait-and-see decisions.

^{Extra}allowing the DSO to provide part of the TSO request. By applying an even greater cost, it is possible to curtail the generators active power for relaxing situations where active power is creating problems in the distribution network. Demand response can also be contemplated to decrease the active power consumption, which in turn will reduce the reactive power consumption, under even greater penalties for this relaxation. These alternatives options will ensure that DSO prioritizes DER and consumers over providing the reactive power service to the TSO.

#### 3.2. First-Stage Constraints

#### 3.3. Second-Stage Constraints

_{CB}, which represents the difference between the tap selection in the present period with the previous one, which is constrained by:

_{TRF}represents the voltage level to be activated in the transformer by the DSO. ${V}_{TRF}^{levels}$ is a parameter representative of all possible taps of the transformer, and X

_{TRF}is the binary variable for selection of a unique tap level. ${V}_{sb}^{ref}$ is the reference of voltage magnitude at the substation before the use of OLTC ability by the transformer, while the final voltage value at the substation is denoted by V

_{sb}. In addition, the cost for changing the tap of the transformer is included in the objective function (5), where Z

_{TRF}is the linearization of the absolute function, as the capacitor banks. Thus, the constraints are:

## 4. Case Study

#### 4.1. 37-Bus Distribution System

#### 4.2. Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Parameters | |

$\Delta P$ | Power deviation in each scenario |

$B$ | Imaginary part in admittance matrix |

$C$ | Cost |

$G$ | Real part in admittance matrix |

$N$ | Number of unit resources |

$p$ | Penalty for external supplier’s flexibility |

$\overline{y}$ | Series admittance of line that connects two buses |

${\overline{y}}_{sh}$ | Shunt admittance of line that connects two buses |

Variables | |

$\theta $ | Voltage angle |

$P$ | Active power |

$Q$ | Reactive power |

$r$ | Reactive power flexibility used in the operating stage |

$rlx$ | Reactive power relaxation in the operating stage |

$R$ | Reactive power flexibility contracted at day-ahead stage |

$RLX$ | Reactive power relaxation at day-ahead stage |

$S$ | Apparent power |

$V$ | Voltage magnitude |

$\overline{V}$ | Voltage in polar form |

${V}_{sb}$ | Voltage at slack bus |

$\Delta V$ | Voltage level activated by the DSO in the transformer |

$X$ | Binary variable |

$Z$ | Auxiliary variable for absolute function linearization |

Subscripts | |

$\omega $ | Index of scenarios |

$cb$ | Index of capacitor bank units |

$CB$ | Capacitor bank abbreviation |

$g$ | Index of generators units |

$i,j$ | Bus index |

$l$ | Index of load consumers |

$L$ | Load consumers abbreviation |

$lv$ | Index of levels (tap changing) for capacitor banks and transformers |

$TSO$ | Transmission system operator |

$t$ | Time index |

$trf$ | Index of transformer units |

$TRF$ | Transformer abbreviation |

Superscripts | |

$act$ | Activation cost of resources in real-time stage |

$cut$ | Generation curtailment |

$Max$ | Maximum limit |

$Min$ | Minimum limit |

$op$ | Operating point of the power resource |

$Q,DW$ | Downward reactive power flexibility |

$Q,UP$ | Upward reactive power flexibility |

$DR$ | Demand response of consumer l |

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**Figure 1.**Two-stage optimization model embedded in the sequential AC-optimal power flow (SOPF) tool [15].

**Figure 2.**37-Bus distribution network (adapted from [18]).

**Table 1.**Reactive power policy for the special scheme [12].

Voltage Level | tan ϕ | |
---|---|---|

Peak Period | Off-Peak Period | |

High Voltage | 0 | 0 |

Medium Voltage (P > 6MW) | 0 | 0 |

Medium Voltage (P ≤ 6MW) | 0.3 | 0 |

Low Voltage | 0 | 0 |

Load. | Bus | Active Power Consumption (kW) | Reactive Power Consumption (kVAr) | ||||
---|---|---|---|---|---|---|---|

Min | Mean | Max | Min | Mean | Max | ||

1 | 3 | 373.2 | 677.9 | 1190.5 | 112.0 | 203.4 | 357.2 |

2 | 4 | 206.1 | 591.2 | 1015.6 | 61.8 | 177.4 | 304.7 |

3 | 6 | 88.4 | 599.0 | 1029.8 | 26.5 | 179.7 | 308.9 |

4 | 7 | 394.7 | 716.9 | 1259.1 | 118.4 | 215.1 | 377.7 |

5 | 9 | 539.0 | 761.8 | 1089.0 | 161.7 | 228.5 | 326.7 |

6 | 10 | 298.7 | 636.6 | 1040.9 | 89.6 | 191.0 | 312.3 |

7 | 12 | 323.0 | 586.5 | 1030.1 | 96.9 | 176.0 | 309.0 |

8 | 14 | 387.0 | 1110.4 | 1907.4 | 116.1 | 325.4 | 567.1 |

9 | 16 | 745.6 | 1589.1 | 2598.3 | 223.7 | 425.6 | 779.5 |

10 | 18 | 509.7 | 720.3 | 1029.8 | 152.9 | 169.7 | 308.9 |

11 | 20 | 88.4 | 599.0 | 1029.8 | 26.5 | 152.1 | 308.9 |

12 | 21 | 373.2 | 677.9 | 1190.5 | 112.0 | 190.9 | 357.2 |

13 | 23 | 365.1 | 778.1 | 1272.3 | 109.5 | 208.4 | 381.7 |

14 | 24 | 539.0 | 761.8 | 1089.0 | 161.7 | 179.5 | 326.7 |

15 | 26 | 323.0 | 586.5 | 1030.1 | 96.9 | 165.1 | 309.0 |

16 | 28 | 178.3 | 511.6 | 878.8 | 53.5 | 149.9 | 261.3 |

17 | 29 | 74.4 | 503.8 | 866.2 | 22.3 | 128.0 | 259.9 |

18 | 31 | 314.0 | 570.2 | 1001.4 | 94.2 | 160.5 | 300.4 |

19 | 32 | 290.4 | 618.9 | 1011.9 | 87.1 | 165.8 | 303.6 |

20 | 34 | 93.5 | 633.4 | 1089.0 | 28.1 | 160.9 | 326.7 |

21 | 36 | 217.9 | 625.3 | 1074.1 | 65.4 | 183.2 | 319.3 |

22 | 37 | 323.0 | 586.5 | 1030.1 | 96.9 | 165.1 | 309.0 |

DER | Number of Units | Total Installed Power | Operating Point P^{op} (MW) | ||
---|---|---|---|---|---|

Min | Mean | Max | |||

CHP | 3 | 2.5 (MVA) | 1.0 | 1.15 | 1.5 |

Wind | 2 | 20 (MVA) | 11.31 | 14.01 | 15.34 |

Transmission system operator (TSO) | 1 | 20 (MVA) | - | - | - |

DER | Upward Cost C^{up} (m.u./kVAr) | Downward Cost C^{dw} (m.u./kVAr) | ||||
---|---|---|---|---|---|---|

Min | Mean | Max | Min | Mean | Max | |

CHP | 0.02 | 0.04 | 0.06 | 0.02 | 0.04 | 0.06 |

Wind | 0.02 | 0.025 | 0.03 | 0.02 | 0.025 | 0.03 |

TSO | 1 | 1 | 1 | 1 | 1 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Abreu, T.; Soares, T.; Carvalho, L.; Morais, H.; Simão, T.; Louro, M.
Reactive Power Management Considering Stochastic Optimization under the Portuguese Reactive Power Policy Applied to DER in Distribution Networks. *Energies* **2019**, *12*, 4028.
https://doi.org/10.3390/en12214028

**AMA Style**

Abreu T, Soares T, Carvalho L, Morais H, Simão T, Louro M.
Reactive Power Management Considering Stochastic Optimization under the Portuguese Reactive Power Policy Applied to DER in Distribution Networks. *Energies*. 2019; 12(21):4028.
https://doi.org/10.3390/en12214028

**Chicago/Turabian Style**

Abreu, Tiago, Tiago Soares, Leonel Carvalho, Hugo Morais, Tiago Simão, and Miguel Louro.
2019. "Reactive Power Management Considering Stochastic Optimization under the Portuguese Reactive Power Policy Applied to DER in Distribution Networks" *Energies* 12, no. 21: 4028.
https://doi.org/10.3390/en12214028