# Active Distribution Network Modeling for Enhancing Sustainable Power System Performance; a Case Study in Egypt

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Examination of the Studied Real Case Study in Egypt

^{2}according to the average values during the last 20 years. The daily duration of sunshine fluctuates between 9 and 11 h [29]. This climate gives New Valley the priority for investment in renewable energy projects.

^{2}and 48 km in length. A detailed description of the studied network and its load distribution is given in Section 5.2.

## 3. Modeling of DN Components

#### 3.1. Modeling of Distribution Line

#### 3.2. Modeling of Transformer Losses

#### 3.3. Modeling of AVR

**For Type-A Regulator:**$${V}_{Source}=\frac{1}{{a}_{R}}\xb7{V}_{Load},{I}_{\begin{array}{c}Sou\\ 6rce\end{array}}={a}_{R}\xb7{I}_{Load}$$$${a}_{R}=\{\begin{array}{c}1+{N}_{R}\xb7Tapforraisetaps\\ 1-{N}_{R}\xb7Tapforlowertaps\end{array}$$**For Type-B Regulator:**$${V}_{Source}={a}_{R}\xb7{V}_{Load},{I}_{Source}=\frac{1}{{a}_{R}}\xb7{I}_{Load}$$$${a}_{R}=\{\begin{array}{c}1-{N}_{R}\xb7Tapforraisetaps\\ 1+{N}_{R}\xb7Tapforlowertaps\end{array}$$

#### 3.4. Modeling of DG Unit

#### 3.5. Modeling of Shunt Capacitor Bank

#### 3.6. Load Models

## 4. Proposed Power-Flow Algorithm

#### 4.1. Module 1: Initialization

- Input the network data (specifications and locations of the network components).
- Input the loads data (locations, consumptions and types of all load points).
- Select the solution accuracy ($\epsilon $) and the maximum number of iterations ($max\_itr$).
- Recall the required parameters related to network components from the database library.

#### 4.2. Module 2: Matrices Construction

- Construct the connection matrix ($CONMAT$) [30], the series impedance matrix ($Z$) and the shunt admittance matrix ($Y$).

#### 4.3. Module 3: BFS Iterations

- Calculate the power injected at each node ${S}_{inj}$ assuming a flat voltage profile. ${S}_{inj}$ is the resultant of the load apparent power ${S}_{L}$ (Equation (12)), the transformer dissipated power ${S}_{T}$ (Equation (4)), the apparent power generated by DG unit ${S}_{g}$ (Equation (10)) and the effective reactive power of capacitor bank ${Q}_{C}$ (Equation (11)) if any.
- Repeat the following BFS iterations:

#### 4.3.1. Backward Sweep Calculations:

- Correct ${S}_{inj}$ considering the load models, DG, SCB and transformer losses.
- Find the current injected to each node using: ${I}_{inj}={\left({S}_{inj}/V\right)}^{*}$.
- Find the current flowed through each segment using: ${I}_{seg}=\left[CONMAT\right]\left[{I}_{inj}\right]$.
- Find the voltage drop across each segment using: ${V}_{drop}=\left[{I}_{seg}\right]\left[Z\right]$.
- Denote the calculated voltage distribution matrix $V$ of the current iteration as ${V}_{old}$.

#### 4.3.2. Forward Sweep Calculations

- Update the matrix $V$ according to the voltage drop ${V}_{drop}$ formerly determined in the backward sweep. Considering the voltage at any arbitrary node k (${V}_{k}$ shown in Figure 5) is the voltage at its predecessor node b (${V}_{b}$) minus the voltage drop across the segment connecting them (${V}_{dropk-1}$).
- Recalculate both voltage and current matrices according to the AVR model.
- Update the loop counter.
- Terminate the loop if each element in the matrix (${V}_{old}\u2013V$) is less than the solution accuracy $\epsilon $, or the loop counter exceeds the maximum number of iterations ($max\_itr$).

#### 4.4. Module 4: Losses Calculations

- Find the power flowed through each segment using: ${S}_{seg}=\left[V\right]{\left[{I}_{seg}\right]}^{*}$
- Find the conductor losses using $\left[{V}_{drop}\right]{\left[{I}_{seg}\right]}^{*}$
- Find the total losses by adding the conductor losses to the transformer losses.
- Print the outputs.

## 5. Simulation Results and Discussions

#### 5.1. Case I: Unbalanced IEEE 37-Node Feeder

^{−6}, the maximum founded deviation in the voltage magnitudes as compared to those given in [46] is less than 0.006%. The maximum deviation of the calculated power losses from those of [46] is less than 0.005%. This test asserted the effectiveness of the presented algorithm to analyze unbalanced DNs.

#### 5.2. Case II: Balanced UEDN Network

#### 5.2.1. PDN Performance

#### 5.2.2. ADN Performance

- The required lands to construct solar power stations are available.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

From node | To node | Code ^{a} | Length (km) | From node | To node | Code ^{a} | Length (km) | From node | To node | Code ^{a} | Length (km) |
---|---|---|---|---|---|---|---|---|---|---|---|

$\mathbf{01}$ | $02$ | $2401$ | $0.1$ | $21$ | $24$ | $1502$ | $2$ | $40$ | $46$ | $1502$ | $0.5$ |

$\mathbf{02}$ | $03$ | $2403$ | $35$ | $24$ | $25$ | $1502$ | $3$ | $46$ | $47$ | $1502$ | $5$ |

$\mathbf{03}$ | $04$ | $4001$ | $0.05$ | $25$ | $26$ | $0702$ | $1$ | $47$ | $48$ | $0702$ | $0.5$ |

$\mathbf{04}$ | $05$ | $4001$ | $0.05$ | $26$ | $27$ | $0702$ | $1$ | $48$ | $49$ | $0702$ | $0.5$ |

$\mathbf{05}$ | $06$ | $2403$ | $5$ | $27$ | $28$ | $0702$ | $1$ | $49$ | $50$ | $0702$ | $1$ |

$\mathbf{06}$ | $07$ | $1502$ | $25$ | $28$ | $29$ | $0702$ | $1.5$ | $50$ | $51$ | $0702$ | $1$ |

$\mathbf{07}$ | $08$ | $1502$ | $23$ | $28$ | $30$ | $0702$ | $4$ | $47$ | $52$ | $1502$ | $5$ |

$\mathbf{08}$ | $09$ | $2401$ | $3$ | $25$ | $31$ | $1502$ | $0.5$ | $52$ | $53$ | $0702$ | $1$ |

$\mathbf{09}$ | $10$ | $1502$ | $12$ | $31$ | $32$ | $1502$ | $4$ | $53$ | $54$ | $0702$ | $0.2$ |

$\mathbf{10}$ | $11$ | $4001$ | $0.05$ | $12$ | $33$ | $2401$ | $0.3$ | $53$ | $55$ | $0702$ | $0.2$ |

$\mathbf{11}$ | $12$ | $4001$ | $0.05$ | $33$ | $34$ | $1502$ | $1$ | $53$ | $56$ | $0702$ | $1$ |

$\mathbf{12}$ | $13$ | $1502$ | $0.5$ | $34$ | $35$ | $1502$ | $1$ | $56$ | $57$ | $0702$ | $2$ |

$\mathbf{13}$ | $14$ | $1502$ | $2.5$ | $35$ | $36$ | $0702$ | $0.5$ | $57$ | $58$ | $0702$ | $0.5$ |

$\mathbf{14}$ | $15$ | $0701$ | $0.1$ | $35$ | $37$ | $0702$ | $0.5$ | $58$ | $59$ | $0702$ | $0.5$ |

$\mathbf{14}$ | $16$ | $0701$ | $0.1$ | $35$ | $38$ | $1502$ | $10$ | $52$ | $60$ | $1502$ | $2$ |

$\mathbf{13}$ | $17$ | $1502$ | $2$ | $38$ | $39$ | $0702$ | $2$ | $60$ | $61$ | $1502$ | $2$ |

$\mathbf{17}$ | $18$ | $0701$ | $0.5$ | $38$ | $40$ | $1502$ | $4$ | $61$ | $62$ | $0702$ | $1.5$ |

$\mathbf{17}$ | $19$ | $1502$ | $1$ | $40$ | $41$ | $0702$ | $1$ | $62$ | $63$ | $0702$ | $0.3$ |

$\mathbf{19}$ | $20$ | $0702$ | $0.3$ | $41$ | $42$ | $0702$ | $1$ | $63$ | $64$ | $0702$ | $1.5$ |

$\mathbf{19}$ | $21$ | $1502$ | $0.5$ | $42$ | $43$ | $0702$ | $3$ | $64$ | $65$ | $0702$ | $0.3$ |

$\mathbf{21}$ | $22$ | $0702$ | $3$ | $43$ | $44$ | $0702$ | $0.5$ | ||||

$\mathbf{22}$ | $23$ | $0702$. | $9$ | $43$ | $45$ | $0702$ | $1.5$ |

^{a}Codes 4001, 2401 and 0701 denote three-core aluminum cables of nominal cross-sectional areas of 400 mm

^{2}, 240 mm

^{2}and 70 mm

^{2}, respectively. Codes 1502 and 0702 denote overhead ACSR of cross-sectional areas of 150/25 mm

^{2}and 70/12 mm

^{2}, respectively. Code 2403 denotes an overhead all aluminum alloy conductor (AAAC) of a cross-sectional area of 240 mm

^{2}.

Solution Variables | ||
---|---|---|

$\mathit{m}\mathit{a}\mathit{x}\_\mathit{i}\mathit{t}\mathit{r}$ | 100 | iterations |

$\mathit{\epsilon}$ | 10^{−6} | - |

$\mathit{f}$ | 50 | Hz |

Utility Grid (UG) Cable Parameters (Codes 701, 2401 and 4001) | |
---|---|

Code | ${z}_{ii}$ (Ω/km) |

0701 | 0.5683 + j 0.11624 |

2401 | 0.1618 + j 0.09676 |

4001 | 0.102 + j 0.090164 |

Overhead Transmission Lines (OHTL) Network Parameters (Codes 702, 1502 and 2403) | |||
---|---|---|---|

$\mathit{T}$ | 70 | $\mathbb{C}$ | |

${\mathit{r}}_{\mathit{d}}$ | 0.04935 | Ω/km | |

${\mathit{D}}_{\mathit{e}}$ | 931.76 | m | |

$\mathit{G}\mathit{M}\mathit{D}$ | 1151.15 | mm | |

Code | ${R}_{ref}$ (Ω/km) | $GMR$ (mm) | $\alpha $ (/$\mathbb{C}$) |

0702 | 0.4130 | 4.7502 | 0.00404 |

1502 | 0.1939 | 6.9426 | |

2403 | 0.1373 | 7.8358 | 0.00347 |

Distribution Transformer Parameters | ||
---|---|---|

${\mathit{S}}_{\mathit{r}}$ | 300 | kVA |

${\mathit{P}}_{\mathit{o}}$ | 576 | Watt |

${\mathit{P}}_{\mathit{c}}$ | 3815 | Watt |

${\mathit{U}}_{\mathit{s}}$ | 4 | % |

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**Figure 3.**Case study location compared to the Egyptian unified national grid. “TH. POWER ST.” is referred to thermal power stations, “HY. POWER ST.” is referred to Hydraulic Power Station and “SS” is referred to Substation.

**Figure 5.**Electric equivalent of an active distribution network (ADN) segment. AVR: automatic voltage regulator; DG: distributed generation.

**Figure 14.**Voltage profile along the UEDN as an ADN compared to PDN under different loading conditions.

Feature | Distribution System | Transmission System |
---|---|---|

Structure | Radial/Weakly meshed | Tightly meshed |

Types of Load | Constant Power (CP)/Constant Current (CC)/Constant Impedance (CI)/Composite | Mostly CP only |

Symmetricity | Unbalanced/Balanced | Balanced |

R/X Ratio | High | Very low |

Generator Nodes | PQ/PV/Composite | Mostly PV only |

**Table 2.**Voltage behavior of the ADN as compared to the passive distribution network (PDN) in case I.

Network | PDN | ADN | |||||
---|---|---|---|---|---|---|---|

Line-to-line | A-to-B | B-to-C | C-to-A | A-to-B | B-to-C | C-to-A | |

Min. Voltage | (pu) | 0.998 | 0.995 | 0.985 | 1.006 | 1.002 | 0.999 |

at Node | 741 | 722 | 741 | 741 | 722 | 741 | |

Max. Voltage | (pu) | 1.044 | 1.025 | 1.035 | 1.031 | 1.019 | 1.025 |

at Node | 701 | 701 | 701 | 701 | 701 | 701 | |

Tap of AVR | 7R | 4R | - | 5R | 3R | - |

Network | PDN | ADN | |||||||
---|---|---|---|---|---|---|---|---|---|

Line | A | B | C | Total | A | B | C | Total | |

Losses (kW) | $26.669$ | $13.804$ | $20.087$ | $60.560$ | $8.118$ | $4.076$ | $5.918$ | $18.112$ |

**Table 4.**Specifications and sittings of the AVR groups in the Upper Egypt distribution network (UEDN).

Location Node | ANSI Type | Rated Current (A) | Connection Type | Voltage Level Setting (V) |
---|---|---|---|---|

$\mathbf{4}$ | $B$ | $300$ | $\mathrm{Closed}\mathrm{Delta}$ | $120$ |

$\mathbf{11}$ | $B$ | $300$ | $\mathrm{Closed}\mathrm{Delta}$ | $115$ |

Location (at Node) | DG Type | Rated Active Power (kW) | Specified Power Factor |
---|---|---|---|

$\mathbf{21}$ | $III,PQ$ | $900$ | $0.9$ |

$\mathbf{46}$ | $III,PQ$ | $1800$ | $0.9$ |

Network | PDN | ADN | |||
---|---|---|---|---|---|

Operation Mode | Day-Time (Full Load) | Night-Time (No Load) | Day-Time (Full Load) | Night-Time (No Load) | |

$SubstationVoltage\left(kV\right)$ | $21.5$ | $22.5$ | $21.5$ | $22.5$ | |

$Min.LoadVoltage$ | $Magnitude\left(kV\right)$ | $18.17$ | $20.83$ | $20.65$ | $20.83$ |

$LocationNode$ | $65$ | $65$ | $65$ | $65$ | |

$Max.LoadVoltage$ | $Magnitude\left(kV\right)$ | $19.14$ | $20.86$ | $20.99$ | $20.86$ |

$LocationNode$ | $15$ | $15$ | $18$ | $15$ | |

${Conductors}^{\prime}Losses$ | kW | $1301.3$ | $1.2$ | $50.1$ | $1.2$ |

% | $28.95$ | $4.97$ | $1.55$ | $4.97$ | |

${Transformers}^{\prime}losses$ | kW | $35.28$ | $22.46$ | $35.28$ | $22.46$ |

% | $0.79$ | $95.03$ | $1.10$ | $95.03$ | |

$TotalLosses$ | kW | $1336.7$ | $23.65$ | $85.33$ | $23.65$ |

% | $29.74$ | $100$ | $2.63$ | $100$ | |

$TapPositionofAVRatnode4$ | $16\mathrm{R}$ | $3\mathrm{L}$ | $7\mathrm{R}$ | $3\mathrm{L}$ | |

$TapPositionofAVRatnode11$ | $16\mathrm{R}$ | $4\mathrm{L}$ | $3\mathrm{L}$ | $4\mathrm{L}$ |

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## Share and Cite

**MDPI and ACS Style**

Radwan, A.A.; Zaki Diab, A.A.; Elsayed, A.-H.M.; Haes Alhelou, H.; Siano, P.
Active Distribution Network Modeling for Enhancing Sustainable Power System Performance; a Case Study in Egypt. *Sustainability* **2020**, *12*, 8991.
https://doi.org/10.3390/su12218991

**AMA Style**

Radwan AA, Zaki Diab AA, Elsayed A-HM, Haes Alhelou H, Siano P.
Active Distribution Network Modeling for Enhancing Sustainable Power System Performance; a Case Study in Egypt. *Sustainability*. 2020; 12(21):8991.
https://doi.org/10.3390/su12218991

**Chicago/Turabian Style**

Radwan, Ali A., Ahmed A. Zaki Diab, Abo-Hashima M. Elsayed, Hassan Haes Alhelou, and Pierluigi Siano.
2020. "Active Distribution Network Modeling for Enhancing Sustainable Power System Performance; a Case Study in Egypt" *Sustainability* 12, no. 21: 8991.
https://doi.org/10.3390/su12218991