# Generation Expansion Planning in the Presence of Wind Power Plants Using a Genetic Algorithm Model

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## Abstract

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## 1. Introduction

- The objective function of this paper is to minimize the sum of expansion costs by considering the four constraints of maximum unit capacity to build, refueling constraints, storage margin, and loss of load probability (LOLP).
- In this paper, in addition to traditional power plants, the presence of wind power plants with a random generation nature is considered.
- Due to the growth of technology for building wind farms, the initial investment required to make these units has decreased. In the present paper, the effect of this price reduction on the influence of wind units on the generation system for a long period of planning is studied.
- Given the importance of the maximum possible use of wind energy in the production system, the maximum possible use of wind power in the GEP process is investigated, provided that the constraints are met.
- The impact of the wind regime on long-term planning studies using two different wind regimes has been shown due to the development of wind unit technology and the increasing reliability of these units as well as different wind regimes. The type of wind regime is selected for two sample cities in Iran. Type 1 wind regime as a weak wind regime and type 2 wind regime as a strong wind regime have been used to obtain wind turbine output.

## 2. Modeling

#### 2.1. Wind Turbine Model

#### 2.2. Wind Farm Model

## 3. Methodology

#### 3.1. Objective Functions

#### 3.1.1. Investment Cost

#### 3.1.2. Salvation Value

#### 3.1.3. Fixed and Variable Operation and Maintenance Cost

#### 3.1.4. The Expected Energy Not Supplied (EENS) Cost

#### 3.2. Constraints

#### 3.2.1. Practical Constraints

#### Fueling Constraint

#### A. Pollution

#### 3.2.2. Technical Constraints

#### B.1. Reserve Margin constraint

#### B.2. Loss of Load Probability (LOLP) Constraint

#### 3.3. GA Optimization

## 4. Data

#### 4.1. Traditional Power Generation Units

#### 4.2. Wind Farm

#### 4.3. Forecast Load

#### 4.4. Objective Function and Constraint Parameters

#### 4.5. Specifications of GA

**,**which also includes the number of wind units in the chromosomes forming a single selectable type, each chromosome will have 42 genes. Integer coding is used to form genes. That is, each gene can have an integer value from zero to the maximum number of constructible units at each programming stage.

## 5. Case Studies

#### 5.1. GEP in the Presence of Wind Farm

#### 5.2. Investigating the Impact of Wind Penetration on GEP

#### 5.3. Investigating the Sensitivity of the Problem of Initial Investment in Wind Farms

## 6. Conclusions

- A model with a higher number of scenarios for the wind farm can be used to increase the accuracy of the calculations.
- In this study, the predicted two-piece linear model was used, while a more accurate model can be used to make the results more realistic.
- Uncertainties in both forecasted load and costs can also be included in the calculations and its effect can be examined.
- Given the problem with the HL1 level, the transmission system is assumed to be quite reliable, which can be considered the transmission network.
- Models can be used to simultaneously consider wind, solar, and other types of renewable energy sources and address the issue.
- In the issue of generation expansion planning, which was examined in this study, only the type of unit, the number and time of units being added to the final design are specified.
- Running the problem by considering the network can determine the location of the units and the impact of the location on the reliability of the system. In this case, different regimes of wind can be applied to different regions, making the results closer to reality.
- This study is conducted as a single bus, therefore the network is not considered. At the next level of system planning so-called transmission expansion planning (TEP), the network should be studied, hence the role of increasing reactive power and low power factor due to the expansion of wind power can be investigated.

## Author Contributions

## Funding

## Conflicts of Interest

## Acronyms

GEP | Generation Expansion Planning |

FOR | Forced Outage Rate |

LOLP | Loss of Load Probability |

$v$ | wind speed variable |

${v}_{cin}$ | (cut-in wind speed) minimum wind speed required to operate the turbine |

${v}_{co}$ | (cut-out wind speed) maximum wind speed terminates turbine power generation |

${v}_{r}$ | (rated wind speed) is the velocity of nominal power of the turbine |

${P}_{r}$ | nominal power of the turbine |

P | equivalent output power vector of the combination of units (MW) |

A | the number of units |

X | output power vector of each wind unit (MW) |

${P}_{i}$ | probability of i being the unit of power output |

K | number of output power levels |

i | number of available units |

${X}_{t}$ | Cumulative vector of ${U}_{t}$ |

${X}_{t,i}$ | capacity of existing units of type i in the t-th period |

$F{C}_{i}$ | constant operating cost of type i ($/MW) |

$M{C}_{i}$ | variable cost of operating unit type i at the t-th stage ($/MWh) |

$EE{S}_{t,i}$ | amount of energy that unit type i provides at the t-th period |

y | operating cost routinely spent during each phase (not at the beginning or end of the phase) |

LDC | Load Duration Curve |

F (Load) | characteristic of the load function of each stage in term of time in the LDC curve |

L1 | level of generation capacity before adding i-th unit capacity |

L2 | level of generation capacity after adding i-th unit capacity |

${R}_{max}$ | maximum system reservations |

${D}_{t}$ | maximum predicted load for the programming stage t |

${Q}_{\mathrm{k}}$ | outage capacitance |

HAWT | Horizontal Axis Wind Turbine |

${P}_{avail}$ | probability of the $CA{P}_{avail}$ |

P | Available Probability |

Capacity (${P}_{avail}$) | Possibility to Access $CA{P}_{avail}$ |

K | output mode for each turbine |

$O.F$ | Objective Function |

$I$ | Investment Cost |

${U}_{t}$ | capacity of the units added at the t-th stage of the planning |

${u}_{t}^{i}$ | capacity of units of type i to be constructed in the t-th phase of the planning |

d | interest rate |

$C{I}_{\mathrm{i}}$ | initial investment cost required for units of type i ($/MW) |

s | number of years considered for each step, which, is often 2 years for planning |

$S$ | Salvation Value |

${\delta}_{t,i}$ | cost-return factor for unit type i |

${T}^{\prime}$ | parameter is used to transfer to the base year |

$EEN{S}_{t}$ | energy not supplied in the t-th stage of planning (MWh) |

$CEENS$ | value of each MWh of energy ($) |

${t}_{k}$ | Time which the system output capacity, ${Q}_{k}$ is greater than the Reserve Margin and load is lost |

${p}_{k}$ | probability that ${Q}_{k}$ is out of capacity |

$O$ | the Outage Cost during the planning period |

${S}_{k}$ | amount of energy that is lost in the system if ${Q}_{k}$ capacity outage occurs |

${U}_{t.max}$ | vector of the maximum capacity of new possible units for the programming stage t |

${M}_{min}^{i}$ | minimum ratios of the type i unit used in the t-th stage of planning, respectively |

${M}_{Max}^{i}$ | maximum ratios of the type i unit used in the t-th stage of planning |

dload | the differential value of the load used to calculate the surface area provided by each power unit |

${R}_{min}$ | minimum system reservations |

${p}_{\mathrm{k}}$ | probability of ${Q}_{\mathrm{k}}$ |

ε | maximum allowed value of LOLP |

FOR | forced outage rate |

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**Figure 10.**Change in the number of optimal design units by changing the cost of investing in regime 2 wind farms.

Probability | Output Power (MW) |
---|---|

$P\left({p}_{w}<0.2\right)=0.4750$ | 0 |

$P\left(0.2\le {p}_{w}<0.6\right)=0.3036$ | 0.4 |

$P\left(0.6\le {p}_{w}<1\right)=0.0854$ | 0.8 |

$P\left(1\le {p}_{w}<1.4\right)=0.0623$ | 1.2 |

$P\left(1.4\le {p}_{w}<1.8\right)=0.0098$ | 1.6 |

$P\left(1.8\le {p}_{w}\right)=0.3036$ | 2 |

Capacity (MW) | Probability |
---|---|

${p}_{1}$ | ${P}_{WTG,1}$ |

${p}_{K}$ | ${P}_{WTG,K}$ |

Number of Units Available | Number of Units Exited | Available Probability (P) | Available Capacity $\left(CA{P}_{avail}\right)$ | Possibility to Access $CA{P}_{avail}$ Capacity $\left({P}_{avail}\right)$ |
---|---|---|---|---|

$0$ | $N$ | ${\mathit{P}}_{\mathbf{1}}\mathbf{=}\mathit{N}\mathbf{\xb7}\mathbf{1}\mathbf{\xb7}\mathit{F}\mathit{O}{\mathit{R}}^{\mathbf{\left(}\mathit{N}\mathbf{-}\mathbf{0}\mathbf{\right)}}$ | $0\times {p}_{1}$ | ${P}_{0}\times {P}_{WTG,1}$ |

$0\times {p}_{K}$ | ${P}_{0}\times {P}_{WTG,K}$ | |||

$i$ | $N-i$ | ${P}_{i}=\left(\begin{array}{c}N\\ i\end{array}\right){\left(1-FOR\right)}^{i}FO{R}^{\left(N-i\right)}$ | $i\times {p}_{1}$ | ${P}_{i}\times {P}_{WTG,1}$ |

$i\times {p}_{K}$ | ${P}_{i}\times {P}_{WTG,K}$ | |||

$N$ | 0 | ${P}_{N}=\left(\begin{array}{c}N\\ N\end{array}\right)\xb7{\left(1-FOR\right)}^{N}$ | $N\times {p}_{1}$ | ${P}_{N}\times {P}_{WTG,1}$ |

$N\times {p}_{K}$ | ${P}_{N}\times {P}_{WTG,K}$ |

Probability | Output Power (MW) |
---|---|

$P\left(CA{P}_{avail}6\right)=0.47$ | 0 |

$P\left(6\le CA{P}_{avail}18\right)=0.304265$ | 12 |

$P\left(18\le CA{P}_{avail}30\right)=0.089295$ | 24 |

$P\left(30\le CA{P}_{avail}42\right)=0.061224$ | 36 |

$P\left(42\le CA{P}_{avail}54\right)=0.028845$ | 48 |

$P\left(54\le CA{P}_{avail}\right)=0.041371$ | 60 |

Probability for Wind Regime 1 | Probability for Wind Regime 2 | Output Power (MW) |
---|---|---|

0.2942 | 0.475 | 0 |

0.174601 | 0.304265 | 12 |

0.165499 | 0.089295 | 24 |

0.184267 | 0.061224 | 36 |

0.096124 | 0.028845 | 48 |

0.084879 | 0.041371 | 60 |

Probability for Wind Regime 1 | Probability for Wind Regime 2 | Output Power (MW) |
---|---|---|

0.2942 | 0.475 | 0 |

0.1734 | 0.3036 | 0.4 |

0.1543 | 0.0854 | 0.8 |

0.1694 | 0.0623 | 1.2 |

0.07714 | 0.0098 | 1.6 |

0.1314 | 0.0639 | 2 |

Planning Stage | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|

Forecasted Load (MW) | 5000 | 7000 | 9000 | 11,000 | 13,000 | 15,000 | 17,000 | 19,000 |

Fuel Mix Ratio | Max (%) | Min (%) |
---|---|---|

Oil | 0 | 30 |

LNG | 0 | 60 |

COAL | 20 | 60 |

PWR | 30 | 60 |

PHWR | 30 | 60 |

Output Power (MW) | Probability for Wind Regime 2 | Probability for Wind Regime 1 |
---|---|---|

0 | 0.2942 | 0.475 |

12 | 0.174601 | 0.304265 |

24 | 0.165499 | 0.089295 |

36 | 0.184267 | 0.061224 |

48 | 0.096124 | 0.028845 |

60 | 0.084879 | 0.041371 |

**Table 10.**Selected optimal plans with the least-cost function, in the presence of wind farm (plan 1) and in the presence of a wind farm (plan 2).

Power Plant | Oil | LNG | COAL | PWR | PHWR | WIND | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Plan | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |

Stage 1 | 3 | 0 | 4 | 2 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |

Stage 2 | 3 | 0 | 2 | 2 | 1 | 2 | 0 | 0 | 1 | 0 | 0 | 2 |

Stage 3 | 0 | 0 | 3 | 4 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |

Stage 4 | 3 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 0 | 3 |

Stage 5 | 4 | 2 | 0 | 2 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 3 |

Stage 6 | 2 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 2 | 0 | 3 |

Stage 7 | 0 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 2 |

Optimal Plan | 1 | 2 |
---|---|---|

Total Cost (M$) | 17,136,679 | 17,245,513 |

Investment Cost of Initial Plan (M$) | 11,461,397 | 11,468,975 |

Operational Cost of Plan (M$) | 3,772,192 | 3,723,465 |

© 2020 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**

Sahragard, A.; Falaghi, H.; Farhadi, M.; Mosavi, A.; Estebsari, A. Generation Expansion Planning in the Presence of Wind Power Plants Using a Genetic Algorithm Model. *Electronics* **2020**, *9*, 1143.
https://doi.org/10.3390/electronics9071143

**AMA Style**

Sahragard A, Falaghi H, Farhadi M, Mosavi A, Estebsari A. Generation Expansion Planning in the Presence of Wind Power Plants Using a Genetic Algorithm Model. *Electronics*. 2020; 9(7):1143.
https://doi.org/10.3390/electronics9071143

**Chicago/Turabian Style**

Sahragard, Ali, Hamid Falaghi, Mahdi Farhadi, Amir Mosavi, and Abouzar Estebsari. 2020. "Generation Expansion Planning in the Presence of Wind Power Plants Using a Genetic Algorithm Model" *Electronics* 9, no. 7: 1143.
https://doi.org/10.3390/electronics9071143