# A Deep Learning-Based Approach for Generation Expansion Planning Considering Power Plants Lifetime

^{1}

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## Abstract

**:**

## 1. Introduction

_{2}emission.

- Investigating the effects of power plants’ lifetime constrain on new and existing plants. This constraint affects the GEP problem due to two practical reasons: 1-Some power plants have less lifetime than the planning horizon. This fact may increase the costs, and the GEP might have more cost than the case with a longer lifetime. 2-Some power plants may have derated efficiency due to aging, or out of date technologies in comparison with newer ones with less fuel consumption. Therefore, they should be replaced by new ones.
- Using a new version of LSTM networks known as Bi-directional LSTM (BLSTM) networks for forecasting the annual peak load. The advantages of BLSTM networks compared to LSTM networks are its two feedforward and feedback loops, which lead to the use of the whole temporal horizon. This feature of BLSTM networks can increase accuracy in time series forecasting tasks.
- Considering the carbon tax policy as a carbon emission reduction method in order to prevent the release of carbon into the environment

## 2. Objective Function

#### 2.1. Investment, Operation, and Maintenance Cost

#### 2.2. Carbon Emission Cost

#### 2.3. Constraints

#### 2.3.1. The Lifetime Constraint

#### 2.3.2. The Reserve Margin Constraint

#### 2.3.3. Maximum Number of New Plants Constraint

#### 2.3.4. Mix Capacity Constraint

#### 2.3.5. The LOLP Constraint

## 3. Deep Learning-Based Approach for Annual Peak Load Forecasting

_{t}), forget (f

_{t}), and output (o

_{t}) gates are calculated, respectively. In addition, Equation (11) shows the cell state, and S

_{t}is the output of LSTM block.:

## 4. Case Studies

#### 4.1. Case 1: Test System

#### 4.2. Forecasting Annual Peak Load

#### 4.3. Case 2: Iran Power System

#### 4.4. Carbon Reduction

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Parameters | |

c_{1} | Cognitive component |

c_{2} | Social component |

$J$ | Fuel type number |

${\underset{\_}{M}}_{t}^{j}$ | Lower bound of j-th fuel type in a year t |

${\overline{M}}_{t}^{j}$ | Upper bound of j-th fuel type in a year t |

$\underset{\_}{R}$ | Lower bound of reserve margin |

$\overline{R}\text{}$ | Upper bound of reserve margin |

$T$ | Time period numbers (years) in the planning horizon |

${\overline{U}}_{t}$ | Maximum manufactural capacity vector (MW) of generation unit types in a year t |

w | Inertia weight |

${\mathrm{\Omega}}_{j}$ | Type indicator set of the j-th generation unit |

$n$ | Total number of input data |

$nh$ | Total number of hidden units |

$no$ | Total number of outputs |

$r$ | Dimension of each input data sequence |

Variables | |

${L}_{t}$ | Retired capacity vector (MW) of generation unit types in a year t |

$LOLP({X}_{t})$ | loss of load probability with ${X}_{t}$, in a year t |

${U}_{t}$ | Added capacity vector (MW) of generation unit types in a year t |

${v}_{a}(k)$ | Velocity of the a-th particle at iteration k |

${x}_{t}^{i}$ | Added capacity (MW) of the i-th unit in a year t |

${X}_{t}$ | Cumulative capacity vector (MW) of generation unit types in a year t |

${y}_{a}(k)$ | Position of the a-th particle at iteration k |

${f}_{t}^{3}\left({L}_{t}\right)$ | Discounted salvage value ($) due to retired capacity ${L}_{t}$ in a year t |

${f}_{t}^{1}\left({U}_{t}\right)$ | Discounted construction cost ($) due to added capacity ${U}_{t}$ in a year t |

${f}_{t}^{2}\left({X}_{t}\right)$ | Discounted operation and maintenance cost due to cumulative capacity ${X}_{t}$ in a year t |

${f}_{t}^{3}\left({X}_{t}\right)$ | Discounted carbon emission cost due to cumulative capacity ${X}_{t}$ in a year t |

$R\left({X}_{t}\right)$ | Capacity reserve margin of ${X}_{t}$ in a year t |

$bc,bf,bi,bo$ | Bias vector for cell block, forget gate, input gate, and output gate, respectively |

$b{h}^{(b)},b{h}^{(f)}$ | Bias vector for backward and forward hidden layer, respectively |

${c}_{t},{f}_{t},{i}_{t}$ | Data vector of cell block, forget gate, and input gate at a time t, respectively |

$c{h}_{t},f{h}_{t},i{h}_{t}$ | Data vector of cell block, forget gate, and input gate at a time t in hidden layer, respectively |

${H}_{t}$ | Total hidden vector layers |

${\overrightarrow{H}}_{t},{\overleftarrow{H}}_{t}$ | Hidden vector for forward and backward layer at a time t, respectively |

${o}_{t}$ | Data vector of output gate at a time t |

$Ofn$ | Output vector of final layer |

$o{h}_{t}$ | Data vector of output gate at a time t in hidden layer |

${S}_{t}$ | State vector of current layer at a state t |

${S}_{t}^{l}$ | State vector of a layer l at a state t |

$S{h}_{t}^{l}$ | State vector of a hidden layer l at a state t |

$\begin{array}{l}Wh{i}_{\hspace{0.17em}},Wh\phi ,\hspace{0.17em}\\ Wh\gamma ,\hspace{0.17em}Who\end{array}$ | Weight vector for output of previous state input gate, forget gate, cell block, and output gate, respectively |

$\begin{array}{l}W{i}_{\hspace{0.17em}},Wi{\phi}_{\hspace{0.17em}},\\ Wi\gamma ,Wio\end{array}$ | Weight vector for input of current state input gate, forget gate, cell block, and output gate, respectively |

$Wh{h}^{(b)},Wh{h}^{(f)}$ | Weight vector of backward and forward layer output data, respectively |

$Wo$ | Weight vector of output layer |

$Wx{h}^{(b)},Wx{h}^{(f)}$ | Weight vector of backward and forward layer input data, respectively |

$\text{}{X}_{t}$ | Input data vector at a time t |

Indices | |

a | Index for particle number |

$i$ | Index for power plant type |

$j$ | Index for fuel type |

$k$ | Index for iteration number |

$t$ | Index for time period |

$l$ | Index for hidden layer |

$t$ | Index for time |

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**Figure 8.**Capacity installed (blue bars) or retired (red bars) in each year for LNG-fired power plants.

**Figure 9.**Capacity installed (blue bars) or retired (red bars) in each year for coal-fired power plants.

**Figure 10.**Capacity installed (blue bars) or retired (red bars) in each year for nuclear power plants (PHWR).

**Figure 11.**Capacity installed (blue bars) or retired (red bars) in each year for oil-fired power plants.

**Figure 12.**Capacity installed (blue bars) or retired (red bars) in each year for nuclear power plants (PWR).

**Figure 13.**Daily forecasted peak load for July to September 2020 by different methods and their yearly peak loads.

Name | No. of Units | Unit Capacity (MW) | Operating Cost ($/kWh) | Fixed O&M Cost ($/kW-mon) |
---|---|---|---|---|

Oil 1 | 1 | 200 | 0.024 | 2.25 |

Oil 2 | 1 | 200 | 0.027 | 2.25 |

Oil 3 | 1 | 150 | 0.030 | 2.13 |

LNG G/T | 3 | 50 | 0.043 | 4.52 |

LNG C/C 1 | 1 | 400 | 0.038 | 1.63 |

LNG C/C 2 | 1 | 400 | 0.040 | 1.63 |

LNG C/C 3 | 1 | 450 | 0.035 | 2.00 |

Coal 1 | 2 | 250 | 0.023 | 6.65 |

Coal 2 | 1 | 500 | 0.019 | 2.81 |

Coal 3 | 1 | 500 | 0.015 | 2.81 |

PWR 1 | 1 | 1000 | 0.005 | 4.94 |

PWR 2 | 1 | 1000 | 0.005 | 4.63 |

Year | Peak (MW) | Year | Peak (MW) |
---|---|---|---|

0 | 5000 | 16 | 17,000 |

2 | 7000 | 18 | 18,000 |

4 | 9000 | 20 | 20,000 |

6 | 10,000 | 22 | 22,000 |

8 | 12,000 | 24 | 24,000 |

10 | 13,000 | 26 | 26,000 |

12 | 14,000 | 28 | 27,000 |

14 | 15,000 | 30 | 30,000 |

Candidate Type | Oil | LNG | Coal | PWR | PHWR |
---|---|---|---|---|---|

Construction upper limit | 5 | 4 | 3 | 3 | 3 |

Capacity (MW) | 200 | 450 | 500 | 1000 | 700 |

Operating cost ($/kWh) | 0.021 | 0.035 | 0.014 | 0.004 | 0.003 |

Fixed O&M cost ($/kW-mon) | 2.20 | 0.90 | 2.75 | 4.60 | 5.50 |

Capital cost ($/kW) | 812.5 | 500.0 | 1062.5 | 1625.0 | 1750.0 |

Lifetime (years) | 20 | 22 | 24 | 26 | 28 |

Name (Fuel Type) | Lifetime (years) | Name (Fuel Type) | Lifetime (years) |
---|---|---|---|

Oil 1 | 6 | LNG C/C 3 | 20 |

Oil 2 | 10 | Coal 1 | 8 |

Oil 3 | 14 | Coal 2 | 12 |

LNG G/T | 4 | Coal 3 | 16 |

LNG C/C 1 | 10 | PWR 1 | 12 |

LNG C/C 2 | 16 | PWR 2 | 16 |

Year | Oil | LNG | PWR | Coal | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

New | Retired | Total | New | Retired | Total | New | Retired | Total | New | Retired | Total | |

2 | 1 | 0 | 1 | 0 | 0 | 0 | 2 | 0 | 2 | 2 | 0 | 2 |

4 | 2 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 2 |

6 | 2 | 0 | 5 | 1 | 0 | 1 | 0 | 0 | 2 | 0 | 0 | 2 |

8 | 0 | 0 | 5 | 0 | 0 | 1 | 2 | 0 | 4 | 0 | 0 | 2 |

10 | 0 | 0 | 5 | 0 | 0 | 1 | 0 | 0 | 4 | 1 | 0 | 3 |

12 | 1 | 0 | 6 | 0 | 0 | 1 | 1 | 0 | 5 | 0 | 0 | 3 |

14 | 4 | 0 | 10 | 0 | 0 | 1 | 1 | 0 | 6 | 1 | 0 | 4 |

16 | 2 | 0 | 12 | 2 | 0 | 3 | 0 | 0 | 6 | 2 | 0 | 6 |

18 | 0 | 0 | 12 | 2 | 0 | 5 | 1 | 0 | 7 | 0 | 0 | 6 |

20 | 4 | 1 | 15 | 2 | 0 | 7 | 2 | 0 | 9 | 0 | 0 | 6 |

22 | 0 | 2 | 13 | 4 | 0 | 11 | 0 | 0 | 9 | 0 | 0 | 6 |

24 | 5 | 2 | 16 | 3 | 0 | 14 | 3 | 0 | 12 | 3 | 2 | 7 |

26 | 1 | 0 | 17 | 0 | 0 | 14 | 1 | 2 | 11 | 2 | 0 | 9 |

28 | 1 | 0 | 18 | 0 | 1 | 13 | 2 | 0 | 13 | 2 | 0 | 11 |

30 | 3 | 1 | 20 | 0 | 0 | 13 | 2 | 0 | 15 | 0 | 0 | 11 |

Method | Total Cost (M $) |
---|---|

Without considering lifetime | 40,248 |

With considering lifetime | 38,231 |

Error Criterion | |||
---|---|---|---|

MAPE (%) | MAE (MW) | RMSE (MW) | |

BLSTM | 1.90 | 1031.74 | 1276.69 |

LSTM | 2.29 | 1243.79 | 1515.57 |

MLP | 3.57 | 1942.65 | 2437.11 |

Year | Peak (MW) | Year | Peak (MW) |
---|---|---|---|

1 | 60,479 | 16 | 80,180 |

2 | 62,613 | 17 | 80,685 |

3 | 64,644 | 18 | 82,143 |

4 | 66,560 | 19 | 82,812 |

5 | 68,354 | 20 | 83,446 |

6 | 70,021 | 21 | 85,632 |

7 | 71,558 | 22 | 86,143 |

8 | 72,967 | 23 | 89,231 |

9 | 74,248 | 24 | 91,968 |

10 | 75,408 | 25 | 92,457 |

11 | 76,451 | 26 | 92,967 |

12 | 77,384 | 27 | 92,692 |

13 | 78,216 | 28 | 93,619 |

14 | 78,954 | 29 | 94,276 |

15 | 79,606 | 30 | 95,889 |

Type | Investment (1000 Rial/kW) | O&M Cost (Rial/kWh) | CO_{2} Generation Rate (ton CO^{2}/MWh) | Existing Capacity (MW) | Plant Life (year) | Unit Size (MW) |
---|---|---|---|---|---|---|

Nuclear | 87,990 | 3150 | 0 | 0 | 60 | 1000 |

Coal based | 80,700 | 2925 | 0.4 | 0 | 40 | 320 |

Combined cycle | 20,411 | 293 | 0.34 | 14,632 | 20 | 480 |

Natural gas | 12,750 | 390 | 0.5 | 21,617 | 15 | 162 |

Steam based | 24,450 | 450 | 0.71 | 15,704 | 30 | 320 |

Hydroelectric | 48,920 | 494 | 0 | 9542 | 50 | 100 |

Wind | 56,430 | 103.2 | 0 | 90 | 22 | 25 |

Solar | 92,700 | 171.9 | 0 | 0 | 20 | 100 |

Photovoltaic | 135,000 | 27.3 | 0 | 0 | 15 | 100 |

Biomass | 121,500 | 1350 | 0 | 0 | 20 | 25 |

Method | Total Cost (M Rial) |
---|---|

Without considering lifetime | 9.54 × 10^{9} |

With considering lifetime | 8.84 × 10^{9} |

Biomass | Natural | Wind | Photovoltaic | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Year | New | Retired | Total | New | Retired | Total | New | Retired | Total | New | Retired | Total |

16 | 0 | 0 | 39 | 0 | 6 | 26 | 1 | 0 | 49 | 0 | 6 | 34 |

17 | 2 | 0 | 41 | 1 | 3 | 24 | 0 | 0 | 49 | 0 | 0 | 34 |

18 | 0 | 0 | 41 | 0 | 0 | 24 | 0 | 0 | 49 | 0 | 4 | 30 |

19 | 0 | 0 | 41 | 2 | 6 | 20 | 0 | 0 | 49 | 3 | 0 | 33 |

20 | 1 | 0 | 42 | 5 | 3 | 22 | 5 | 0 | 54 | 3 | 6 | 30 |

21 | 1 | 6 | 37 | 3 | 0 | 25 | 3 | 0 | 57 | 5 | 6 | 29 |

22 | 3 | 0 | 40 | 5 | 5 | 25 | 1 | 0 | 58 | 0 | 5 | 24 |

23 | 5 | 4 | 41 | 1 | 4 | 22 | 5 | 6 | 57 | 4 | 4 | 24 |

24 | 6 | 6 | 41 | 6 | 0 | 28 | 6 | 6 | 57 | 6 | 0 | 30 |

25 | 3 | 6 | 38 | 3 | 0 | 31 | 3 | 6 | 54 | 1 | 2 | 29 |

26 | 3 | 6 | 35 | 2 | 1 | 32 | 1 | 3 | 52 | 1 | 1 | 29 |

27 | 6 | 3 | 38 | 6 | 1 | 37 | 6 | 0 | 58 | 6 | 2 | 33 |

28 | 0 | 1 | 37 | 1 | 1 | 37 | 2 | 6 | 54 | 0 | 0 | 33 |

29 | 5 | 0 | 42 | 0 | 1 | 36 | 5 | 5 | 54 | 3 | 0 | 36 |

30 | 3 | 2 | 43 | 4 | 1 | 39 | 3 | 4 | 53 | 3 | 4 | 35 |

**Table 13.**Total carbon produced by Iran power system with and without considering carbon emissions constraint.

Method | Total Carbon (Ton) |
---|---|

Without considering the carbon emission constraint | 1.5492 × 10^{6} |

With considering the carbon emission constraint | 1.2731 × 10^{6} |

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## Share and Cite

**MDPI and ACS Style**

Dehghani, M.; Taghipour, M.; Sadeghi Gougheri, S.; Nikoofard, A.; Gharehpetian, G.B.; Khosravy, M. A Deep Learning-Based Approach for Generation Expansion Planning Considering Power Plants Lifetime. *Energies* **2021**, *14*, 8035.
https://doi.org/10.3390/en14238035

**AMA Style**

Dehghani M, Taghipour M, Sadeghi Gougheri S, Nikoofard A, Gharehpetian GB, Khosravy M. A Deep Learning-Based Approach for Generation Expansion Planning Considering Power Plants Lifetime. *Energies*. 2021; 14(23):8035.
https://doi.org/10.3390/en14238035

**Chicago/Turabian Style**

Dehghani, Majid, Mohammad Taghipour, Saleh Sadeghi Gougheri, Amirhossein Nikoofard, Gevork B. Gharehpetian, and Mahdi Khosravy. 2021. "A Deep Learning-Based Approach for Generation Expansion Planning Considering Power Plants Lifetime" *Energies* 14, no. 23: 8035.
https://doi.org/10.3390/en14238035