# Renewable Generation and Transmission Expansion Planning Coordination with Energy Storage System: A Flexibility Point of View

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation and Approach

#### 1.2. Literature Review

#### 1.3. Contributions

- None of the previous studies on CNEP consider the flexibility index of power systems. However, it is important in a power system in the presence of RESs to modify the generation injection and/or consumption patterns that are not suitable from a power balancing viewpoint due to the uncertainties of RESs. This index can be improved in the power system using the optimal planning of energy storage systems such as batteries.
- Many research works reviewed above take into account DC power flow constraints in their CNEP models. This simplification results in the elimination of reactive power studies in an expansion planning problem. It should be noted that the capacity of lines and power sources also depends on the reactive power as well as the active power, and without considering the reactive power, the CNEP solution may lead to impractical results.
- Some works use evolutionary methods to solve the CNEP problem. These methods search for different directions of the solution space, and their progress is usually slow. Therefore, the computation time of evolutionary methods is high. In addition, their convergence to the global optimum for the CNEP problem cannot be guaranteed.

- Modeling the coordinated network expansion planning in the power system according to a hybrid method of optimal planning of renewable and flexible sources and TEP to improve the operation and the flexibility indices.
- Obtaining the linear model of the proposed strategy, considering the least calculation error concerning the original method using linearized AC optimal power flow equations.
- Using scenario-based stochastic programming based on a hybrid approach with the roulette wheel mechanism and Kantorovich method to model the uncertainty of the load, the energy price, and the RES power.

#### 1.4. Paper Organization

## 2. Problem Formulation

#### 2.1. Stochastic CNEP Problem

^{max}) is the function of wind speed/solar radiation for a wind/solar farm. Additionally, in constraint (10), if the RES i is constructed, ${x}_{i}^{R}$ = 1; otherwise, ${x}_{i}^{R}$ = 0.

#### 2.2. The Linear CNEP Model

- The difference in the voltage phases of the two ends of a transmission line is under 6 degrees or 0.105 radians.
- Since the magnitude of bus voltages in the transmission network should be between 0.95 and 1.05 per unit, the magnitude of bus voltages is very close to 1 per unit.

^{2}, $\mathsf{\Delta}V\times ({\theta}_{i,t,y,\omega}-{\theta}_{j,t,y,\omega})$ and $\mathsf{\Delta}{V}_{i}\times \mathsf{\Delta}{V}_{j}$ are small enough to ignore, which is the case in this paper. Hence, Equations (4) and (5) are rewritten as below.

^{6}. Also, the linearization procedure of Equation (23) is described in the next section.

_{k}denotes the number of linearized parts. For example, if 180 square planes are used for the linearization of a circular plane, n

_{k}and Δα will be equal to 180 and 2, respectively. Consequently, the planes x ≤ r and y ≤ r correspond to k = 0 and k = 45. Therefore, the linear approximation of (23) and (8) is as follows.

#### 2.3. Uncertainties Model

^{max}) are considered to be the sources of uncertainty. In this paper, the roulette wheel mechanism (RWM) [27] for the generation of scenario samples is used for this case. It is noted that the RWM generates scenarios for load and price forecasting errors based on the normal distribution function [39], for the maximum RES active power based on Weibull distribution functions [27]. The Kantorovich method [27] is selected in this paper to reduce the number of scenarios, where the proposed scenario generation/reduction algorithm details are presented in [27].

## 3. Numerical Results and Discussion

#### 3.1. IEEE 6-Bus Test System

- Modeling of the TEP problem based on DC power flow equations (DCTEP) as an MILP problem.
- Modeling of the TEP problem based on nonlinear AC power flow equations (NACTEP) as an MINLP problem.
- Modeling of the TEP problem based on the linear approximation of AC power flow equations (LACTEP) as an MILP problem.

- Case I: The stochastic TEP method based on the linear AC power flow.
- Case II: The stochastic linear AC power flow-based CNEP (LAC-CNEP) method, considering renewable sources and the planning of transmission lines.
- Case III: The proposed stochastic LAC-CNEP method that is formulated in (29)–(31).

- Reduce the operation cost: The operation cost in case II is 3,045,670 $, a reduction of 9.57% with respect to the TEP model. This term is 13.13% for the coordinated renewable sources and transmission expansion planning method.
- Reduce the investment cost: In the proposed CNEP method (case III), there is one constructed line that is between busses 2 and 6, while the TEP model includes two constructed lines.
- Improve the voltage profile: In case III, the maximum voltage drop is 0.053 p.u., while it is 0.065 and 0.059 p.u. in cases I and II, respectively. Therefore, the CNEP strategy can improve the voltage profile by about 18.46%.
- Obtain high flexibility: Based on Table 7, the CNEP method includes system flexibility of 10.93 as well as 0.2186 million $ flexibility benefit, where it is high concerning cases I and II.

#### 3.2. IEEE 24-Bus Network

^{5}$, and it is constant to 2.5 × 10

^{5}if FC changes between 10

^{5}and 10

^{6}$. Also, the expected operation cost will be increased if FC increases between 0 and 10

^{5}$, and it is constant to 60 M$ if FC changes between 10

^{5}and 10

^{6}$. It is noted that the increase in FC causes the number of flexible sources or ESSs to be increased in the power system to obtain the high flexibility benefit; hence, the operation cost will be increased because a high number of ESSs is used in the power system in this condition. As a result, the CNEP can provide a transmission network with a lot of flexibility by setting a high flexibility incentive price. A suitable cost of operation value is also required. Finally, Table 9 presents the values of maximum voltage drop, system flexibility, and problem convergence. Accordingly, the maximum voltage drop from 1.05 p.u. is 0.064 p.u., which is less than the allowed value, i.e., 0.1 (1.05–0.95) p.u. Also, system flexibility is 19.4. In the end, these capabilities are calculated in 21 s, where the solution situation is optimal. Thus, the proposed method can obtain a reliable optimal solution in a low calculation time.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

ch, dch | Binary variable of charging and discharging state inflexible source (without unit) |

E | Stored energy in the flexible source |

F^{+}, F^{−} | Upward and downward flexibility active power |

PF^{ch}, PF^{dch} | Charging and discharging active power of flexible source |

PG, QG | Active and reactive power of generation unit |

PL, QL | Active and reactive power flow of line |

PR | Active power of RES |

SF | System flexibility (without unit) |

V, ΔV, θ | Magnitude, deviation, and angle (in radian) of voltage |

x, x^{R}, x^{F} | The binary variable of line, RES, and flexible source construction (without unit) |

A | Bus incidence matrix (if a line existed between buses i and j, A_{b,j} is equal to 1, or otherwise zero) |

C | Energy or operation price in $/MWh |

CF | Coincidence factor |

E^{ini} | Initial energy of flexible source in p.u. |

E^{min}, E^{max} | Minimum and maximum energy of flexible source in p.u. |

FC | Flexibility price ($) |

g, b | Conductance and susceptance of a line in p.u. |

IC^{L}, IC^{R}, IC^{F} | Investment cost of line, RES, and flexible source in $ |

PD, QD | Active and reactive load in p.u. |

PF^{max} | Maximum charge/discharge rate in p.u. |

PR^{max} | Maximum RES active power in p.u. |

V^{min}, V^{max} | Minimum and maximum value of voltage magnitude in p.u. |

SL^{max} | Maximum capacity of line in p.u. |

SG^{max} | Maximum capacity of generation unit in p.u. |

ρ | Probability of scenario |

λ | Energy price ($/MWh) |

η^{ch}, η^{dch} | Charging and discharging efficiency of flexible source |

(i, j), t, y, ω, k | Indices of bus, time, year, scenario, linearization segments of circular constraint |

ϕ_{i}, ϕ_{t}, ϕ_{y}, ϕ_{ω,} ϕ_{k} | Sets of bus, time, year, scenario, linearization segments of circular constraint |

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**Figure 3.**Structure of 6-bus network [47].

**Figure 5.**Structure of 6-bus network that resulted from applying the proposed problem in the last year by using (

**a**) NACTEP, (

**b**) LACTEP, and (

**c**) DCTEP.

**Figure 6.**Structure of 6-bus network that resulted from applying the proposed problem in the last year.

**Table 1.**Load characteristics of 6-bus network [47].

Bus | Active Load (MW) | Reactive Load (MVAr) |
---|---|---|

1 | 80 | 16 |

2 | 240 | 48 |

3 | 40 | 8 |

4 | 130 | 32 |

5 | 240 | 48 |

**Table 2.**Line characteristics of 6-bus network [47].

Line | From-To Bus | Resistance (pu) | Reactance (pu) | Construction Cost (M$) | Capacity (MVA) |
---|---|---|---|---|---|

1 | 1–2 | 0.04 | 0.4 | 0 | 100 |

2 | 1–3 | 0.038 | 0.38 | 38 | 100 |

3 | 1–4 | 0.06 | 0.6 | 0 | 80 |

4 | 1–5 | 0.02 | 0.2 | 0 | 100 |

5 | 2–3 | 0.01 | 0.1 | 0 | 200 |

6 | 2–4 | 0.04 | 0.4 | 0 | 100 |

7 | 2–6 | 0.01 | 0.1 | 60 | 300 |

8 | 3–5 | 0.01 | 0.1 | 0 | 300 |

9 | 3–6 | 0.048 | 0.48 | 48 | 100 |

10 | 4–6 | 0.01 | 0.1 | 90 | 300 |

**Table 3.**Generator characteristics of 6-bus network [47].

Bus | SG^{max} (MVA) | Operation Price ($/MWh) |
---|---|---|

1 | 173 | 10 |

3 | 390 | 8 |

6 | 642 | 12 |

Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Load percent | 0.8 | 0.85 | 0.9 | 0.95 | 1 |

Parameter | DCTEP | NACTEP | LACTEP |
---|---|---|---|

Operation cost ($) | 3,062,000 | 3,224,000 | 3,062,000 |

Investment cost (M$) | 90 | 90 | 90 |

Total cost (M$) | 93.062 | 93.224 | 93.062 |

Constructed lines | 4–6 | 4–6 | 4–6 |

Daily active power Loss (MWh) | 0 | 3.23 | 0 |

Daily Reactive power Loss (MVARh) | 0 | 5.83 | 0 |

Computation time (s) | 4 | 432 | 4 |

Solution situation | Optimal | Local optimal | Optimal |

Parameter | LACPF |
---|---|

Expected operation cost ($) | 3,368,200 |

Investment cost (M$) | 150 |

Total cost (M$) | 153.3682 |

Constructed lines | 2–6, 4–6 |

Computation time (s) | 5 |

Solution situation | Optimal |

Parameter | Case I | Case II | Case III |
---|---|---|---|

Total expected operation cost ($) | 3,368,200 | 2,926,000 | 3,045,670 |

Investment cost (M$) | 150 | 60 | 60 |

Flexibility benefit (M$) | - | 0 | 0.2186 |

Constructed lines | 2–6, 4–6 | 2–6 | 2–6 |

Maximum voltage drop from 1.05 per unit (p.u.) | 0.065 | 0.059 | 0.053 |

System flexibility | - | 0 | 10.93 |

Line | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Initial-Final bus | 15–21 | 15–24 | 16–17 | 16–19 | 17–18 |

Construction cost (M$) | 100 | 100 | 100 | 90 | 90 |

Line | 6 | 7 | 8 | 9 | 10 |

Initial-Final bus | 17–22 | 18–21 | 19–20 | 20–23 | 21–22 |

Construction cost (M$) | 100 | 100 | 110 | 100 | 90 |

Parameter | Value |
---|---|

Maximum voltage drop from 1.05 per unit (p.u.) | 0.064 |

System flexibility | 19.4 |

Calculation time (s) | 21 |

Solution situation | Optimal |

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**MDPI and ACS Style**

Ansari, M.R.; Pirouzi, S.; Kazemi, M.; Naderipour, A.; Benbouzid, M. Renewable Generation and Transmission Expansion Planning Coordination with Energy Storage System: A Flexibility Point of View. *Appl. Sci.* **2021**, *11*, 3303.
https://doi.org/10.3390/app11083303

**AMA Style**

Ansari MR, Pirouzi S, Kazemi M, Naderipour A, Benbouzid M. Renewable Generation and Transmission Expansion Planning Coordination with Energy Storage System: A Flexibility Point of View. *Applied Sciences*. 2021; 11(8):3303.
https://doi.org/10.3390/app11083303

**Chicago/Turabian Style**

Ansari, Mohammad Reza, Sasan Pirouzi, Mostafa Kazemi, Amirreza Naderipour, and Mohamed Benbouzid. 2021. "Renewable Generation and Transmission Expansion Planning Coordination with Energy Storage System: A Flexibility Point of View" *Applied Sciences* 11, no. 8: 3303.
https://doi.org/10.3390/app11083303