# A Novel Security Framework for the Enhancement of the Voltage Stability in a High-Voltage Direct Current System

## Abstract

**:**

## 1. Introduction

## 2. Literature Survey

#### Recent Literature Related to HVDC Systems Is Detailed Below

- Initially, an IEEE 50-bus system is designed using a MATLAB simulation.
- In addition, a novel Adaptive Neural Spider Monkey Algorithm (ANSMA) is developed to address the voltage stability security issues in HVDC systems.
- The developed ANSMA model is utilized to reduce the generator’s agenda with the organization of margin constraints and voltage stability.
- Analysis of the commutation margin index is conducted to improve the security range in power system transmission.
- Subsequently, the proposed model is applied in an IEEE 50-bus system, and several main metrics are measured.
- Finally, the effectiveness of the proposed model is determined by comparing the key metrics with those of existing models in terms of voltage stability, optimal power flow, security range, and so on.

## 3. System Model and Problem Statement

^{T}

_{gk}and Q

^{T}

_{gk}represent the active and reactive power that are produced at the bus $k,l$ with time period T; P

^{T}

_{hk}and Q

^{T}

_{hk}denote the requirements of active and reactive power; V

_{k}and V

_{l}are the magnitudes of the voltage; g

_{kl}is the susceptance and B

^{C}

_{kl}is the conductance between the buses k and l; n denotes the number of buses; and θ

^{T}

_{kl}is the voltage of the phase angle between the buses k and l with time period T.

^{min}

_{gk}and Q

^{min}

_{gk}denote the minimum boundaries of the real and reactive power in the bus k, and g

_{n}represents the generator bus.

## 4. Proposed ANSMA Methodology

#### ANSMA Model for Voltage Stability

_{k}, load angle L

_{φ}, real power P

_{k}, and reactive power Q

_{k}, are given to the input layer of the network. The data initialization process using the ANSMA model in the input layer is detailed in Equation (9):

_{k min}and V

_{k max}denote the minimum and maximum levels of bus voltage in the k

^{th}bus, and U(0, 1) denotes a random number uniformly distributed in the range (0, 1). The fitness function of the model is expressed in Equation (10), which is utilized as the stability margin of the bus. In addition, the stability margin is defined as the variance between the operating load level and the load ability level. The process of the ANSMA network model is represented in Figure 3.

_{Vk}denotes the voltage stability, and I

_{Vk}denotes the voltage instability condition. Herein, the utilized voltage level in each line is calculated, and that which has levels of less than 1 V is considered as voltage stability. Furthermore, if the voltage level is greater than 1 V, it is considered as voltage instability. Moreover, voltage stability is increased based on the planning, maintenance, and operation of a generation system. Consequently, voltage stability is enhanced using Equation (11):

_{k}denotes the voltage stability margin, δ

_{L}represents the load reduction factor for improving voltage stability, and g

_{M}represents the generation of the maintaining factor.

- Load scheduling

_{L}and CL

_{n}denote the load scheduling and the classification of n number of loads based on the location and duty of the loads. Furthermore, ϕ denotes the angle between the loads, and e

_{kl}denotes the electrical parameters that include power factor, efficiency, and nominal/observed ratings. This load scheduling process is utilized for arranging the generators.

- Enhanced Voltage Stability

- Voltage security margin (VSM)

Algorithm 1: ANSMA for voltage stability | |

Start | |

{ | |

Create the IEEE 50 bus | |

Initialize the input parameters V_{k}, L_{φ}, P_{k}, and Q_{k} //bus voltage, load angle, real power, and reactive power | |

Input parameters are trained to the system | |

Calculate the stability margin | |

If 0 < V ≥ 1.1 then S_{vij} //voltage stability | |

Else | |

Voltage instability | |

End if | |

Voltage stability improvement() | |

For all(k) | |

Consider R_{k} //voltage stability margin | |

Calculate ProbV_{k} | |

End for | |

Load scheduling() | |

For all(k) | |

Consider the variation in loads | |

Identify the location, electrical parameters, and angle of the loads | |

Calculate ${S}_{L}$ using Equation (12) //load scheduling | |

End for | |

Voltage security margin() | |

If high voltage stability | |

Then | |

High security | |

End if | |

Optimal outcomes //(voltage stability, power flow, and high security) | |

} | |

Stop |

## 5. Result and Discussion

#### 5.1. Case Study for IEEE 50-Bus System

_{k}, reactive power Q

_{k}, and bus voltage V

_{k}were considered for the IEEE 50-bus system, and these input variables are initialized using Equation (9). The IEEE 50-bus system involves 10 synchronous generators and 2 HVDC transmissions, which are illustrated in Figure 5. Therein, the utilized generators are denoted as G41 to G50 and two HVDC transmissions. Herein, the HVDC transmission capacities are considered as 1000 MW, and the generator capacity of the system is considered as 4800 MW. Additionally, the stability margin of the proposed model is calculated using Equation (10). In this equation, the voltage level of the generator is considered as 0 < V ≥ 1.1. If the voltage level is lower than 1.1 V, it is considered as stable voltage; otherwise, it is unstable. Thus, the proposed model calculates the voltage level and enhances the voltage stability using Equation (11) while maintaining the loads and generators. In this model, the load scheduling process is carried out using Equation (12) based on the location of loads that are employed to arrange the generators in the IEEE 50-bus system. When the voltage stability is maintained, the security of the system is improved. In this IEEE 50-bus system, the inner HVDC model and the exterior power source are utilized to attain a dynamic load center. The smallest VSM of the local power grid is larger than the normal operation of the power grid because of the technical specifications for system security and voltage stability.

#### 5.2. Discussion

## 6. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**Performance comparison of power flow of the proposed ANSMA model with those of existing methods in IEEE 50-bus system.

Main Objective Functions and Variables | HMIDC [22] | AC/DC Hybrid Grid [18] | MRFR [23] | Proposed (ANSMA) |
---|---|---|---|---|

P_{G41} (MW) | 210.7 | 155.1242 | 145.345 | 130.56 |

P_{G42} (MW) | 100 | 77.6136 | 126.667 | 120.45 |

P_{G43} (MW) | 127.56 | 19.6631 | 107.45 | 56.69 |

P_{G48} (MW) | 27 | 34.7131 | 54.78 | 46.35 |

P_{G50} (MW) | 30 | 30.032 | 34.78 | 27.45 |

Q_{G41} (VAR) (p.u) | 825 | 670 | 850 | 430 |

Q_{G42} (VAR) (p.u) | 355 | 540 | 430 | 150 |

Q_{G43} (VAR) (p.u) | 257 | 375 | 260 | 55 |

Q_{G48} (VAR) (p.u) | 737 | 420 | 175 | 78 |

Q_{G50} (VAR) (p.u) | 250 | 125 | 270 | 32 |

P_{conv} (in p.u) | - | 1.0765 | 1.1 | 1.023 |

Power loss (MW) | 17.56 | 24.5 | 36.67 | 10.67 |

Cost (USD/hr) | 3759 | 456.25 | 765.50 | 207.46 |

Time (s) | 45 | 60 | 55 | 15 |

**Table 2.**Performance comparison of voltage deviation of the proposed ANSMA model with those of existing methods in IEEE 50-bus system.

Main Objective Functions and Variables | HMIDC [22] | AC/DC Hybrid Grid [18] | MRFR [23] | Proposed (ANSMA) |
---|---|---|---|---|

V_{41} (in p.u)
| 1.3 | 1.0835 | 1.0765 | 1.0693 |

V_{42} (in p.u)
| 1.05 | 1.0835 | 1.0765 | 1.0877 |

V_{43} (in p.u)
| 1.01 | 0.9811 | 1.0724 | 1.0263 |

V_{48} (in p.u)
| 1.1 | 1.0724 | 1.0656 | 1.036 |

V_{50} (in p.u)
| 1.03 | 1.0639 | 1.035 | 1.062 |

V_{dc} (in p.u)
| - | 1.0852 | 1.045 | 1.0831 |

Author | Method | Advantages | Disadvantages |
---|---|---|---|

Qi Tao and Yusheng Xue [16] | Margin-based security frame | Enhance the security | Instability range in load variation condition |

Kaiqi sun et al. [17] | Hybrid systems | Improve the flexibility and reliability of power flows | Designing the model takes more time to complete |

Ningyu Zhang et al. [18] | Hybrid grid | Enhance the security of IEEE 39-bus system | This model is complex and takes more time to design |

Enrico M. Carlini et al. [19] | Transmission network in HVDC | Dynamic and steady state performance | Very small stability range |

Bo Zhou et al. [20] | Dynamic reserve model | Reduce the parameter constraints | Very little measured stability |

Proposed | ANSMA | Optimal power flow, high security, and high stability in the IEEE 50-bus system | - |

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**MDPI and ACS Style**

Alsaduni, I.
A Novel Security Framework for the Enhancement of the Voltage Stability in a High-Voltage Direct Current System. *Processes* **2023**, *11*, 1028.
https://doi.org/10.3390/pr11041028

**AMA Style**

Alsaduni I.
A Novel Security Framework for the Enhancement of the Voltage Stability in a High-Voltage Direct Current System. *Processes*. 2023; 11(4):1028.
https://doi.org/10.3390/pr11041028

**Chicago/Turabian Style**

Alsaduni, Ibrahim.
2023. "A Novel Security Framework for the Enhancement of the Voltage Stability in a High-Voltage Direct Current System" *Processes* 11, no. 4: 1028.
https://doi.org/10.3390/pr11041028