# 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

- Liu, D.; Li, Z.; Xu, H. HVDC Commutation Failures Detection for Security and Stability Control Based on Local Electrical Quantities. In Proceedings of the PURPLE MOUNTAIN FORUM 2019-International Forum on Smart Grid Protection and Control; Lecture Notes in Electrical Engineering. Springer: Singapore, 2020; pp. 247–255. [Google Scholar] [CrossRef]
- Elgamasy, M.M.; Taalab, A.-M.I.; Kawady, T.A.; Izzularab, M.A.; Elkalashy, N.I. Wave propagation differential protection scheme for VSC-HVDC transmission systems. Electr. Power Syst. Res.
**2020**, 189, 106826. [Google Scholar] [CrossRef] - Linke, F.; Alhomsi, H.; Westermann, D. Investigation of the critical fault clearing time in HVDC-systems on the angle stability of generators in the AC system using protection zones. In Proceedings of the NEIS 2020 Conference on Sustainable Energy Supply and Energy Storage Systems, Hamburg, Germany, 14–15 September 2020. [Google Scholar]
- Yan, Y.; Sun, N.; Zhang, N.; Zhao, H.; Li, S. Hierarchical Reliability Evaluation to Security and Stability Control System of Power Systems. In Proceedings of the 2020 5th Asia Conference on Power and Electrical Engineering (ACPEE), Chengdu, China, 4–7 June 2020. [Google Scholar]
- Sennewald, T.; Linke, F.; Westermann, D. Preventive and Curative Actions by Meshed Bipolar HVDC-Overlay-Systems. IEEE Trans. Power Deliv.
**2020**, 35, 2928–2936. [Google Scholar] [CrossRef] - Chen, B.; Yim, S.-I.; Kim, H.; Kondabathini, A.; Nuqui, R. Cybersecurity of Wide Area Monitoring, Protection and Control Systems for HVDC Applications. IEEE Trans. Power Syst.
**2020**, 36, 592–602. [Google Scholar] [CrossRef] - Wu, X.; Xiao, L.; Yang, J.; Xu, Z. Design method for strengthening high-proportion renewable energy regional power grid using VSC-HVDC technology. Electr. Power Syst. Res.
**2019**, 180, 106160. [Google Scholar] [CrossRef] - Jiang, T.; Zhang, R.; Li, X.; Chen, H.; Li, G. Integrated energy system security region: Concepts, methods, and implementations. Appl. Energy
**2020**, 283, 116124. [Google Scholar] [CrossRef] - Wu, C.; Zhang, D.; He, J. A Novel Protection Scheme for MMC-HVDC Transmission Lines Based on Cross-Entropy of Charge. IEEE Access
**2020**, 8, 222800–222812. [Google Scholar] [CrossRef] - Zhu, Z.; Yan, J.; Lu, C.; Chen, Z.; Tian, J. Two-Stage Coordinated Control Strategy of AC/DC Hybrid Power System Based on Steady-State Security Region. IEEE Access
**2020**, 8, 139221–139243. [Google Scholar] [CrossRef] - Abbasipour, M.; Milimonfared, J.; Yazdi, S.S.H.; Rouzbehi, K. Power injection model of IDC-PFC for NR-based and technical constrained MT-HVDC grids power flow studies. Electr. Power Syst. Res.
**2020**, 182, 106236. [Google Scholar] [CrossRef] - Cheng, J.; Dou, F.; Wang, W.; Le, X.; Zhen, H. Regional Generator Excitation Control Strategy for HVDC Commutation Failure Suppression. In Proceedings of the 2020 12th IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), Nanjing, China, 20–23 September 2020. [Google Scholar]
- Wang, J.; Xu, Q.; Dai, P.; Xin, H. A Recovery Method for HVDC Systems Following AC System Faults. In Proceedings of the 2020 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), Weihai, China, 13–15 July 2020. [Google Scholar]
- Glende, E.; Wolter, M. Tracing HVDC Flows using the proportional sharing principle. In Proceedings of the 2020 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe), The Hague, The Netherlands, 26–28 October 2020. [Google Scholar]
- Musca, R.; Bizumic, L. Primary Frequency Control in the Power System of Continental Europe including the Dynamics of the HVDC Link France-Great Britain. In Proceedings of the 2020 AEIT International Annual Conference (AEIT), Catania, Italy, 23–25 September 2020. [Google Scholar]
- Tao, Q.; Xue, Y. Quantitative Assessment for Commutation Security Based on Extinction Angle Trajectory. J. Mod. Power Syst. Clean Energy
**2021**, 9, 328–337. [Google Scholar] [CrossRef] - Sun, K.; Xiao, H.; Pan, J.; Liu, Y. A Station-Hybrid HVDC System Structure and Control Strategies for Cross-Seam Power Transmission. IEEE Trans. Power Syst.
**2020**, 36, 379–388. [Google Scholar] [CrossRef] - Zhang, N.; Wu, S.; An, H.; Zhu, X. Security-Constraint Unit Commitment for AC/DC Transmission Systems with Voltage Stability Constraint. J. Electr. Eng. Technol.
**2020**, 15, 2459–2469. [Google Scholar] [CrossRef] - Carlini, E.M.; Vergine, C.; Gadaleta, C.; Aluisio, B.; Migliori, M.; Dicorato, M.; Trovato, M.A.; Forte, G. Static and dynamic evaluation of different architectures for an actual HVDC link project. IEEE Trans. Power Deliv.
**2020**, 35, 2782–2790. [Google Scholar] [CrossRef] - Zhou, B.; Fang, J.; Ai, X.; Yang, C.; Yao, W.; Wen, J. Dynamic Var Reserve-Constrained Coordinated Scheduling of LCC-HVDC Receiving-End System Considering Contingencies and Wind Uncertainties. IEEE Trans. Sustain. Energy
**2020**, 12, 469–481. [Google Scholar] [CrossRef] - Akhand, M.; Ayon, S.I.; Shahriyar, S.; Siddique, N.; Adeli, H. Discrete Spider Monkey Optimization for Travelling Salesman Problem. Appl. Soft Comput.
**2019**, 86, 105887. [Google Scholar] [CrossRef] - Li, D.; Sun, M.; Fu, Y. A General Steady-State Voltage Stability Analysis for Hybrid Multi-Infeed HVDC Systems. IEEE Trans. Power Deliv.
**2020**, 36, 1302–1312. [Google Scholar] [CrossRef] - Sun, K.; Xiao, H.; Liu, S.; Liu, Y. A machine learning-based fast frequency response control for a VSC-HVDC system. CSEE J. Power Energy Syst.
**2020**, 7, 688–697. [Google Scholar] - Abdul Baseer, M.; Almunif, A.; Alsaduni, I.; Zubair, M.; Tazeen, N. An adaptive power point tracker in wind photovoltaic system using an optimized deep learning framework. Energy Sources Part A Recovery Util. Environ. Eff.
**2022**, 44, 4846–4861. [Google Scholar] [CrossRef] - Zubair, M.; Awan, A.B.; Baseer, M.A.; Khan, M.N.; Abbas, G. Optimization of parabolic trough based concentrated solar power plant for energy export from Saudi Arabia. Energy Rep.
**2021**, 7, 4540–4554. [Google Scholar] [CrossRef] - Baseer, M.A.; Alsaduni, I.; Zubair, M. A Novel Multi-Objective Based Reliability Assessment in Saudi Arabian Power System Arrangement. IEEE Access
**2021**, 9, 97822–97833. [Google Scholar] [CrossRef] - Abdul Baseer, M.; Alsaduni, I.; Zubair, M. Novel hybrid optimization maximum power point tracking and normalized intelligent control techniques for smart grid linked solar photovoltaic system. Energy Technol.
**2021**, 9, 2000980. [Google Scholar] [CrossRef] - Baseer, M.; Praveen, P.R.; Zubair, M.; Khalil, A.G.A.; Al Saduni, I. Performance and Optimization of Commercial Solar PV and PTC Plants. Int. J. Recent Technol. Eng.
**2020**, 8, 1703–1714. [Google Scholar] [CrossRef] - Praveen, P.R.; Awan, A.B.; Zubair, M.; Baseer, M.A. Performance Analysis and Optimization of a Parabolic Trough Solar Power Plant in the Middle East Region. Energies
**2018**, 11, 741. [Google Scholar] [CrossRef][Green Version] - Jeeninga, M.; De Persis, C.; Van der Schaft, A. DC power grids with constant-power loadsPart I: A full characterization of power flow feasibility, long-term voltage stability and their correspondence. IEEE Trans. Autom. Control
**2022**, 68, 2–17. [Google Scholar] [CrossRef] - Wang, X.; Wu, H.; Wang, X.; Dall, L.; Kwon, J.B. Transient Stability Analysis of Grid-Following VSCs Considering Voltage-Dependent Current Injection during Fault Ride-through. IEEE Trans. Energy Convers.
**2022**, 37, 2749–2760. [Google Scholar] [CrossRef] - Meraihi, Y.; Gabis, A.B.; Ramdane-Cherif, A.; Acheli, D. Advances in Coyote Optimization Algorithm: Variants and Applications. In Advances in Computational Intelligence and Communication; Springer: Cham, Switzerland, 2023; pp. 99–113. [Google Scholar]
- Csurcsia, P.Z.; Decuyper, J.; Renczes, B.; De Troyer, T. Nonlinear Modelling of an F16 Benchmark Measurement. In Nonlinear Structures & Systems; Springer: Cham, Switzerland, 2023; Volume 1, pp. 49–60. [Google Scholar]
- Gao, J.; Chen, S.; Li, X.; Zhang, J. Transient Voltage Control Based on Physics-Informed Reinforcement Learning. IEEE J. Radio Freq. Identif.
**2022**, 6, 905–910. [Google Scholar] [CrossRef] - Mohamed, M.A.E.; Mohamed, S.M.R.; Saied, E.M.M.; Elsisi, M.; Su, C.-L.; Hadi, H.A. Optimal Energy Management Solutions Using Artificial Intelligence Techniques for Photovoltaic Empowered Water Desalination Plants under Cost Function Uncertainties. IEEE Access
**2022**, 10, 93646–93658. [Google Scholar] [CrossRef] - Rahman, M.M.; Saha, S.; Majumder, M.Z.H.; Suki, T.T.; Akter, F.; Haque, M.A.S.; Hossain, M.K. Energy Conservation of Smart Grid System Using Voltage Reduction Technique and Its Challenges. Evergreen
**2022**, 9, 924–938. [Google Scholar] [CrossRef] - Mozaffari, H.; Houmansadr, A. E2FL: Equal and Equitable Federated Learning. arXiv
**2022**, arXiv:2205.10454. [Google Scholar] - Roshani, G.H.; Hanus, R.; Khazaei, A.; Zych, M.; Nazemi, E.; Mosorov, V. Density and velocity determination for single-phase flow based on radiotracer technique and neural networks. Flow Meas. Instrum.
**2018**, 61, 9–14. [Google Scholar] [CrossRef] - Mozaffari, H.; Houmansadr, A. Heterogeneous private information retrieval. In Proceedings of the Network and Distributed Systems Security (NDSS) Symposium, San Diego, CA, USA, 23–26 February 2020. [Google Scholar]
- Alqudah, A.; Mohaidat, M.; Altawil, I. Control of variable speed drive (VSD) based on diode clamped multilevel inverter using direct torque control and fuzzy logic. In Proceedings of the 2013 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT), Amman, Jordan, 3–5 December 2013. [Google Scholar]
- Baseer, M.A.; Kumar, V.V.; Izonin, I.; Dronyuk, I.; Velmurugan, A.K.; Swapna, B. Novel Hybrid Optimization Techniques to Enhance Reliability from Reverse Osmosis Desalination Process. Energies
**2023**, 16, 713. [Google Scholar] [CrossRef]

**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