# Minimum Frequency and Voltage Stability Constrained Unit Commitment for AC/DC Transmission Systems
## 1 Introduction  
The high-voltage direct current (HVDC) system can not only transmit high-capacity power in long-distance, but also regulate power flexibly based on multiple control modes [1; 2]. At the present time, the line-commutated converter (LCC) and voltage source converter (VSC) [3] are two main technologies for HVDC transmission. However, in China, LCC-HVDC has dominated the scene of high-capacity power transportation and plays an important role in transmitting renewable power from the power supply region to heavy load centers. As more LCC-HVDC projects were put into operation, how to operate them to guarantee stability and improve economy of the power grid became a problem which need to be solved urgently. In recent years, some effort has been spent by power engineers and researchers to investigate the optimum operation scheme of the alternating current /direct current (AC/DC) hybrid power system, such as researching the transmission power limits with temperature [4; 5; 6]. The simplest approach is to treat HVDC transmissions as constant power injections or withdrawals. Then the existing mature models and algorithms of unit commitment (UC), economic dispatch (ED), and optimal power flow(OPF) can still be suitable for the AC/DC hybrid grid. However, such simplified technology ignores HVDC's operational characteristic and the interaction between the AC and DC system. Another method is establishing the detail model of the HVDC during operation optimization. For example, authors in [7] introduced comprehensive representation of HVDC transmission in operation optimization of the AC/DC hybrid system while increasing the complexity of the model. To solve such problem efficiently, linear power flow equations were used to model the AC and DC transmission grids so as to decrease the complexity of the whole model in [8]. Another method is utilizing Benders decomposition (BD) algorithm to decompose the large scale model into a master problem and several sub-problems. Then the economic dispatch problem can be solved by efficient iterative algorithms [9]. Similarly, authors in [10; 11; 12] obtained a solution for the security-constrained unit commitment (SCUC) problem more effectively with BD. In addition, the annealing algorithm, which is used as the solver of the planning model containing bundled wind-thermal generation and the HVDC, belongs to the field of artificial intelligence optimization algorithms [13]. Despite the hybrid AC/DC power system, operation could be improved partly by the above achievement, it is worth pointing out that there are still some significant challenges in the receiving-end of hybrid grids to overwhelm:  
1. Low frequency risk. HVDC blocked accident is one of the most serious faults in the operation. It can always be triggered by continuous commutation failures or DC lines failures. With such wind power as random source penetrating into the power grid, the HVDC blocked risk will increase [14]. After HVDC transmissions are fed into the power grid, the system operator should prepare much more spinning reserve for dealing with its blocked fault because of HVDC's larger capacity than thermal plants. Meanwhile, renewable power transferred by the HVDC is preferred to traditional fossil fuel, resulting in less online thermal plants, which are currently the main reserve power providers. On account of increasing reserve demand and decreasing reserve suppliers, low frequency fault might happen after the HVDC is blocked. For example, Jinsu's HVDC bipolar block on 19 September 2015 lead to grid frequency in eastern China, reducing to 49.557 Hz, violating the minimum frequency requirement. 2. Voltage stability problem [15]. For the purpose of consuming power easier in the receiving-end grid, HVDC systems are always fed into the metropolitan area with heavy load and fewer power plants. Such feature lead to lower voltage and weak voltage support ability. In addition, based on switching the devices' characteristic, LCC-HVDC need lots of reactive power while transmitting active power massively.