# Decision Optimization for Power Grid Operating Conditions with High- and Low-Voltage Parallel Loops
## 1 Introduction  
The high and low-voltage parallel loop is a kind of power grid structure, in which transmission lines of different voltage levels are looped by transformers at the sending and receiving ends. With the rapid development of higher-voltage power grids, parallel loops [1] have become more and more common. Parallel flow in a parallel loop would make unbalanced power flow in a power system, which leads to higher power losses. In some cases, parallel loop would even threaten the security and stability of a power system [2]. On the one hand, low-voltage transmission lines of parallel loops would bear a quite heavy load after faults on high-voltage transmission lines, which may cause cascading trips of low-voltage transmission lines [3]. On the other hand, parallel operation of high- and low-voltage transmission lines also leads to a high level of short circuit current, which may exceed the interrupting capacity of circuit breakers. Therefore, considering energy saving and system security and stability, some methods must be presented to solve these problems. There are many studies that have tried to apply Flexible AC Transmission System (FACTS) technologies to eliminate parallel flow or control power flow in parallel loops [1; 2; 3; 4]. These studies only improve the operational characteristics of power systems, however, they cannot solve the problemscaused by parallel loops radically from the aspect of power grid structure. Especially for higher-voltage power grids, the use of FACTS is quite limited. Fortunately, it has been proved that switching specific transmission lines could make power flow more balanced [5], reduce power loss [6] and decrease short circuit current [7]. And some studies have been carried out to find the optimal line switching scheme [8; 9]. Accordingly, the parallel loop problem mentioned above can be solved by switching specific low-voltage transmission lines at appropriate location and time. However, it is difficult to describe this problem as an accurate mathematical model [10]. It is actually a complicated mixed-integer programming problem, which is multi-objective, non-linear and discrete. In order to simplify the calculation complexity, the decision process of opening parallel loops is usually divided into two stages: scheme generation and scheme evaluation. The generation of opening schemes used to only depend on engineering experiences. But things are changing gradually. There are studies employing linear programming algorithms to find the optimal line switching scheme with minimum power loss [11; 12]. These studies only consider the branch active power flow constraint, and the bus voltage constraint is neglected. Simulation results in [13] show that the neglect of bus voltage constraint may cause the failure of optimization. A line switching optimization method considering bus voltage constraint is proposed in [14], which could effectively eliminate over-limited power flows. In [15], the Benders decomposition technology is applied to network reconfiguration, which could deal with the constraints of static security and transient stability simultaneously. But this method is barely able to be used in actual large-scale power systems, due to its high complexity. The evaluation of opening schemes should consider static security, transient stability, short circuit current and operation economy of power systems. A comprehensive evaluation method for opening schemes is proposed in [16], which combines AHP (analytic hierarchy process) with fuzzy evaluation algorithms. The AHP is used to establish the hierarchical model to describe the operational characteristics of power systems. In this model, five performance indices and corresponding membership functions are presented. After detailed analysis and calculations for each opening scheme, the optimal one is obtained by two-level fuzzy evaluation. All of the previous studies only discuss parallel loop opening issues in pure AC power grids.