Multi-train modeling and simulation integrated with traction power supply solver using simplified Newton–Raphson method

Abstract

Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be determined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss-Seidel, conventional Newton-Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton-Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton-Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system (BTS) of Thailand with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton-Raphson method and just over 6 % faster than the current injection method.

Ước lượng năng lượng thu hồi tại các trạm điện kéo dựa trên mô hình mạng công suất

“…Rabih A. Jabr [8] [9], Hammad Alnuman và các cộng sự [10] bổ sung thêm tính năng ước lượng giá trị điện trở trên lưới tiếp xúc và đường ray tương ứng với vị trí tương quan giữa các đoàn tàu ở từng thời điểm di chuyển; đồng thời thay thế mô hình nguồn dòng bằng mô hình nguồn áp cho các TĐK. Trong mô hình này, năng lượng tái sinh có khả năng thu hồi được mô phỏng và xác định trên điện trở hãm mắc song song với các nguồn dòng điện, các nguồn dòng điện này chính là các đoàn tàu.…”

Development of an Electrical Model for Multiple Trains Running on a DC 4th Rail Track

“…To study the size of ESS, where to locate it and how it is controlled requires a sophisticated voltage model capable of supporting multiple train simulations [5]. T. Kulworawanichpong [6] solved the power flow of a multi-train model by using a simplified Newton-Raphson method. B. Mohamed, P. Arboleya and C. Gonzalez-Moran [7] have provided a method called a Modified Current Injection to solve the electric railway power flow, whether the substations were reversible or non-reversible.…”

“…cb train E I V dt (6) where cb I is the current passing through the braking resistor of the train, and train V is the voltage seen by the train.…”

Optimal energy saving in DC railway system with on-board energy storage system by using peak demand cutting strategy

“…A train model is presented by a controlled current model, I tr ¼ P tr =V tr . In this paper, the current injection method (CIM) [1] has been applied in the power flow calculation. The updated parameters are obtained by setting up the nodal equations as in Eq.…”

“…Many countries in Asia such as Thailand, Singapore and India have plans to expand the existing routes in their mass transit systems to cover all urban areas [1]. Energy efficiency and management are undoubtedly the big challenges in the railway systems [2].…”