Abstract This paper presents a new unbalanced three-phase governor power flow formulation using the three-phase current injection equations (TCIM) expressed as a function of voltages expressed in rectangular coordinates. The proposed technique considers the representation of the primary frequency regulation for synchronous generators, as well as, voltage and frequency regulation in a droop-based control for distributed generation units (DGs). The static response of the generation governor, droop control equations and an equation to define the network reference angle for a given value are incorporated into the modeling. As the system is unbalanced, an internal additional bus, having balanced voltages, was created for each synchronous generator. As a consequence, two additional equations were included to keep internal voltages balanced. The inclusion of new equations results in an augmented formulation which is then linearized and solved using the Newton–Raphson method, in which the original structure of the Jacobian matrix from the current injections method is preserved. The proposed formulation allows the distribution of the active losses among the generating units as well as the determination of the frequency deviation due to variations, either in the total amount of generation or in the total system load. Any bus (load or generation bus) of the system can be chosen as the system reference bus. The results obtained using the unbalanced three-phase 6-bus test system were validated using the well known RTDS (real time digital simulator). The 25-bus islanded test system was also used in the simulations with the inclusion of synchronous generation (SG) units to demonstrate the effectiveness of the proposed methodology.

中文翻译：

---

一种新的基于电流注入法的不平衡三相调速器潮流公式

摘要 本文使用三相电流注入方程 (TCIM) 提出了一种新的不平衡三相调速器潮流公式，该方程表示为以直角坐标表示的电压的函数。所提出的技术考虑了同步发电机的初级频率调节的表示，以及分布式发电机组 (DG) 的基于下垂的控制中的电压和频率调节。发电调速器的静态响应、下垂控制方程和用于定义给定值的网络参考角的方程都包含在建模中。由于系统不平衡，因此为每个同步发电机创建了一个具有平衡电压的内部附加总线。因此，包括两个额外的方程来保持内部电压平衡。包含新方程会产生一个增强公式，然后使用 Newton-Raphson 方法对其进行线性化和求解，其中保留了当前注入方法中雅可比矩阵的原始结构。建议的公式允许在发电机组之间分配有功损耗，以及确定由于变化引起的频率偏差，无论是在发电总量还是在总系统负载中。可以选择系统的任何总线（负载或发电总线）作为系统参考总线。使用不平衡三相 6 母线测试系统获得的结果使用众所周知的 RTDS（实时数字模拟器）进行验证。