**Multi-Objective Optimal Reactive Power Planning under Load Demand and Wind Power Generation Uncertainties Using** ε**-Constraint Method**

### **Amir Hossein Shojaei 1, Ali Asghar Ghadimi 2, Mohammad Reza Miveh 3, Fazel Mohammadi 4,\* and Francisco Jurado 5**


Received: 14 March 2020; Accepted: 16 April 2020; Published: 20 April 2020

**Abstract:** This paper presents an improved multi-objective probabilistic Reactive Power Planning (RPP) in power systems considering uncertainties of load demand and wind power generation. The proposed method is capable of simultaneously (1) reducing the reactive power investment cost, (2) minimizing the total active power losses, (3) improving the voltage stability, and (4) enhancing the loadability factor. The generators' voltage magnitude, the transformer's tap settings, and the output reactive power of VAR sources are taken into account as the control variables. To solve the probabilistic multi-objective RPP problem, the ε-constraint method is used. To test the e ffectiveness of the proposed approach, the IEEE 30-bus test system is implemented in the GAMS environment under five di fferent conditions. Finally, for a better comprehension of the obtained results, a brief comparison of outcomes is presented.

**Keywords:** ε-Constraint method; multi-objective optimization; reactive power planning (RPP); uncertainty; wind farms
