Quasi-dynamic Load and Battery Sizing and Scheduling for Stand-Alone Solar System Using Mixed-integer Linear Programming

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.Comment: 6 pages, 3 figures, accepted at The IEEE Conference on Control Applications (CCA

Reliability of Dynamic Load Scheduling with Solar Forecast Scenarios

This paper presents and evaluates the performance of an optimal scheduling algorithm that selects the on/off combinations and timing of a finite set of dynamic electric loads on the basis of short term predictions of the power delivery from a photovoltaic source. In the algorithm for optimal scheduling, each load is modeled with a dynamic power profile that may be different for on and off switching. Optimal scheduling is achieved by the evaluation of a user-specified criterion function with possible power constraints. The scheduling algorithm exploits the use of a moving finite time horizon and the resulting finite number of scheduling combinations to achieve real-time computation of the optimal timing and switching of loads. The moving time horizon in the proposed optimal scheduling algorithm provides an opportunity to use short term (time moving) predictions of solar power based on advection of clouds detected in sky images. Advection, persistence, and perfect forecast scenarios are used as input to the load scheduling algorithm to elucidate the effect of forecast errors on mis-scheduling. The advection forecast creates less events where the load demand is greater than the available solar energy, as compared to persistence. Increasing the decision horizon leads to increasing error and decreased efficiency of the system, measured as the amount of power consumed by the aggregate loads normalized by total solar power. For a standalone system with a real forecast, energy reserves are necessary to provide the excess energy required by mis-scheduled loads. A method for battery sizing is proposed for future work.Comment: 6 pager, 4 figures, Syscon 201

Coordination of OLTC and Smart Inverters for Optimal Voltage Regulation of Unbalanced Distribution Networks

Photovoltaic (PV) smart inverters can improve the voltage profile of distribution networks. A multi-objective optimization framework for coordination of reactive power injection of smart inverters and tap operations of on-load tap changers (OLTCs) for multi-phase unbalanced distribution systems is proposed. The optimization objective is to minimize voltage deviations and the number of tap operations simultaneously. A novel linearization method is proposed to linearize power flow equations and to convexify the problem, which guarantees convergence of the optimization and less computation costs. The optimization is modeled and solved using mixed-integer linear programming (MILP). The proposed method is validated against conventional rule-based autonomous voltage regulation (AVR) on the highly-unbalanced modified IEEE 37 bus test system and a large California utility feeder. Simulation results show that the proposed method accurately estimates feeder voltage, significantly reduces voltage deviations, mitigates over-voltage problems, and reduces voltage unbalance while eliminating unnecessary tap operations. The robustness of the method is validated against various levels of forecast error. The computational efficiency and scalability of the proposed approach are also demonstrated through the simulations on the large utility feeder.Comment: Accepted for Electric Power Systems Research. arXiv admin note: text overlap with arXiv:1901.0950