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While renewable power generation and vehicle electrification are promising solutions to reduce greenhouse gas emissions, it faces great challenges to effectively integrate them in a power grid. The weather-dependent power generation of renewable energy sources, such as Photovoltaic (PV) arrays, could introduce significant intermittency to a power grid. Meanwhile, uncontrolled PEV charging may cause load surge in a power grid. This paper studies the optimization of PEV charging/discharging scheduling to reduce customer cost and improve grid performance. Optimization algorithms are developed for three cases: 1) minimize cost, 2) minimize power deviation from a pre-defined power profile, and 3) combine objective functions in 1) and 2). A Microgrid with PV arrays, bi-directional PEV charging stations, and a commercial building is used in this study. The bi-directional power from/to PEVs provides the opportunity of using PEVs to reduce the intermittency of PV power generation and the peak load of the Microgrid. Simulation has been performed for all three cases and the simulation results show that the presented optimization algorithms can meet defined objectives.

In recent years, Microgrid is becoming an increasingly popular concept. It has flexibility to react grid supply variation and robustness to overcome grid disturbance due to its self-supporting capability. Usually, key components of a Microgrid include residential or commercial loads and localized Renewable Energy Sources (RESs) such as photovoltaic arrays, wind turbine, energy storage and Plug-in Electric Vehicles (PEVs). Renewable energy sources and green vehicles are critical to deal with the dependence of fossil energy as well as greenhouse gas emissions. According to the global greenhouse gas emission data published by the United States Environmental Protection Agency [

PV generated power depends significantly on weather conditions. For example, cloud could result in irradiance variation and introduce the intermittency of PV generated power. This will lead to power imbalance and frequency/voltage fluctuation in Microgrids. Although, battery packs of PEVs can function as energy swap systems to mitigate the above issue by charging and discharging, the approach of using PEV batteries has limitation and operational constraints. Firstly, PEV batteries have charge/discharge power limits based on the level of charging stations. PEVs might not be able to mitigate power imbalance when the power imbalance amount is greater than the PEV charge/discharge limits. Secondly, from PEV driver perspective, frequently charge and discharge might accelerate battery degradation.

A number of researchers have investigated PEV charging load modeling and optimal control in power grid. Ahourai et al. [

This paper studies the optimization of PEV charging/discharging in Microgrids with PV arrays. The objective functions of the optimization algorithms are defined considering both for PEV driver benefits and Microgrid performance, including minimization of charging cost, minimization of Microgrid power deviation, and combining these two objectives. The simulation for different objective functions is performed with two optimization methods. The rest of the paper is organized as follows. Section 2 describes the modeling of the Microgrid and its components. Section 3 discusses the objective functions for the optimization of PEV charging/discharging control. Section 4 presents the optimization methods and the simulation results. Section 5 concludes the presented work.

the PEV driver. Meters are placed to measure power consumption of each component and breakers are designed to protect Microgrid from over-current. The weather and location information required in Microgrid model is based on Arizona Phoenix during summer time, and a unit power factor is assumed. The Microgridis modeled using Grid Lab-D [

The commercial building load model is a data-based load profile extracted from Commercial and Residential Hourly Load Profiles for all TMY3 Locations in the United States published by EERE [^{2} [

The solar irradiance that PV array receives can be calculated by (1)

where

where

The simulation parameters of PV array model in Grid Lab-D are listed in

Solar parameters | Value |
---|---|

Panel type | Single crystal silicon |

Orientation azimuth angle | 180˚ (facing south) |

Panel tilt angle, | 33.5˚ |

Efficiency, | 0.15 |

Array area | 64.4 m^{2} |

efficiency of single crystal silicon PV arrays typically varies from 13% to 17%. We select the median energy conversion efficiency of 15%. The PV array area is referenced from Canadian Solar CS6P-255P Black Solar Panel. Each PV array consists of 40 CS6P-255P panels. The area of a single CS6P-255P panel is ^{2}).

The variation of PV array output power due to the change of weather condition is considered in this model. The shading factor,

In this Microgrid model, PEV charging stations are modeled as AC level II EVSE units with 6.6 kW maximum charging/discharging rate. The power demand/output of

where

The total PEV charge/discharge power for all EVSE units can be expressed as

where,

where

The objective of this optimization problem is to minimize the overall PEV charging cost in the Microgrid. Consider time period of 24 hours with time steps of

where

The constraints of this optimization problem are defined in (8), (9) and (10).

1) Single PEV charge and discharge rate should not exceed power limit.

where

2) PEV battery SOC should not exceed an acceptable SOC range

where

3) At PEV leaving time, battery should be charged above lowest acceptable SOC, but lower than SOC upper threshold

where

From Microgrid point of view, large deviation between the local load demand and grid supply capability is not acceptable. In some energy plan, electricity supplier will publish day-ahead load forecasting information commonly with TOU as a guild of customer power usage. The published information is not only the prediction of customer power consumption activity, but also as power supply plan in one day ahead. By following the day-ahead load signal, Micro Grid can contribute to main grid load regulation and benefit from TOU price plan.

For this optimization problem, we assume that the power supplier published day-ahead load schedule is as shown in

where

The objective of third optimization problem is to minimize charging cost and Microgrid power deviation simultaneously. The objective function is defined as shownin (12)

where,

The optimization of PEV charging/discharging scheduling is investigated in a Microgrid described in Section 2. It is assumed that EVSE model has following information: PEV arriving time, initial SOC and vehicle leaving time. The simulation is performed with the number of PEVs and their arriving time, leaving time, and initial SOC listed in

This section presents the optimization of PEV charging/discharging scheduling using MILP method. The objective function and constraints for minimizing PEV charge cost are defined in Section 3.1. For the MILP method, the objective function in (7) is modified to

EVSE | PEV sequence | |||
---|---|---|---|---|

PEV | Arriving Time | Leaving Time | Initial SOC | |

EVSE1 | PEV11 | 5:00 am | 9:00 am | 30 |

PEV12 | 9:12 am | 13:06 pm | 40 | |

PEV13 | 13:12 pm | 21:00 pm | 50 | |

EVSE2 | PEV21 | 7:00 am | 11:00 am | 40 |

PEV22 | 11:30 am | 15:00 pm | 50 | |

PEV23 | 15:30 pm | 20:00 pm | 40 | |

EVSE3 | PEV31 | 9:00 am | 11:48 am | 55 |

PEV32 | 12:00 pm | 16:30 pm | 33 | |

PEV33 | 16.42 pm | 22:00 pm | 41 |

SOC constraints | values |
---|---|

Lower SOC threshold, | Vehicle initial SOC |

Upper SOC threshold, | 100% |

Lowest acceptable SOC at leaving time, | 90% |

where

Based on TOU rate in

The objective function to minimize the power deviation of the Microgrid has been defined in (11). Constraints of PEV charge/discharge are defined in (8), (9) and (10). Due to the nonlinear feature of the objective function, this optimization problem is solved using Nonlinear Programming technique. We assume that the TOU rate and available PEVs in Microgrid are the same as MILP method in Case 1. The simulation results obtained by Nonlinear Programming method are shown in Figures 16-25. Comparing with MILP method, the PEV charging/ discharging rate using Nonlinear Programming method can be any value between [−6.6 kW, 6.6 kW] as shown in

strate that the Nonlinear Programming method can also meet the SOC requirement defined in (9) and (10). The accumulated PEV charge price using Nonlinear Programming method are shown in

The objective function for Case 3 optimization approach with combined objectives is defined in (12). To find a proper value for the weightingfactor a, two sweep testsare performed. The first sweep test selects the range of a values from 0.1 to 0.9 with a step size of 0.1. The second sweep test selects the range of a values from 0.01 to 0.09 with a step size of 0.01. The values of PEV charge bill and the Root Mean Square Error (RMSE) of power deviation in (12) are calculated for all the test points. Selected calculation results from the sweep tests are listed in

EVSEs | PEV charge final price | ||
---|---|---|---|

PEV | Case 1: charge cost minimization ($) | Case 2: power deviation minimization ($) | |

EVSE1 | PEV11 | 0.84 | 0.80 |

PEV12 | 0.72 | 1.04 | |

PEV13 | 0.82 | 1.37 | |

EVSE2 | PEV21 | 0.61 | 0.69 |

PEV22 | 0.99 | 1.06 | |

PEV23 | 1.49 | 1.85 | |

EVSE3 | PEV31 | 0.42 | 0.61 |

PEV32 | 1.56 | 1.59 | |

PEV33 | 1.27 | 1.67 | |

Total | 8.72 | 10.68 |

Tradeoff coefficient a | 0.01 | 0.03 | 0.05 | 0.07 | 0.09 | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 |
---|---|---|---|---|---|---|---|---|---|---|

PEV total bill ($) | 8.29 | 8.53 | 9.83 | 10.19 | 10.34 | 10.38 | 10.60 | 10.64 | 10.65 | 10.66 |

RMSE of power deviation | 59.52 | 51.43 | 16.66 | 11.06 | 9.28 | 8.91 | 7.61 | 7.56 | 7.54 | 7.54 |

In this paper, a Microgrid model has been built with commercial building load, PV array generation and bi- directional PEV charging/discharging stations. The optimization of PEV charging/discharging schedule has been studied with three different objective functions and two optimization methods. The first objective function is to minimize the PEV charging cost; the second objective function is to minimize Microgrid power deviation; and the third objective function combines the first two objective functions. The simulation results show that the optimization with combined objectives can achieve relative low charging cost with acceptable Microgrid power deviation. The simulation results also illustrate that the charging/discharging of PEVs provides grid service to reduce the intermittency of PV power generation. In future study, we will focus on decentralied PEV charging/ discharging control for a PEV fleet in larger scale smart grid with renewable energy sources.

Chong Cao,Ming Cheng,Bo Chen, (2016) Optimal Scheduling of PEV Charging/Discharging in Microgrids with Combined Objectives. Smart Grid and Renewable Energy,07,115-130. doi: 10.4236/sgre.2016.74008