Framework Description

The aim is to propose a decentralized energy scheduling algorithm for the community to schedule the appliance’s operation ofH householdsh= [_1,...,H]. Each consumer is assumed to be equipped with shiftable and nonshiftable appliances, an energy storage system (ESS), a photovoltaic panel (PV), and an EV.

The ESS, PV, and EV are referred to in the rest of the sections as distributed energy resources. Consumers are considered to have different consumption behaviors.

It is assumed that all the households possess the technical features capable of energy and information transfer from and to other households. Some of the notations previously introduced in Subsection 2.2.2 are reused here with a slight difference (subscript h is added to the notations introduced before).

The energy exchange among the consumers has been carried out thanks to the bidirec-tional ways of communication enabled by the SG concept. We consider that each household is equipped with a virtual switch in order to visualize the energy direction and the parties that are participating (i.e., sell and purchase). The virtual switches are considered to be open to transfer/receive energy to/from the neighbors or can be closed, as shown in Fig. 2.27.

Figure 2.27: Community-level framework consisting of multiple smart households.

The number of virtual switches is determined based on the number of interconnected households participating in the DR program. The presented method aims to minimize con-sumers’ electricity bills and maximize the usage of locally generated energy (i.e., distributed energy resources) under a ToU dynamic electricity tariff. A hybrid optimization framework is proposed here and consists of an appliances scheduling component to shift the major

loads from on-peaks to off-peaks. Furthermore, the scheduling component coordinates the distributed energy resources in the neighborhood. The scheduling is formulated as an opti-mization problem using a MIP algorithm. A limitation on the energy drawn from the grid is imposed to avoid peak rebounds while shifting to off-peaks.

As some of the households may have remaining on-site generated energy, an energy market is created as a part of the scheduling algorithm. The market allows the participants to sell and purchase (i.e., exchange) the unconsumed energy on the neighborhood level. This strategy will avoid the overloading and the congestion of the grid since another energy source is available. The energy market is modeled based on a noncooperative game-theoretical setup. Each player participating in the market game seeks to maximize their profit. The game-theory model is responsible for making decisions to define the virtual switchers that will be open and close (i.e., indicate the seller and the buyer) and on the amount of energy to be sold and purchased by each household.

The proposed algorithm requires the players to raise the flag to indicate how much they want to sell or purchase. Hence, their privacy is not invaded since they should not show their chosen strategy to schedule their households appliances to the rest of the participants.

The decision is then updated and adapted by the scheduling component to re-coordinate the distributed energy resources. This process will be repeated (making decisions, updating scheduler entries, and scheduling) until the end of the scheduling horizon.

Time and Energy Flexible Appliances Model

As an extension to what was discussed in Section 2.4 , the EV is considered here to supply all the household appliances. Hence, the ESS and the EV are considered as energy sources when charged to a certain level along with the grid and power generated by the PV. The EV charging is improved here to be more flexible compared to the previously discussed charging strategy.

• The EV is handled as a soft load, which means that it can charge, discharge or remain idle between the arrival timet_h,arand departure timet_h,dp (as previously used). Thus, the energy consumed can change from one time to the other. For simplicity, the state-of-energy (SoE) is adopted here instead of the state-of-charge to avoid confusion and long equations.

Information about the consumers’ traveling pattern can be retrieved and includes the number of days the EV traveled, indicated byEV_h,ndand the distance traveled, denoted byEV_h,dst. The features of the EV’s battery are given with the technical specifications of the EV, where the highlights are on the EV capacity E_h,EV, and the maximum distance range EV_h,mrg that the EV can travel with its fully charged battery. Based on the mentioned features and information, the EV’s initial state-of-energy for each household when parked in the household can be estimated as follow

SoE_h,EV^th,ar _,init= ¹⁻(EV_h,ndEV_h,dst)

EV_h,mrg , (2.35)

thus, the SoE of the hth EV, SoE_h,EV^k , is available at each time slot when the EV is

plugged in the household by

SoE_h,EV^k =SoE_h,EV^th,ar_,init+P OW_h,EV^k _,ch−P OW_h,EV^k _,dis∆t for k=t_h,ar,

SoE_h,EV^k =SoE_h,EV^k−1 +P OW_h,EV^k _,ch−P OW_h,EV^k _,dis∆t for k= [t_h,ar+_1...t_h,dp]_, (2.36) whereP OW_h,EV^k _,ch andP OW_h,EV^k _,dis are the charging and discharging powers at time slot k in householdh; respectively.

As the EV’s charging rate can be different in each time slot, its charging power of at time slot k cannot violate the hard energy constraint set by the manufacturer P OW_EV,rate. Since the EV may be used as an energy source to household h, the discharging power rate is considered to be similar to the charging rate, where

0≤P OW_h,EV^k _,ch≤P OW_EV,rateon^k_EV,

0≤P OW_h,EV^k _,dis≤P OW_EV,rate(1−on_EV)^k, (2.37) whereon^k_EV is a binary variable to prevent the charging and discharging of the EV at the same time slotk.

The charging of EV should reach a recommended levelSoE_h,EV,max and not discharge to lower than SoE_h,EV,min to prolong the battery life cycle’s longevity. The SoE at the departure of the EV in household h is expressed as

SoE_h,EV,min≤SoE_h,EV^th,dp ≤SoE_h,EV,max. (2.38)

• Similarly, the ESS can charge flexibly to reach its capacity E_h,ESS starting from an initial SoE, SoE_h,ESS,init. Due to the manufacturer configuration, the charging of the ESS, P OW_h,ESS,ch^k , should not exceed a given rate P OW_ESS,rate. The same rate is considered for the discharging of the ESS. The overlap of charging and discharging of the ESS is prevented using the binary variable on^k_ESS

0≤P OW_h,ESS,ch^k ≤P OW_ESS,rateon^k_ESS,

0≤P OW_h,ESS,dis^k ≤P OW_ESS,rate(₁−on_ESS)^k_. ^(2.39) The ESS energy level can be calculated at the beginning of the scheduling horizon and at every time slot as follow

SoE_h,ESS¹ =SoE_h,ESS,init+P OW_h,ESS,ch¹ −P OW_h,ESS,dis¹ ∆t,

SoE_h,ESS^k =SoE_h,ESS^k−1 +P OW_h,ESS,ch^k −P OW_h,ESS,dis^k ∆t for k= [_2,...,N_slot]_, (2.40) Renewable Energy Model: Photovoltaic Panel

It is assumed that all the households possess a PV panel with similar technical specifications.

The PV panel’s power production is modeled physically with the impact of solar irradiance

and panels’ configurations. The power generated by the PV at time slot k of household h, P OW_{h,P V}^k , is predicted as follows

P OW_{h,P V}^k =n_h,sn_h,prp_{P V} Ir^k Ir_{ST C}

!

, (2.41)

wheren_h,s and n_h,p are the number of modules in series and parallel of household h; respec-tively. rp_{P V},Ir_{ST C} and Ir^k are the rated power of PV model and irradiance in Standard Test Conditions and irradiance at k; respectively.

Figure 2.28 shows an example of the power generated based on the proposed PV model.

The irradiance information is based on one-day historical data in Budapest. The PV-generated power in the example is used for the rest of the study.

Figure 2.28: Power generated due to the photovoltaic panel.