A novel energy management strategy to reduce gird dependency using electric vehicles storage in coordination with solar power

Abstract

The effective coordination of solar photovoltaic (solar PV) with Electrical Vehicles (EV) can substantially improve the micro grid(MG) stability and economic benefits. This paper presents a novel Energy Management System (EMS) that synchronizes EV storage with Solar PV and load variability. Reducing grid dependency and energy cost of the MGs are the key objectives of the proposed EMS. A smart EV prioritization based control strategy is developed using fuzzy controller. Probabilistic approach is designed to estimate the EV usage expectancy in the near time zone that helps smart decision on choosing EVs. Minimizing battery degradation and maximizing EV storage exploitation are the key objectives of EV prioritization. On the other hand, Water Filling Algorithm (WFA) is used for Optimal Storage Distribution (OSD) in each zone of energy need for load flattening. The proposed EMS is implemented in a real time on-grid MG scenario and different case studies have been investigated to realize the impact of proposed EMS. A comprehensive cost analysis has been conducted and the efficacy of the proposed EMS is analysed.

Keywords

Solar PV EV storage WFA load flattening EV ranking

1 Introduction

Penetration of renewables and EVs with the existing grid creates numerous challenges. To deal with these issues it is necessary to have adequate energy storage system which is not an economical choice. In this context, EV fleets in micro grids, organizations, working places and corporate buildings are the most significant zones where EV fleet can transform like a virtual storage unit [1]. Numerous studies have been focused on effective EMS for EV fleets to coordinate with renewables and load fluctuations [2]. For MGs, there has been many EMS strategies developed for EVs in off-grid mode [3 –8] and on-grid mode [9 –15]. Strategies are developed to maximize the economic befit for owners [3 –5] and fleet/utility [6 –8].

With estimated mobility data of EVs, PV power output, EV’s SoC, dynamic grid pricing, etc.; [6] has considered with and without authentication of EV plugging with smart pricing, [7] used both short and long term statistical analysis, [3] developed EMS using real statistics of EV mobility data, [4] has proposed dynamic EV EMS strategy, [5] has designed online EV control strategy with solar PV, and [8] has used mobility data and Global Positioning System (GPS) to estimate EV charging patterns.

On-grid MG EV strategies have been developed for economic benefits in [9 –11], for minimal charging cost at charging fleets [12 –15], and to minimize queuing time for charging at the fleet [16, 17]. [9] has considered smart price concept, and [11] has considered RES’s intermittency, and [13] has accounted uncertainties in EV mobility along with smart pricing, [14] has considered grid price dynamics. Battery degradation is taken in to account in [12] and [15], but, the critical aspects of battery degradation are not addressed fully. It is not easy to examine battery degradation with consideration of all the factors that leverage battery degradation. However, the impact of V2 G and G2 V should be taken into account while EVs are being exploited for grid support.

In [16 –20], driving patterns have been taken into consideration to maximize the accuracy of EV charging evaluation. However, these strategies need forecasted data of EV charging, mobility data, PV power and smart price in order to optimize EV EMS. Authors have developed a prioritization where EV’s mean waiting time is estimated by considering the available charging ports, arrival times, and charging target of the other EVs staying at the fleet [21]. Here, the service quality is estimated based on waiting span of each EV. In [22], authors have investigated the impact of the target SoC of EVs on charging instants and proposed a fast charging model or fleet operators. [23], has developed an algorithm to maximize the economic benefit of the EV owner using forecasting of electricity prices.

Optimal EV EMS, taking into consideration of autonomy and constraints of flexibility of EV owners, become crucial [24]. The entire power grid, V2 G approaches take advantage of EVs in order to provide grid support such as frequency and voltage regulation in [25]. [26], has developed an EMS with EV as a distributed spinning reserve, where each one acts individually in sync with frequency deviation at the point of common coupling. Load regulation and spinning reserves are taken as the ancillary support to be provided by EVs in [27]. [28], has proposed a decentralized scheduling EMS, where EVs are supposed to compensate the stochastic nature of RES and load. Most of these EMS must ensure the large amounts of connected EVs with which substantial support through V2 G and G2 V is expected in the real time scenario [26 –28].

The best way to append pliability to the MG is by EV’s through their V2 G and G2 V functionalities. Different strategies to utilize EVs for grid support have been studied in [29, 30] and the impacts of V2 G and G2 V are analyzed in [31]. EV charging/discharging strategies should be as smart as possible in order to sync with the grid fluctuations [32]. Heuristic algorithms such as Earliest Deadline First (EDF) or Least Laxity First (LLF) can handle such a contingency situations. However, this may lead to negative impact on the battery longevity. On the other hand, Model Predictive Control (MPC) is an optimization-based control method that can be used to track signals for which forecasts are available in real-time [33]. It can be used by an EV fleet operator to track regulation signals, as described in [34]. So, there will not be frequent transitions in charge rates which will lead to enhance battery life. It is not much focused on key aspects of battery degradation and maximizing EV storage usage simultaneously.

The remaining version of this paper is articulated as follows: Section 2 provides overview of proposed EMS with the help of flow chart representation and the remaining is dedicated to description of MG entities. Modelling of energy economics is presented in section 3. In section 4 Optimal Energy distributions is explained using WFA. EV usage expectancy is formulated in section 5 whereas section 6 explains whole processes of EV prioritization. In section 7, a case study has been presented to investigate the impact of proposed EMS in different scenarios.

2 Proposed EMS and system description

The proposed EMS is implemented in a micro grid environment which is an educational organization. It consists of Solar PV plant, EV fleet, DG set and load. Through the coordination of Solar PV, EV fleet and DG set, it is intended to minimise the total operating energy cost and grid dependency. Here, the load is considered to be not flexible. The solar PV power is stochastic in nature, so, we don’t have control over it. The DG set, which is one of the costly power generations, is used for emergency needs of the micro grid. DG power can be scheduled in accordance with the EMS requirement. However, it is not the primary support for the EMS. The major support for the EMS is expected from EV fleet. EV fleet can be considered as two different entities simultaneously: flexible load and virtual storage. The remaining part of this section is dedicated to model different components of the MG.

The proposed EMS uses the historical data of EV arrival and departure in order to estimate the EV availability and its storage capacity available for V2 G and G2 V operations. Also, the solar PV and load demand are estimated based on the past data. EMS will coordinate EVs with solar Power and load demand in such a way that grid intake power always below the authenticated power (maximum demand $P_{\max}^{g, d}$ ). More importantly, EMS ensures the trip requirement (target SoC before the time of departure) for each EV.

The EMS proposed in this article is well depicted as a flowchart (Fig. 1) that follows the below steps:

Day span of 24 hours has been to 96 intervals.

Collecting EV mobility data and estimating the EV availability at fleet.

Collecting solar power, load demand to identify the zones of energy need for load flattening.

OED among the intervals of each zone using WFA.

Probabilistic approach to deduce EV usage chance during near time intervals.

EV ranking using Fuzzy controller EVs based on prioritization criterion to support EMS.

Fig. 1

Demonstration of Proposed EMS.

2.1 Solar PV plant

Harvesting solar PV power in India has become aspiring target for the government to reach 100 GW by 2022. Solar PV power depends on irradiance and temperature which is given by (1) [35]. $P_{t}^{pv} = P^{stc} \frac{G_{t}^{a}}{G^{stc}} (1 + (T_{t}^{c} - T^{stc}) C^{c})$ (1)

P^stc = PV output power at Standard Test Condition (STC), in W.

$G_{t}^{a}$ =Irradiance on the panel at ‘t’ in W/m².

G^stc=Irradiance at STC (1000 W/m²).

$T_{t}^{c}$ =Temperature of The Solar PV cell at‘t’ in °C.

T^stc=STC temperature (25 °C).

C^c=Temperature Coefficient (–0.258).

The uncertainty in solar irradiation can be modelled using beta distribution (3) and to that of temperature can be assessed using normal distribution (4) [36]. Here, α and β shaping values for the time interval t which can estimated using mean (μ) and standard deviation (σ) of the past data [42]. $F_{si} = {\begin{matrix} {SI}^{(α - 1)} {(1 - SI)}^{(β)} & 0 ⩽ SI ⩽ 1 \\ 0 & otherwise \end{matrix}$ (2) $β = (1 - μ) (\frac{μ (1 + μ)}{σ^{2}} - 1)$ (3) $α = \frac{μ β}{1 - μ}$ (4) The Probability Distribution Function (PDF) of the temperature is given by (5) [37]. $F_{pv} = \frac{1}{\sqrt{2 π σ_{pv}}} e^{- \frac{{(t - μ_{pv})}^{2}}{2 σ_{pv}^{2}}}$ (5)

Here, T_a represents the ambient temperature.

2.2 EV and fleet

2.2.1 EV mobility data

It is essential to estimate the available probability of EVs at fleet in order to schedule to cope up with EMS. EV mobility model provides information about EVs availability for energy support and their readiness with required SoC and Laxity. Here the term, ‘Laxity’ indicates the flexible time duration that the EV can support EMS. The employee biometric data is used to extract the EV arrival and departure timings (using past data). The EV mobility data is not considered during holidays as it leads to inaccurate probabilities.

Arrival and departure times of each EV for Monday of all weeks during the odd and even semesters are shown in Tables 1 and 2. Probability Density functions (PDFs) are obtained for arrival and departure for each weekday (Monday to Saturday) using normal distribution given by (6). $F_{ev} = \frac{1}{\sqrt{2 π σ_{ev}}} e^{- \frac{{(t - μ_{ev})}^{2}}{2 σ_{ev}^{2}}}$ (6)

Table 1

EV mobility data (Monday’s of all weeks)

Table 2

Arrival times of E 001 of all weeks in the odd & Even semester

The mileage and the battery capacity are assumed to be same for all the EVs.

EV LAXITY: The laxity of EV is given by (7) and is denoted in terms of intervals. Higher the Laxity higher the vehicle flexibility for grid support and vice-versa [38]. Here, the third term is the time need for EV to get the charge to fill it up to target SoC. $L_{ev}^{i, t} = t_{d}^{i} - t - \frac{({SoC}_{ev}^{i, t = t_{d}} - {SoC}_{ev}^{i, t}) E_{ev}^{i, cap}}{P_{rate}^{i, t}}$ (7)

2.2.2 Estimation of available EV’s storage capacity for V2 G and G2V

For Monday, in the t^th interval, the probability of i^th EV arrival is taken as $p_{i, t}^{a}$ and that of for departure is taken as $p_{i, t}^{d}$ . The respective cumulative probabilities of i^th EV in t^th interval are denoted as $p_{i, t}^{a, c}$ and $p_{i, t}^{d, c}$ for arrival and departure respectively. By considering both arrival and departure probabilities, the availabilityprobability of each EV at fleet in each interval can estimate using the (8). $p_{i}^{j} = p_{i, t}^{a, c} - p_{i, t}^{d, c}$ (8) Let there are N numbers of EV gathering at the fleet. L, is the vector EV’s travel lengths. (9) $L = [l_{1} l_{2} l_{3} \dots \dots \dots . l_{N}]$ (9) Estimated SoC vector at the time of arrival is estimated using (10). ${SoC}_{ev}^{arr} = M / C [l_{1} l_{2} l_{3} \dots \dots \dots . l_{N}]$ (10) Drop in SoC due to trip is estimated using (11). ${SoC}_{i, ev}^{new} = {SoC}_{i, ev}^{old} - (E_{ev}^{old, i} - γ l) / E_{ev}^{cap, i}$ (11)

Here, ${SoC}_{i, ev}^{new}$ is nothing but ${SoC}_{i, ev}^{arr}$

The SoC levels of PEVs those are participating in EMS support can be estimated using (12) & (13) for discharging and charging cases respectively. ${SoC}_{i, ev}^{t + 1} = {SoC}_{i, ev}^{t} - (E_{ev}^{t, i} - E_{ev}^{t + 1, i}) / E_{ev}^{cap, i}$ (12) ${SoC}_{i, ev}^{t + 1} = {SoC}_{i, ev}^{t} + (E_{ev}^{t + 1, i} - E_{ev}^{t, i}) / E_{ev}^{cap, i}$ (13)

The probability of i^th EV storage availability during t^th interval is $p_{i}^{j} * C * {SoC}_{i}^{t}$ .

From each EV, for G2 V, the storage space available is estimated using (14). $e_{i, j}^{g 2 v} = p_{i}^{t} * C * (1 - {SoC}_{i}^{t} - 0.2)$ (14) From each EV, for V2 G, the stored energy available is estimated using (15). $e_{i, j}^{v 2 g} = p_{i}^{t} * C * ({SoC}_{i}^{t} - 0.2)$ (15) The vector of storage availability for G2 V and total storage availability are represented by the (16) and (17) respectively. $E_{i}^{g 2 v} = [e_{i}^{1, g 2 v} e_{i}^{2, g 2 v} e_{i}^{3, g 2 v} \dots \dots \dots \dots . e_{i}^{N, g 2 v}]$ (16) $S_{i}^{g 2 v} = A = \sum_{j = 1}^{N} e_{i}^{t, g 2 v}$ (17) The vector of stored energy available for V2 G and total stored energy availability are $E_{i}^{v 2 g} = [e_{i}^{1, v 2 g} e_{i}^{2, v 2 g} e_{i}^{3, v 2 g} \dots \dots \dots \dots . e_{i}^{N, v 2 g}]$ (18) $S_{i}^{v 2 g} = A = \sum_{j = 1}^{N} e_{i}^{t, v 2 g}$ (19)

2.3 EV battery degradation

EV battery degradation depends so many factors such as SoC, Temperature, DoD, charge rate and other factors. It is always suggested to limit DoD and SoC levels. Keeping battery unused for longer duration with high SoC will excel the capacity fading. Also, fullest discharging (high DoD) causes capacity fading due to increase in battery resistance [39].

In this article, battery degradation is considered while scheduling EVs for EMS. It is assumed that the temperature is maintained at an optimal level for healthy battery operation. Here, the battery care is taken in view of DoD and SoC by following two guidelines [40]: 1. Don’t allow to reach its peak SoC and unused, 2. Don’t let it go for higher DoD. The EV battery degradation cost related to DoD and SoC are expressed by (20) and (21) which are taken from [41] and [42]. The total degradation cost ( $C_{bd}^{T}$ ) due to SoC and DoD is given by (22). $C_{bd}^{DoD} = \frac{C_{b}^{i} * E_{b}^{i} * c_{d}^{cs} + C_{d}^{lbr}}{C_{b}^{life} * L_{b}^{i} * DoD} * E_{dc}^{i}$ (20) $C_{bd}^{SoC} = C_{b}^{i} \frac{c_{d}^{cs} * {SoC}_{avg}^{i, d} - c_{d}^{ci}}{8760 * C_{f} * L_{b}^{i}}$ (21) $C_{bd}^{T} = C_{bd}^{SoC} + C_{bd}^{DoD}$ (22)

$C_{bd}^{DoD}$ =Degradation cost related to DoD.

$C_{bd}^{SoC}$ =Degradation cost related to SoC.

$c_{d}^{cs}$ =degradation coefficient related to cost-slope = 1.59×10^–5.

$c_{d}^{ci}$ =degradation coefficient related to cost-intercept=6.41×10^–6.

C_f=Capacity fade (assumed to be 20% of maximum capacity, $E_{b}^{i}$ ).

$C_{b}^{i}$ =Battery cost per kWh ($300).

$E_{b}^{i}$ =Battery capacity in kWh.

$L_{b}^{i}$ =Battery life (10 years /5000 cycles).

$C_{d}^{lbr}$ =Battery replacement labor cost ($240).

3 Modeling of energy economics

3.1 Cost of grid power

The tariff structure for consumer in Indian energy market follows ‘flat rate tariff’ which is under the regulation of Central Electricity regulation System (CERS). It is also known as three-part tariff which includes: fixed cost (a) semi-fixed cost (b) and variable cost (c). It depends on maximum load (kW) and number of units consumed (kWh)

The maximum demand which is authenticated from the grid utilityis $P_{\max}^{g, d}$ . The minimum amount of power up to which the charges are fixed is 80% of $P_{\max}^{g, d}$ . It is calculated as below:

For, 0 to 80% of $P_{\max}^{g, d}$ , the charge is $P_{\max}^{g, d} * 0.8 * C_{d}^{g}$ (Fixed Charges).80 to 100% of $P_{\max}^{g, d}$ , the charge is $P_{\max}^{g, l} * C_{d}^{g}$ (Semi-Fixed charges). Greater than 100% of $P_{\max}^{g, d}$ , the charge is $P_{\max}^{g, l} * C_{d}^{g} + P_{extra}^{g, l} * C_{d}^{g}$ (With penalty).

Here, $P_{\max}^{g, l}$ is the maximum power drawn from the grid during the given month.

$C_{d}^{g}$ =Grid demand cost per 1 kVA = Rs. 475.

$C_{e}^{g}$ =Grid energy cost per 1 kWH = Rs. 7.56.

$U_{e}^{g}$ =Number of units consumed per month.

The minimum number of units for which the charges are fixed is 7000 kWh. For, 0 to 7000kWh, the charge is $7000 * C_{e}^{g}$ (Fixed Charges).>7000kWh, the charge is $U_{e}^{g} * C_{e}^{g}$ (Variable Charges).

Grid Power cost = Fixed cost+Semi fixed cost+Variable cost+Penalty Charges $\begin{matrix} C_{T}^{g} = {P_{\max}^{g, d} * 0.8 * 475 + 7000 * C_{e}^{g}} + {P_{\max}^{g, l} * 475} \\ + {U_{e}^{g} * C_{e}^{g} + P_{\max}^{g, l} * 475} + {P_{extra}^{g, l} * 475} \end{matrix}$ (23)

3.2 Cost of solar PV power

The total cost of solar PV power can be divided into two parts as shown in (24). $C_{T}^{pv} = C_{int}^{pv} + C_{opr}^{pv}$ (24)

Here,

$C_{T}^{pv} =$ Total solar PV power cost.

$C_{int}^{pv} =$ Initial Cost of solar PV.

$C_{opr}^{pv} =$ Operational Cost of solar PV.

The initial cost is converted to cost per year(25) by considering, $C_{int}^{pv}$ , interest rate (q) and lifetime (S_pv). $C_{int / y}^{pv} = C_{int}^{pv} \frac{q {(1 + q)}^{S_{pv}}}{{(1 + q)}^{S} - 1}$ (25)

Now the (24) is modified to represent annual cost of solar PV power given by (26). Also, the cost of solar PV power per each month can be obtained by (27). $C_{/ y}^{pv} = C_{int / y}^{pv} + C_{opr}^{pv}$ (26) $C_{/ m}^{pv} = (C_{int / y}^{pv} + C_{opr}^{pv}) / 30$ (27)

3.3 DG power cost

In view of flexibility and emergency perspective DG can be used as a substitution for grid supply. In spite of its high cost per unit, for micro grid applications, DG will be useful for reliable power. The total cost of DG power is represented by (28). $\begin{matrix} Total DG power cost = Initial cost + operating cost \\ C_{T}^{dg} = C_{int}^{dg} + C_{opr}^{dg} \end{matrix}$ (28) $\begin{matrix} DG operating cost = Fuel cost + startup = cost \\ C_{opr}^{dg} = C_{f}^{dg} + C_{stup}^{dg} \end{matrix}$ (29)

Here, $C_{T}^{dg} =$ Total cost of DG power per month.

$C_{int}^{dg} =$ Initial Cost of DG per month.

$C_{opr}^{dg} =$ Operational Cost of DG (fuel cost+Start-up cost).

$C_{f}^{dg}$ =Fuel cost per month.

$C_{stup}^{dg}$ =DG start-up cost per month.

3.3.1 Initial cost of DG set

The total initial cost is converted to year by considering, $C_{int}^{dg}$ , interest rate (q) and lifetime (S_dg) in years (30). $C_{int / y}^{dg} = C_{int}^{dg} \frac{q {(1 + q)}^{S_{dg}}}{{(1 + q)}^{S} - 1}$ (30) The total cost of DG power is modified as shown in (31) to represent annum cost equivalent of DG set and that of per month is given by (32). $C_{/ y}^{dg} = C_{int / y}^{dg} + C_{opr}^{dg}$ (31) $C_{/ m}^{dg} = (C_{int / y}^{dg} + C_{opr}^{dg}) / 30$ (32)

3.3.2 Fuel cost of DG set

The fuel consumption per kWh of a DG set is represented by quadratic equation, given by (33) [43]. $F_{opr}^{dg} = \sum_{t = 1}^{96} \sum_{j = 1}^{m} \sum_{t = 1}^{96} (α H_{t, j}^{dg} + β P_{t, j}^{dg} + γ {(P_{t, j}^{dg})}^{2}) t$ (33)

The DG coefficients α, βandγ are taken as 10 $, 0.0133 $/kWh and 0.002 $/kWh² [44].

3.3.3 DG start-up cost per month

The DG start-up cost per month is calculated using (34). It depends on the number of times that the DG has switched on during the given month. $C_{stup}^{dg} = \sum_{j = 1}^{m} \sum_{k = 1}^{\bar{u}} C_{k, j}^{dg}$ (34)

$C_{k, j}^{dg}$ =Starting cost j^th DG

Here, $\bar{u}$ represents the vector of m DG’s switching (OFF to ON) times in a given month. $\bar{u} = {u_{1} u_{2} u_{3} \dots \dots \dots . u_{m}}$

The number of times that each DG was switched ON (u_j) can be calculated using (35). $u_{j} = \frac{1}{2} \sum_{t = 1}^{96} (1 + s (t) - s (t - 1))$ (35)

3.4 EV charging cost

EV Charging cost is calculated for each day based on initial (at the time of arrival) and final (at the time of departure) SoC of each EV (36). The total cost of EV charging is calculated per month using (37). $C_{d, i}^{ev} = ({SoC}_{i}^{dep} - {SoC}_{i}^{arr}) * E_{i} * C_{e}^{g} - C_{inc}^{ev} * Q_{i}^{ev}$ (36) $C_{C}^{ev} = \sum_{d = 1}^{31} \sum_{i = 1}^{n} C_{i, d}^{ev}$ (37)

Here, $Q_{i}^{ev}$ is the amount of energy transaction done via V2 G and G2 V for which the regulation cost is paid to EV owner as an incentive ( $C_{inc}^{ev}$ ). The amount of Energy transacted $Q_{i}^{ev}$ is calculated using (38). $Q_{i}^{ev} = \sum_{d = 1}^{31} \sum_{i = 1}^{96} {P_{i}^{ev} * t} - {({SoC}_{i}^{dep} - {SoC}_{i}^{arr}) {* E}_{i}}$ (38)

4 Optimal energy distribution

The amount of power need from grid is estimated using (39) using past data. The amount of energy need from grid in each interval is estimated using (40). (41) Represents the amount of energy required from EV storage in order to ensure that the grid intake power is less than $P_{\max}^{g, d}$ . The same is represented pictorially in Fig. 2. Total amount of energy need in each zone is estimated using (42). $P_{need}^{t, grid} = {- P_{solar}^{t} + P_{load}^{t} + P_{ev}^{t, ch}}$ (39) $E_{need}^{t, grid} = \sum_{i = t}^{t + 15} P_{need}^{t, grid} t$ (40) $E_{need}^{t, ev} = E_{need}^{t} - E_{spec}^{grid}$ (41) Where $E_{spec}^{grid} = \sum_{i = t}^{t + 15} P_{need}^{grid} t$ $E_{need}^{z} = \sum_{t = 1}^{M} E_{need}^{ev, t}$ (42)

Fig. 2

Optimal energy dispatch using WFA in a charging zone.

In this section, the optimal distribution of available storage in each zone is accomplished. In each zone, the amount energy capacity available from EV storage and energy need for the load flattening is used for the optimal allocation of EV storage among the intervals in each zone. WFA is used for this OSD which is generally used in communication systems for optimal power allocation among the channels with different noise levels [45]. Consider a zone (charging) as depicted in Fig. 2 with M number of intervals. The value of μ for each interval represents the optimum EV storage space that could be charged.

4.1 Problem formulation

Here, the objective is to minimize ΔP and is formulated as the minimization of variance as given by (43). To deal with PEVs battery power, (43) is converted energy form (44). Here, the key constraint is that the total energy distribution in each zone should not exceed available energy from all PEVs. This is in contrast with power constraint in communication channel power allocation using WFA. $\begin{matrix} \min, (P_{ev, t}^{reg}, z) = \min, \sum_{t = 1}^{M} (P_{need}^{t, grid} \\ + \sum_{i = 1}^{n} P_{ev, i, t}^{charge} \pm \sum_{i = 1}^{n} P_{ev, i, t}^{reg} - P_{grid}^{spec})^{2} \end{matrix}$ (43) $\begin{matrix} \min, (E_{ev, t}^{reg}, z) = \min, \sum_{t = 1}^{M} (E_{need}^{t, grid} \\ + \sum_{i = 1}^{x} E_{ev, i, t}^{charge} + E_{ev, t}^{reg} - E_{grid}^{spec})^{2} \end{matrix}$ (44) Constraint on power availability in each t is (45) $\sum_{i = 1}^{y} P_{ev, t, i}^{reg} ⩽ \sum_{i = 1}^{y} P_{ev, t, i}^{avail, ch} For charging zone$ (45) Constraint on energy usage in each t is (46) $\sum_{i = 1}^{M} E_{i}^{need} ⩽ E_{ev, t = 1}^{avail, z, ch} For charging zone$ (46) This power constraint has been included in energy constraint (47) $If E_{ev, t = 1}^{avail, z, ch} ⩾ \sum_{i = 1}^{y} P_{ev, t, i}^{avail, ch} t$ (47) $Then E_{ev, t = 1}^{avail, z, ch} = \sum_{i = 1}^{y} P_{ev, t, i}^{avail, ch} t$ (48) Using Lagrange multiplier, (49) is obtained. $\begin{matrix} \min, L (E_{ev, t}^{reg}, λ) = \sum_{t = 1}^{M} (E_{need}^{t, grid} + \sum_{i = 1}^{x} E_{ev, i, t}^{charge} \\ + E_{ev, t}^{reg} - E_{grid}^{spec})^{2} + 2 (\sum_{t = 1}^{M} E_{ev, t}^{reg} - E_{ev, t = 1}^{avail, z, ch}) \end{matrix}$ (49) $E_{need}^{i, t, grid} + \sum_{i = 1}^{x} (E_{ev}^{cap, i} - E_{ev}^{i, t}) + \sum_{i = 1}^{y} E_{ev, t}^{reg} - E_{grid}^{spec} - λ = 0$ (50) By simplifying the above equation, (51) obtained. $\sum_{i = 1}^{y} E_{ev, t}^{reg} - E_{grid}^{spec} - λ + α = 0$ (51) $\sum_{i = 1}^{y} E_{ev, t}^{reg} + E_{other}^{t} = E_{grid}^{spec} + λ$ (52) $Where, E_{other}^{t} = E_{need}^{t, grid} + \sum_{i = 1}^{x} (E_{ev}^{cap, 1} - E_{ev}^{i, t})$ (53) Here, $E_{other}^{t}$ indicates the sum of grid energy need and EV charging load. In (52), RHS is independent of t and let $E_{grid}^{spec} + λ = μ$ $\sum_{i = 1}^{y} E_{ev, t}^{reg} + E_{other}^{t} = μ$ (54) $\sum_{i = 1}^{y} E_{ev, t}^{reg} = μ - E_{other}^{t}$ (55)

The optimal value of μ is obtained with the help of bisection method, with € =0.01. The optimum value of μ decides the optimum $E_{ev, t}^{reg}$ for t in zone z.

4.2 WFA algorithm for energy allocation

Input: $E_{spec}^{grid}$ , €, $E_{pev, t = 1}^{avail, z, ch}$ , $E_{ev, t, i}^{charge}$ for t = 1,2,3 ... M in zone ‘z’

Output: μ and $E_{pev, t}^{reg}$ for t = 1,2 ... M in zone ‘z’

1. Initialize: μ_min= $E_{grid}^{spec}$ and μ_max= $E_{grid}^{spec} + E_{pev, z 1 = t}^{avail, ch}$

2. While, (μ max-μ min)> € then do ...

3. μnew=(μ_min+μ_max)/2

4. Calculate $\sum_{i = 1}^{x + y} E_{ev, i}^{reg} = f (μ - E_{other}^{t})$ ; for t = 1,2...M

5. $f (y (t)) = {\begin{matrix} \sum_{i = 1}^{y} P_{ev, i, t}^{avail, ch} Δ t & y (t) ⩾ P_{ev, i, t}^{avail, ch} Δ t \\ y (t) & 0 ⩽ y (t) ⩾ P_{ev, i, t}^{avail, ch} Δ t \\ 0 & y (t) < 0 \end{matrix}$

6. Calculate $E_{ev, z}^{reg} = \sum_{t = 1}^{M} y (t)$

7. if $E_{ev, z}^{reg} > E_{ev, t = 1}^{avail, z, ch}$

8. μ_max = μ_new

9. else if $E_{ev, z}^{reg} < E_{ev, t = 1}^{avail, z, ch}$

10. μ_min = μ_new

11. End if

12. End while

13. Repeat the above steps for all t.

14. End

5 EV estimating usage expectancy

In order to reduce rapid transitions between V2 G and G2 V, it is better to continue the battery status for the next consecutive intervals if it is viable. Also, it is not recommended to have peak SoC for longer time duration which discussed in section 2.2.4. But, in order to maximize the EV storage usage, one should use the battery to its fullest extent with consideration of battery degradation.

In this aspect, it is very much useful if one could estimate the usage expectancy of an EV near time intervals. It can be realized using the probability of state transition ( $p_{ij}^{t + 1}$ ). After the arrival of an EV, There are three possible states: CH(Charging state), DC (Discharging state) and IDL (Idle state).

The vector or zone transition probabilities are represented by the vector $P_{z} = [p_{z}^{1} p_{z}^{2} p_{z}^{3} p_{z}^{4} p_{z}^{5} \dots \dots \dots . p_{z}^{96}]$ . It is obtained from the date of energy need from EVs for load flattening.

The zone transition probabilities as depicted in Fig. 4 estimated for individual zones based on the formula given by (56). $p_{z}^{t + 1} = (1 - \frac{τ_{z}^{k}}{τ_{z}^{\max}})$ (56) Here, $τ_{z}^{k}$ =k^th interval in zone z(counted from right to left)and $τ_{z}^{T}$ is the total number of intervals in zone z. In each zone, as $τ_{z}^{k}$ tends to reach $τ_{z}^{T}$ the zone transition probability approaches zero. $p_{j, 11}^{t + 1} = {1 - {SoC}_{j}^{t} - {SoC}_{j}} {* p}_{avl}^{t + 1} * {1 - p_{z}^{t + 1}}$ (57)

Fig. 3

Illustration of possible state transitions for an EV.

Fig. 4

Process of obtain zone transition probabilities.

Where, SoC_j is the change in SoC due to charging or discharging in the previous interval.

5.1 Transition probability ‘CH → DC’,

p_{12}^{t}

The transition probability from the charging mode to discharging mode is estimated using the usage probability for discharging and available probability. The usage probability is framed as the conditional probability (58) similar to that of (57). $p_{j, 2}^{t + 1} = p_{SoC}^{ch, t} {* p}_{avl}^{t + 1} = {{SoC}_{j}^{t} + {SoC}_{j}} {* p}_{avl}^{t + 1}$ (58) Now, the transition probability is estimated using the (59) with the help of zone transition probability. $p_{j, 12}^{t + 1} = {1 - {SoC}_{j}^{t} + {SoC}_{j}} {* p}_{avl}^{t + 1} {* p}_{z}^{t + 1}$ (59)

5.2 Transition probability ‘CH → IDL’,

p_{13}^{t}

The probability ( $p_{3}^{t + 1}$ ) that an EV goes to idle state in t + 1 interval is determined by its SoC and its mode of operation (charge/discharge) at t^th interval. So, the probability $p_{3}^{t + 1}$ can be determined using (60) for charging modes in t^th interval.

For charging mode in t^th interval, probability that EV goes to idle state can be estimated from the SoC level as (60). The probability of transition from charging mode to idle mode is given by (61). $p_{j, 3}^{t + 1, idl} = {{SoC}_{j}^{t} + {SoC}_{j}} {* p}_{avl}^{t + 1}$ (60) $p_{j, 13}^{t + 1, idl} = {{SoC}_{j}^{t} + {SoC}_{j}} {* p}_{avl}^{t + 1} * {1 - p_{z}^{t + 1}}$ (61)

5.3 Transition probability ‘DC → CH’,

p_{21}^{t}

It is opposite to the case of ‘CH→DC’. The transition probability from the discharging mode to charging is estimated using the usage probability for charging and available probability. The usage probability is framed as the conditional probability is (62) similar to that of (57). $p_{j, 1}^{t + 1} = p_{SoC}^{dc, t} {* p}_{avl}^{t + 1} = {1 - {{SoC}_{j}^{t} - {SoC}_{j}}} {* p}_{avl}^{t + 1}$ (62) Now, the transition probability is estimated using (64) by including the zone transition probability ( $p_{z}^{t + 1}$ ). $p_{j, 21}^{t + 1} = {1 - {{SoC}_{j}^{t} - {SoC}_{j}}} {* p}_{avl}^{t + 1} {* p}_{z}^{t + 1}$ (63)

5.4 Transition probability ‘DC → DC’,

p_{22}^{t}

This case is similar and opposite to the case of CH→CH. Usage probability of EV in the interval ‘t+1’ for discharging given that the EV was in discharging mode in the previous interval ’t’ is given by (65). Here, in order to use the EV for discharging purpose, battery should have the SoC > 0.2 given that the EV is available at the fleet. Hence, it is a conditional probability which is expressed using (64). $p_{j, 2}^{t + 1} = p_{j, SoC}^{dc, t + 1} {* p}_{j, avl}^{t + 1} = {{SoC}_{j}^{t} - {SoC}_{j}} {* p}_{avl}^{t + 1}$ (64) Now, the transition probability of the given EV from discharging to discharging mode from interval t to t + 1 is obtained by using the zone transition probability ${1 - p_{z}^{t + 1}}$ using (65). $p_{j, 22}^{t + 1} = {{SoC}_{j}^{t} - {SoC}_{j}} {* p}_{avl}^{t + 1} * {1 - p_{z}^{t + 1}}$ (65)

5.5 Transition probability ‘DC → IDL’,

p_{23}^{t}

This case is similar to the case of CH→IDL. The probability ( $p_{3}^{t + 1}$ ) that an EV goes to idle state in t + 1 interval is determined by its SoC and its mode of operation (discharge) at t^th interval. So, the probability $p_{3}^{t + 1}$ can be determined using the eq. (11)for discharging modes in t^th interval.

For charging mode in t^th interval, probability that EV goes to idle state can be estimated from the SoC level as given by (66). The probability of transition from charging mode to idle mode is given by (67). $p_{j, 3}^{t + 1, 3} = {1 - {{SoC}_{j}^{t} - {SoC}_{j}}} {* p}_{avl}^{t + 1}$ (66) $p_{j, 23}^{t + 1, idl} = {1 - {{SoC}_{j}^{t} - {SoC}_{j}}} {* p}_{avl}^{t + 1} * {1 - p_{z}^{t + 1}}$ (67)

5.6 Transition probability ‘IDL → CH’,

p_{31}^{t}

This is the opposite case of CH→IDL. It is important to note that EV will remain in idle state if there is no zone transition ( $p_{z}^{t + 1} = 0$ ). Once, the zone transition occurs in t + 1 interval,then the probability of usage EV in CH mode can be estimated using (68) and (69).

If the current zone is CH, i.e, next zone is DC. The EV is in idle position due to its max SoC in the current zone. As the next zone is DC, there is no chance to use the given EV in CH mode. So, EV continues in IDL state. $p_{j, 31}^{t + 1} = 0$ (68) If the current zone is DC, (i.e, next zone is CH) the reason for IDL state of the given EV is that the SoC is at its minimum level. However, the transition to CH depends on (1-SoC). So, the transition probability is given by (69) $p_{j, 31}^{t + 1} = {1 - {SoC}_{j}^{t}} {* p}_{avl}^{t + 1} {* p}_{z}^{t + 1}}$ (69)

5.7 Transition probability ‘IDL → DC’,

p_{32}^{t}

This is opposite to case (h). If the current zone is CH, i.e, next zone is DC. The EV is in idle position due to its max SoC in the current zone. As the next zone is DC and the chance of EV getting into DC mode depends on SoC and it represented by (70). there is no chance to use the given EV in CH mode. So, EV continues in IDL state. $p_{j, 32}^{t + 1} = {1 - {SoC}_{j}^{t}} {* p}_{avl}^{t + 1} {* p}_{z}^{t + 1}}$ (70)

If the current zone is DC, (i.e, next zone is CH) the reason for IDL state of the given EV is that the SoC is at its minimum level. As the next zone is CH, the chance of getting into CH mode of operation is zero. $p_{j, 32}^{t + 1, 3} = 0$ (71)

5.8 Transition probability ‘IDL → IDL’,

p_{33}^{t}

The EV will be still in IDL state until the zone transition takes place. So, the probability of being in IDL state depends on ( $1 - p_{z}^{t + 1}$ ). It also depends on type of upcoming zone and current SoC level.

If next zone transition from CH to DC, the transition probability depends on (1-SoC) as shown in (72). For the opposite case, the transition probability is given by (73). $p_{j, 33}^{t + 1} = (1 - p_{z}^{t + 1}) {* p}_{avl}^{t + 1} * (1 - {SoC}_{j}^{t})$ (72) $p_{j, 33}^{t + 1} = (1 - p_{z}^{t + 1}) {* p}_{avl}^{t + 1} * {SoC}_{j}^{t}$ (73) The conditional probability can be used to represent the probability of being in CH state in t + 1 given that the EV was in CH state in interval t. Here, $p ({CH}_{j}^{t + 1} / {CH}_{j}^{t}) = p_{j, 11}^{t + 1}$ $p ({CH}_{j}^{t} \cap {CH}_{j}^{t + 1}) = p ({CH}_{j}^{t}) * p ({CH}_{j}^{t + 1} / {CH}_{j}^{t})$ (74) $p ({CH}_{j}^{t} \cap {DC}_{j}^{t + 1}) = p ({CH}_{j}^{t}) * p ({DC}_{j}^{t + 1} / {CH}_{j}^{t})$ (75) $p ({CH}_{j}^{t} \cap {CH}_{j}^{t + 1}) = p ({CH}_{j}^{t}) * p ({DC}_{j}^{t + 1} / {CH}_{j}^{t})$ (76)

6 EV prioritization

In order to maximize the EV storage usage, it is very important to take a wise decision to choose the EVs based on SoC and Laxity. On the other hand, It is also important to consider the battery degradation due to its V2 G and G2 V functionalities (while supporting the EMS).In this regard, as explained in section 2.2.4, it is desirable to maintain low DoD and moderate ‘average SoC’ levels during the V2 G and G2 V operations. Also, it has to be ensured that the peak SoC is not still for longer time duration. In this context, the importance of EV prioritization is depicted in Fig. 1 which depicts in two aspects: available power and usage expectancy. The other aspects of prioritization i.e, based on DoD and SoC are not encrypted in the Fig. 6. The Fig. 6 is self-explanatory from which one can understand the impact of EV ranking. For instant, at 54^th interval EV1 has been used in V2 G mode instead of EV4. At 51^st interval for which more power is needed when compared with 54^th interval, EV1 can’t be used as it got drained to 0.2 SoC. Usage of EV4 at 54^th interval instead of EV1 would let to have EV1 to participate in V2 G at 61^st interval.

Fig. 5

Probability tree showing transition probabilities for the next two intervals.

Fig. 6

Demonstrating impact of EV prioritization.

6.1 Fuzzy logic controller based EV ranking

Fuzzy controller helps to design a decision process through human intuition and logic [46].In this work the four decision variables (SoC, laxity, Usage expectancy and DoD) are used for prioritization process. Here, The first two inputs comes under fleet perspective and the last two comes under EV perspective. Rank of each EV is decided in utility perspective and customer perspective separately. Hence, two fuzzy controllers are designed with two input variables and one output.

Each input and output are assigned with five membership functions (Fig. 7). Here, first fuzzy controller (FC1) assigns rank based on SoC and laxity and FC2 assigns rank based on usage probability and DOD. FC1 aim is to maximize EV usage by strategically planning EVs usage timings based on their SoC and laxity values. FC2 aim is to maximize the battery degradation. The average of the ranks obtained from FC1 and FC2 is taken as the rank of the EV at given t.

Fig. 7

Fuzzy controller (FC1) membership functions.

6.2 Fuzzy rule base

In charging zone, for a given EV, if SoC is high then the rank should be low and vice versa (fleet perspective based on SoC). Lower the Laxity lower will be the flexibility of PEV usage for grid support and hence EV is given highest rank in order to use it as early as possible. Higher the value of DoD higher will be the rank in discharging zone and vice-versa. The EV with the highest usage expectancy could be assigned with lowest rank. The fuzzification rule base for utility perspective (FC1) is shown in Table 3 for charging and discharging zones and FC2, will follow the same pattern as FC1.

Table 3
Fuzzy rule base for FC1

Priority is assigned for each EV depending on rank assigned to it. Higher the rank lesser will be the priority and vice-versa. Based on the priority, EVs are allowed to participate in EMS support. $V_{rank}^{t} = {[\begin{matrix} 0.87 & 0.32 & . & . & . & . & 0.52 & 0.47 \end{matrix}]}_{1 \times N}$ $V_{pri}^{t} = {[\begin{matrix} N - 5 & 8 & . & . & . & . & N - 6 & 5 \end{matrix}]}_{1 \times N}$

The impact of the prioritization on load flattening and other aspects (battery degradation) is discussed in the result section. Also, the role of each decision parameter in the prioritization process is presented with different cases.

7 Case study and result analysis

The proposed EMS strategy is examined in an ON-Grid MG scenario (Educational Institution) hosting 2 DGs of 100 KVA each, solar PV of 500 kW capacity, 50 EVs each of 32kWh, 6 kW power rate. The other technical specifications are furnished in Table 4.The efficacy of the proposed EMS in different cases is reported with the help of results obtained. The authenticated maximum demand from the grid ( $P_{\max}^{g, d}$ ) is curtailed down by 50 kVA and the implications on energy cost are studied for three different cases: Case 1 : 500 kVA max demand ( $P_{\max}^{g, d}$ ), Case 2 : 450 kVA (10% reduction in $P_{\max}^{g, d}$ ) and Case 3 : 400 kVA (20% reduction in $P_{\max}^{g, d}$ ).

Table 4
Technical specifications of MG entities

The individual contribution of OED and SEVP are investigated by through different case studies: Case (a): With proposed EMS, Case (b): Without WFA, Case (c): Without EV ranking, Case (d): EV Ranking without Laxity and SoC as decision variables, Case (e): EV Ranking without Usage expectancy and DoD as decision variables.

7.1 Economic analysis

Total energy cost is investigated in aforementioned case studies. Comparison is done with reference to the case with no EMS. For case (a), the impact on $C_{T}^{op}$ with and without EMS is depicted in Fig. 8. There is appreciable reduction in $C_{T}^{op}$ with the proposed EMS in three cases of max grid demand, $P_{\max}^{g, d}$ . It is observed that $C_{T}^{op}$ is reduced by 11%, 12.6% and 14.3% in case 1, 2 and 3 respectively.The individual participation of EMS and prioritization are also demonstrated in Fig. 8. Optimal distribution of energy among the intervals in each zone plays a key role in betterment of EV storage exploitation (Case (b)). It is seen in terms of minimization of both ΔP_sd and $C_{T}^{op}$ . In Case (c), EVs are chosen randomly to participate in energy transactions (no prioritization). The proposed strategy relays on WFA for optimal energy distribution. This leads to increase in P_a and reduction in $C_{T}^{op}$ as depicted in Fig. 8.

Fig. 8

Cost comparison depicting individual contribution of OSD and prioritization.

Case (c) is purely EV prospective as the decision variables are DoD and Usage expectancy. It leads to better SoC profile or in others words battery will last for longer duration. But, the negative impact on energy cost is inevitable as demonstrated in Fig. 9. Similarly, there is proportional negative impact on load flattening as well (Fig. 9). In case (e), can be designated as the case of utility favour which in contrast to case (d). Here, the battery degradation is not considered during its usage for utility support. However, the micro grid operating cost will get reduce in this scenario. Figure 9 demonstrates all the cases pertaining to prioritization.

Fig. 9

Cost comparison demonstrating impact of decision variables in EV ranking.

7.2 Load profile

In the comparison analysis of load flattening, case 1 has been considered. The individual contribution of OSD and prioritization (i.e. cases (b) and (c)) and decision variables of EV ranking (i.e. cases (d) and (e)) has been projected in Fig. 10. Case (d), which is in contrast to the case (e), EV battery degradation, is taken care form the perspective of EV prioritization by involving DoD and usage expectancy are as the only decision variables. Here, the benefit to the micro grid operator has not been and hence it reflects on the load flattening. In case (e), SoC and Laxity are only the decision variables which are pertaining to benefit of maximization of EV storage exploitation.

One of the decision variables that accounts for better way of EV storage exploitation is Laxity. With the absence of Laxity as a decision variable during the prioritization, load flattening is not achieved at its maximum possible extent. On the other hand, with the absence of the decision variable, ‘usage expectancy’, SoC profile goes in an undesirable manner. In order to provide a statistical view of load flattening, mean and standard deviations of the respective cases are demonstrated in Figs. 11 and 12 respectively.

Fig. 10

Comparison of P in all case studies (case (a) –(e)).

Fig. 11

Comparison of mean and variability of grid power (case (a) –(e)).

Fig. 12

Comparison of standard deviation of grid power (case (a) –(e)).

For case 1, load flattening is achieved with a standard deviation (ΔP_sd) of 111 kW by the proposed EMS strategy, whereas the ΔP_sd without EMS is 228 kW as depicted in Fig. 10. Case (e) has minimum ΔP_sd followed be cases (a), (d), (b) and (c).

7.3 SoC profile

SoC profile is intended to maintain at its minimum average levels in order to avoid low SoC (high DoD) and peak SoC as these two cases causes early battery degradation. In this regard, It is taken care from the prioritization perspective by involving DoD and Usage expectancy as decision variables. The same can be understood from the process of prioritization. As described in Fig. 13, for case (e), SoC and Laxity are only the decision variables that benefits MG operator. In contrast, the case (d) favours battery health. Here, battery is taken care enough while taking decision on EV ranking. In Figs. 13 and 14, the SoC profiles are compared for case (a) and (e) and with reference to the case (d).

Fig. 13

Comparison of SoC profiles for case (a) and (d).

Fig. 14

Comparison of SoC profiles for case (a) and (e).

The impact of decision variables on SoC profile, load flattening and aggregate fleet power is studied for different cases (Fig. 14). The statistical comparison gives little deeper insight on how the SoC profile is varying. SoC profiles can be analyzed using Fig. 15(a) where mean and variability are depicted pictorially. In case (d), the mean SoC is maintained minimum followed by case (a), (c) and (d). The deviation from mean SoC also follows the same sequence as it displayed in Fig. 11.

Fig. 15

(a) Depiction of mean and variability of SoC profile, (b) Load flattening and (c) Aggregate Fleet EV power available at fleet.

The impact on aggregate EV power availability from the fleet is shown in Fig. 15(c) for different cases. This power directly resembles load flattening as well Fig. 15(b). It will have direct impact on it. Here in Case e, it is seen that maximum power from fleet is available due the absence of decision variables: Usage expectancy and DoD. For the same, SoC profile is not in a desirable way which eventually leverages degradation. The opposite case (Case d) can be investigated with the absence of decision variables: SoC and laxity.

8 Conclusion

The proposed EV strategy is mainly intended in two aspects: reducing grid dependency (load flattening) and minimizing energy cost. Here, the probabilistic analysis is used to predict the availability or chance of using the battery for V2 G or G2 V during upcoming intervals. It helps to take a decision on whether to use the EV battery or not in view of battery degradation. Load flattening is achieved using the WFA through optimal dispatch of available EV storage in each interval of the given zone. WFA optimizes the usage of EV storage in each zone based on available and needful energies for load flattening. Later, fuzzy controller is used to prioritise the EVs for V2 G or G2 V support in each interval. The effectiveness of the proposed control strategy is investigated for an educational organization. Comprehensive result analysis is carried out in different case studies individual impact of OSD and prioritization has been investigated. There is a substantial reduction in grid energy cost of the MG. This control strategy helps to minimize the grid dependency through effective utilization of Solar PV and EV storage and hence avoids expenditure on additional storage and diesel generators to support the power intermittencies.

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A novel energy management strategy to reduce gird dependency using electric vehicles storage in coordination with solar power

Abstract

Keywords

1 Introduction

2 Proposed EMS and system description

2.2.1 EV mobility data

3.1 Cost of grid power

5 EV estimating usage expectancy

Table 3 Fuzzy rule base for FC1

Table 4 Technical specifications of MG entities

References

Table 3
Fuzzy rule base for FC1

Table 4
Technical specifications of MG entities