Aggregator Index for 24-Hour Energy Flexibility Evaluation in an ADN Including PHEVs

This paper proposes obtaining maximum and minimum daily cumulative energy curves and introduces novel hourly and daily energy flexibility indices. Also, it develops a generic methodology that quantifies and formulates energy flexibility as the possible power increase (P_in) or decrease (P_dec) within operational limits. The proposed method can be applied to derive maximum and minimum energy flexibility curves for different devices and aggregate them to extract hourly or daily energy flexibility indices based on the calculation area between daily cumulative energy curves in an hour and 24 hours. The proposed energy flexibility estimation is evaluated by doing offline digital time-domain simulations on a 100-bus home-residential active distribution network (ADN), including flexible equipment/devices (e.g., washing machines, dishwashers, domestic heat water, battery, photovoltaic (PV) panels, and plug-in hybrid electric vehicle (PHEV) charging stations) in MATLAB/Simulink software environment. Then, a price-sensitive model of every flexible equipment is introduced, and ultimately, the effect of electricity price changes on energy flexibility is evaluated. The simulations and comparisons of the energy flexibility potential of different pricing scenarios effectively prove the proposed strategy’s effectiveness, accuracy, and authenticity.

Nomenclature

AbbreviationExpansion

$\boldsymbol {E}_{ \boldsymbol {c}} \boldsymbol {.max}$ :	Daily aggregated maximum cumulative energy curve.
$\boldsymbol {E}_{ \boldsymbol {c}} \boldsymbol {.nor}$ :	Daily aggregated normal state cumulative energy curve.
$\boldsymbol {E}_{ \boldsymbol {c}} \boldsymbol {.min}$ :	Daily aggregated minimum cumulative energy curve.
$\boldsymbol {P}_{{ \boldsymbol {inc}}_{\left [{ \boldsymbol {t}_{ \boldsymbol {1}} \boldsymbol {.} \boldsymbol {t}_{ \boldsymbol {2}} }\right ]}}$ :	Power-increasing flexibility in $\left [{ t_{1}.t_{2} }\right ]$ .
$\boldsymbol {P}_{{ \boldsymbol {dec}}_{\left [{ \boldsymbol {t}_{ \boldsymbol {1}} \boldsymbol {.} \boldsymbol {t}_{ \boldsymbol {2}} }\right ]}}$ :	Power-decreasing flexibility in $\left [{ t_{1}.t_{2} }\right ]$ .
$\boldsymbol {m}_{ \boldsymbol {max.} \boldsymbol {t}_{ \boldsymbol {1}}}$ :	The slop of maximum cumulative energy curve in [$t_{1},t_{1}+1$ ].
$\boldsymbol {m}_{ \boldsymbol {nor.} \boldsymbol {t}_{ \boldsymbol {1}}}$ :	The slop of normal state cumulative energy curve in [$t_{1},t_{1}+1$ ].
$\boldsymbol {m}_{ \boldsymbol {min.} \boldsymbol {t}_{ \boldsymbol {1}}}$ :	The slop of minimum cumulative energy curve in [$t_{1},t_{1}+1$ ].
$\overline {(A_{1},.., A_{n})}$ :	Average of $\boldsymbol {(} \boldsymbol {A}_{ \boldsymbol {1}}. \ldots . \boldsymbol {A}_{ \boldsymbol {n}} \boldsymbol {)}$ .
$\boldsymbol {f}_{{ \boldsymbol {inc}}_{ \boldsymbol {t}_{ \boldsymbol {1}}}}$ :	Hourly energy flexibility index, $t_{1}=1.2. \ldots .24$ .
$\boldsymbol {f}_{{ \boldsymbol {inc}}_{ \boldsymbol {t}_{ \boldsymbol {1}}}}$ :	Hourly energy flexibility index, $t_{1}=1.2. \ldots .24$ .
$\boldsymbol {F}_{ \boldsymbol {inc}}$ :	24-hour energy flexibility index.
$F_{dec}$ :	24-hour energy flexibility index.
$FHs$ :	Flexibility hours provided by home appliances.
$N$ :	Number of households that participate in a flexibility program.
$P_{G}\left ({ t,i }\right )$ :	Generation power of household $i$ at time step $t$ .
$P_{C}\left ({ t,i }\right )$ :	Consumption power of household $i$ at time step $t$ .
$P_{EX}\left ({ t,i }\right )$ :	Exchanged power between household $i$ at time step $t$ .
${Pr}_{t}$ :	Day-ahead price at time step $t$ .
${Pr}_{av}$ :	The average price of the day-ahead price profile.
$SOC\left ({ t,i }\right )$ :	Battery’s state of charge of household $i$ at time step $t$ .
${SOC}_{min}$ :	Permissible minimum state of charge.
${SOC}_{min}$ :	Permissible maximum state of charge.
$P_{ch}$ :	Maximum power charging.
$P_{disch}$ :	Minimum power charging.
$N_{BESS}$ :	Total number of battery energy storage systems.

SECTION I. Introduction

A. Motivation and Incitement

Flexibility has become a vital issue today for the reliability and security of the electrical energy supply. Power system flexibility is the ability of a power system to reliably and cost-effectively manage the variability and uncertainty of demand and supply across all relevant timescales. There is a growing necessity for flexibility for the following reasons:

• Increasing the share of renewable energy resources in the energy supply basket,

• Dispersion and intermittent attributes of renewable energy resources,

• Decentralized growth of energy storage systems,

• Electrical load demand increment in the transportation and heating sector because of fossil-fueled systems replacement politics with highly efficient electrical equipment like PHEVs and electrical heat waters [1], and,

• Decrement of the number of traditional controllable power plants.

• Flexibility estimation is essential for planning and managing power systems. Generally, flexibility requirements are considered holistically, both from the overall system perspective and from the more local perspectives [2]:

• From an overall system perspective, flexibility requirements are related to maintaining a stable frequency and secure energy supply.

• From a more local perspective, flexibility requirements are related to maintaining bus voltages and securing transfer capacities.s

The temporary and intermittent nature of renewable energy leads to increased utilization of advanced control systems to enable the flexibility potential of the demand side by a suitable integration system [3]. Households have a vital role in energy flexibility programs on the demand side, as the home sector accounts for approximately 40% of global energy consumption [4]. Also, more than 70% of total electricity in the United States and 90% in Hong Kong is consumed by the building sector [5], [6]. Application of distributed energy resources (DER) technologies such as solar photovoltaic (PV), combined heat and power, electric vehicles (EVs), and energy storage have enabled active building loads by reducing demand and satisfying energy, capacity, and ancillary services requirements [7], [8], [9].

B. Literature Review

In [10], the effect of converting power to heat has been examined, various power-to-heat options have been categorized, and the authors have introduced an analytical model formulation of heat pumps and heat water storage as energy flexibility options. PHEVs can provide energy flexibility by controlling the charging process according to motivations and even act as a distributed storage system on the demand side for supplying required energy in emergencies [11].

In [12], the flexibility potential of the residential appliance has been estimated according to survey data, but it has not explained how the user behavior is modeled. In [13], the flexibility potential of residential households has been estimated according to a fixed percentage of their consumption. However, it has not mentioned how these percentages can be obtained. In [14], the flexibility estimation has been performed in detail, but this study’s survey data are related to non-flexible appliances. In [15], [16], and [17], the flexibility potential of residential appliances has been estimated according to extrapolated consumption data of smart appliances. Besides, [18] has estimated the flexibility potential of households based on data from only one household with flexible appliances. In [19], the electric load shapes and demand response behavior has been characterized, and the modeling methods have been applied to evaluate demand response effectiveness. The definition of energy flexibility can be found in numerous studies and reviews [20], [21], [22]. The common view of these definitions is the ability of the grid to manage predictable or unpredictable changes. However, a more general and industrially-applicable definition is “Power system flexibility is the ability of a power system to reliably and cost-effectively manage the variability and uncertainty of demand and supply across all relevant timescales.”

C. Literature Review

This paper presents a method based on the area between daily cumulative energy curves. By exploiting these curves, the value of energy flexibility potential is estimated. The main contributions of this paper are as follows:

• Formulating the energy flexibility based on maximum, minimum, and normal daily cumulative energy curves,

• Defining energy flexibility hourly and 24-hours indices,

• Comparing the energy flexibility potential between different energy management scenarios,

• Introducing the price-sensitive models of various home appliances, and

• Assessment of the effect of price changes in three-step daily price profiles on energy flexibility.

SECTION II. Energy Flexibility Estimation Method

Household maximum and minimum daily cumulative energy consumption curves are determined by flexible appliances and energy generation and storage systems such as washing machines, dishwashers, domestic heat water (DHW), batteries, and solar panels. The distribution grid aggregators aggregate daily averages of cumulative household energy consumption in a specific area. The total maximum and minimum cumulative energy curves determine power-increasing and power-decreasing flexibility over a certain period.

In this paper, energy flexibility is defined as the ability to increase or decrease the consumption power of a particular area in a given period, referred to as power-increasing flexibility and power-decreasing flexibility, respectively. (see Fig. 1) [20]. $$\begin{align*} \text {P}_{\text {inc}} [\text {t}_{1},\text {t}_{2} ]&=\text {P}_{1} -\text {P}_{\text {ref}} \\ & =\left \{{\left ({ {\frac {\text {E}_{\text {c,max}} (\text {t}_{2} )-\text {E}_{\text {c,normal}} (\text {t}_{1} )}{\text {t}_{2} -\text {t}_{1}}} }\right )}\right . \\ &\left .{\quad -\left ({ {\frac {\text {E}_{\text {c,normal}} (\text {t}_{2} )-\text {E}_{\text {c,normal}} (\text {t}_{1} )}{\text {t}_{2} -\text {t}_{1}}} }\right ) }\right \} \\ &=\left ({ {\frac {\text {E}_{\text {c,max}} (\text {t}_{2} )-\text {E}_{\text {c,normal}} (\text {t}_{2} )}{\Delta \text {T}}} }\right ) \\ \text {P}_{\text {dec}} [\text {t}_{1},\text {t}_{2} ]&=\text {P}_{2} -\text {P}_{\text {ref}} \\ &=\left \{{\left ({ {\frac {\text {E}_{\text {c,min}} (\text {t}_{2} )-\text {E}_{\text {c,normal}} (\text {t}_{1} )}{\text {t}_{2} -\text {t}_{1}}} }\right )}\right . \\ &\left .{\quad -\left ({ {\frac {\text {E}_{\text {c,normal}} (\text {t}_{2} )-\text {E}_{\text {c,normal}} (\text {t}_{1} )}{\text {t}_{2} -\text {t}_{1}}} }\right )}\right \} \\ &=\left ({ {\frac {\text {E}_{\text {c,min}} (\text {t}_{2} )-\text {E}_{\text {c,normal}} (\text {t}_{2} )}{\Delta T}} }\right ) \tag{1}\end{align*}$$

FIGURE 1.

Daily aggregated cumulative energy curves.

SECTION III. Energy Flexibility Indices

In this paper, hourly and 24-hours indices compare numerous more flexible scenarios. As shown in Fig. 2, to calculate the hourly maximum/minimum energy flexibility index, the area between the maximum/minimum aggregated cumulative energy curve and the normal aggregated cumulative energy curve every hour is calculated. It is divided into the total area between the maximum aggregated cumulative energy curve and the minimum aggregated cumulative energy curve every hour (sampling rate of cumulative energy curves: 4 samples per hour). $$\begin{align*} \text {m}_{\text {max},\text {t}_{1}}& =\frac {\text {E}_{\text {c,max}} (\text {t}_{1} +1)-\text {E}_{\text {c,max}} (\text {t}_{1} )}{(\text {t}_{1} +1)-(\text {t}_{1} )} \\ &=\text {E}_{\text {c,max}} (\text {t}_{1} +1)-\text {E}_{\text {c,max}} (\text {t}_{1} ) \\ \text {m}_{\text {nor},\text {t}_{1}} &=\frac {\text {E}_{\text {c,nor}} (\text {t}_{1} +1)-\text {E}_{\text {c,nor}} (\text {t}_{1} )}{(\text {t}_{1} +1)-(\text {t}_{1} )} \\ &=\text {E}_{\text {c,nor}} (\text {t}_{1} +1)-\text {E}_{\text {c,nor}} (\text {t}_{1} ) \\ \text {m}_{\text {min},\text {t}_{1}} &=\frac {\text {E}_{\text {c,min}} (\text {t}_{1} +1)-\text {E}_{\text {c,min}} (\text {t}_{1} )}{(\text {t}_{1} +1)-(\text {t}_{1} )} \\ &=\text {E}_{\text {c,min}} (\text {t}_{1} +1)-\text {E}_{\text {c,min}} (\text {t}_{1} ) \tag{2}\\ \text {E}_{\text {c,max}} (\text {t})-\text {E}_{\text {c,max}} (\text {t}_{1} )&=\text {m}_{\text {max},\text {t}_{1}} \times (t-\text {t}_{1} ) \\ \text {E}_{\text {c,max}} (\text {t})&=\left ({ {\text {m}_{\text {max},\text {t}_{1}}} }\right )\times \text {t} \\ &\quad +\left [{ {\text {E}_{\text {c,max}} (\text {t}_{1} )-\left ({ {\text {m}_{\text {max},\text {t}_{1}} \times \text {t}_{1}} }\right )} }\right ] \\ \text {E}_{\text {c,max}} (\text {t})&=\left [{ {\text {A}(\text {t}_{1} )\times t} }\right ]+\text {B}(\text {t}_{1} ) \\ \text {E}_{\text {c,nor}} (\text {t})-\text {E}_{\text {c,nor}} (\text {t}_{1} )&=\text {m}_{\text {nor},\text {t}_{1}} \times (t-\text {t}_{1} ) \\ \text {E}_{\text {c,nor}} (\text {t})&=\left ({ {\text {m}_{\text {nor},\text {t}_{1}}} }\right )\times \text {t} \\ &\quad +\left [{ {\text {E}_{\text {c,nor}} (\text {t}_{1} )-\left ({ {\text {m}_{\text {nor},\text {t}_{1}} \times \text {t}_{1}} }\right )} }\right ] \\ \text {E}_{\text {c,nor}} (\text {t})&=\left [{ {C(\text {t}_{1} )\times \text {t}} }\right ]+\text {D}(\text {t}_{1} ) \\ \text {E}_{\text {c,min}} (\text {t})-\text {E}_{\text {c,min}} (\text {t}_{1} )&=\text {m}_{\text {min},\text {t}_{1}} \times (t-\text {t}_{1} ) \\ \text {E}_{\text {c,min}} (\text {t})&=\left ({ {\text {m}_{\text {min},\text {t}_{1}}} }\right )\times t \\ &\quad +\left [{ {\text {E}_{\text {c,min}} (\text {t}_{1} )-\left ({ {\text {m}_{\text {min},\text {t}_{1}} \times \text {t}_{1}} }\right )} }\right ] \\ \text {E}_{\text {c,min}} (\text {t})&=\left [{ {\text {E}(\text {t}_{1} )\times \text {t}} }\right ]+\text {F}(\text {t}_{1} ) \tag{3}\end{align*}$$ $$\begin{align*}\text {S}_{\text {inc},\text {t}_{1}} &=\sum \limits _{\text {i}=\left ({ {4\times \text {t}_{1} -3} }\right )}^{\left ({ {4\times \text {t}_{1} -1} }\right )} {\int _{\text {i}}^{\text {i}+1} {\int _{\text {E}_{\text {c,nor}} (\text {t})}^{\text {E}_{\text {c,max}} (\text {t})} {\text {dE}\times \text {dt}}}} \\ &=\sum \limits _{\text {i}=\left ({ {4\times \text {t}_{1} -3} }\right )}^{\left ({ {4\times \text {t}_{1} -1} }\right )} {\frac {\left ({ {A(\text {t}_{1} )-\text {C}(\text {t}_{1} )} }\right )}{2}} \\ &\quad \times \left [{ {2\text {i}+1} }\right ]+\left ({ {\text {B}(\text {t}_{1} )-\text {D}(\text {t}_{1} )} }\right ) \\ \text {S}_{\text {dec},\text {t}_{1}}& =\sum \limits _{\text {i}=\left ({ {4\times \text {t}_{1} -3} }\right )}^{\left ({ {4\times \text {t}_{1} -1} }\right )} {\int _{\text {i}}^{\text {i}+1} {\int _{\text {E}_{\text {c,min}} (\text {t})}^{\text {E}_{\text {c,nor}} (\text {t})} {\text {dE}\cdot \text {dt}}}} \\ & =\sum \limits _{\text {i}=\left ({ {4\times \text {t}_{1} -3} }\right )}^{\left ({ {4\times \text {t}_{1} -1} }\right )} {\frac {\left ({ {\text {C}(\text {t}_{1} )-\text {E}(\text {t}_{1} )} }\right )}{2}} \\ &\quad \times \left [{ {2\text {i}+1} }\right ]+\left ({ {\text {D}(\text {t}_{1} )-\text {D}(\text {t}_{1} )} }\right ) \tag{4}\\ \text {f}_{\text {inc},\text {t}_{1}} &=\frac {\text {S}_{\text {inc},\text {t}_{1}}}{\text {S}_{\text {total},\text {t}_{1}} }=\frac {\text {S}_{\text {inc},\text {t}_{1}}}{\text {S}_{\text {inc},\text {t}_{1}} +\text {S}_{\text {dec},\text {t}_{1}} } \\ &\quad \left ({ {0\,\,\le \,\,\text {f}_{\text {inc},\text {t}_{1}} \,\le \,\,1} }\right ) \\ \text {f}_{\text {dec},\text {t}_{1}} &=\frac {\text {S}_{\text {dec},\text {t}_{1}}}{\text {S}_{\text {total},\text {t}_{1}} }=\frac {\text {S}_{\text {dec},\text {t}_{1}}}{\text {S}_{\text {inc},\text {t}_{1}} +\text {S}_{\text {dec},\text {t}_{1}} } \\ &\quad \left ({ {0\,\,\le \,\,\text {f}_{\text {dec},\text {t}_{1}} \,\le \,\,1} }\right ) \tag{5}\end{align*}$$ $$\begin{align*}\text {F}_{\text {inc}} &=\frac {\sum \nolimits _{\text {t}_{1=1}}^{24} {\text {f}_{\text {inc},\text {t}_{1}}} }{24} \\ &=\left ({ {\overline {\text {f}_{\text {inc},1} \,,\,\,\text {f}_{\text {inc},2} \,,\,\ldots \,,\,\text {f}_{ \text {inc},24}}} }\right ) \\ \text {F}_{\text {dec}} &=\frac {\sum \nolimits _{\text {t}_{1=1}}^{24} {\text {f}_{\text {dec},\text {t}_{1}}} }{24} \\ &=\left ({ {\overline {\text {f}_{\text {dec},1} \,,\,\,\text {f}_{\text {dec},2} \,,\,\ldots \,,\,\text {f}_{\text {dec},24}}} }\right ) \tag{6}\end{align*}$$

FIGURE 2.

The area between aggregated cumulative energy curves.

SECTION IV. Price-Sensitive Model of Loads Equipment

This paper estimates the energy flexibility provided by home appliances and storage units. A price-sensitive load model must be defined to examine the effect of price variation on energy flexibility in the day-ahead electricity price profile. The following presents a price-sensitive model of home appliances like washing machines, dishwashers, domestic heat water, and lighting load. Also, batteries’ charging and discharging algorithms belong to buildings equipped with photovoltaic panels and plug-in hybrid electric vehicles (PHEVs) batteries.

A. Washing Machine and Dishwasher Price-Sensitive Model

Time of use (TOU) and hours of participation in flexibility programs (FHs) have been shown in Table 1. In [23], the consumption profile of washing machines and dishwashers has been presented. Also, owners are given a day-ahead electricity price profile, and they can select the optimum TOU of every appliance according to its TOU, FHs, and cost of energy consumption based on the day-ahead electricity price profile in the range of [TOU-FHs, TOU-FHs].

TABLE 1 TOU and Fhs Information on Washing Machines and Dishwashers

In this price-sensitive model, the starting point is moved in the time steps in the range of [TOU-FHs, TOU-FHs]. In every step, the cost of energy consumption is calculated according to the consumption power profile and day-ahead electricity price profile. Finally, the optimum time of use (${TOU}_{opti})$ of the appliance is obtained with the object of minimum cost of energy consumption.

B. Domestic Heat Water (DHW) Price-Sensitive Model

In this model, to consider the prosperity of households, the temperature of water in the storage tank should be kept within [$T_{min},T_{max}]$ which are selected by the households.

For simplification of this model, $T_{min}~and~T_{max}$ is considered the same for all households. According to Fig. 3, in every time step, the reference temperature ($T_{ref})$ of DHW is obtained according to $T_{min}$ , $T_{max}$ Maximum and minimum price in the day-ahead electricity price profile and electricity price in that time-step. If in time step t, the water temperature of the tank of DHW is higher than $T_{ref.t}$ ; the DHW heater turns off; otherwise, the heater will be turned on. $$\begin{align*} \text {T}_{\text {ref,t}} &=\text {T}_{\text {min}} +\left \{{{\left ({ {\text {Pr}_{\text {t}} -\text {Pr}_{\text {max}}} }\right )\times \frac {\text {T}_{\text {max}} -\text {T}_{\text {min}}}{\text {Pr}_{\text {min}} -\text {Pr}_{\text {max}}}\,} }\right \} \\ &\quad \text {t}=1,2,\ldots,96 \tag{7}\end{align*}$$

FIGURE 3.

Calculating reference temperature in time step $t$ .

The daily power consumption profile of households’ DHW is needed to derive the price-sensitive daily cumulative energy curve. Table 2 considers three random distributions to gather households’ daily hot water consumption.

TABLE 2 Random Distribution of Households’ Heat Water Consumption

In every time step, the equilibrium temperature of ${DHW}_{i}$ ($T_{eq}(t,i))$ is calculated according to the hot water consumption of ${DHW}_{i}$ (${HWC}_{i})$ , the temperature of residual water in the DHW’s tank ($T_{res,w}(t,i))$ , total volume of ${DHW}_{i}$ ($V_{i})$ , and the temperature of the water, which is replaced with consumed hot water ($T_{w})$ . $$\begin{align*}\text {T}_{\text {eq}} (\text {t},\text {i})&=\left ({ {\frac {\text {HWC}(\text {t},\text {i})}{\text {V}_{\text {i}}}\times \text {T}_{\text {w}}} }\right ) \\ &\quad +\left ({ {\frac {\text {V}_{\text {i}} -\text {HWC}(\text {t},\text {i})}{\text {V}_{\text {i}}}\times \text {T}_{\text {res},\text {w}} (\text {t},\text {i})} }\right ) \\ &\quad \text {t}=1,2,\ldots,96\,\,\,\,\,\,\,\,\,\,\,\,\,\& \,\,\,\,\,\,\,\text {i}=1,2,\ldots,\text {N} \tag{8}\end{align*}$$

In this paper, the volume of DHW’s tank in all households and the temperature of cold water ($T_{w})$ , is considered 100 Litr and 18°, respectively, for simplification. Comparison between $T_{eq}\left ({ t,i }\right )$ and $T_{ref.t}$ in every time step is specified whether the $DHW_{i}$ should be turned on or not. If $T_{eq}\left ({ t,i }\right )$ be less than $T_{ref.t}$ , then the $DHW_{i}$ in the time step, $t$ will be turned on; otherwise, it will be turned off. The energy consumption of DHW in a time step when it is turned on is calculated by the below relation. $$\begin{equation*} \text {E}_{\text {DHW}} (\text {t},\text {i})^{\text {kWh}}=\text {P}_{\text {DHW}_{\text {i}}}^{\text {kW}}\times 0.25^{\text {h}} \tag{9}\end{equation*}$$

For simplification, $P_{DHW}$ is considered 1kW for all of DHWs.

C. Charging and Discharging Algorithm of the Building’s Battery

This paper considers the battery storage system for households with a PV system. The charging and discharging strategy of a building’s battery has been designed in Fig. 4 based on every household’s total generation and consumption and the day-ahead price profile. The maximum and minimum state of charge (${SOC}_{max}$ , ${SOC}_{min})$ and the maximum power of the Charger in charging mode (G2V) and discharging mode (V2G) are considered the limiting factors in this planning. Finally, the energy consumption and generation of the batteries in every time step are calculated by the below relation. $$\begin{align*} \text {E}_{\text {BATT}} (\text {t}\,,\text {i})&=\left [{ {\text {SOC}(\text {t}+1\,,\,\text {i})\,\,-\,\,\text {SOC}(\text {t}\,,\,\text {i})} }\right ] \\ &\quad \times \text {CAP}_{\text {BATT}} \,\,\,\,\,\,\forall \text {t}\in \,1,2,\ldots,96 \tag{10}\end{align*}$$

FIGURE 4.

The charging and dischrging algoritm for battry energy storage systems.

The specification of the energy storage system of buildings is shown in Table 3.

TABLE 3 The Specification of the Energy Storage System of Buildings

D. Charging and Discharging Algorithm of PHEVS’ Battery

This paper supposed that 50% of households possess PHEVs inclined to contribute flexibility programs and exchange power from the battery to the grid (V2G) or conversely (G2V). In the other word, according to the day-ahead price profile, the minimum and maximum permissible state of charge (${PSOC}_{min}, {PSOC}_{max})$ specified by PHEV owners, the charging and discharging strategy are designed. In this study, it is supposed that 20% of PHEVs contribute flexibility programs only at parking lots of buildings, and 30% contribute flexibility programs only at stations nearby the workplace. The others contribute flexibility programs at both places. Table 4 shows information such as arrival time, departure time, initial SOC, and location of the PHEVs.

TABLE 4 The Information of the PHEVs in the Flexibility Program

In the proposed charging and discharging strategy, the PHEVs are charged when the hourly electricity price be less than the average price of the day-ahead price profile, and the SOC of the battery must not be higher than ${PSOC}_{max}$ . On the other hand, the PHEVs are discharged when the hourly electricity price is higher than the average price of the day-ahead price profile, and the SOC of the battery must not be less than ${PSOC}_{min}$ . Finally, the energy consumption and generation of every PHEV’s battery in every time step is calculated by the below relation. $$\begin{align*} \text {E}_{\text {BATT}}^{\text {PHEV}} (\text {t}\,,\text {i})&=\left [{ {\text {SOC}(\text {t}+1\,,\,\text {i})\,\,-\,\,\text {SOC}(\text {t}\,,\,\text {i})} }\right ] \\ &\quad \times \text {CAP}_{_{\text {BATT}}}^{\text {PHEV}} \,\,\,\,\,\forall \text {t}\in \,1,2,\ldots,96 \tag{11}\end{align*}$$

SECTION V. Case Study

In this section, a microgrid with 100 households is considered. Some of those have home appliances such as a Washing- machine, dishwasher, and DHW participating in flexibility programs. Also, some households have equipment such as PV panels, Battery Energy Storage Systems, and PHEVs participating in flexibility programs. In Fig. 5, the outline of the sample microgrid is shown. The final goal of this study is the collection of generation or consumption energy data of the different sections of the study case and estimating the energy flexibility of a sample microgrid due to the information gathered from households and the microgrid’s components. The day-ahead electricity price information of two various price scenarios is shown in Table 5. Pricing criteria are based on low, medium, and full load times.

TABLE 5 The Day- Ahead Electricity Price Information

FIGURE 5.

The outline of the sample microgrid.

SECTION VI. Simulation Results

Two scenarios are provided in this paper to validate the proposed method for estimating energy flexibility potential.

A. Scenario 1: Evaluation of Energy Flexibility Potential of Proposed Microgrid in Section (V)

In this study case, 60 PV units were considered randomly for distributed generation of the houses. The total daily power generation of PV panels has been illustrated in Fig. 6. In Figs. 7 and 8 illustrate the washing machine and dishwasher’s maximum, minimum, and daily cumulative energy curves. Also, in Figs, normal daily cumulative energy by applying price-sensitive models. 7 and 8.

FIGURE 6.

Total power generation of PV panels [25].

FIGURE 7.

Daily cumulative energy profiles of washing machines.

FIGURE 8.

Daily cumulative energy profiles of dishwashers.

The impact of electricity price on displacement TOU of the washing machines and dishwashers is evident in Figs. 7 and 8, respectively. As expected, because of the low electricity price in the time range of 00:00 to 08:00 in price profile 1, some of the washing machines and dishwashers, which are allowed to start during this period according to parameters like TOU and FHs, set earlier to decrease total cost of energy consumption. Whereas due to price profile 2, the minimum price is related to the range of 16:00 to 24:00.According to Figs. 7 and 8, as much as the electricity price is approached at the minimum price of the day-ahead prices, the normal cumulative energy of washing machines and dishwashers is approached to maximum daily cumulative energy curves.

On the other hand, the normal cumulative energy of washing machines and dishwashers is approached to minimum daily cumulative energy curves when the electricity price is approached to the maximum price of the day-ahead prices, provided that the displacement of TOU of the objective appliance is possible. Fig. 9 shows the maximum and minimum daily cumulative Energy profiles of DHWs. Also, the normal daily cumulative energy by considering the daily price impact on the energy consumption of DHWs has been calculated. For this purpose, two operation mode has been designed below.

• Operation Mode 1: Calculating normal daily cumulative energy by applying price impact on consumption energy of DHWs, so that According to section II-B, the reference temperature of DHWs in every time step is specified based on Fig. 3.

• Operation Mode 2: Calculating normal daily cumulative energy by not applying price impact on consumption energy of DHWs so that the reference temperature of DHWs in every time step is selected randomly within [$T_{min},T_{max}$ ].

FIGURE 9.

Daily cumulative energy consumption of DHWs.

As illustrated in Fig. 9, in the range of 00:00 to 08:00, the reference temperature OM1 is higher than the reference temperature OM2. Therefore, the energy consumption of the DHWs, in OM1 is more than in OM2. In the range of 08:00 to 16:00, the electricity price has been maximum, and the reference temperature has been $T_{min}$ Furthermore, the heater of the DHW s sets off. The equilibrium temperature of DHWs’ storage tank is decreasing by heat water consumption of households until the equilibrium temperature of DHWs’ storage tank equals $T_{min}$ . At this moment, the DHW sets on. Finally, in the range of 16:00 to 24:00, the price of electricity is decreased, and the reference temperature becomes more than $T_{min}$ and energy consumption of DHWs is increased. In Fig. 10, the maximum and minimum daily cumulative energy curves have been achieved by charging and discharging all BESSs at the beginning of the day. The normal daily cumulative energy has been calculated due to factors used in the BESSs charging and discharging flowchart in Fig. 4. These factors are SOC of BESSs, hourly electricity price, generation power, and consumption power of every household.

FIGURE 10.

Daily cumulative energy profiles of BESSs.

Considering three types of PHEVs’ owners’ contribution in this study case that is mentioned in Table 3, and due to the day-ahead electricity price information in Table 4, the daily cumulative energy profiles of three groups of PHEVs are calculated (Fig. 11). In this study case, the average daily electricity price is equal to 0.086667 ${\$}$ /kWh according to the day-ahead electricity price. All PHEVs are expected to be in charging mode within [00:00–08:00], as the electricity price in this period is less than the average electricity price of the day-ahead electricity price profile. Due to the absence of PHEVs that belong to the type2 within [00:00–06:00], despite the proper condition for PHEVs charging, the cumulative energy of this group has been equal to zero.

FIGURE 11.

Daily cumulative energy profiles of PHEVs.

Finally, as seen in Fig. 12, the total daily cumulative energy curves related to the objective zone are achieved by summing all the maximum, minimum, and normal curves of various sectors contributing to the flexibility program. According to the provided strategy in Section II, the hourly power-increasing flexibility and hourly power-decreasing flexibility are calculated, which is mentioned in Figs. 13 and 14, respectively. By comparison of electricity prices information in Table 4, it is expected that the total consumption power related to price profile 2, in the range of [16:00,24:00], will be increased. Consequently, in the range of [16:00,24:00], hourly power-increasing flexibility in price profile 2 is less than in price profile 1. In other words, the hourly power-decreasing flexibility in price profile 2 is more than the hourly power-decreasing flexibility in price profile 1. All the above results are evident in Figs. 12–​14.

FIGURE 12.

Total daily cumulative energy profiles.

FIGURE 13.

Hourly power increasing flexibility.

FIGURE 14.

Hourly power decreasing flexibility.

According to the relations presented in Section III, hourly increased and decreased energy flexibility indices are calculated for price profiles 1 and 2. Hourly energy flexibility rate is described with the help of hourly increased and decreased energy flexibility indices. When the energy flexibility index is approached 1, energy flexibility is increased. Due to the hourly increase and decreased energy flexibility indices profile in Figures 15 and 16, in the range of [17:00,24:00], the tendency to increase power in price profile 1 is higher than in price profile 2. On the contrary, the tendency to power decrease in price profile 2 is more than in price profile 1. For daily increasing and decreasing energy flexibility assessment, daily increased and decreased energy flexibility are presented by indices that realize the daily energy flexibility potential comparison possibility between diverse scenarios. According to Fig. 17, daily increased and decreased energy flexibility indices are achieved by calculating the average of the hourly increased and decreased energy flexibility indices, respectively. Generally, the daily increased energy flexibility index in price profile 1 is more than the daily increased energy flexibility index in price profile 2. On the contrary, the daily decreased energy flexibility index in price profile 2 is more than the daily decreased energy flexibility index in price profile 1.

FIGURE 15.

Hourly increased energy flexibility indexes profile.

FIGURE 16.

Hourly decreased energy flexibility indexes profile.

FIGURE 17.

Daily increased and decreased energy flexibility indexes.

B. Scenario 2: Comparison With a Previously-Reported Flexibility Evaluation Technique [24]

In [24], three EV charging strategies have been presented, and their energy flexibility potential has been evaluated. Minimum Time (MT), economic Model Predictive Control (eMPC), and Optimal Control with Minimum Cost and Maximum Flexibility (OCCF) have been considered for each Charger in the charging station. Maximum charging power in fast mode has been considered 50kW, and the battery capacity of an EV is 80kWh. To analyze the proposed charging strategies, the EV charger schedule for one charging station has been reported in Table 6. The power profile of EV charger (I) with the different strategies has represented in Fig. 18. The proposed strategy of this paper determines the maximum and minimum cumulative energy curves of this scenario. All the cumulative energy curves have represented in Fig. 19.

TABLE 6 EV Charger (i) Schedule

FIGURE 18.

Power profiles of EV Charger (I) with the different strategies.

FIGURE 19.

Cumulative energy curves of EV Charger (I).

According to Fig. 19 and the proposed energy flexibility estimation strategy, daily increasing and decreasing energy flexibility indices are calculated (Fig. 20). According to Fig. 20 and Table 4 in [24], the OCCF strategy is more flexible than the eMPC strategy and eMPC strategy is more flexible than MT strategy from increasing power potential prospective. Also, the MT strategy is more flexible than the eMPC strategy, and the eMPC strategy is more flexible than the OCCF strategy from decreasing power potential perspective. The results effectively prove the accuracy and authenticity of the method presented in this paper.

FIGURE 20.

Daily increasing and decreasing energy flexibility indexes of EV Charger (I) with the different strategies.

SECTION VII. Conclusion

This paper presents and formulates a novel approach to estimating energy flexibility. We propose a generic methodology that quantifies and formulates energy flexibility as possible power increases and decreases within operational limits. Utilizing this formulation, energy flexibility indices were introduced that allow comparisons between various pricing scenarios. The maximum and minimum cumulative energy curves for a day were obtained, along with indices of energy flexibility created hourly and daily. We derived maximum and minimum energy flexibility curves for different types of devices. We extracted hourly or daily energy flexibility indices using the calculation areas between daily cumulative energy curves recorded in one hour and one day. Additionally, the price-sensitive models corresponding to each load were introduced to apply the reaction of loads to pricing politics. This makes it possible to change energy flexibility by changing electricity prices over a specific period. The proposed energy flexibility estimation strategy was evaluated using offline digital time-domain simulations in MATLAB/Simulink software on a home-residential grid. The simulation results and comparisons of the presented energy flexibility potential of different pricing scenarios revealed that the proposed strategy is effective, accurate, and authentic.