A Multi-Objective Optimization Approach towards a Proposed Smart Apartment with Demand-Response in Japan

Abstract

In Japan, residents of apartments are generally contracted to receive low voltage electricity from electric utilities. In recent years, there has been an increasing number of high voltage batch power receiving contracts for condominiums. In this research, a high voltage batch receiving contractor introduces a demand–response in a low voltage power receiving contract, which maximizes the profit of a high voltage batch receiving contractor and minimizes the electricity charge of residents by utilizing battery storage, electric vehicles (EV), and heat pumps. A multi-objective optimization algorithm calculates a Pareto solution for the relationship between two objective trade-offs in the MATLAB${}^{\circledR }$ environment.

1. Introduction

The use of renewable energy resources is necessary to generate electricity to help mitigate environmental problems. In Japan, the introduction of renewable energies, specifically photovoltaic (PV) systems, is rapidly expanding. However, PV has the disadvantage that its output power fluctuates depending on the weather conditions. Furthermore, PV cannot generate electricity at night or early in the morning due to the absence of the Sun. Therefore, in order to supply electricity even during the period when PV cannot generate electricity, the use of battery storage is effective. Currently, many researchers are working on a new home energy management system (HEMS) with PV, wind generators (WG), and storage systems. The work in [1] introduced PV coupled with battery banks and proposed energy consumption models for smart homes using demand–response. The energy scheduling problem of smart houses with PV, diesel generators, and batteries and the unit commitment problem of power generation companies were described in [2]. The work in [3] proposed a probabilistic model of HEMS using a demand–response program, taking into account the uncertainties of EV availability and renewable power generation. The researchers in [4] compared proportional-integral-derivative (PID) and model predictive control of home air conditioning with PV and demand–response. S.van der Stelt et al. discussed the technical and economic feasibility of combining energy storage systems and demand-side management, and HEMS scheduled the allocation of energy sent from PV systems, batteries, and grid to meet household power demand [5]. The structure and functional models of smart HEMS that use PV, WG, geothermal energy, and biomass were outlined in [6], where the scheduling of home appliances was considered to reduce electricity charges, as well as improve energy efficiency. The work in [7] described the benefits and possibilities of demand–response in smart grids.

It is possible for the EV to play the role of a storage battery during parking at home. Many researchers are studying a system that not only powers EVs from homes, but also powers homes from EVs. The work in [8] proposed a stochastic dynamic programming framework for optimal energy management of smart homes with plug-in electric vehicles’ (PEV) energy storage with vehicle-to-grid (V2G), vehicle-to-home (V2H), and grid-to-vehicle (G2V) modes of operation. Ozan Erdinc et al. discussed dynamic pricing and demand–response strategies with bidirectional availability of EV and energy storage systems [9]. The work in [10] proposed an evaluation of a framework for smart households that have introduced an electric vehicle with an interactive power flow function, an energy storage system, and a small distributed power generation unit. The work in in [11] also dealt with V2H, V2V, and V2G technologies.

On the other hand, there is an increasing number of bulk high voltage traders (aggregators) contracting to receive power from a power company at high voltage and sell it to apartment residents in Japan. The received power contract at high voltage has the advantage of a low price per kWh. Therefore, the difference between the electricity charge from the apartment and the electricity business is a benefit for the aggregator.

In this study, a smart apartment model is presented, which maximizes the profit of the bulk high voltage trader and minimizes the electricity charges of smart apartment residents. NSGA-II is applied as a multi-objective optimization method in the MATLAB${}^{\circledR }$ environment. This algorithm calculates Pareto solutions of two objective functions.

The remainder of this paper is organized as follows. Section 2 refers to a hot water supply system using a smart condominium model and a heat pump using a solar heat collector introduced to the smart apartment. Section 3 refers to real-time pricing applied as a demand response approach. Section 4 describes the objective functions and constraints of this study. Section 5 describes the optimization method used in this study. Section 6 represents simulation conditions and simulation results with analysis. The conclusions are given in Section 7.

2. Smart Apartment Model

Figure 1 shows the smart apartment building model considered in this study [12,13]. The photovoltaic system (PV) and the storage battery was introduced into the apartment model [14]. The rated power of PV was 20 kW. Storage battery capacity and rated inverter output were 2000 kWh and 20 kW, respectively. In addition, 10 units of the heat pump (HP) with a coefficient of performance (COP) value of 3.5 and solar heat collectors (SC) were introduced in the smart apartment model [15,16,17]. The smart apartment included 100 households.

Figure 2 shows the proposed contract between a smart apartment, an electric utility, and a bulk high voltage trader. Bulk high voltage traders receive high voltage power by entering a high voltage contract with an electric utility. After that, the high voltage power is converted to a low voltage, and the power is supplied to the smart apartment, which has a low voltage contract. High voltage power supply contracts have the advantage of low cost. Therefore, the difference between the electricity charges received from the apartment and the electricity charges paid to the electricity supplier is the benefit of the bulk high voltage trader.

In addition, bulk high voltage traders apply real-time pricing as a demand–response method to equalize the power load on the apartment. The storage battery, EV, and HP are used to adjust the power load. By applying real-time pricing, bulk high voltage traders can reduce the basic charge for incoming contracts with utilities. On the other hand, the residents of the apartment will reduce their electricity bills by adjusting the power consumption. The reduced electricity charges will be indicated by the bulk high voltage trader.

Hot Water Supply System from HP Using a Solar Collector

In this paper, we considered three SCs as an auxiliary heat source for the heat pumps [18]. The area of SC, $A_{SC}$, and SC efficiency, ${\eta }_{SC}$, were $1.6{\mathrm{m}}^2$ and $60\%$, respectively. The hot water supply system using SC can be formulated by Equations (1)–(7) [19]. The characteristic of hot water temperature depends on the ambient temperature, solar insolation, and time. The characteristic is obtained as follows:

$$\frac{d{T}_h}{dt}=\frac{Q_h}{1000A_w}$$

(1)

$$\frac{d{Q}_h}{dt}=-{\alpha }_h(T_h-T)$$

(2)

where $T_h$ (${}^{\circ }$C) is the water temperature in the storage tank, $Q_h$ (J) denotes the quantity of heat in the tank, $A_w$ (ℓ) is the capacity of the storage tank, ${\alpha }_h$ is the specific heat of the water, and T (${}^{\circ }$C) indicates the ambient temperature. The amount of heat from solar irradiation is obtained by the following equation:

$$Q_a={\eta }_{SC}{I}_{a}n{A}_{SC}$$

(3)

where $I_a$ (J) and n are the solar irradiation and the number of SC panels, respectively. The heat loss by supplying hot water $Q_{tl}$ (cal), the added heat by the city’s water supply $Q_{sw}$ (cal), the amount of the hot water supply $A_{tl}\left(l\right)$, the amount of the city’s water supply $A_{sw}$ (L), and the heat from SC $Q_e$ (J) are calculated as follows:

$$Q_{tl}=1000A_{tl}{T}_h$$

(4)

$$Q_{sw}=1000A_{sw}{T}_w$$

(5)

$$A_{tl}=A_{sw}=\frac{T_l-T_w}{T_h-T_w}{A}_l$$

(6)

$$Q_e=1000A_w(T_e-T_h)$$

(7)

where $T_l$ (${}^{\circ }$C) is the temperature of the hot water supply, $T_w$ (${}^{\circ }$C) stands for the temperature of the city’s water supply, $A_l$ (L) indicates the amount of the hot water supply, and $T_e$ (${}^{\circ }$C) is the target temperature.

3. Demand–Response Method

In this section, the demand–response method used in this study and the modeling of the load response to price are described. Section 3.1 describes the real-time pricing of the demand–response method used in this study. Section 3.2 describes the load response modeling.

3.1. Overview of Demand–Response

Demand–response is a mechanism where end-users change their pattern of electricity consumption to cope with the variation of electricity rates implied by the utility, or they can lower their power usage in case of an emergency such as system imbalance, or high electricity market price by being involved in schemes like incentive pricing or new tariffs [7]. If power generation is performed with a high cost power source such as thermal power generation during peak hours of power demand, it may be possible to suppress power generation with a high cost power source by suppressing power demand through demand–response.

There are three ways to change the use of electricity in demand–response by the participation of consumers. These are reducing their energy consumption through load curtailment strategies, moving energy consumption to a different time period, and using on site standby generated energy, thus limiting their dependence on the main grid. The load reduction strategy is achieved by lowering the brightness level of the room lighting or by setting the air conditioner temperature appropriately. The movement of energy consumption is achieved by moving energy demand from a period of higher power costs to a period of lower costs, such as pre-cooling a building. Limiting the dependency on the main grid can be achieved by using the power generated on site, utilizing storage technology, stopping industrial facilities at night, or moving a part of production to other industrial facilities.

On the other hand, consumers can participate in the demand–response program through the aggregator. In addition, if the user is provided with sufficient incentives, the user can adjust the usage to reduce the peak-to-average ratio of load demand or minimize energy costs.

3.2. Modeling of Real-Time Pricing

In this study, real-time pricing is used as a demand–response method. The demand–response equation is based on the sigmoid function equation. The equation for the real-time price is shown as follows:

$$C_{Lt}=\frac{w}{1+\exp \{d\times (P_{La}-P_{Lt}-k)\}}+l$$

(8)

where $P_{La}$ and $P_{Lt}$ are the average load power of the apartment (kW) and the total load power of the apartment (kW), respectively. Moreover, w, d, k, and l are the parameters of the real-time pricing where wis the difference between the current power demand and the average power demand, d is the magnitude of the sigmoid function slope, k is the average power demand, and l is the average electricity charges. The electric power company can adjust these parameters to lead load demand. In this study, these parameters were optimized in order to maximize the profit of the trader and minimize the electricity charges for the consumers.

The demand–response characteristics of each dweller are illustrated in Figure 3. The load was adjusted by changing the price depending on demand–response. The load fluctuation became smaller after the adjustment. In this study, it was assumed that the power demand–response of each dweller was based on each characteristics in Figure 3. From Figure 3, the load reduced when the electricity price was high and increased when the electricity price was low.

4. Formulation of Objective Functions and Constraints

In this paper, it was assumed that the electric power demand and hot water consumption of apartment dwellers and the output power from PV for a full day could be predicted. The multi-objective optimization problem that was formulated in this study had two objectives. The first objective was to minimize the total electric charges of apartment dwellers. The second objective was to maximize the profit of the trader of bulk high voltages. The simulation period was assumed to be one day because it was difficult to create one month demand data for HP and EV, and the calculation time was long in long term simulation. In this study, to formulate the problem as a two objective minimizing optimization problem, the profit of the trader was reversed. The multi-objective optimization problem is defined as follows:

• The objective functions are:

  $$\min M_{day}=\sum _{t\in T}^T\{P_{Lt}{C}_{Lt}+P_{EVrt}{C}_{EVrt}-P_{It}{C}_{It}-P_{Im}{C}_{Im}\}$$

  (9)

  $$\min C_M=\sum _{t\in T}^T\left\{P_{Lt}{C}_{Lt}\right\}$$

  (10)

  where: $M_{day}$: profit of trader for a full day (Yen), $C_{Lt}$: real-time price (Yen/kWh), $P_{EVrt}$: consumption power of EV (kW), $C_{EVrt}$: price of EV consumption (Yen/kWh), $P_{It}$: interconnection power flow (kW), $C_{It}$: price of purchasing power in high voltage contract (Yen/kWh), $P_{Im}$: maximum of interconnection power flow (kW), $C_{Im}$: basic fees on power receiving contract with electric utility (Yen/kW), and $C_M$: total electricity charges of dwellers for a full day (Yen).

These functions were subjected to following conditions

(i)

The total amount of load power variation constraint:

$$|\Delta U_L|<0.05\times U_L$$

(11)

(ii)

The amount of load power variation for each dweller constraint:

$$|\Delta U_{ln}|<0.1\times U_{ln}$$

(12)

(iii)

The upper/lower bound of the real-time price constraint:

$$10<C_L<35$$

(13)

(iv)

The profit of the trader constraint:

$$M_{day}<0$$

(14)

(v)

The parameters of the real-time pricing constraint:

$$w>0,d>0$$

(15)

(vi)

The adverse power currents constraint:

$$P_{lit}\ge 0$$

(16)

(vii)

The demand–response peak constraint:

$$P_{Rm}\le P_{Lm}$$

(17)

(viii)

SOC constraint for a full day:

$$0.2\times {\xi }_{Bm}\le {\xi }_{Bt}\le {\xi }_{Bm}$$

(18)

(ix)

SOC constraint at 24:00:

$${\xi }_{B(t=0)}\le {\xi }_{B(t=24)}$$

(19)

(x)

Active power of fixed battery constraint:

$$|P_{Bt}|\le P_{Bm}$$

(20)

(xi)

SOC of EV constraint for a full day:

$$0.2\times {\xi }_{EVm}\le {\xi }_{EVt}\le {\xi }_{EVm}$$

(21)

(xii)

SOC of EV constraint at 24:00:

$${\xi }_{EV(t=0)}\le {\xi }_{EV(t=24)}$$

(22)

(xiii)

Active power of EV constraint:

$$|P_{EVt}|\le P_{EVm}$$

(23)

(xv)

Interconnection point power flow constraint:

$$P_{Im}\le P_{Lm}$$

(24)

where: $U_L$: the amount of load power in the apartment for a full day (kWh), $\Delta U_L$: variation of the amount of load between before and after the demand–response (kWh), $U_{ln}$: amount of power consumption of dweller n for a full day (kWh), $\Delta U_{ln}$: variation of the amount of power consumption between before and after the demand–response of dweller n (kWh), $P_{lnt}$: the load power of dweller n after demand–response (kW), $P_{Lm}$: maximum load power of the apartment after demand–response (kW), $P_{Pm}$: predicted maximum load power of the apartment (kW), ${\xi }_{Bt}$: SOC of a fixed battery (%), ${\xi }_{Bm}$: maximum SOC of a fixed battery (%), $P_{Bt}$: active power of a fixed battery (kW), $P_{Bm}$: maximum active power of a fixed battery (kW), ${\xi }_{EVt}$: SOC of EV (%), ${\xi }_{EVm}$: maximum SOC of EV (%) (100%), $P_{EVt}$: active power of EV (kW), $P_{EVm}$: maximum active power of EV (kW).

5. Optimization Method

In this study, there were two objective functions: minimization of electricity costs for condominium customers and maximization of profits for high voltage bulk traders. Because there were two objective functions, the non-dominated classification genetic algorithm-II (NSGA-II) was used as a multi-objective optimization method [20,21,22]. The algorithm of NSGA-II is described in Section 5.1.

5.1. Algorithm of NSGA-II

In NSGA-II, two independent populations are used, the saving population Ptand the population Qt for performing searches using genetic operations such as crossover and mutation. The population $P_t$ storing non-dominated individuals is the parent population, and the population $Q_t$ will be used for searching the child population. The flow of the NSGA-II algorithm is shown as follows.

Step 1:

Combine the parent population and the child population to generate $R_t$ = $P_t$∪$Q_t$ Perform non-dominated sorting on $R_t$, and classify all individuals according to the front.

Step 2:

Generate a new population $P_t=\phi$. Let variable $i=1$. Execute $P_{t+1}$ and $i=i+1$ until $|P_{t+1}|+|F_i|<N$ is satisfied.

Step 3:

Perform congestion degree sorting, and add $N-|P_{t+1}|$ individuals, which were the most diverse, to $P_{t+1}$.

Step 4:

Based on $P_{t+1}$, create a new child population $Q_{t+1}$ using crowded tournament selection, crossover, and mutation.

Thus, in NSGA-II, the top N individuals of the population $R_t$, which is a combination of the parent population $P_t$ and the child population $Q_t$, are selected to be the parent-child body $P_{t+1}$ of the next generation. In addition, the search individual $Q_t$ is selected from the parent individual $P_t$ using congestion tournament selection, and a search using genetic operations is performed using a superior parent individual $P_t$. At this time, storing $P_t$ and $Q_t$ separately prevents the loss of the excellent solution found in the search. A conceptual diagram of updating the parent population $P_t$ of NSGA-II is shown in Figure 4.

6. Simulation Analysis

In this section, the simulation conditions and simulation results of this study are described. The simulation conditions are described in Section 6.1, and the simulation results of this study are described in Section 6.2.

6.1. Simulation Conditions

In this study, a sunny and a cloudy day were considered. In addition, simulations are performed assuming that the daily EV usage, the output of the solar power generation system, and the amount of hot water supplied from each hot water tank could be predicted in advance. Figure 5, Figure 6 and Figure 7 show the daily EV usage, photovoltaic power generation, and hot water supply, respectively. Ten EVs were installed in the apartment building. In this study, it was assumed that the condominium residents paid 50 yen/kWh. The total load of the entire apartment other than the assumed controllable load is shown in Figure 8. The total power consumption of the load in Figure 8 was 1000 kWh. The electricity charges for a conventional electricity contract (low voltage) were 25 yen/kWh. Therefore, if a conventional electricity contract were agreed upon, the total electricity charges would be 25,000 yen. This should be noted in comparison with the proposed contract. Otherwise, the power rate over time at high voltage was assumed, as shown in Figure 9. In this study, the NSGA-II population size was set to 200 and the number of generations to 15,000.

6.2. Simulation Results

Figure 10 shows a Pareto solution calculated by NSGA-II. As shown in Figure 10, the total electricity bill for all solutions was less than 25,000 yen. In addition, bulk high voltage traders were recognized to be profitable with all solutions. The real-time price for all solutions is shown in Figure 11. To level load demand every time, traders need to apply real-time pricing and perform peak load and bottom-up by using fixed batteries. According to Figure 11, the real-time price would be higher if the load demand was high. Figure 12 shows the simulation results of Solution (A). Figure 12a shows the real-time price as a curve. The load demand before demand–response is also shown as a bar graph in Figure 12a. In Figure 12a, the real-time price will be higher if the load demand is high. The load demand after demand–response is shown as a curve in Figure 12b. According to Figure 12b, it can be confirmed that the load demand leveled. Figure 12c shows the electricity bill for each resident after demand–response. It can be observed that all residents could reduce their fees. Figure 12d,e show the load demand of two dwellers before and after the demand–response. One gained the greatest profit and the other gained the least profit by demand and response. In Figure 12d, the load demand decreased if the real-time price was high. In contrast, Figure 12e shows little difference before and after the demand–response. Figure 12f,g shows the power consumption from HP and the temperature of hot water in the storage tank, respectively. According to Figure 12f, most HPs operated during the daytime to consume the output power from the PV system. In addition, the temperature of hot water in the storage tank rose with the operation of HP. Figure 12h,i shows the state of charge (SOC) of the fixed battery and the SOC of the EV. In Figure 12h, the fixed battery charged in the morning and discharged during the day. As shown in Figure 12i, due to the constraints, all EVs would be charged to more than 50% by 24:00.

Figure 12j shows the transmitted power from the grid. Compared to the natural Load, the difference between the peak (highest load demand) and valley (lowest load demand) was smaller. The interconnection power flow was leveled to perform peak-cut.

Figure 13 shows the Pareto front when there was almost no power generated by PV. From Figure 13, the optimum point was determined as Point (B). The profit of bulk high voltage traders in (B) was 1913 yen, and the electricity bill was 21,630 yen. In this case, the profits of bulk high voltage traders were decreasing compared to Point (A) of Figure 10. The simulation results for Solution (B) are shown in Figure 14a–c. The EV and storage battery were discharged at night.

The costs for the consumer and the profits of the aggregator (utility) are introduced in

Table 1. Profit vs. cost representation of two Pareto solutions.

Profit/Cost	Solution (A)	Solution (B)
Profit of Bulk voltage utility (Yen)	4275	1913
Consumer Cost (Electricity charges) (Yen)	19,800	21,630

. It was evident that Solution (A) was better than Solution (B), which means if PV power output were less, then the bulk voltage supplier authority would lose its profit, and consequently, electricity charges would be higher.

7. Conclusions

In this study, smart condominiums were proposed in which high voltage collective power receivers could reduce the electricity charges when they entered into high voltage power receiving contracts with electric power providers. This was done by leveling the interconnection power flow between the condominium and the power system. In the proposed smart condominium, the high voltage power receivers could optimize the power flow at the interconnection point by optimizing the operation of storage batteries, EVs, and heat pumps installed in the condominium and further reduce the electric power purchased from the electric power company. The profits obtained by leveling the interconnection power flow through the optimal operation of demand–response and controllable load would increase the profits of the high voltage power receiver and reduce the electricity charges of the entire smart condominium. However, there was a trade-off between increasing profits for high voltage bulk power receivers and reducing electricity charges for the entire smart condominium.

Therefore, in this study, NSGA-II, which is a multi-objective optimization algorithm, was used to determine the real-time price to be presented to the apartment dwellers by the high voltage collective power receiver and to plan the optimal operation of the controllable load. From the results of the optimal operation plan, the Pareto solution was calculated for the profit of the high voltage bulk power receiver and the total amount of electricity charges for the entire apartment. Based on the calculated Pareto solution, it was shown that the profit of the high voltage bulk power receiver and the electricity charges of the entire apartment could be adjusted by the optimum operation of demand–response and controllable load. Furthermore, PV generated power could benefit both the utility and consumers.