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Power utilization strategy in smart residential community using non-cooperative game considering customer satisfaction and interaction
Electric Power Systems Research 166 (2019) 178–189
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Power utilization strategy in smart residential community using noncooperative game considering customer satisfaction and interaction
T
Chunyan Li , Wenyue Cai, Hongfei Luo, Qian Zhang ⁎
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, 400044 China
ARTICLE INFO
ABSTRACT
Keywords: Distributed photovoltaic generation Smart power utilization Clustering analysis Electricity consumption satisfaction Non-cooperative game
The development of smart grids and photovoltaic (PV) generation has led to the popularization and access of distributed PV energy among residential communities. However, the interactions among residential customers significantly affect the power utilization strategy of PV consumption. To encourage customers to participate in PV consumption, this study proposes an optimal smart power utilization model by using a non-cooperative game for a residential community with distributed PV energy. First, a benefit maximization model for distributed PV energy is established to determine an optimal PV output. Second, according to the consumption habits and load curves of residential customers, a power utilization model of community customers is built considering electricity consumption satisfaction by performing clustering analysis. Finally, a non-cooperative game model is built for the PV power supplier and customers in the community. A Nash equilibrium point is also obtained based on the balance between the maximum benefit of PV power and the minimum electricity bills for customers. This approach is useful to encourage customers to consume PV energy in local areas. The case studies indicate that the proposed model can be applied to achieve the maximum benefit of PV power; furthermore, it allows customers to meet their own needs while reducing their electricity payments.
1. Introduction The depletion of fossil energy and the increasing trend of energy consumption demand have promoted the generation of renewable energy, and PV power is considered to be the most promising renewable energy in the future because of its flexibility and universality [1]. However, the construction of PV power needs to be coordinated with the consumption of solar energy to solve the abandoned solar energy problem and improve the development of low carbon energy. In addition, PV panels need to be effectively placed on rooftops for the longterm construction of distributed PV power generation. Accordingly, how to involve residential customers in the full utilization of PV power has become a popular research field. With regard to smart grids, the studies on electricity consumption patterns of residential customers mainly focus on the establishment of DR scheduling models by adjusting and optimizing the scheduling strategy [2–4]. However, most of the models fail to consider the decline in customer satisfaction when the operation states of electrical appliances change quickly during scheduling [5]. For instance, the satisfaction toward electric vehicle usage is based on the requested plugout times, requested battery state of charges, willingness to pay highcharging energy prices, etc. [6]. In terms of satisfaction of using ⁎
appliances, adding the penalty of customer comfort level for scheduling of a particular appliance or changing of living environment like temperature has been investigated [7–9]. To maintain the balance between energy saving and comfortable lifestyle, consumers' consumption preferences of executing DR tasks were evaluated by user convenience rate or appliances consumption preferences [10,11]. Meanwhile, user preference was also modeled as a waiting time associated with a cost [12]. Nevertheless, the previous studies neither comprehensively explained electrical appliances usage preference nor carefully calculated the different satisfaction stages at different consumption levels. In other words, a uniform definition for “satisfaction”, which considers the above state changes for different customers, is lacking. The SRD is a typical physical model that depicts the future development of smart grid construction, and the design, configuration, function, and key techniques have been fully discussed [13,14]. The SRD was integrated with renewable energy, and its pricing scheme was subsequently built to minimize the total electricity bills of all customers; however, the benefit of utilizing renewable generation was rarely discussed [15,16]. Therefore, an intensive analysis is required when determining the specific strategy for electricity consumption in accordance with generation benefits of SRDs. In terms of multi-user smart power utilization, the described
Corresponding author. E-mail address: [email protected] (C. Li).
https://doi.org/10.1016/j.epsr.2018.10.006 Received 8 June 2018; Received in revised form 6 September 2018; Accepted 9 October 2018 0378-7796/ © 2018 Elsevier B.V. All rights reserved.
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Nomenclature
di
Abbreviations
wi qi
PV SRD DR
Photovoltaic Smart residential district Demand response
C S1 S2 Wmax qh, t
Parameters and variables
qtPV qFPV ,t qPV PV pt pft pst ptGRID n qmust ,t n qcontrol ,t
qtn qtGRID N I J tistart , tiend [ i, i] [ j, j]
The portion of PV power that supplies directly to the customers The portion of PV power that supplies directly to the grid The total amount of PV power The incentive price that customers pay for PV power supplier The on-grid price of PV power The subsidy for PV supply financed by the government The price that customers purchase the electricity from the grid, also known as retail price The electricity of the uncontrollable electrical appliances of customer n at time t The electricity of the controllable electrical appliances of customer n at time t The total demand of customer n at time t The electricity purchased from the grid The set of customers in SRD The set of non-interruptible electrical appliances The set of interruptible electrical appliances The startup and shutdown time of electrical appliance The allowable operation time interval for the ith non-interruptible electrical appliance The allowable operation time interval for the jth interruptible electrical appliance
The total operation time of appliance that requires to complete a given work The rated power of the appliance The amount of electricity required to complete the specified task The electricity payments The electricity payment satisfaction The electricity usage satisfaction The maximum capacity of a customer's power line The power of the uncontrollable electrical appliances at
h H
time t The original operational states of electrical appliances i and j at time t xi,t, xj,t The optimized operational states of electrical appliances i and j at time t All customers who participate in the scheduling Qn The electricity plan of customer n F The payoff function q n , {q1, ..., qn 1, qn + 1, ..., q N } The set of the total demand of all other customers expect customer n within the time range that PV has an effective output c A price constant of the incentive price k A coefficient of the incentive price that greater than 0 qN * The optimal power consumption plan for customers G The non-cooperative game q n , {q1 , ..., qn 1 , qn + 1 , ..., q N } The optimal strategy combination of other users in the game except customer n λ The parameter in evaluating comprehensive result of satisfaction S′ The overall satisfaction of the customers ptiPV , ptiPV1 The incentive price at ith iteration and (i-1)th iteration respectively ε the tolerated error
x i0, t , xj0, t
approaches were aimed at optimizing household energy costs in SRDs [17,18]. From the perspective of cost reduction, game theory was used
to analyze the characteristics of interaction among users, customer benefits, and effective energy scheduling strategies [19,20]. A bi-level
Fig. 1. Typical SRD with distributed PV power supply. 179
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game was formulated in [21] to minimize customer costs at the community level and aggregator cost at the market level, but this approach needs to collect and broadcast energy demand requests to each customer, which is difficult to achieve in reality. With real-time pricing mechanism under different PV installed capacities and battery capacities, the Nash equilibrium was found applicable for consumers with different levels of DR capability [22]. In addition, game theory has been applied to maximize customer payoff while guaranteeing the system reliability and meeting users' electricity demands in power systems integrated with wind farm [23]. A real-time DR model based on game theory is presented to coordinate the energy consumption behavior of consumers, and the effectiveness of the method is verified in terms of improving the economic benefits and PV energy sharing [24]. The superiority of the game algorithm has been proved for load redistribution attack and defense in power systems [25]. However, to the best of our knowledge, an appropriate and flexible PV incentive pricing that can encourage different customers to participate in PV consumption has not yet been investigated, and thus, this gap is the main scope of the present study. In accordance with the study of [26], the present work proposes a multi-user smart power utilization strategy based on the non-cooperative game in SRD integrated with distributed PV power. Customers can be clustered according to their consumption habits and load curves. Hence, the power utilization model, which considers the satisfaction of electricity utilization, is built. Then, from the two perspectives of PV power supply and customer demand, the non-cooperative game is played by focusing on the interactions of residential customers. The main contributions of this paper are summarized as follows:
• • •
2.1. Benefits of PV supply The PV supply in Fig. 1 is used as an example for benefit analysis. The capital cost of a given PV panel is fixed under certain technical conditions, whereas the benefits vary with many factors, such as the directions and amounts of power flow changes. Therefore, the benefit maximization model for PV power supply is
Max Ben efit = t T PV
q PV = t T pV
(qtPV
+
qtPV ptPV +
t T PV
PV qFPV , t pft + q pst
qFPV ,t )
(1) (2)
Eq. (1) indicates that the benefits of the PV power supply consist of the following three parts:
• The cost of the PV power that is directly supplied to the customers in the SRD; • The income received by directly selling the PV power to the grid; • The government subsidy for PV generation. Sometimes PV outputs are small at low temperatures or less solar radiation. To ensure that customer loads have a high-quality stable power supply, the amount of PV power supplied directly to the customer should be zero, which indicates that the load extracts all the electricity from the grid, as shown by Eqs. (3)–(5).
qtPV = 0
(3)
qtPV + qFPV ,t <
n qmust ,t
(4)
n N
To encourage customers to fully utilize PV power, a benefit maximization model is built considering the customer comprehensive satisfaction of power consumption, i.e., electricity payment satisfaction and electricity usage satisfaction. The smart power utilization model of SRD customers is established based on clustering analysis and household electrical appliances modeling, which is beneficial for PV consumption in the community. Based on the non-cooperative game, the power utilization strategy among SRD customers is proposed. The flexible PV incentive price, that closely related to the PV power and customer demand, is used as a lever to stimulate the customer to optimize power consumption. Hence, the balance between the maximum benefit of the PV power and the minimum of electricity payment is achieved.
qtn
n (qmust ,t
=
n N
+
n qcontrol ,t )
=
n N
qtGRID
(5)
By contrast, when PV outputs are large in high-temperature or solar radiation, the customers can select either PV power or the power from the grid to supply the loads, as shown by Eqs. (6) and (7).
qtn = qtPV + qtGRID n N
qtPV
+
qFPV ,t
n qmust ,t n N
(6) (7)
2.2. Analysis of PV incentive pricing
The rest of this paper is organized as follows. The benefit analysis of PV power supply is introduced in Section 2. The smart power utilization model of customers that considers satisfaction is presented in Section 3. The proposed non-cooperative game is discussed in Section 4. The simulated results are provided in Section 5, and the conclusions are drawn in Section 6.
The typical PV outputs and SRD load curves have different characteristics. During the time range in which PV has an effective output, e.g., 8:00 a.m.–6:00 p.m., the peak of the load profile and that of the PV output usually do not match. Therefore, customers need to be encouraged to transfer loads and consume maximal PV energy. SRD customers are only willing to take part in the scheduling if the impact on their lives is minimal and if the derived benefits are sufficient. Consequently, a competitive PV incentive price should be offered to SRD customers to encourage them to consume PV power, i.e., to transfer their loads and optimize the operation time of controllable appliances. According to the benefit maximization model of PV power supply in Eq. (1), PV incentive price ptPV is related to PV output. To consume maximal PV power, customers should actively participate in the consumption of PV power. In particular, when PV output is large, the PV incentive price should be relatively low and vice versa. Considering the mediation of the PV incentive price on SRD customers, the PV incentive price should also be related to customer demands. In other words, the PV incentive price has an inverse relationship with the gap between PV output and customer electricity demands. The greater the gap is, the lower the PV incentive price will be, which suggests the likelihood of having more PV energy for consumption. By contrast, the smaller the
2. SRD with distributed PV power supply Fig. 1 shows a typical SRD with distributed PV energy. PV energy can be directly connected to the distribution terminals or SRD customers, or it can be sold to the grid. The loads in the SRD can obtain power not only from the grid but also from PV. On the one hand, the PV power supplier aims to acquire the maximum benefit of PV generation; on the other hand, the SRD customers want to obtain adequate and lowcost electricity. For PV outputs with intermittent characteristics, the consumption of PV energy in a local area is an important consideration in keeping the system in stable and economical state. Therefore, balance needs to be maintained between the maximum PV power benefit and the minimum customer payments. 180
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gap is (i.e., the smaller the amount of retained PV power), the lesser the need to encourage customers to transfer their loads, thus the higher PV incentive price will be. For PV suppliers, the PV incentive price should be greater than the PV on-grid price to derive relatively greater benefits. By contrast, for the customers, the PV incentive price should be lesser than the price directly purchased from the grid, i.e., the retail price, as shown in Eq. (8).
pft < ptPV < ptGRID
according to their consumption characteristics: uncontrollable, noninterruptible, and interruptible electrical appliances. Uncontrolled electrical appliances refer to those types that are operated at certain times, such as lighting, television, computers, etc. These types cannot be considered for optimal scheduling. Non-interruptible and interruptible electrical appliances are both controllable appliances, and their common feature involves the completion of scheduled work at certain times. The changes in the startup and shutdown states of controllable appliances have relatively smaller impact on customer life. Non-interruptible electrical appliances refer to appliances that need to be turned on and can be turned off only when their tasks are completed. Examples include washing machines, dryers, dishwashers, disinfection cabinets. According to their working characteristics, as long as these appliances have been turned on, they will continue working until their default tasks have been completed, such that
(8)
3. Smart power utilization model of SRD customers To consume more PV power, partial loads should be shifted from the time when the demand is higher than the PV output to the time when the demand is comparatively low. Therefore, in this section, the different customer electricity consumption characteristics and the power utilization model are discussed.
tistart
i
i
i i
3.1. Clustering analysis of SRD customers
tiend
t
i
i
I
(10)
di
wi x i, t = wi di = qi
t= i
The consumption behavior of each household is difficult to analyze because the number of households in SRD varies from tens to thousands. Moreover, different customers have varying electricity consumption patterns and load curves, which renders the analysis even more complex. To simplify the problem, the customers are usually classified into several types, which can be solved by using two classification techniques: supervised learning and unsupervised learning methods [27]. Unsupervised learning, also known as clustering analysis, has the advantage of grouping in data without data label [28]. Clustering analysis is, therefore, adopted in this paper to classify customer types. The SRD customers were classified into five types by combining the collected consumption information from smart meters with the different profiles of customer behaviors [29], as shown in Fig. 2. Meanwhile, the characteristics of each type are described as follows:
tiend
(11) (12)
tistart = di
x i, t = 1
t
[tistart , tiend]
x i, t = 0
t
[tistart , tiend]
(13)
For the sake of simplicity, this study assumes that all of the appliances operate at a rated power. Thus, the operation state xi,t = 1 means the appliance is running; and xi,t = 0 means that the appliance has stopped working. By contrast, interruptible electrical appliances merely need to finish their tasks at certain times, which indicate that their operation times are arbitrary. These types of appliance include air-conditioners, water heaters, water pumps, electric vehicles, etc. Similarly, we can obtain the model of the interruptible electrical appliances as follows:
• Type A: The electricity consumption is low, which mainly contains
j
power loss. Customers of this type include households that do not use electricity all day, such as vacant homes, or the homeowner is outside on a trip, etc.
j
t
j
j
j
x j, t = 0
J
dj t t
[ j, j] [ j, j ]
small peak in the morning and a bigger peak in the evening with a longer duration. In addition, less electricity is consumed at daytime. Customers mainly include office workers who do not stay home during daytime.
• Type C: Daytime electricity consumption is maintained at a certain level with negligible fluctuations; higher power consumption occurs at noontime, and shorter duration of peak hours are observed at nighttime. Customers mainly include elderly families, office workers who rest at home at noon, etc.
• Type D: Total electricity consumption is high among customers.
Peaks occur at noon and in the evening. Customers likely include families with elderly and office workers. Type E: High level of electricity consumption is maintained during daytime, while the valley of electricity consumption appears at nighttime. Consumers mainly include commercial customers along residential streets.
3.2. Models of household electrical appliances Fig. 2. Load curves of different clusters.
The household electrical appliances can be divided into three types 181
(14) (15)
xj, t = {0,1}
• Type B: Peaks and valleys are apparent in the load profile, i.e., a
•
(9)
(16)
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satisfaction are both applied to determine the different levels of SRD customer satisfaction on the basis of the different power consumption plans.
j
wj xj, t = wj dj = qj
(17)
t= j
The total amount of operation time should be equal before and after scheduling. Moreover, an upper limit is designated for the total power consumption for all the controllable appliances in each period. Based on these rules, we have
x i0, t
x i, t = t T
xj0, t
x j, t =
(19)
t T
wi x i, t + i I
When customers use electricity, they simultaneously prefer less electricity payments and high electricity consumption satisfaction. Hence, the smart power utilization model of SRD customers includes two parts: electricity payment satisfaction and power consumption satisfaction. On the basis of the clustering analysis of customers in Section 3.1, the smart power utilization models for each type of customers are established, as shown in Eqs. (26)–(28). No electrical appliances need to be operated for Type A customers, which means that scheduling cannot be conducted and that the satisfaction based on power consumption cannot be considered. On this basis, the objective function of the electricity payment for Type A is
(18)
t T
t T
3.4. Smart Power utilization model of SRD customers
wj xj, t
Wmax
qh, t
j J
(20)
h H
3.3. Satisfaction of power consumption
(ptPV qtPV + ptGRID qtGRID )
C=
qmust , t + qcontrol, t = qtPV + qtGRID qcontrol, t =
x i, t wi + i I
The power consumption levels of Type B, C, and D customers are more flexible than that of Type A because of the utilization of controllable appliances, which can take part in the scheduling. Although customers differ in terms of their sensitivity toward electricity payments, the satisfaction of electricity payment and the satisfaction of power consumption should both be considered in the modeling of each customer type. The power utilization model is expressed as Eq. (27).
max F =
(21)
t T
xj, t wj
(23)
As shown in Eq. (21), the lower the payment is, the higher the degree of satisfaction will be. Electricity payment satisfaction is therefore defined as
(ptPV qtPV S1 = 1
+
max S1.
ptGRID qtGRID )
t T
(ptGRID (qmust , t + qcontrol, t )
(24)
S2 = 1
wj x j0, t
x i, t + j J
wi x i0, t + i I
wj xj0, t j J
(28)
4. Power utilization model based on non-cooperative game
Electricity consumption plans are subsequently assumed to be optimized. Similarly, the higher the S1 is, the greater the electricity payment satisfaction will be. Electricity usage satisfaction is defined as customer's adaptability of the current living conditions. It is assumed that customers will voluntarily choose a certain electricity plan to derive the highest satisfaction for power consumption. Therefore, electricity usage satisfaction can be expressed as
wi xi0, t
(27)
In this study, Eqs. (8)–(20), (22), and (23) are the constraints of the model.
× 100%
t T
i I
max S1 max S2
For the customers of Type E, the electricity consumption during the day is at a high level with negligible fluctuations. On the one hand, the electrical appliances of Type E customers essentially include uncontrollable appliances; on the other hand, they need to consider the comfort of their guests in their shops. Consequently, the highest satisfaction of power consumption is acquired, and only electricity payment needs to be considered as follows:
(22)
j J
(26)
max S1
The customer satisfaction (i.e., with electricity plan) in this study consists of two parts, namely, electricity payment satisfaction and electricity usage satisfaction. Based on the appliance modeling in Section 3.2, electricity payment satisfaction is defined as the degree of satisfaction of users when paying electricity charges. Thus, under the same electricity consumption conditions, the lesser electricity bill the customers pay, the more they are satisfied with the consumption plans. Hence, electricity payments can be expressed as
The proposed method for modeling the interaction among SRD customers is formulated as a typical game problem with incomplete, static and finite information. In the interaction process, PV power suppliers intend to maximize their benefits, whereas SRD customers intend to reduce the electricity payments while meeting their satisfactions. This process is consistent with that of finding effective decisions in solving the conflict between maximizing PV power benefits and minimizing customer electricity payments by two or more individuals, which can be solved by game theory [30]. Meanwhile, the proposed power utilization model is formulated as a multi-objective optimization problem. Game theory has the advantages of better global searching ability and faster convergence speed compared with other optimization techniques. In addition, many applications have done by using the game theory on these problems [24,25]. Therefore, an algorithm based on game theory is proposed to solve the proposed power utilization model.
x j, t × 100% (25)
Take the original power consumption plan chosen by the customer as the basis. If the optimized power consumption plan is exactly the same as the original plan, i.e., the customer does not change consumption habits, then the customer will feel the most comfortable, and thus, electricity usage satisfaction will be the highest. By contrast, if the optimized power consumption plan is completely different from the original plan, then the scheme will drastically change the consumption habits and cause a negative impact on the customer’s life. Under this circumstance, the electricity usage satisfaction will be at its worst state. In summary, electricity payment satisfaction and electricity usage
4.1. Game modeling The Normal Form Representation is adopted in this paper, and all the players involved in the game choose their own strategies at the same time [31]. 182
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• Payoff: The payoff function is expressed as
A non-cooperative game of smart power utilization for the customers in the SRD is defined asG = {Q1, ..., Q N ; u1, ..., uN } , which is composed of player N, strategy Q and payoff u. The details are described as follows:
un (qn ,
q n) =
F=
t T PV
ptPV qtn
(29)
It is a game problem that all players pursue their own objects. For PV power suppliers, it is necessary to maximize their benefits; whereas for SRD customers, they intend to reduce the electricity payments while meeting their satisfactions. Therefore, customers participate in the game by changing the electricity consumption at each time interval, then find their own optimal electricity consumption strategy.
• Player: Customer who participate in the scheduling in the SRD that = {1,2,..., N }. is regarded as a player, wheren Strategy: Every customer selects the electricity plan •
Qn = {qtn t T PV } in accordance with his or her requirements, where qtn represents the electricity demand of the electrical appliances that is obtained from the corresponding smart power utilization model in Section 3.
Fig. 3. Flowchart of the model. 183
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4.2. Proof of nash equilibrium existence
Step 2 Solve the power utilization model considering customer’s satisfaction independently; Step 3 If the calculated value of qn(k) is different from qn(k-1), go to step 4, else go to step 6; Step 4 Update qn(k) in the smart power utilization model; Step 5 Collect qn(k) in the system from smart meters;
In order to find the optimal set of strategies to meet the needs of all customers for the whole system, the Nash equilibrium of the game needs to be determined. No player can benefit by changing strategies if every player n has chosen a strategy Qn while the other players keep theirs unchanged, then the current set of strategy choices {Q1 *, ..., Q N *} is a Nash equilibrium. The existence of Nash equilibrium of this model is proved as follows:
un (qn , q n) =
k qtPV + qFPV ,t
c t T PV
ptPV = c
qtn
qtn
n N
k qtPV + qFPV ,t
n N
qtn
Step 6 If qtPV
q n)
qtn 2
=
(30)
(31)
2k < 0
5. Case studies 5.1. Basic data
(32)
where un (qn , q n) is a concave function of qtn. Therefore, the Nash equilibrium exists in the proposed non-cooperative game according to Nash equilibrium existence theorem [31]. The optimal power consumption plan for all the customers {q1 , q2 , ..., q N } is the Nash equilibrium solution for the non-cooperative game G. Hence, when a customer in the system adopts the optimal policy, none of the other customers can bypass the existing strategy, i.e., a new strategy cannot be established, to increase his or her benefit.
un (qn , q
n
)
un (qn , q
n
)
qn
Qn,
n
, go to step 7; else, update ptPV , then go
to step 2; Step 7 Print out customer's optimal consumption qn(*) and optimal PV incentive price ptPV (*) . Each customer optimizes his or her electricity consumption behavior individually in the game model based on the PV incentive price, that is, the optimization process of each customer is an independent iteration at each period until the Nash equilibrium is obtained, and the supply is matched with the demand.
The two-order partial derivatives for qtn are obtained as 2un (qn ,
qtn n
A distributed PV power generation system is built with a capacity of 150 kW. The PV power can connect to the grid through the inverter, which can either supply energy for SRD customers or sell energy to the grid. The SRD has 300 households, of which 30 are willing to transform their line to access PV power. Among the 30 households, 3 customers are part of Type A, 7 customers are part of Type B, 10 customers are part of Type C, 9 customers are part of Type D, and 1 customer is from the Type E. The uncontrollable electrical appliances include light, TV, computer, refrigerator, cooker, etc. The controllable appliances include dishwasher, disinfection cabinet, air-conditioner, water heater, washing machine, electric vehicle, etc. The characteristics and parameters of both types of electrical appliances are shown in Table A.1 in the Appendix. The upper limit of the total power consumption of all controllable electrical appliances at each time is shown in Table A.2 in the Appendix. The multi-user power consumption system with distributed PV power supply consists of the PV power supply and 30 customers. The PV output is shown as a red dotted line in Fig. 4, and the effective output time is from 8:00 a.m. to 6:00 p.m. In the same figure, the demand of the customers over 24 h is depicted as a black solid line. The load fluctuates at daytime, and higher demands are observed at nighttime than in the other times of the day. This study assumes that the PV ongrid price is 0.41 $/kWh while the subsidy price is 0.42 $/kWh. The three Type A customers have low power consumption and can be ignored. For simplicity, only Type B, C, D, and E customers are considered in the succeeding section. The original power consumption plans of the customers for each type are shown in Fig. 2.
(33)
4.3. Algorithm design and implementation An algorithm is proposed to maximize the benefits of PV power and obtain optimal consumption, which is shown in Fig. 3. Each customer needs to play a game between PV power supplier and other customers, to reach a balance between increasing PV benefits and reducing electricity payments at Nash equilibrium point. The PV incentive price ptPV is related to both the PV output and customer demands. In other words, the PV incentive price has an inverse relationship with the net generation between PV output and customer electricity demands. When in the time of high PV, the net generation is large, which indicates more PV power needs to be consumed. Hence, a low PV incentive price is initially established to encourage consumers to shift their controllable loads independently based on their requirements of satisfaction and electrical appliance working parameters. In turn, PV incentive price will adjust due to the changes in consumption behaviors, and the process will continue until Nash equilibrium is reached. During the implementation of the algorithm, each customer optimizes his or her electricity consumption behavior individually after receiving the PV incentive price, the adjustment of customer behavior will affect the power consumption and the supply-demand matching status, then the PV incentive price is further readjusted. The process will be repeated until the PV incentive price and the customer electricity consumption are no longer changed. In this way, the dynamic adjustment between electricity price and DR resources is accomplished. The ultimate PV incentive price is the price accepted by all SRD customers, and the electricity consumption of each customer has reached the optimum, i.e., the state of Nash equilibrium has achieved. In Fig. 3, the red dotted box is a distributed optimization algorithm that finds the Nash equilibrium solution, which is described as follows: Step 1 Initialize qn(0) and q−n(0), and receive the PV incentive price PV pt ;
Fig. 4. PV output and load curve. 184
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5.2. Analytical results
compared with the customers in Case I (Fig. 4), those in Case II will choose electricity consumption plans they are most satisfied with on the basis of their own habits. The corresponding PV output, customer demands and PV incentive price of Case II and Case III are shown in Fig. 5(a) and (b) respectively. The PV output shown in Fig. 5(a) is greater than the demand between 11:00a.m. and 4:00p.m. This is due to the fact that customers arbitrarily choose their electricity plans to meet their satisfactions without considering optimal scheduling. While in Case III, the smart power utilization algorithm based on game theory is adopted, the optimization results of Case III in Fig. 5(b) shows that the PV incentive price between 11:00a.m. and 4:00p.m. is decreased and the customers’ electricity consumptions are increased compared to that of Case II. Therefore, the PV power consumption has been maximized in Case III.
Three cases are discussed as follows:
• Case I: The customers will choose their electricity plans without • •
considering their satisfaction. They will choose the power consumption plan according to the upper power limit constraint. Case II: The customers will adaptively choose their electricity plans and consider their satisfaction. Case III: The smart power utilization algorithm based on game theory is adopted and the customer satisfaction is considered. The results are analyzed from the following aspects:
• Supply and demand matching. • PV incentive price. • Comprehensive income analysis. • Comparison of power consumption in different cases. • Comparison of power consumption satisfaction in different cases.
5.2.2. PV incentive price The PV incentive price is the same as the grid price in Cases I and II without optimal scheduling, which indicates that customers do not have additional benefits, and they prefer to purchase electricity from the grid to maximize their own interests. Thus, all the PV power is acquired by the grid through the inverter. In Case III, the incentive price with values between the PV on-grid
5.2.1. Supply and demand matching In Cases I and II, the optimal strategy is not considered. However,
Fig. 5. Supply and demand in Cases II and III (a) Cases II, (b) Cases III. 185
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price and the retail price is determined by using the non-cooperative game model. The incentive price is offered to customers to encourage PV power consumption. Then, based on the game between customers and the PV power, the Nash equilibrium is reached. The final PV incentive price is shown in Fig. 6. When the PV output is high, such as the period from 11:00 a.m. to 4:00 p.m., the PV incentive price is significantly lower than the retail price. This scenario implies that customers will likely use PV electricity to minimize electricity payments. The solar energy in this scenario is fully absorbed. 5.2.3. Comprehensive income analysis The comprehensive incomes for the above cases are shown in Table 1. Case I and II depict the PV incomes from power generation. PV incentive price is not considered, and all the SRD customers absorb electricity from the grid. Type B and D customers in Case II obtain higher electricity payments than those in Case I because they adjust their electricity consumption plans to reach the highest degree of satisfaction, whereas Type C and E customers have relatively lower electricity payments. In Case III, the PV power supplier can achieve comparatively higher benefits after optimization. The SRD customers consume PV power, and they also cut down their electricity payments (i.e., by consuming PV power, the prices are lowered). Compared with Case II, the income of the PV supplier is higher by 7.8% and the payments of Type B, C, D, and E customers are lower by 9.6%, 13.1%, 12.8%, and 14.0% in Case III, respectively. Then, compared with Case I, the payments of Type B, C, D, and E customers in Case III are lower by 1.05%, 14.8%, 7.8%, and 29.0% respectively.
Fig. 6. Optimized PV incentive price. Table 1 Comparison of comprehensive income Cases
Case I Case II Case III
PV Income/$
Electricity payment of customers/$ Type B
Type C
Type D
Type E
294.38 294.38 317.47
10.43 11.42 10.32
10.84 10.63 9.24
13.61 14.40 12.55
22.14 18.29 15.73
5.2.4. Comparison of power consumption in different cases In Case I, as long as the power consumption does not exceed the upper limit, the customers will not change their original consumption habits. Therefore, the consumption of customers is the same as their previous consumption (Fig. 2). The power consumption of different types of customers are compared between Cases II and III (Figs. 7 and 8). The PV incentive price is cheaper than the retail price in Cases II and III, and Type B customers can adjust the operation time of their controllable electrical appliances to adequately consume PV power. Given that Type C customers mostly stay at home during the day, the available operation times of the controllable appliances have relatively lesser restrictions, which suggest that the scheduling rate of the load is high. For the sake of reducing electricity payment, the customers transfer the operation time of some controllable electric appliances to the period with low incentive price, e.g., the period from 2:00 p.m. to 4:00 p.m. Similar to Type C, the load scheduling rate of Type D is also high. To reduce electricity payment, the operation times of some controllable electric appliances are also transferred to the period with low PV incentive price. As a consequence of the high satisfaction for power consumption of Type E customers, and because their electrical appliances mainly consist of uncontrollable electrical appliances, the consumption plans are not adjusted in Cases II and III. However, the electricity payments are reduced because of the relatively lower PV incentive price. The consumption changes in Cases I and II are compared and shown in Fig. 9. Given that consumers tend to use electricity in the evening, all types of customers increase their electricity consumption at night from the perspective of customer satisfaction. In terms of original consumption in Case I, Types B and D appear with two peaks, namely, from 6:00 a.m. to 9:00 a.m. and from 6:00 p.m. to 10:00 p.m., respectively, as shown in Fig. 2. In Case II, however, Type D customers reduce their consumption between 4:00 p.m. and 6:00 p.m., while Type B customers reduce their consumption between 3:00 p.m. and 5:00 p.m. Type E customers have high power consumption during the day to meet their satisfaction requirements, and their daytime electricity consumption does not change significantly and instead mostly decrease at nighttime.
Fig. 7. Power consumption of customers in Case II.
Fig. 8. Power consumption of customers in Case III. 186
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Fig. 9. Power consumption changes in Cases I and II.
Fig. 10. Power consumption changes in Cases II and III.
The power consumption changes in Cases II and III are compared and shown in Fig. 10. Except for those in Type E, the customers increase their electricity consumption when PV has an effective output, which verifies the effectiveness of the PV incentive price in guiding customers to consume PV power.
Table 2 Power consumption satisfaction of different types of customers Customers
Type Type Type Type
B C D E
Case II
Case III
S1
S2
S1
S2
−0.095 0.019 −0.058 0.174
0.686 0.253 0.261 0.216
0.01 0.14 0.077 0.28
0.896 0.344 0.414 0.216
5.2.5. Comparison of power consumption satisfaction in different cases The power consumption satisfaction levels of different types of customers are shown in Table 2, in which Case I is designated as the benchmark of the comparison. To evaluate the comprehensive result of satisfaction, parameter λ can be set as follows:
Table 3 Overall satisfaction of different types of customers Case II
Case III
S = S1 + (1
Type Type Type Type
0.2955 0.136 0.1015 0.195
0.453 0.242 0.2455 0.248
where 0 ≤ λ ≤ 1. Furthermore, the overall satisfaction of the customers can be expressed (Table 3), i.e., λ = 0.5. In Case II, the electricity payment satisfaction of Type B and D customers are less than that of the other types of customers because of the relatively higher electricity bills, and their electricity usage satisfaction is higher than their electricity payment satisfaction.
B C D E
187
) S2
(34)
Customers
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Consequently, Type B and D customers changed their manner of using electricity mainly because their power consumption needs are met. The electricity charges decreased and the needs were simultaneously met for the other types of customers. In Case III, the satisfaction levels of all customer types increased after the PV incentive pricing. However, the electricity usage satisfaction of Type E customers was the same because of their high satisfaction for power consumption, and their increased satisfaction was derived from the additional benefits from consuming PV power. In summary, the customer electricity consumption plans are guided by the non-cooperative game model and the consideration of an incentive price that is closely related to PV output and load demands. The game is implemented from two aspects, namely, customers versus PV power supplier and a single customer versus other customers. At the Nash equilibrium point, the benefits of PV power supply are increased and the electricity payments are reduced for customers under the condition of having to satisfy their own demands. The effectiveness of the model is verified by the case studies.
has the following characteristics: 1. The specific situation of each type of customer is considered in the electricity plans. The SRD customers can independently adjust their power consumption by the non-cooperative game. When the game is balanced, the optimal policy combination among all players is obtained. 2. The PV incentive price, which acts as a supply–demand lever, can guide the customer in optimizing the distribution of power consumption. By applying the incentive price, which is closely related to PV output and customer electricity demands, the customers are then motivated to participate in PV power consumption. Our approaches are valid for small scale like a typical SRD. For large-scale systems, with the increase of the customers, renewable energy types and network nodes, the customer clustering analysis and the game strategy among customers will be more complex. In addition, the uncertainties of renewable energy output and customer response and the related power system constraints should be also taken into account. Therefore, it will be the key work in our future research to establish more complex scheduling models and strategies among customers, renewable energy and grids.
6. Conclusion Power consumption optimization is conducted from two levels in this study. First, the PV incentive price, which is closely related to PV output and customer demand, is established to optimize the smart power utilization. Then, by establishing the Nash equilibrium point, the balance is achieved between the maximum benefits of PV power and the minimum electricity payments of customers. The proposed strategy
Acknowledgement This work is supported by National Natural Science Foundation of China(NSFC) [grant number 51247006].
Appendix A
Table A.1 Parameters of controllable electrical appliances Electrical appliance
Type
Rated Power/(kW)
Dishwasher Disinfection Cabinet Air Conditioning Water Heater Washing Machine Electric Vehicle
Non Non Int Int Non Int
1.0 0.52 5.2 5.8 0.75 3.5
Note: “Non” − non-interruptible electrical appliances; “Int” − interruptible electrical appliances.
Table A.2 Upper limit of power at each time. Time
Upper Limit/(kW)
7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00
4.5 4.5 6 6 6 6 6 6 6 6 6 6 5 5
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Power utilization strategy in smart residential community using noncooperative game considering customer satisfaction and interaction
T
Chunyan Li , Wenyue Cai, Hongfei Luo, Qian Zhang ⁎
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, 400044 China
ARTICLE INFO
ABSTRACT
Keywords: Distributed photovoltaic generation Smart power utilization Clustering analysis Electricity consumption satisfaction Non-cooperative game
The development of smart grids and photovoltaic (PV) generation has led to the popularization and access of distributed PV energy among residential communities. However, the interactions among residential customers significantly affect the power utilization strategy of PV consumption. To encourage customers to participate in PV consumption, this study proposes an optimal smart power utilization model by using a non-cooperative game for a residential community with distributed PV energy. First, a benefit maximization model for distributed PV energy is established to determine an optimal PV output. Second, according to the consumption habits and load curves of residential customers, a power utilization model of community customers is built considering electricity consumption satisfaction by performing clustering analysis. Finally, a non-cooperative game model is built for the PV power supplier and customers in the community. A Nash equilibrium point is also obtained based on the balance between the maximum benefit of PV power and the minimum electricity bills for customers. This approach is useful to encourage customers to consume PV energy in local areas. The case studies indicate that the proposed model can be applied to achieve the maximum benefit of PV power; furthermore, it allows customers to meet their own needs while reducing their electricity payments.
1. Introduction The depletion of fossil energy and the increasing trend of energy consumption demand have promoted the generation of renewable energy, and PV power is considered to be the most promising renewable energy in the future because of its flexibility and universality [1]. However, the construction of PV power needs to be coordinated with the consumption of solar energy to solve the abandoned solar energy problem and improve the development of low carbon energy. In addition, PV panels need to be effectively placed on rooftops for the longterm construction of distributed PV power generation. Accordingly, how to involve residential customers in the full utilization of PV power has become a popular research field. With regard to smart grids, the studies on electricity consumption patterns of residential customers mainly focus on the establishment of DR scheduling models by adjusting and optimizing the scheduling strategy [2–4]. However, most of the models fail to consider the decline in customer satisfaction when the operation states of electrical appliances change quickly during scheduling [5]. For instance, the satisfaction toward electric vehicle usage is based on the requested plugout times, requested battery state of charges, willingness to pay highcharging energy prices, etc. [6]. In terms of satisfaction of using ⁎
appliances, adding the penalty of customer comfort level for scheduling of a particular appliance or changing of living environment like temperature has been investigated [7–9]. To maintain the balance between energy saving and comfortable lifestyle, consumers' consumption preferences of executing DR tasks were evaluated by user convenience rate or appliances consumption preferences [10,11]. Meanwhile, user preference was also modeled as a waiting time associated with a cost [12]. Nevertheless, the previous studies neither comprehensively explained electrical appliances usage preference nor carefully calculated the different satisfaction stages at different consumption levels. In other words, a uniform definition for “satisfaction”, which considers the above state changes for different customers, is lacking. The SRD is a typical physical model that depicts the future development of smart grid construction, and the design, configuration, function, and key techniques have been fully discussed [13,14]. The SRD was integrated with renewable energy, and its pricing scheme was subsequently built to minimize the total electricity bills of all customers; however, the benefit of utilizing renewable generation was rarely discussed [15,16]. Therefore, an intensive analysis is required when determining the specific strategy for electricity consumption in accordance with generation benefits of SRDs. In terms of multi-user smart power utilization, the described
Corresponding author. E-mail address: [email protected] (C. Li).
https://doi.org/10.1016/j.epsr.2018.10.006 Received 8 June 2018; Received in revised form 6 September 2018; Accepted 9 October 2018 0378-7796/ © 2018 Elsevier B.V. All rights reserved.
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Nomenclature
di
Abbreviations
wi qi
PV SRD DR
Photovoltaic Smart residential district Demand response
C S1 S2 Wmax qh, t
Parameters and variables
qtPV qFPV ,t qPV PV pt pft pst ptGRID n qmust ,t n qcontrol ,t
qtn qtGRID N I J tistart , tiend [ i, i] [ j, j]
The portion of PV power that supplies directly to the customers The portion of PV power that supplies directly to the grid The total amount of PV power The incentive price that customers pay for PV power supplier The on-grid price of PV power The subsidy for PV supply financed by the government The price that customers purchase the electricity from the grid, also known as retail price The electricity of the uncontrollable electrical appliances of customer n at time t The electricity of the controllable electrical appliances of customer n at time t The total demand of customer n at time t The electricity purchased from the grid The set of customers in SRD The set of non-interruptible electrical appliances The set of interruptible electrical appliances The startup and shutdown time of electrical appliance The allowable operation time interval for the ith non-interruptible electrical appliance The allowable operation time interval for the jth interruptible electrical appliance
The total operation time of appliance that requires to complete a given work The rated power of the appliance The amount of electricity required to complete the specified task The electricity payments The electricity payment satisfaction The electricity usage satisfaction The maximum capacity of a customer's power line The power of the uncontrollable electrical appliances at
h H
time t The original operational states of electrical appliances i and j at time t xi,t, xj,t The optimized operational states of electrical appliances i and j at time t All customers who participate in the scheduling Qn The electricity plan of customer n F The payoff function q n , {q1, ..., qn 1, qn + 1, ..., q N } The set of the total demand of all other customers expect customer n within the time range that PV has an effective output c A price constant of the incentive price k A coefficient of the incentive price that greater than 0 qN * The optimal power consumption plan for customers G The non-cooperative game q n , {q1 , ..., qn 1 , qn + 1 , ..., q N } The optimal strategy combination of other users in the game except customer n λ The parameter in evaluating comprehensive result of satisfaction S′ The overall satisfaction of the customers ptiPV , ptiPV1 The incentive price at ith iteration and (i-1)th iteration respectively ε the tolerated error
x i0, t , xj0, t
approaches were aimed at optimizing household energy costs in SRDs [17,18]. From the perspective of cost reduction, game theory was used
to analyze the characteristics of interaction among users, customer benefits, and effective energy scheduling strategies [19,20]. A bi-level
Fig. 1. Typical SRD with distributed PV power supply. 179
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game was formulated in [21] to minimize customer costs at the community level and aggregator cost at the market level, but this approach needs to collect and broadcast energy demand requests to each customer, which is difficult to achieve in reality. With real-time pricing mechanism under different PV installed capacities and battery capacities, the Nash equilibrium was found applicable for consumers with different levels of DR capability [22]. In addition, game theory has been applied to maximize customer payoff while guaranteeing the system reliability and meeting users' electricity demands in power systems integrated with wind farm [23]. A real-time DR model based on game theory is presented to coordinate the energy consumption behavior of consumers, and the effectiveness of the method is verified in terms of improving the economic benefits and PV energy sharing [24]. The superiority of the game algorithm has been proved for load redistribution attack and defense in power systems [25]. However, to the best of our knowledge, an appropriate and flexible PV incentive pricing that can encourage different customers to participate in PV consumption has not yet been investigated, and thus, this gap is the main scope of the present study. In accordance with the study of [26], the present work proposes a multi-user smart power utilization strategy based on the non-cooperative game in SRD integrated with distributed PV power. Customers can be clustered according to their consumption habits and load curves. Hence, the power utilization model, which considers the satisfaction of electricity utilization, is built. Then, from the two perspectives of PV power supply and customer demand, the non-cooperative game is played by focusing on the interactions of residential customers. The main contributions of this paper are summarized as follows:
• • •
2.1. Benefits of PV supply The PV supply in Fig. 1 is used as an example for benefit analysis. The capital cost of a given PV panel is fixed under certain technical conditions, whereas the benefits vary with many factors, such as the directions and amounts of power flow changes. Therefore, the benefit maximization model for PV power supply is
Max Ben efit = t T PV
q PV = t T pV
(qtPV
+
qtPV ptPV +
t T PV
PV qFPV , t pft + q pst
qFPV ,t )
(1) (2)
Eq. (1) indicates that the benefits of the PV power supply consist of the following three parts:
• The cost of the PV power that is directly supplied to the customers in the SRD; • The income received by directly selling the PV power to the grid; • The government subsidy for PV generation. Sometimes PV outputs are small at low temperatures or less solar radiation. To ensure that customer loads have a high-quality stable power supply, the amount of PV power supplied directly to the customer should be zero, which indicates that the load extracts all the electricity from the grid, as shown by Eqs. (3)–(5).
qtPV = 0
(3)
qtPV + qFPV ,t <
n qmust ,t
(4)
n N
To encourage customers to fully utilize PV power, a benefit maximization model is built considering the customer comprehensive satisfaction of power consumption, i.e., electricity payment satisfaction and electricity usage satisfaction. The smart power utilization model of SRD customers is established based on clustering analysis and household electrical appliances modeling, which is beneficial for PV consumption in the community. Based on the non-cooperative game, the power utilization strategy among SRD customers is proposed. The flexible PV incentive price, that closely related to the PV power and customer demand, is used as a lever to stimulate the customer to optimize power consumption. Hence, the balance between the maximum benefit of the PV power and the minimum of electricity payment is achieved.
qtn
n (qmust ,t
=
n N
+
n qcontrol ,t )
=
n N
qtGRID
(5)
By contrast, when PV outputs are large in high-temperature or solar radiation, the customers can select either PV power or the power from the grid to supply the loads, as shown by Eqs. (6) and (7).
qtn = qtPV + qtGRID n N
qtPV
+
qFPV ,t
n qmust ,t n N
(6) (7)
2.2. Analysis of PV incentive pricing
The rest of this paper is organized as follows. The benefit analysis of PV power supply is introduced in Section 2. The smart power utilization model of customers that considers satisfaction is presented in Section 3. The proposed non-cooperative game is discussed in Section 4. The simulated results are provided in Section 5, and the conclusions are drawn in Section 6.
The typical PV outputs and SRD load curves have different characteristics. During the time range in which PV has an effective output, e.g., 8:00 a.m.–6:00 p.m., the peak of the load profile and that of the PV output usually do not match. Therefore, customers need to be encouraged to transfer loads and consume maximal PV energy. SRD customers are only willing to take part in the scheduling if the impact on their lives is minimal and if the derived benefits are sufficient. Consequently, a competitive PV incentive price should be offered to SRD customers to encourage them to consume PV power, i.e., to transfer their loads and optimize the operation time of controllable appliances. According to the benefit maximization model of PV power supply in Eq. (1), PV incentive price ptPV is related to PV output. To consume maximal PV power, customers should actively participate in the consumption of PV power. In particular, when PV output is large, the PV incentive price should be relatively low and vice versa. Considering the mediation of the PV incentive price on SRD customers, the PV incentive price should also be related to customer demands. In other words, the PV incentive price has an inverse relationship with the gap between PV output and customer electricity demands. The greater the gap is, the lower the PV incentive price will be, which suggests the likelihood of having more PV energy for consumption. By contrast, the smaller the
2. SRD with distributed PV power supply Fig. 1 shows a typical SRD with distributed PV energy. PV energy can be directly connected to the distribution terminals or SRD customers, or it can be sold to the grid. The loads in the SRD can obtain power not only from the grid but also from PV. On the one hand, the PV power supplier aims to acquire the maximum benefit of PV generation; on the other hand, the SRD customers want to obtain adequate and lowcost electricity. For PV outputs with intermittent characteristics, the consumption of PV energy in a local area is an important consideration in keeping the system in stable and economical state. Therefore, balance needs to be maintained between the maximum PV power benefit and the minimum customer payments. 180
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gap is (i.e., the smaller the amount of retained PV power), the lesser the need to encourage customers to transfer their loads, thus the higher PV incentive price will be. For PV suppliers, the PV incentive price should be greater than the PV on-grid price to derive relatively greater benefits. By contrast, for the customers, the PV incentive price should be lesser than the price directly purchased from the grid, i.e., the retail price, as shown in Eq. (8).
pft < ptPV < ptGRID
according to their consumption characteristics: uncontrollable, noninterruptible, and interruptible electrical appliances. Uncontrolled electrical appliances refer to those types that are operated at certain times, such as lighting, television, computers, etc. These types cannot be considered for optimal scheduling. Non-interruptible and interruptible electrical appliances are both controllable appliances, and their common feature involves the completion of scheduled work at certain times. The changes in the startup and shutdown states of controllable appliances have relatively smaller impact on customer life. Non-interruptible electrical appliances refer to appliances that need to be turned on and can be turned off only when their tasks are completed. Examples include washing machines, dryers, dishwashers, disinfection cabinets. According to their working characteristics, as long as these appliances have been turned on, they will continue working until their default tasks have been completed, such that
(8)
3. Smart power utilization model of SRD customers To consume more PV power, partial loads should be shifted from the time when the demand is higher than the PV output to the time when the demand is comparatively low. Therefore, in this section, the different customer electricity consumption characteristics and the power utilization model are discussed.
tistart
i
i
i i
3.1. Clustering analysis of SRD customers
tiend
t
i
i
I
(10)
di
wi x i, t = wi di = qi
t= i
The consumption behavior of each household is difficult to analyze because the number of households in SRD varies from tens to thousands. Moreover, different customers have varying electricity consumption patterns and load curves, which renders the analysis even more complex. To simplify the problem, the customers are usually classified into several types, which can be solved by using two classification techniques: supervised learning and unsupervised learning methods [27]. Unsupervised learning, also known as clustering analysis, has the advantage of grouping in data without data label [28]. Clustering analysis is, therefore, adopted in this paper to classify customer types. The SRD customers were classified into five types by combining the collected consumption information from smart meters with the different profiles of customer behaviors [29], as shown in Fig. 2. Meanwhile, the characteristics of each type are described as follows:
tiend
(11) (12)
tistart = di
x i, t = 1
t
[tistart , tiend]
x i, t = 0
t
[tistart , tiend]
(13)
For the sake of simplicity, this study assumes that all of the appliances operate at a rated power. Thus, the operation state xi,t = 1 means the appliance is running; and xi,t = 0 means that the appliance has stopped working. By contrast, interruptible electrical appliances merely need to finish their tasks at certain times, which indicate that their operation times are arbitrary. These types of appliance include air-conditioners, water heaters, water pumps, electric vehicles, etc. Similarly, we can obtain the model of the interruptible electrical appliances as follows:
• Type A: The electricity consumption is low, which mainly contains
j
power loss. Customers of this type include households that do not use electricity all day, such as vacant homes, or the homeowner is outside on a trip, etc.
j
t
j
j
j
x j, t = 0
J
dj t t
[ j, j] [ j, j ]
small peak in the morning and a bigger peak in the evening with a longer duration. In addition, less electricity is consumed at daytime. Customers mainly include office workers who do not stay home during daytime.
• Type C: Daytime electricity consumption is maintained at a certain level with negligible fluctuations; higher power consumption occurs at noontime, and shorter duration of peak hours are observed at nighttime. Customers mainly include elderly families, office workers who rest at home at noon, etc.
• Type D: Total electricity consumption is high among customers.
Peaks occur at noon and in the evening. Customers likely include families with elderly and office workers. Type E: High level of electricity consumption is maintained during daytime, while the valley of electricity consumption appears at nighttime. Consumers mainly include commercial customers along residential streets.
3.2. Models of household electrical appliances Fig. 2. Load curves of different clusters.
The household electrical appliances can be divided into three types 181
(14) (15)
xj, t = {0,1}
• Type B: Peaks and valleys are apparent in the load profile, i.e., a
•
(9)
(16)
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satisfaction are both applied to determine the different levels of SRD customer satisfaction on the basis of the different power consumption plans.
j
wj xj, t = wj dj = qj
(17)
t= j
The total amount of operation time should be equal before and after scheduling. Moreover, an upper limit is designated for the total power consumption for all the controllable appliances in each period. Based on these rules, we have
x i0, t
x i, t = t T
xj0, t
x j, t =
(19)
t T
wi x i, t + i I
When customers use electricity, they simultaneously prefer less electricity payments and high electricity consumption satisfaction. Hence, the smart power utilization model of SRD customers includes two parts: electricity payment satisfaction and power consumption satisfaction. On the basis of the clustering analysis of customers in Section 3.1, the smart power utilization models for each type of customers are established, as shown in Eqs. (26)–(28). No electrical appliances need to be operated for Type A customers, which means that scheduling cannot be conducted and that the satisfaction based on power consumption cannot be considered. On this basis, the objective function of the electricity payment for Type A is
(18)
t T
t T
3.4. Smart Power utilization model of SRD customers
wj xj, t
Wmax
qh, t
j J
(20)
h H
3.3. Satisfaction of power consumption
(ptPV qtPV + ptGRID qtGRID )
C=
qmust , t + qcontrol, t = qtPV + qtGRID qcontrol, t =
x i, t wi + i I
The power consumption levels of Type B, C, and D customers are more flexible than that of Type A because of the utilization of controllable appliances, which can take part in the scheduling. Although customers differ in terms of their sensitivity toward electricity payments, the satisfaction of electricity payment and the satisfaction of power consumption should both be considered in the modeling of each customer type. The power utilization model is expressed as Eq. (27).
max F =
(21)
t T
xj, t wj
(23)
As shown in Eq. (21), the lower the payment is, the higher the degree of satisfaction will be. Electricity payment satisfaction is therefore defined as
(ptPV qtPV S1 = 1
+
max S1.
ptGRID qtGRID )
t T
(ptGRID (qmust , t + qcontrol, t )
(24)
S2 = 1
wj x j0, t
x i, t + j J
wi x i0, t + i I
wj xj0, t j J
(28)
4. Power utilization model based on non-cooperative game
Electricity consumption plans are subsequently assumed to be optimized. Similarly, the higher the S1 is, the greater the electricity payment satisfaction will be. Electricity usage satisfaction is defined as customer's adaptability of the current living conditions. It is assumed that customers will voluntarily choose a certain electricity plan to derive the highest satisfaction for power consumption. Therefore, electricity usage satisfaction can be expressed as
wi xi0, t
(27)
In this study, Eqs. (8)–(20), (22), and (23) are the constraints of the model.
× 100%
t T
i I
max S1 max S2
For the customers of Type E, the electricity consumption during the day is at a high level with negligible fluctuations. On the one hand, the electrical appliances of Type E customers essentially include uncontrollable appliances; on the other hand, they need to consider the comfort of their guests in their shops. Consequently, the highest satisfaction of power consumption is acquired, and only electricity payment needs to be considered as follows:
(22)
j J
(26)
max S1
The customer satisfaction (i.e., with electricity plan) in this study consists of two parts, namely, electricity payment satisfaction and electricity usage satisfaction. Based on the appliance modeling in Section 3.2, electricity payment satisfaction is defined as the degree of satisfaction of users when paying electricity charges. Thus, under the same electricity consumption conditions, the lesser electricity bill the customers pay, the more they are satisfied with the consumption plans. Hence, electricity payments can be expressed as
The proposed method for modeling the interaction among SRD customers is formulated as a typical game problem with incomplete, static and finite information. In the interaction process, PV power suppliers intend to maximize their benefits, whereas SRD customers intend to reduce the electricity payments while meeting their satisfactions. This process is consistent with that of finding effective decisions in solving the conflict between maximizing PV power benefits and minimizing customer electricity payments by two or more individuals, which can be solved by game theory [30]. Meanwhile, the proposed power utilization model is formulated as a multi-objective optimization problem. Game theory has the advantages of better global searching ability and faster convergence speed compared with other optimization techniques. In addition, many applications have done by using the game theory on these problems [24,25]. Therefore, an algorithm based on game theory is proposed to solve the proposed power utilization model.
x j, t × 100% (25)
Take the original power consumption plan chosen by the customer as the basis. If the optimized power consumption plan is exactly the same as the original plan, i.e., the customer does not change consumption habits, then the customer will feel the most comfortable, and thus, electricity usage satisfaction will be the highest. By contrast, if the optimized power consumption plan is completely different from the original plan, then the scheme will drastically change the consumption habits and cause a negative impact on the customer’s life. Under this circumstance, the electricity usage satisfaction will be at its worst state. In summary, electricity payment satisfaction and electricity usage
4.1. Game modeling The Normal Form Representation is adopted in this paper, and all the players involved in the game choose their own strategies at the same time [31]. 182
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• Payoff: The payoff function is expressed as
A non-cooperative game of smart power utilization for the customers in the SRD is defined asG = {Q1, ..., Q N ; u1, ..., uN } , which is composed of player N, strategy Q and payoff u. The details are described as follows:
un (qn ,
q n) =
F=
t T PV
ptPV qtn
(29)
It is a game problem that all players pursue their own objects. For PV power suppliers, it is necessary to maximize their benefits; whereas for SRD customers, they intend to reduce the electricity payments while meeting their satisfactions. Therefore, customers participate in the game by changing the electricity consumption at each time interval, then find their own optimal electricity consumption strategy.
• Player: Customer who participate in the scheduling in the SRD that = {1,2,..., N }. is regarded as a player, wheren Strategy: Every customer selects the electricity plan •
Qn = {qtn t T PV } in accordance with his or her requirements, where qtn represents the electricity demand of the electrical appliances that is obtained from the corresponding smart power utilization model in Section 3.
Fig. 3. Flowchart of the model. 183
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4.2. Proof of nash equilibrium existence
Step 2 Solve the power utilization model considering customer’s satisfaction independently; Step 3 If the calculated value of qn(k) is different from qn(k-1), go to step 4, else go to step 6; Step 4 Update qn(k) in the smart power utilization model; Step 5 Collect qn(k) in the system from smart meters;
In order to find the optimal set of strategies to meet the needs of all customers for the whole system, the Nash equilibrium of the game needs to be determined. No player can benefit by changing strategies if every player n has chosen a strategy Qn while the other players keep theirs unchanged, then the current set of strategy choices {Q1 *, ..., Q N *} is a Nash equilibrium. The existence of Nash equilibrium of this model is proved as follows:
un (qn , q n) =
k qtPV + qFPV ,t
c t T PV
ptPV = c
qtn
qtn
n N
k qtPV + qFPV ,t
n N
qtn
Step 6 If qtPV
q n)
qtn 2
=
(30)
(31)
2k < 0
5. Case studies 5.1. Basic data
(32)
where un (qn , q n) is a concave function of qtn. Therefore, the Nash equilibrium exists in the proposed non-cooperative game according to Nash equilibrium existence theorem [31]. The optimal power consumption plan for all the customers {q1 , q2 , ..., q N } is the Nash equilibrium solution for the non-cooperative game G. Hence, when a customer in the system adopts the optimal policy, none of the other customers can bypass the existing strategy, i.e., a new strategy cannot be established, to increase his or her benefit.
un (qn , q
n
)
un (qn , q
n
)
qn
Qn,
n
, go to step 7; else, update ptPV , then go
to step 2; Step 7 Print out customer's optimal consumption qn(*) and optimal PV incentive price ptPV (*) . Each customer optimizes his or her electricity consumption behavior individually in the game model based on the PV incentive price, that is, the optimization process of each customer is an independent iteration at each period until the Nash equilibrium is obtained, and the supply is matched with the demand.
The two-order partial derivatives for qtn are obtained as 2un (qn ,
qtn n
A distributed PV power generation system is built with a capacity of 150 kW. The PV power can connect to the grid through the inverter, which can either supply energy for SRD customers or sell energy to the grid. The SRD has 300 households, of which 30 are willing to transform their line to access PV power. Among the 30 households, 3 customers are part of Type A, 7 customers are part of Type B, 10 customers are part of Type C, 9 customers are part of Type D, and 1 customer is from the Type E. The uncontrollable electrical appliances include light, TV, computer, refrigerator, cooker, etc. The controllable appliances include dishwasher, disinfection cabinet, air-conditioner, water heater, washing machine, electric vehicle, etc. The characteristics and parameters of both types of electrical appliances are shown in Table A.1 in the Appendix. The upper limit of the total power consumption of all controllable electrical appliances at each time is shown in Table A.2 in the Appendix. The multi-user power consumption system with distributed PV power supply consists of the PV power supply and 30 customers. The PV output is shown as a red dotted line in Fig. 4, and the effective output time is from 8:00 a.m. to 6:00 p.m. In the same figure, the demand of the customers over 24 h is depicted as a black solid line. The load fluctuates at daytime, and higher demands are observed at nighttime than in the other times of the day. This study assumes that the PV ongrid price is 0.41 $/kWh while the subsidy price is 0.42 $/kWh. The three Type A customers have low power consumption and can be ignored. For simplicity, only Type B, C, D, and E customers are considered in the succeeding section. The original power consumption plans of the customers for each type are shown in Fig. 2.
(33)
4.3. Algorithm design and implementation An algorithm is proposed to maximize the benefits of PV power and obtain optimal consumption, which is shown in Fig. 3. Each customer needs to play a game between PV power supplier and other customers, to reach a balance between increasing PV benefits and reducing electricity payments at Nash equilibrium point. The PV incentive price ptPV is related to both the PV output and customer demands. In other words, the PV incentive price has an inverse relationship with the net generation between PV output and customer electricity demands. When in the time of high PV, the net generation is large, which indicates more PV power needs to be consumed. Hence, a low PV incentive price is initially established to encourage consumers to shift their controllable loads independently based on their requirements of satisfaction and electrical appliance working parameters. In turn, PV incentive price will adjust due to the changes in consumption behaviors, and the process will continue until Nash equilibrium is reached. During the implementation of the algorithm, each customer optimizes his or her electricity consumption behavior individually after receiving the PV incentive price, the adjustment of customer behavior will affect the power consumption and the supply-demand matching status, then the PV incentive price is further readjusted. The process will be repeated until the PV incentive price and the customer electricity consumption are no longer changed. In this way, the dynamic adjustment between electricity price and DR resources is accomplished. The ultimate PV incentive price is the price accepted by all SRD customers, and the electricity consumption of each customer has reached the optimum, i.e., the state of Nash equilibrium has achieved. In Fig. 3, the red dotted box is a distributed optimization algorithm that finds the Nash equilibrium solution, which is described as follows: Step 1 Initialize qn(0) and q−n(0), and receive the PV incentive price PV pt ;
Fig. 4. PV output and load curve. 184
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5.2. Analytical results
compared with the customers in Case I (Fig. 4), those in Case II will choose electricity consumption plans they are most satisfied with on the basis of their own habits. The corresponding PV output, customer demands and PV incentive price of Case II and Case III are shown in Fig. 5(a) and (b) respectively. The PV output shown in Fig. 5(a) is greater than the demand between 11:00a.m. and 4:00p.m. This is due to the fact that customers arbitrarily choose their electricity plans to meet their satisfactions without considering optimal scheduling. While in Case III, the smart power utilization algorithm based on game theory is adopted, the optimization results of Case III in Fig. 5(b) shows that the PV incentive price between 11:00a.m. and 4:00p.m. is decreased and the customers’ electricity consumptions are increased compared to that of Case II. Therefore, the PV power consumption has been maximized in Case III.
Three cases are discussed as follows:
• Case I: The customers will choose their electricity plans without • •
considering their satisfaction. They will choose the power consumption plan according to the upper power limit constraint. Case II: The customers will adaptively choose their electricity plans and consider their satisfaction. Case III: The smart power utilization algorithm based on game theory is adopted and the customer satisfaction is considered. The results are analyzed from the following aspects:
• Supply and demand matching. • PV incentive price. • Comprehensive income analysis. • Comparison of power consumption in different cases. • Comparison of power consumption satisfaction in different cases.
5.2.2. PV incentive price The PV incentive price is the same as the grid price in Cases I and II without optimal scheduling, which indicates that customers do not have additional benefits, and they prefer to purchase electricity from the grid to maximize their own interests. Thus, all the PV power is acquired by the grid through the inverter. In Case III, the incentive price with values between the PV on-grid
5.2.1. Supply and demand matching In Cases I and II, the optimal strategy is not considered. However,
Fig. 5. Supply and demand in Cases II and III (a) Cases II, (b) Cases III. 185
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price and the retail price is determined by using the non-cooperative game model. The incentive price is offered to customers to encourage PV power consumption. Then, based on the game between customers and the PV power, the Nash equilibrium is reached. The final PV incentive price is shown in Fig. 6. When the PV output is high, such as the period from 11:00 a.m. to 4:00 p.m., the PV incentive price is significantly lower than the retail price. This scenario implies that customers will likely use PV electricity to minimize electricity payments. The solar energy in this scenario is fully absorbed. 5.2.3. Comprehensive income analysis The comprehensive incomes for the above cases are shown in Table 1. Case I and II depict the PV incomes from power generation. PV incentive price is not considered, and all the SRD customers absorb electricity from the grid. Type B and D customers in Case II obtain higher electricity payments than those in Case I because they adjust their electricity consumption plans to reach the highest degree of satisfaction, whereas Type C and E customers have relatively lower electricity payments. In Case III, the PV power supplier can achieve comparatively higher benefits after optimization. The SRD customers consume PV power, and they also cut down their electricity payments (i.e., by consuming PV power, the prices are lowered). Compared with Case II, the income of the PV supplier is higher by 7.8% and the payments of Type B, C, D, and E customers are lower by 9.6%, 13.1%, 12.8%, and 14.0% in Case III, respectively. Then, compared with Case I, the payments of Type B, C, D, and E customers in Case III are lower by 1.05%, 14.8%, 7.8%, and 29.0% respectively.
Fig. 6. Optimized PV incentive price. Table 1 Comparison of comprehensive income Cases
Case I Case II Case III
PV Income/$
Electricity payment of customers/$ Type B
Type C
Type D
Type E
294.38 294.38 317.47
10.43 11.42 10.32
10.84 10.63 9.24
13.61 14.40 12.55
22.14 18.29 15.73
5.2.4. Comparison of power consumption in different cases In Case I, as long as the power consumption does not exceed the upper limit, the customers will not change their original consumption habits. Therefore, the consumption of customers is the same as their previous consumption (Fig. 2). The power consumption of different types of customers are compared between Cases II and III (Figs. 7 and 8). The PV incentive price is cheaper than the retail price in Cases II and III, and Type B customers can adjust the operation time of their controllable electrical appliances to adequately consume PV power. Given that Type C customers mostly stay at home during the day, the available operation times of the controllable appliances have relatively lesser restrictions, which suggest that the scheduling rate of the load is high. For the sake of reducing electricity payment, the customers transfer the operation time of some controllable electric appliances to the period with low incentive price, e.g., the period from 2:00 p.m. to 4:00 p.m. Similar to Type C, the load scheduling rate of Type D is also high. To reduce electricity payment, the operation times of some controllable electric appliances are also transferred to the period with low PV incentive price. As a consequence of the high satisfaction for power consumption of Type E customers, and because their electrical appliances mainly consist of uncontrollable electrical appliances, the consumption plans are not adjusted in Cases II and III. However, the electricity payments are reduced because of the relatively lower PV incentive price. The consumption changes in Cases I and II are compared and shown in Fig. 9. Given that consumers tend to use electricity in the evening, all types of customers increase their electricity consumption at night from the perspective of customer satisfaction. In terms of original consumption in Case I, Types B and D appear with two peaks, namely, from 6:00 a.m. to 9:00 a.m. and from 6:00 p.m. to 10:00 p.m., respectively, as shown in Fig. 2. In Case II, however, Type D customers reduce their consumption between 4:00 p.m. and 6:00 p.m., while Type B customers reduce their consumption between 3:00 p.m. and 5:00 p.m. Type E customers have high power consumption during the day to meet their satisfaction requirements, and their daytime electricity consumption does not change significantly and instead mostly decrease at nighttime.
Fig. 7. Power consumption of customers in Case II.
Fig. 8. Power consumption of customers in Case III. 186
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Fig. 9. Power consumption changes in Cases I and II.
Fig. 10. Power consumption changes in Cases II and III.
The power consumption changes in Cases II and III are compared and shown in Fig. 10. Except for those in Type E, the customers increase their electricity consumption when PV has an effective output, which verifies the effectiveness of the PV incentive price in guiding customers to consume PV power.
Table 2 Power consumption satisfaction of different types of customers Customers
Type Type Type Type
B C D E
Case II
Case III
S1
S2
S1
S2
−0.095 0.019 −0.058 0.174
0.686 0.253 0.261 0.216
0.01 0.14 0.077 0.28
0.896 0.344 0.414 0.216
5.2.5. Comparison of power consumption satisfaction in different cases The power consumption satisfaction levels of different types of customers are shown in Table 2, in which Case I is designated as the benchmark of the comparison. To evaluate the comprehensive result of satisfaction, parameter λ can be set as follows:
Table 3 Overall satisfaction of different types of customers Case II
Case III
S = S1 + (1
Type Type Type Type
0.2955 0.136 0.1015 0.195
0.453 0.242 0.2455 0.248
where 0 ≤ λ ≤ 1. Furthermore, the overall satisfaction of the customers can be expressed (Table 3), i.e., λ = 0.5. In Case II, the electricity payment satisfaction of Type B and D customers are less than that of the other types of customers because of the relatively higher electricity bills, and their electricity usage satisfaction is higher than their electricity payment satisfaction.
B C D E
187
) S2
(34)
Customers
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Consequently, Type B and D customers changed their manner of using electricity mainly because their power consumption needs are met. The electricity charges decreased and the needs were simultaneously met for the other types of customers. In Case III, the satisfaction levels of all customer types increased after the PV incentive pricing. However, the electricity usage satisfaction of Type E customers was the same because of their high satisfaction for power consumption, and their increased satisfaction was derived from the additional benefits from consuming PV power. In summary, the customer electricity consumption plans are guided by the non-cooperative game model and the consideration of an incentive price that is closely related to PV output and load demands. The game is implemented from two aspects, namely, customers versus PV power supplier and a single customer versus other customers. At the Nash equilibrium point, the benefits of PV power supply are increased and the electricity payments are reduced for customers under the condition of having to satisfy their own demands. The effectiveness of the model is verified by the case studies.
has the following characteristics: 1. The specific situation of each type of customer is considered in the electricity plans. The SRD customers can independently adjust their power consumption by the non-cooperative game. When the game is balanced, the optimal policy combination among all players is obtained. 2. The PV incentive price, which acts as a supply–demand lever, can guide the customer in optimizing the distribution of power consumption. By applying the incentive price, which is closely related to PV output and customer electricity demands, the customers are then motivated to participate in PV power consumption. Our approaches are valid for small scale like a typical SRD. For large-scale systems, with the increase of the customers, renewable energy types and network nodes, the customer clustering analysis and the game strategy among customers will be more complex. In addition, the uncertainties of renewable energy output and customer response and the related power system constraints should be also taken into account. Therefore, it will be the key work in our future research to establish more complex scheduling models and strategies among customers, renewable energy and grids.
6. Conclusion Power consumption optimization is conducted from two levels in this study. First, the PV incentive price, which is closely related to PV output and customer demand, is established to optimize the smart power utilization. Then, by establishing the Nash equilibrium point, the balance is achieved between the maximum benefits of PV power and the minimum electricity payments of customers. The proposed strategy
Acknowledgement This work is supported by National Natural Science Foundation of China(NSFC) [grant number 51247006].
Appendix A
Table A.1 Parameters of controllable electrical appliances Electrical appliance
Type
Rated Power/(kW)
Dishwasher Disinfection Cabinet Air Conditioning Water Heater Washing Machine Electric Vehicle
Non Non Int Int Non Int
1.0 0.52 5.2 5.8 0.75 3.5
Note: “Non” − non-interruptible electrical appliances; “Int” − interruptible electrical appliances.
Table A.2 Upper limit of power at each time. Time
Upper Limit/(kW)
7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00
4.5 4.5 6 6 6 6 6 6 6 6 6 6 5 5
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