Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system

Applied Energy 190 (2017) 1126–1137

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system q Yibo Jiang, Jian Xu ⇑, Yuanzhang Sun, Congying Wei, Jing Wang, Deping Ke, Xiong Li, Jun Yang, Xiaotao Peng, Bowen Tang The School of Electrical Engineering, Wuhan University, Wuhan 430072, China

h i g h l i g h t s
Improving the utilization of wind power by the demand response of residential hybrid energy system.
An optimal scheduling of home energy management system integrating micro-CHP.
The scattered response capability of consumers is aggregated by demand bidding curve.
A stochastic day-ahead economic dispatch model considering demand response and wind power.

a r t i c l e

i n f o

Article history: Received 13 October 2016 Received in revised form 9 January 2017 Accepted 14 January 2017

Keywords: Demand response Residential hybrid energy system Wind power fluctuations Micro-CHP Economic dispatch

a b s t r a c t As the installed capacity of wind power is growing, the stochastic variability of wind power leads to the mismatch of demand and generated power. Employing the regulating capability of demand to improve the utilization of wind power has become a new research direction. Meanwhile, the micro combined heat and power (micro-CHP) allows residential consumers to choose whether generating electricity by themselves or purchasing from the utility company, which forms a residential hybrid energy system. However, the impact of the demand response with hybrid energy system contained micro-CHP on the large-scale wind power utilization has not been analyzed quantitatively. This paper proposes an operation optimization model of the residential hybrid energy system based on price response, integrating micro-CHP and smart appliances intelligently. Moreover, a novel load aggregation method is adopted to centralize scattered response capability of residential load. At the power grid level, a day-ahead stochastic economic dispatch model considering demand response and wind power is constructed. Furthermore, simulation is conducted respectively on the modified 6-bus system and IEEE 118-bus system. The results show that with the method proposed, the wind power curtailment of the system decreases by 78% in 6-bus system. In the meantime, the energy costs of residential consumers and the operating costs of the power system reduced by 10.7% and 11.7% in 118-bus system, respectively. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Wind power, which is a kind of clean energy, has received wide attention and support from the whole world. However, the stochastic variability of wind power output become increasingly significant as the growing wind power capacity. Since the ramping

q This work was supported in part by the National Key Research and Development Program of China (2016YFB0900105), in part by the National Natural Science Foundation of China (51477122). ⇑ Corresponding author. E-mail address: [email protected] (J. Xu).

http://dx.doi.org/10.1016/j.apenergy.2017.01.030 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved.

ability of thermal units cannot cope with such large power fluctuation, the power output of wind farm is limited in the power system scheduling [1]. According to the latest statistics of China’s National Energy Administration, as of the first half of 2016, the total installed capacity of large-scale wind farms has been up to 137 million kilowatts. Whereas the average utilization time of wind power is only 917 h and the average wind power curtailment is 21% [2]. Therefore, the stochastic variability of wind power output is gradually becoming a bottleneck restricting the development and utilization of wind power [3]. It should be noted that this variability, which leads to the mismatch of demand and generated power, means the variable wind power output caused by

Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137

1127

Nomenclature

Dt T pein,t peout,t pgas,t gtotal,t ein,t eout,t X sx,t px,t PNx Pmin x Pmax x T start x T end x T last x T total x

gx

hin,t hout,t hmin in hmax in eair

jair

hfr,t hmin fr hmax fr

wfr

ufr Xfr Afr,t

vprim,t vaux,t

ustart,t uclose,t Tref eprim,t emin prim emax prim emin prim emax prim eramp hprim,t

time step set of time periods price when consumers imported electricity at time t price when consumers sold electricity at time t natural gas price total gas used at time t electricity imported at time t electricity sold to the grid at time t set of home smart appliances on/off state of device x at time t output power of device x at time t rated power device x minimum output power of device x at time t maximum output power of device x at time t the first time that device x can start up the last time that device x must shut down successive operation time of device x required operation time of device x efficiency of device x inside temperature of the house at time t forecasted outside temperature of the house at time t minimum inside temperature of the house maximum inside temperature of the house factor of inertia of air thermal conductivity inside temperature of the fridge at time t minimum inside temperature of the fridge maximum inside temperature of the fridge warming effect of the usage of the fridge per time cooling effect of an ON state of the fridge per time warming effect of an OFF state of the fridge per time activity level of fridge at time t on/off state of the micro-CHP prime mover at time t on/off state of the micro-CHP auxiliary burner at time t binary variable denoting start up of the prime mover at time t binary variable denoting shut down of the prime mover at time t start-up time of the fuel cell electric power generated by the prime mover at time t minimum electric power generated by prime mover maximum electric power generated by prime mover minimum electric power generated by prime mover maximum electric power generated by prime mover electric ramp capacity of the prime mover heat power generated by the prime mover at time t

intermittence of wind energy. Many scholars have proposed the demand response technology using the regulating capability of load to balance the wind power variability [4,5]. With the microCHP and smart home appliances, residential users turn from passive energy consumers to elastic loads, and they gradually have the demand response capability. Since micro-CHP has the characteristics of gas and electricity coupling, users can build residential hybrid energy systems and meet their electricity demand from both the power grid and the natural gas network. Hence, the interaction between this kind of residential users and power system needs to be further analyzed. At the level of power system, some existing research considers demand response in the scheduling problem. Ref. [6] presents an economic model of demand response, which explains the change of consumption pattern and cross-period shift of loads. Ref. [7] makes an integration of demand response programs and dynamic

haux,t hs,t hd,t

ge gh gaux

gprim,t gaux,t gref di pb Dpe Ncus Ntes G N E NG NW ND di,t min

heat power generated by the auxiliary burner at time t heat power stored by tank at time t heat power needed by consumers at time t electric efficiency of the prime mover thermal efficiency of the prime mover thermal efficiency of the auxiliary burner gas consumed by the prime mover at time t gas consumed by the auxiliary burner at time t gas used for heating up the reforming unit during startup demand curve aggregated from all consumers under node i benchmark price curve unit price changes the number of HEMSs under a node the number of points for testing demand curve the directed graph that reflect the grid structure set of nodes set of lines set of thermal units set of wind units set of loads electric load of load i at time t

di;t

minimum load of load i at time t

max di;t

maximum load of load i at time t generation dispatch of thermal unit i at time t minimum capacity of thermal unit i maximum capacity of thermal unit i generation dispatch of wind unit i at time t maximum capacity of wind unit i actual available power of wind unit i at time t underestimation cost coefficient of wind unit i overestimation cost coefficient of wind unit i maximum transmission capacity of the line from node i to j up regulation reserves provided by thermal unit i at time t down regulation reserves provided by thermal unit i at time t confidence level for having sufficient up regulation reserves confidence level for having sufficient down regulation reserves

pi,t Pmin i Pmax i wi,t wmax i wa,i,t kun,i kov,i Pmax L;i;j ru,i,t rd,i,t cu cd

economic dispatch. A market clearing mechanism considering both demand-side and supply-side bidding is described in Ref. [8]. In addition, a bi-level optimization model of system-wide demand response management is presented in Ref. [9]. Some research also considers the coordination of demand response and wind power. Ref. [10] studies the bidding strategy of Load Serving Entities (LSEs), taking into account the stochasticity of wind power by probabilistic scenarios. In Ref. [11], a robust optimal dispatching model, which combines robust optimization and dynamic optimization, is constructed, considering demand response and its impact on wind power in various cases. Ref. [12] proposed a probabilistic unit commitment model with incentive-based demand response and high wind power, using an operational-cycle-based algorithm. A demand response market is designed in Ref. [13], and the quantity of residential demand response is optimized. In Ref. [14], the interruptible-load based and coupon-based demand

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response capability of virtual power plants is analyzed. Ref. [15] considers the demand response and wind power in the operating strategy of gas-electricity integrated energy systems. The above literatures discuss the demand response in power system dispatching and analysis the characteristics of demand response based on statistical model. However, with the popularity of micro-CHP that has the features of gas and electric coupling, the traditional load statistics regularity is no longer applicable to residential hybrid energy system. To explore the response characteristics of this kind of load, the physical model is supposed to be constructed. At the residential level, there have been some literatures focusing on the characteristics and modeling method of micro-CHP. Refs. [16,17] study the strategy of ‘‘heat-lead” for micro-CHP, maintaining the temperature in the water storage tank constant. This operation strategy is used by most micro-CHP currently. In Ref. [18], the output and efficiency of different micro-CHP is analyzed under various operation strategies. Ref. [19] mathematically models three types of micro-CHPs and two different strategies. A mechanism of using micro-CHP for demand response is proposed in Ref. [20], in which the working conditions of micro-CHP varies based on the electricity price change. Ref. [21] compares two different operation strategies for a heat-driven residential natural gas-fired CHP system. For smart home appliances, the home energy management system (HEMS) dispatches the operation of all appliances centrally and automatically [22]. Ref. [23] proposes an energy dispatch framework, aiming to reduce electricity expenditure and waiting time of each controllable device under the excitation of time-dependent electricity price. Ref. [24] presents a novel algorithm of energy dispatching, considering the uncertainty of operation time of home appliances and intermittent power generation by renewable energy. A mathematical optimization model of residential energy center considering users’ preference and satisfaction is introduced in Ref. [25], in which the use, storage and production of residential energy loads are optimized in an effective and real-time way. In the existing researches, the independent operation strategy of micro-CHP and smart appliances is used to optimize the energy consumption of single family. However, the coordination between micro-CHP and smart appliances remains to be discussed, and the power regulation capability of the residential load cluster has not been quantitatively analyzed. Micro-CHP allows residential consumers to choose whether generating electricity by themselves or purchasing from the utility company, which forms a residential hybrid energy system. Regarding to the hybrid energy system, Refs. [26–29] discuss the design and operation strategies of hybrid micro-generation system. Refs. [26,27] point out that the key to build sustainable energy systems is effectively integrating non-conventional renewable energies, with thriftiness and energy efficiency, and offer design and operation strategies based on homeostatic control. A business optimal design method of a small grid-connected hybrid energy system is proposed in Ref. [28], the objective function is to minimize the life cycle cost of the system, ensuring certain level of system reliability at the same time. Ref. [29] focuses on exergy optimality, and presents a new theoretical approach for developing grid-connected sustainable hybrid energy systems, which based on exergy and energy management, cybernetics and homeostatic control. Consequently, the hybrid energy system is investigated in details, but the demand response capability of residential hybrid energy system contained micro-CHP dealing with large-scale wind power has not been fully discussed. In summary, the micro-CHP is proved to have demand response capability in literatures. However, in the existing research, how to utilize this part of response capability to improve large-scale wind power utilization is not investigated, and the interaction of residential hybrid energy system and power system is not quantitatively analyzed. Therefore, motivated by those issues, this paper

proposes a complete framework regarding to the demand response of residential hybrid energy system from both residential load and power system dispatching aspects. At the residential level, this paper introduces micro-CHP into HEMS to further explore users’ potential of demand response and aggregates the scattered demand response capability of residential consumers. At the level of power grid scheduling, this paper establishes a stochastic economic dispatching model to analyze the impact of the residential hybrid energy system on the wind power utilization. The main contributions of this paper can be summarized as below: (1) A price-response-based energy supply optimization model of the residential hybrid energy system is constructed, in which the micro-CHP and smart home appliances are integrated intelligently. The coordination of micro-CHP and smart appliances is considered and the power regulation capability of residential hybrid energy system is analyzed. (2) A load aggregation method is proposed to aggregate the scattered demand response capability of residential load. Demand bidding curve of consumers group is presented to describe the cluster features of residential users. (3) The paper establishes a stochastic day-ahead dispatch model considering demand response and wind power, using versatile distribution model to describe the stochasticity of wind power, and maximizes social surplus. This model analyzes the interaction between the residential hybrid energy system and power system. The following of this paper is organized as follows: Section 2 describes the framework of residential demand response. Section 3 introduces the optimization model and operating principle of the residential hybrid energy system. A stochastic day-ahead dispatch model considering demand response and wind power is established in Section 4. Section 5 analyzes the impact of the residential hybrid energy system on the wind power utilization of the windintegrated power system based on simulation results. The conclusion is drawn in Section 6.

2. Framework of residential demand response The physical architecture of the power system and the operation process of the electricity market are demonstrated in Fig. 1. Residential and commercial consumers are generally connected at the end of the power grid, while large-scale wind farms are generally connected directly to the power transmission network. At the demand level, the residential consumers utilize microCHPs to establish a residential hybrid energy system. These consumers can choose whether using nature gas to generate electricity by themselves or purchasing electricity from the utility companies. In addition, this power supply model has been implemented in various countries [16–21]. This residential hybrid energy system is operating efficiently because of the high-energy utilization efficiency of micro-CHP. Furthermore, the conjunction with the power grid ensures the power supply reliability. The energy price, the external environment (such as air temperature and weather) and consumers’ personal habits are the input of HEMS, and can influence the choice whether purchasing electricity from utility companies or generating electricity by micro-CHP. Due to the capability to change their load curve resulted by the residential hybrid energy system based on the energy price [20], the system can be employed to demand response program. Demand aggregators, such as LSEs, centralize scattered response capability and transact it in the wholesale market. At the level of power grid, ISO cannot dispatch the output of residential hybrid energy system directly, because the devices belong

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4

1

Wind power forecast

2

generator Wind power

5

6

Supply curve

3

Dispatch ISO

Transmission Grid

Aggregated Demand curve Electric price

Commercial Building

Demand aggregator (e.g. LSEs) Pay willness Customer Customer Consumers Consumers

Residential Customer Distribution Grid

Outdoor environment

Gas price

Gas grid

Gas grid

Fig. 1. Framework of residential demand response.

to the consumers. Nevertheless, ISO can stimulate users to change their load curve by real-time price, which is one of the inputs of HEMS. As the operation cost of wind power is significantly lower than that of thermal power, the wind power output affects the price when the proportion of wind power is high. The real-time price, which contains the information of the wind power variability, is released to each LSE, and subsequently be distributed to each consumer to prompt demand response. Based on this principle, ISO utilizes the demand bid curve and the supply bid curve uploaded by power suppliers to clear the market by the economic dispatch model. After that, the calculated market clearing price is sent to each participant. The market clearing principle of ISO is demonstrated in Fig. 2, in which the demand bid curve and the supply bid curve are mostly a stepwise curve or a piecewise broken line. The supply bid curve increases monotonically and the demand bid curve decreases monotonically. In general, the maximization of total social surplus is the objective in the dispatch considering demand response [10]. Total social surplus is the sum of surpluses of all users, while users’ surplus is the sum of producer surplus and consumer surplus. From the geometric view, it is equal to the area

Price Bidding ($/MWh) Supply Bid Curve

under the supply bid curve and above the demand bid curve, shown as the shaded area in Fig. 2. The intersection of two curves corresponds to the market clearing price and the total social surplus is maximum at this point. 3. Modeling and aggregation of residential hybrid energy system Table 1 lists typical smart home appliances and their operating characteristics. There are two types of output of smart home appliances: constant power and variable power. Based on their operating characteristics, they can be further classified by interruption and transitivity. ‘‘” indicates the appliance is not interruptible or not transitive; ‘‘U” indicates the appliance is interruptible or transitive. To explore users’ potential of demand response, the paper embeds micro-CHP into the HEMS and establishes a priceresponse-based energy supply optimization model for residential hybrid energy system. The schematic diagram of the residential hybrid energy system is shown in Fig. 3. The residential hybrid energy system in this paper consists of smart home appliances and micro-CHP. All appliances are automatically managed by HEMS to ensure consumer comfort

Table 1 Classification of electrical appliances. Type

Power characteristics

Interruption

Transitivity

Dishwasher Air-conditioner Refrigerator Washer Dryer Lighting and Entertainment

Constant Power Variable Power Variable Power Constant Power Constant Power Constant Power

U U U   

U U U U U 

P* Demand Bid Curve 0

d*

Quantity (MWh)

Fig. 2. Principle of market clearing.

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Smart meter

Light

Dish Washer

Washer

Water Heater

Electricty Freezer

AC

Micro CHP

Natrual gas

Electric flow

Gas flow

Message flow

Fig. 3. Structure of residential hybrid energy system.

and minimize residential energy cost. The HEMS is integrated in the smart meter and optimizes the operating of all appliances 24 h a day. The optimization target of HEMS is shown as (1).

min cost ¼ Dt 

T X

ðpein;t ein;t  peout;t eout;t þ pgas;t g total;t Þ

ð1Þ

t¼1

where pein,t and peout,t are the price of purchasing and selling electricity at time t respectively. pgas,t is the price of purchasing nature gas. ein,t and eout,t are the quantity of electricity imported and sold at time t. gtotal,t is the total quantity of gas used at time t. (1) represents the total energy cost of home users to meet their energy demand.

where ½T start ; T end x x  is the time range that appliance x may run for; is the continuous working time of appliance x. When the appliT last x ance is Transitive and interruptible appliances, such as a dishwasher, are only subject to (5). The appliance that is not interruptible but is transitive, such as a washing machine, is subject to both (4) and (5). Non-interruptible and non-transferable is subject to (4) such as a lighting device. (6) describes the relationship of start-up time of different appliances (for example, the dryer should start after the washing machine ends its work): T X sx1 ;t P T total x1 ðsx2 ;t  sx2 ;t1 Þ

ð6Þ

t¼1

3.1. Modeling of smart home appliances The set of smart home appliances is assumed to be X, and 0–1 variable sx,t is introduced to indicate the start/stop state of the appliance x 2 X at the time t. sx,t = 1 denotes the appliance is on; sx,t = 0 denotes the appliance is off. (2) and (3) describe the actual power output of constant power appliances and variable power appliances respectively.

px;t ¼ sx;t  P Nx

ð2Þ

6 px;t 6 sx;t  Pmax sx;t  Pmin x x

ð3Þ

(4) and (5) are introduced to describe the interruption and transitivity of smart home appliances. (4) describes the operating characteristics of appliances that cannot be interrupted. Such appliances, once started, must operate continuously until its work is completed. (5) describes the transitivity of appliances whose operating time can be adjusted. last TX x 1

sx;tþi P ðsx;t  sx;t1 Þ;

t 2 ½T start ; T end  T last þ 1 x x x

ð4Þ

i¼0

i¼0

hin;tþ1 ¼ eair hin;t þ ð1  eair Þðhout;t  pAC;t =jair Þ

ð7Þ

hfr;tþ1 ¼ hfr;t þ Dtðwfr Afr;t  ufr sfr;t þ Xfr Þ

ð8Þ

pfr;t ¼ PNfr  sfr;t

ð9Þ

max min 6 hfr;t 6 hmax hmin in 6 hin;t 6 hin ; hfr fr

delay

TX x

where T total is the required operating time of appliance x; x1, x2 are x the appliance running first and the appliance running later respectively. In particular, as for temperature-controlled loads such as air conditioners and refrigerators, their power consumption is related to the setting temperature and the ambient temperature. Therefore, it is essential to establish models for temperature-controlled loads separately. The principle of classical thermodynamics is introduced to describe the energy exchange of air conditioning system and external system [30], and the rise and drop temperature coefficients are used to represent the temperature in the refrigerator storage compartment [25]. (7)–(10) indicate the power demand of temperature-controlled appliances and describe the inertia of temperature change.

sx;T start þi P 1; 0 6 x

T delay x

6

T end x



T start x



T last x

ð5Þ

ð10Þ

where pAC,t and pfr,t express the power demand of the air conditioner and refrigerator at the time t respectively; hfr,t is the temperature

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inside the refrigerator at the time t; Afr indicates the actual use level of the refrigerator; wfr is the temperature rise per unit time due to being used by the user; ufr expresses the temperature drop per unit time due to the operation of the refrigerator compressor; sfr,t indicates the start/stop state of the refrigerator at the time t; Ofr is the temperature rise per unit time due to cold loss of the refrigerator.

hs;tþ1 ¼ hs;t þ hprim;t þ haux;t  hd;t

ð15Þ

g prim;t ¼ eprim;t =ge þ T ref  g ref  ustart;t

ð16Þ

g totol;t ¼ g prim;t þ g aux;t

ð17Þ

eprim;t =ge ¼ hprim;t =gh

ð18Þ

3.2. Modeling of micro-CHP

g aux;t ¼ haux;t =gaux

ð19Þ

A micro-CHP consists of a prime mover, an auxiliary burner and a heat storage tank, and the energy flows in the micro-CHP is shown in Fig. 4. The prime mover provides both electricity and heat simultaneously. The electric energy generated by micro-CHP can be used locally and the surplus is sold to the utility company. The heat produced is stored in the heat storage tank. The auxiliary burner can be a boiler or an electric heat pump [31] and it produces heat only. (11)–(23) are introduced to describe the operation of micro-CHP mathematically. (11)–(13) are the start/stop constraints. (14)–(19) indicate the energy balance constraints. (20)– (23) are the output constraints. Four 0–1 variables vprim,t, vaux,t, ustart,t, uclose,t are introduced to describe the start/stop state of micro-CHP. vprim,t = 1 indicates the prime mover is on at the time t; vprim,t = 0 indicates the prime mover is off at the time t; vaux,t is in the same way. ustart,t = 1 indicates the prime mover starts up at the time t; uclose,t = 1 indicates the prime mover shuts down at the time t. (11) describes the relationship of the start/shut state and running state of the prime mover; (12) indicates the prime mover can only start or shut at the time t; (13) indicates the start process constraint of the prime mover.

where eprim,t denotes the generated electric power by the prime mover at the time t; ein,t and eout,t are the power purchased and sold from the utility company at the time t respectively; gx is the energy efficiency of the appliance x; hs,t is the heat energy of the hot water stored in the tank at the time t; hprim,t and haux,t are the heat produced by the prime mover and the auxiliary burner at the time t respectively; hd,t is the residential heat demand the time t; gaux,t and gprim,t respectively denote the amount of natural gas consumed by the auxiliary burner and the prime mover at the time t; gref is the amount of natural gas consumed by the fuel cell in one reforming; gtotal,t is the total amount of natural gas consumed by the micro-CHP at the time t. (20) and (21) indicate the upper and lower limit constraints of the output of the prime mover; (22) is the ramping constraint of the prime mover; (23) is the upper and lower limit constraints of the thermal power of the auxiliary burner.

v prim;t  v prim;t1 ¼ ustart;t  uclose;t

ð11Þ

ustart;t þ uclose;t 6 1

ð12Þ

ustart;ti 6 v prim;t ; 0 6 i 6 T ref  1

ð13Þ

max emin prim  sa;t 6 eprim;t 6 eprim  sa;t

sa;t ¼ v prim;t 

T ref 1

X

ustart;t

ð21Þ

jeprim;t  eprim;t1 j 6 eramp

ð22Þ

haux  v aux;t 6 haux;t 6 haux  v aux;t

ð23Þ

i¼0

min

where Tref is the time required for the start process of the prime mover. (14) describes the supply and demand balance of electric power of residential consumers. The amount of hot water stored in the heat storage tank, the gas consumption of the auxiliary burner and the total gas consumption of the micro-CHP can be calculated by (15)–(17) respectively. (18) describes the correspondence between power generation and heat production of the prime mover. (19) calculates the gas consumption of the auxiliary burner.

eprim;t þ ein;t ¼

X px;t

,

gx þ eout;t

ð14Þ

x2X

Power grid

eout

ð20Þ

max

where sa,t is an intermediate variable determines the power output of the prime mover. 3.3. Aggregation of load The consumer demand bidding curve at a certain time reflects the relationship between the electricity price and the power consumption at this time. In order to investigate the response of the residential hybrid energy system to the electricity price, the paper uses the following method to obtain the demand bidding curves of individual consumers, and then aggregates them into the demand bidding curve of all consumers at one node of the power transmission network. Specific steps are as follows:

ed

ein

Electricity demand

eprim gprim Prime mover

Gas netwok

hprim Storage tank

gaux Auxiliary burner Gas flow

haux

hd

Heat demand

hs

Power flow Fig. 4. Energy flows in the micro-CHP.

Heat flow

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Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137

erally, the economic dispatch model is used to clear the supply and demand balance [32]. 4.1. Modeling A directed graph G = (N, E) is defined to represent the topology structure of the transmission network, where N = {1, 2, . . . , N} is the set of nodes; the ordered pair (i, j) 2 E is the directed edge from node i to node j. The paper introduces auxiliary 0–1 variables BG;i;iG , BW;i;iW and BD;i;iD to respectively denote the location of thermal units, wind farms and demands in the network. BG;i;iG ¼ 1 indicates that the thermal power unit iG is located at the node i, so do BW;i;iW and BD;i;iD . The objective function of the economic dispatch model considered in this paper is as follows:

XX XX max ui;t ðdi;t Þ  C G;i;t ðpi;t Þ t2T i2ND



XX

t2T i2NG

ðC un;j;t ðwi;t Þ þ C ov ;j;t ðwi;t ÞÞ

ð25Þ

t2T i2NW

where di,t is the load value; pi,t is the output power of the thermal power unit and wi,t is the dispatch value of wind power. The first term in this formula is consumer gross surplus; the second term describes the fuel cost of the thermal power unit; The third and fourth terms are wind power underestimation and overstimulation costs respectively. The calculation formula of each term is as follows:

Fig. 5. Flow chart of demand bidding curve aggregation.

Z ui;t ðdi;t Þ ¼

Firstly, we repeatedly change the benchmark electricity price at a certain time and maintain the electricity price of other time fixed. The modified electricity price is input to the residential load model to explore the demand bidding curve of an individual consumer at a certain time. The paper ignores the constraints of the power distribution network and assumes that the aggregated electric demand at a node is equal to the linear superposition of all consumers’ demand at this node. Then, the demand bidding curve of the consumers group at a certain time is obtained. Finally, the above method is repeated for other time in sequence. The flow chart of demand bidding curve aggregation is shown in Fig. 5. Where pb = [pb,1, pb,2, . . . , pb,T] and pe = [pe,1, pe,2, . . . , pe,T] are the benchmark price curve and the price curve used to test demand response respectively; Ntes is the number of tested points; Ncus is the number of consumers at the node i. This paper takes Ntes = 5 and T = 24. ein,c,t and eout,c,t are the qualities of electricity purchased and sold by consumer c at the time t; di is the demand matrix after aggregating all consumers at the node i, which can be expressed as:

2

   di;1;Ntes

3

di;1;1 6 di;2;1 6 di ¼ 6 6 .. 4 .

di;1;2 di;2;2 .. .

   di;2;Ntes 7 7 7 .. .. 7 . . 5

di;T;1

di;T;2

   di;T;Ntes

ð24Þ

di;t

dmin i;t

g i;t ðdi;t Þddi;t

C G;i;t ðpi;t Þ ¼ ai p2i;t þ bi pi;t þ ci Z

wmax i

C un;i;t ðwj;t Þ ¼ kun;i

ð27Þ

ðwa;i;t  wi;t Þf i ðwa;i;t Þdwa;i;t

ð28Þ

wi;t

Z C ov ;i;t ðwi;t Þ ¼ kov ;i

wi;t

0

ðwi;t  wi;t;a Þf i ðwa;i;t Þdwa;i;t

ð29Þ

where gi,t(di,t) is the demand bidding curve of the node i at the time t. The piecewise broken line is used in this paper to represents the demand bidding curve. Therefore ui,t(di,t) is a piecewise quadratic function. ai, bi, ci are cost parameters of the thermal power unit; fi(wa,i,t) is the PDF function of the conditional probability distribution of the actual output of wind power, which is obtained from the statistics of historical data of wind farms; kun,i and kov,i are wind power underestimation and overestimation cost coefficients respectively, which represent the costs of the dispatch department due to underestimating or overestimating the actual wind power output [33]; wa,i,t denotes the actual wind power output, which is a stochastic variable in this paper. The constraints of the economic dispatch model include:

X

BG;i;iG piG ;t þ

X

The element in the t row of di is the demand corresponding to different prices under this node at the time t. In addition, considering that not all consumers have installed HEMS in the actual system, ein,t is taken as the day-ahead load forecast and eout,t is set as 0 for traditional residential consumers not installing HEMS.

iG 2NG

4. Day-ahead stochastic economic dispatch considering demand response and wind power

pi;t  pi;t1 6 RUi ;

After calculating the demand bidding curves, LSEs upload them to ISOs. ISOs utilize the demand bidding curves and the supply bidding curve uploaded by power suppliers to make dispatching. Gen-

ð26Þ

¼

X

iW 2NW

X

pL;i;j;t 

j:ði;jÞ2E

X

BD;i;iD diD ;t

iD 2ND

pL;k;i;t

i 2 N; t 2 T

ð30Þ

k:ðk;iÞ2E

6 pi;t 6 P max Pmin i i

pi;t1  pi;t 6 RDi min

BW;i;iW wiW ;t 

max

di;t 6 di;t 6 di;t

i 2 NG ; t 2 T i 2 NG ; t 2 T

ð31Þ ð32Þ

i 2 NG ; t 2 T

ð33Þ

i 2 ND ; t 2 T

ð34Þ

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Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137 max Pmax L;i;j 6 pL;i;j;t 6 P L;i;j ;

; 0 6 wi;t 6 wmax i

ði; jÞ 2 E; t 2 T

ð35Þ

i 2 NW ; t 2 T

ð36Þ

0 6 r u;i;t 6 minfPmax  pi;t ; RU i g i

ð37Þ

0 6 r d;i;t 6 minfpi;t  Pmin ; RDi g i

ð38Þ

( Pr

X

r u;i;t P

i2NG

( Pr

X

i2NG

X

Cg ,i ,t ( pi ,t )

) ðwj;t  wa;j;t Þ

P cu

Cg ,i ,t ( pimin )

ð39Þ

r d;i;t P

X

0

) ðwa;j;t  wj;t Þ

P cd

ð40Þ

4.2.1. The fuel cost of thermal power unit The fuel cost is a quadratic function of the unit active power output. The paper utilizes the method in Ref. [34] to divide the quadratic function into a plurality of linear segments. In each linear segment, there is a linear relationship between the cost and the output power of the generator, according to Fig. 6. 4.2.2. Consumer gross surplus The consumer gross surplus function is the integral of the demand bidding curve, as seen in (26). Since the piecewise linear function is used to describe the demand bidding curve, the consumer gross surplus function is a piecewise quadratic function. The paper uses the same way as that for the quadratic function of the fuel cost, and introduce the successive linearization method to linearize each segment of the quadratic consumer gross surplus function. 4.2.3. The underestimation and overestimation cost of wind power G(wi,t) represents the total cost of wind power. That is,

Gðwi;t Þ ¼ C un;i;t ðwi;t Þ þ C ov ;i;t ðwi;t Þ

ð41Þ

Since G(wi,t) is a non-explicit integral function, this paper evenly scatters the independent variable wi,t of the function in its value range [0,wmax,i] as 1000 points, uses the numerical integration method to obtain corresponding G(wi,t) value of different wi,t. Then

pmax ,i

pi ,t

4.2.4. Reserve capacity chance-constraints The versatile distribution proposed in [35] is employed here to describe the stochasticity of wind power. Since the inverse function of the cumulative distribution function (CDF) of the versatile distribution has analytic expression, (39) and (40) in the model can be transferred into (42) and (43), respectively.

X

wj;t 

j2NW

j2NW

As (25)–(40), the proposed economic dispatch model is a nonlinear programming problem, where the nonlinear terms are composed of four parts: fuel cost of the thermal power unit in the objective function; consumer gross surplus; wind power underestimation and overestimation costs; and chance-constraints of reserve capacity. In order to reduce solving difficulty, it is necessary to linearize the nonlinear problems.

T2,i

the piecewise linear function is introduced to fit G(wi,t), and the non-linear G(wi,t) function is transformed into a piecewise linear function.

X

4.2. Transformation of model and solving method

T1,i

Fig. 6. Diagram of fuel cost.

j2NW

where (30) is the constraint of power balance based on the DC power flow model; (31) describes output power upper and lower limits of the thermal power unit; (32) and (33) are the ramping constraints of the thermal power unit; the upper and lower limits of load adjustment is expressed by (34); (35) is the power limitation of transmission line; (36) is the constraint of the wind turbine generator output power; (37)–(40) are the constraints of reserve capacity, in which ru,i,t and rd,i,t are the upward and downward reserve of the thermal power unit; cu and cd are the confidence intervals where the thermal power unit in the system can ensure sufficient capacity to adjust upwards and downwards. Overall, (25)–(40) constitute the day-ahead stochastic economic dispatch model considering demand response and wind power.

pimin

3, t , i

2, t , i

1, t , i

j2NW

X

r u;i;t 6 F 1 R ð1  c u Þ

ð42Þ

r d;i;t P F 1 R ðc d Þ

ð43Þ

i2NG

wj;t þ

X i2NG

Consequently, the model is converted into a mixed-integer linear programming problem, and the commercial software, such as IBM ILOG CPLEX, can solve the problem. 5. Numerical case studies The proposed model is tested on a modified 6-bus system and a modified IEEE 118-bus system respectively. The paper analyzes the impact of the demand response of the residential hybrid energy system on the wind power utilization on the 6-bus system. In addition, the further simulation is experimented on 118-bus system to analyze the operation cost of the power system and the residential consumers. Some assumptions are made in both two test-systems, which are listed as following: (1) In the electricity market, the customers’ electricity tariff is calculated by the real-time price. To simplify calculation, it is assumed that the electricity sale price is the same as the electricity purchase price, and the price of natural gas is constant. (2) Residential demand accounts for 40% of the total demand, and one third of the customers have hybrid energy system that response to the real-time price automatically by HEMS. (3) In addition to micro-CHP, other gas loads are not affected by the demand response. Moreover, the natural gas supply is stable. 5.1. 6-Bus system The modified 6-bus system is shown in Fig. 7. In this system, 3 thermal power units are connected to Bus 1, Bus 2 and Bus 6 respectively. The total installed capacity of these thermal power units is 420 MW, and the parameters of thermal power units are

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Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137

G1

G2

L1

2

1

4

3

5 L2

6 WG

L3

G3

Fig. 7. Diagram of 6-bus system.

Table 2 Generator’s data. Unit

Pmax

Pmin

Ramp

a

b

c

G1 G2 G3

220 100 100

100 10 10

55 45 45

0.05 0.01 0.01

10 22 22

100 162 162

Fig. 8. Demand bid curve.

High wind power output

listed in Table 2. A wind farm is connected to Bus 5 and the installed capacity is 200 MW. The wind power overestimation and underestimation cost coefficients take 120$/MWh and 60$/ MWh [36], and the confidence interval of the chance-constraint, i.e., cu and cd, are set as 0.95. Loads are connected in Bus 3, Bus 4 and Bus 5, respectively. The configuration of micro-CHP in the simulation is introduced in Section 3.2, and the maximum electric power of micro-CHP is 3 kW. The prime mover of micro-CHP is a proton exchange membrane fuel cell (PEMFC). 3 kW micro-CHP device is selected by considering the electricity and heat demands of local residential consumers, and the other types of residential hybrid energy systems can also be analyzed by the method proposed in this paper. The electricity and heat energy conversion efficiency of the prime mover are 30% and 70%, respectively. The heat energy conversion efficiency of the auxiliary burner is assumed to be 100%, ignoring the heat energy loss in combustion [20]. The volume of the heat storage tank is 150 L, and the water temperature in the tank is maintained between 68 °C and 72 °C. Based on the method proposed in Section 3.3, the various electricity prices are used as the input of the residential hybrid energy system model to gain the demand bidding curve of the single consumer. Then all the consumers on the same node are aggregated to obtain the demand bidding curve of the consumers group. Demand bidding curve reflects the demand response capacity of the residential consumers. Due to the temporal correlation of the residential demand, the demand bidding curves of each time are diverse. Fig. 8 shows an aggregated demand bidding curve at 9:00 and 23 demand bidding curves of other times are generated. With the electricity price rising, the electricity that consumers purchase from the utility company gradually reduced, the curve is monotonically decreasing. The stochastic economic dispatch model proposed in Section 4.1 is employed to do market clearing and calculate the electricity price at all time. Fig. 9 describes the impact of the variable wind power output on the electricity price of the system. The black line in the figure represents the forecast wind power curve and the blue1 one represents the electricity price. Because of the low power generation cost of wind power, the power system integrates as much 1 For interpretation of color in Fig. 9, the reader is referred to the web version of this article.

Low wind power output

Fig. 9. Electricity price and wind power output.

wind power as possible that affects the total power generation cost of the system. The fluctuation of day-ahead planned electricity price is closely related to the forecast value of wind power output. When the output power of the wind farm is high, such as 9:00 and 16:00, the planned electricity price decreases compared to that of the adjacent points. While when the output power of the wind farm is low, such as 5:00 and 19:00, the price grows. The electricity purchased from the utility company and the gas consumption are calculated by the proposed residential hybrid energy system model, when consumers respond to the real-time price. For the consumers who do not respond to the price, the electric power consumption of all home appliances are non-interruptible and non-transferable. The micro-CHP adopts the traditional ‘‘heat-lead” operation strategy that the micro-CHP operates according to the heat demand. Figs. 10 and 11 show the comparison of exchange power of residential consumers and the gas consumption respectively, where the electricity consumption represents the quantity of electricity purchased from the utility company. It should be noted that the residential gas consumption in the figure only includes the gas consumed for heating, because other gas-consuming devices are assumed unchangeable gas loads in this paper. The unit of natural gas in Fig. 11 is converted into MWh based on its heat value. Since the variability of wind power output leads to the fluctuation of the electric price, which is the input of HEMS, the residential hybrid energy system can perceive the variation of wind power and adjust the operation of

Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137

Fig. 10. Residential electricity consumption in Day 1.

Fig. 11. Residential gas consumption in Day 1.

micro-CHP and smart home appliances. When the wind power output is high, residential hybrid energy system automatically increases the quantity of electricity purchased from the utility company and reduces the output of the micro-CHP. Accordingly, the electricity consumption raises and the gas consumption decreases, as seen at t = 9 and 16 in Figs. 10 and 11. Moreover when the wind power output is low, the electricity and gas consumption show an opposite trend, as seen at t = 5, 11 and 19. In order to show the residential demand response more intuitively, the variations of the electricity and gas consumption before and after demand response are illustrated in Fig. 12. Consumers respond to the energy price by micro-CHPs, which use natural gas as energy source. Hence, the change of electricity consumption leads to the variation of gas consumption that shows a complementary trend. In order to analyze the impact of the residential demand response on the wind power utilization under different wind power variability, the paper calculates the wind power curtailment for 8 different days. The peak/valley difference of wind power and the number of hours with a wind energy fluctuation larger than 10 MW/20 MW are used to describe the wind power variability. The wind power curve in Fig. 10 corresponds to the wind power output for Day 1 in Table 3. The calculation results of wind power utilization are listed in Table 3. When the wind power fluctuates greatly, as Day 2, the wind power curtailment in one day is at 330 MWh if the residential consumers do not respond to the energy price. However, with the demand response of residential

1135

Fig. 12. Variations of electricity and gas consumption in Day 1.

hybrid energy system, the wind power curtailment decreases 85%. In the case that the wind power fluctuates narrowly, as Day 5, the wind power curtailment is also reduced by 67% with demand response. In general, the method described in this paper can keep down the wind power curtailment of the system to about 60 MW, down 78% on average in one day. Moreover, the reduction of wind power curtailment is highest with the most strongly fluctuating wind power output. Since the ratio of demand response obviously influences the effect of the presented method, the paper calculates the wind power curtailment under different ratios of demand response at the same day, as shown in Fig. 13. 100% in the abscissa indicates that all the residential consumers who have the smart home appliances and micro-CHPs respond to the energy price, and 0 means no residential consumers respond. The curve in Fig. 13 looks like an exponential form in shape. With the ratio of demand response increasing, the wind power curtailment of the system gradually decreases. When the ratio of demand response is around 60%, the wind power curtailment caused by the mismatch of demand and generated power is almost eliminated, thus the effect of demand response begins to saturate. 5.2. 118-Bus system The original system data source of the IEEE 118-bus system is http://motor.ece.iit.edu/data/SCUC_118test.xls. This test system consists of 54 conventional thermal power units and 186 transmission lines. The total thermal power installed capacity of this system is 7200 MW, and the maximum load is 6800 MW. The changes of basic load in one day for each load points are assumed the same. A large-scale wind farm is connected to Bus 65 and the wind power installed capacity is 3000 MW. Moreover, the wind power forecast curves using in this case is the amplification of that in the 6-bus system according to the installed capacity of wind farms. The proposed day-ahead stochastic economic dispatch model calculates the system operation cost, and the wind power forecast curve is the expansion of that showed in Fig. 8 according to the wind farm size. The simulation results are listed in Table 4, in which the thermal power cost is the fuel cost of thermal unit, and the wind power cost is the sum of wind power overestimation and underestimation cost. As seen from the table, since the mismatch of load and generated power reduces due to the regulation of demand, the wind power cost with demand response decrease 60.24%, and the energy supply by wind power increases 5.54%. Meanwhile the power generated by thermal unit decrease, and

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Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137

Table 3 Comparison of wind power curtailment under different wind power fluctuation. Number of Day

Peak/valley difference in wind Power (MW)

Number of hours with a wind power variability larger than 10 MW

Number of hours with a wind power variability larger than 20 MW

Wind power curtailment with demand response (MWh)

Wind power curtailment without demand response (MWh)

Decrement of wind power curtailment (%)

Day Day Day Day Day Day Day Day

87.59 88.97 86.63 85.09 73.23 89.71 91.00 82.22

8 10 12 10 8 12 12 11

2 7 6 3 2 4 4 5

52.12 49.46 51.26 70.77 76.31 63.34 54.09 64.83

203.96 330.01 214.75 276.08 229.50 328.77 255.39 322.75

74.45 85.01 76.13 74.37 66.75 80.73 78.82 79.91

1 2 3 4 5 6 7 8

tion of micro-CHP and HEMS automatically manages smart home appliances according to the energy price, the electricity cost decreases 27.71%. Consequently, the total energy cost is 11.7% lower than that of traditional consumer.

The wind power curtailment decreases with the increase of the demand response ratio

6. Conclusions

Fig. 13. Wind power curtailment under different demand response ratio.

the thermal power cost reduces 3.91%. Overall, the total operation cost of the system per day with demand response decreases 10.7%. For residential consumers, the one-month operation cost of the traditional operation strategy and the strategy proposed in this paper is compared. In the traditional operation strategy, microCHP and smart home appliances are independent, and do not respond to the change in energy price. The simulation results are listed in Table 5, the gas consumption of the residential hybrid energy system is higher than the traditional consumer, which means more energy are supplied by micro-CHP. As a result of that, the gas cost of hybrid energy system increases 11.04%. In the contrast, because the electricity consumption is lower and the opera-

This paper employs the demand response capability of residential hybrid energy system to improve the wind power utilization of the system. At the residential level, a centralized optimal operation of the residential hybrid energy system is proposed, which integrates micro-CHP and smart appliances. The demand response capability of scattered residential load is centralized by a novel load aggregation method. At the power grid level, a day-ahead stochastic economic dispatch model considering demand response and wind power is proposed, and the successive linearization method and the versatile distribution are used to simplify the optimization problem. Simulation results show that the method proposed can enhance the utilization of wind power and reduce the energy costs of residential consumers and the operating costs of the power system. In the 6-bus system, the total wind power curtailment decreases by an average of 78%. In the 118-bus system, the operating costs of the system drops by 10.7%. Meanwhile, the energy cost of the residential consumer decrease by 11.7%, thus achieving a win-win situation between the power grid and users. It should be noted that, to facilitate calculation and analysis, the paper assumes that LSEs are pure load aggregators. However, in the actual electricity market, LSEs develop different marketing programs for their own interests, and those programs affect the ratio of demand response. In addition, the paper does not consider the constraint of the natural gas pipeline network on natural gas supply, which need to be further studied in the future.

Table 4 Comparison of system operation cost. Item

Thermal power cost ($)

Wind power cost ($)

Energy supply by thermal power (MWh)

Energy supply by wind power (MWh)

Total cost ($)

With demand response Without demand response

1,355,250 1,410,391

77,019 193,729

99,864 100,265

39,036 36,988

1,432,269 1,604,120

Table 5 Comparison of residential energy cost. Item

Gas consumption (kWh)

Electricity consumption (kWh)

Gas cost ($)

Electricity cost ($)

Total energy cost ($)

Traditional residential consumer Hybrid energy residential consumer

74.1 82.3

316.77 282.78

32.6 36.2

46.2 33.4

78.8 69.6

Y. Jiang et al. / Applied Energy 190 (2017) 1126–1137

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