Stochastic profit-based scheduling of industrial virtual power plant using the best demand response strategy

Applied Energy 164 (2016) 590–606

Contents lists available at ScienceDirect

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

Stochastic profit-based scheduling of industrial virtual power plant using the best demand response strategy Seyyed Mostafa Nosratabadi, Rahmat-Allah Hooshmand ⇑, Eskandar Gholipour Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran

h i g h l i g h t s
VPPs and IVPPs are defined for energy management of aggregated generations.
IVPP can manage industrial microgrid containing some relevant load and generation.
A stochastic modeling is proposed to schedule optimal generations in competition market.
Wind generation and day-ahead and spot market prices are considered to be stochastic.
A new DRL program selection scheme is presented in the scheduling procedure.

a r t i c l e

i n f o

Article history: Received 6 September 2015 Received in revised form 7 December 2015 Accepted 8 December 2015 Available online xxxx Keywords: Virtual power plant Stochastic scheduling Industrial microgrid Demand response load Mixed integer non-linear programming

a b s t r a c t One of the main classified microgrids in a power system is the industrial microgrid. Due to its behaviors and the heavy loads, its energy management is challengeable. Virtual Power Plant (VPP) can be an important concept in managing such problems in this kind of grids. Here, a transmission power system is considered as a Regional Electric Company (REC) and the VPPs comprising Distributed Generation (DG) units and Demand Response Loads (DRLs) are determined in this system. This paper focuses on Industrial VPP (IVPP) and its management. An IVPP can be determined as a management unit comprising generations and loads in an industrial microgrid. Since the scheduling procedure for these units is very important for their participation in a short-term electric market, a stochastic formulation is proposed for power scheduling in VPPs especially in IVPPs in this paper. By introducing the DRL programs and using the proposed modeling, the operator can select the best DRL program for each VPP in a scheduling procedure. In this regard, a suitable approach is presented to determine the proposed formulation and its solution in a Mixed Integer Non-Linear Programming (MINLP). To validate the performance of the proposed method, the IEEE Reliability Test System (IEEE-RTS) is considered to apply the method on it, while some challenging aspects are presented. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Clarification of the problem Since the penetration of Distributed Generation (DG) resources is rapidly increasing in power systems, taking into consideration of the control of the network, provision of ancillary services, and improvement of the network performance are greatly essential. Thus, providing new ways to control the generation and provision of appropriate infrastructure is required for participation in the electricity market. A possible solution to satisfy the aspects ⇑ Corresponding author. E-mail addresses: [email protected] (S.M. Nosratabadi), [email protected] (R.-A. Hooshmand), [email protected] (E. Gholipour). http://dx.doi.org/10.1016/j.apenergy.2015.12.024 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

mentioned above is to use the concept of Virtual Power Plant (VPP). The set of loads, DGs, and storage of electrical energy resources aggregated together are called VPP [1,2]. The use of new control methods with DG resources in power networks while considering security levels, quality, reliability, and power availability has converted these networks to dynamic ones to determine the microgrid concept [3]. Due to the nature of the loads of these networks, they are divided into the categories of residential, commercial, and industrial loads [4]. Because an industrial microgrid normally consists of industrial loads, industrial workshops, industrial factories, and industrial parks, it is therefore of utmost importance. An industrial smart microgrid can be considered attached to the main grid in the form of a VPP to pursue several important objectives.

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

591

Nomenclature C. Constants A. Indices number of time periods Nt number of spot market price scenarios Nsp Np number of market price scenarios Nw number of wind power scenarios k NVPP number of loads in kth VPP j total number of DG units Ng B. Variables ProfitVPPk obtained profit of kth VPP ($) IncomeVPPk obtained revenue of kth VPP ($) CostVPPk obtained cost of kth VPP ($) IncomeDRLs obtained revenue of DRLs ($) IncomeDGs obtained revenue of DG units ($) CostLoads obtained cost of loads ($) CostDGs obtained cost of DG units ($) CostLshed obtained cost of load shedding ($) DLjwp ðtÞ value of load change for load j in time period t (MW) Pi ðtÞ sold power of unit i in time period t (MW) Piwp ðtÞ sold power of unit i in each scenario and time period t (MW) PWT sold power of wind turbine WP in each scenario and wp ðtÞ time period t (MW) CostL ðtÞ cost of load L in time period t ($/MWh) S:P:Pwpsp ðtÞ purchased power from spot market in each scenario and time period t (MW) Psp value of purchased power from spot market in each scewp ðtÞ nario and time period t (MW) LShed load shedding value for consumer j in each scenario and jwp ðtÞ time period t (MW) WT uDG binary variables equal to 1 if the DG units and the wind i ;u powers are scheduled to be committed EL ðtÞ consumed energy in time period t for loads

v j ðtÞ

binary variable equal to 1 if load j is on in time period t

Ploss nr ðtÞ dn ðtÞ

power loss through line ðn; rÞ in period t (MW) voltage angle at node n in period t (rad)

Microgrids and VPPs share important features like the ability to integrate demand response; generation of distributed renewable energy; and storage at the distribution level. Some market participants share a lot with these two platforms; however, there are differences [5,6]:
Microgrids may be in the grid-tied or grid-connected form, but VPPs are always in the grid-tied form.
Microgrids can pose themselves as an island separated from the larger power grid, but VPPs do not recommend this type of contingency.
Microgrids normally require some levels of storage; however, the presence or absence of storage in VPPs is possible.
Microgrids depend on hardware innovations such as smart inverters and switches, whereas VPPs heavily depend on smart metering and information technology.
Microgrids include a fixed set of resources within a limited geographical area, whereas VPPs can combine a wide variety of resources in large geographic areas, and match them.
Microgrids are normally traded only in the form of retail distribution, while the VPPs can build a bridge to the wholesale market.

aw ; bp ; csp probability of wind, market price and spot market price scenarios demand ratio in time period t IVðtÞ incentive value in time period t for each kWh load reduction L0j ðtÞ initial value of demand in time period t (MW) psp ðtÞ spot market price in time period t ($/MWh) pp ðtÞ market price in time period t ($/MWh) eLT self-elasticity of demand considering load type LT in p ðtÞ time period t LT aLT ; b constant factors of load type LT Penaltywp ðDLj ðtÞÞ penalty value of load change for load j in time period t PVðtÞ penalty value in time period t for each kWh load change CDRðtÞ contract level of DRLs in time period t (MW) SUC iwp ; SDC iwp cost due to the startup and shutdown of unit iin each scenario ($) ki cost of produced power by DG unit i ($/MWh) kw cost of produced wind power by unit w ($/MWh)

CðtÞ

fLT j

load shedding factor for different load types

VOLLj ðtÞ value of loss load for consumer j in period t ($/MWh) Pmin ; Pmax minimum and maximum power of each DG unit I i i (MW) PWT;min ; P WT;max minimum and maximum power of each wind turbine (MW) LIVPP loads in each IVPP (MW) j down Lramp ramp down rate of load j (MW/s) j Lramp j

up

ramp up rate of load j (MW/s)

EAFðonÞ j EAFðoff Þ j LSj ðtÞ

minimum on time for EAF (s)

Bnr

absolute value of the imaginary part of the admittance of line ðn; rÞ (per unit) maximum power flow through line ðn; rÞ in period t (MW)

s s

max

f nr

minimum off time for EAF (s) maximum value of load shedding in time period t (MW)


Microgrids face legal and political hurdles, while VPPs can now be performed on the current structure and legal tariffs. Because of these advantages, VPP management is taken into account here since its importance can be more manifest for industrial environments. Here, it is supposed that the main grid is a transmission network acting under a Regional Electric Company (REC). Usually a REC has several generation units that can operate as a GENCO or as a VPP. One of the VPPs that this paper focuses on is the Industrial VPP (IVPP). Because the IVPP comprises industrial loads, then one of the main goals is to minimize the load shedding in the existing industrial network at the microgrid. This is also very important, because the industrial loads are looking for different ways to obtain the required electricity to avoid the stoppage of production cycles. This energy can be supplied by participation in the spot and balancing markets. Also, by cooperation in a suitable DRL program, IVPP can manage the interruptible loads which require an appropriate modeling in transmission systems. By solving the problem, an optimal solution will be extracted via an optimization problem satisfying different generation, load, market, and system constraints.

592

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

The method proposed here is the formulation of the scheduling problem with the aims of the maximization of the profit and minimization of load shedding cost as an optimization problem. With regard to the real world actions, this formulation is stochastic and the three main parameters of wind power, day-ahead market price, and spot market price are uncertain. With this clarification, from the VPP point of view, the best introduced DRL program can be selected to have the maximum profit and from the IVPP point of view, minimization of load shedding is also more important. 1.2. Literature review Nowadays, some papers [7–31] have focused on VPP and different aspects related to this concept and also on the interactions between them and the power system. With regard to issues such as energy costs, renewable generations, and also distributed generation at the distribution level, VPP assesses the uncertainty of renewable generations; considers congestion and loss constraints; investigates the issues related to demand response and interruptible loads, and dimensions associated with the reliability of the system. In [7], a robust optimization tool is presented for selfscheduling of VPPs in the uncertain environment of power markets. The VPP is generally composed of renewable sources, storage systems, interruptible loads, and small conventional power plants. Thus, to ensure the commercial profit, it needs to negotiate some bilateral contracts in advance prior to participating in the dayahead market. For this, a mixed integer linear programming model based on robust optimization approach is proposed to enable informed decision making under different levels of uncertainty. A method for utilization of interruptible load in the distribution system using the thermal mass of a building to defer power consumption from electric space heating is presented in [8]. The power consumption for heating is controlled by an operational VPP. In [9], a coordinated control method of VPP, which includes photovoltaic (PV) systems and controllable loads, is proposed so that the power output of the VPP can be flexibly set in a wide range. To achieve this, power output of the PV systems and operating modes of controllable loads are coordinated by solving a mixed integer programming problem. In [10], a novel demand response scheme is presented that avoids the need to predict the price elasticity of demand or demand forecast. This is done based on the consumers’ submissions of candidate load profiles ranked in the preference order. The load aggregator then performs the final selection of individual load profiles subject to the total system cost minimization. The proposed model incorporates a billing mechanism with a scheme implemented in a context of a VPP aggregating load and generation units. The evaluation of a hybrid system consisting of wind, solar, hydrogen and thermal power systems in the concept of VPP strategy is realized in [11]. An economic load dispatching strategy that can interactively adapt to the real measured wind and solar power production values is proposed. The effects of the stochastic nature of solar and wind energy systems are considered in order to participate in the electricity market with higher benefits. The wind power is inherently intermittent and cannot be accurately predicted even in short time; thus increasing the imbalance costs paid by wind farm owners. To cope with these problems, constructing a VPP is proposed in [12] that presents a stochastic profit-based model for day-ahead operational planning of a combined system. The VPP owner considers a portion of its hydro plant’s capacity to compensate the wind power forecast errors. The proposed optimization problem is a mixed integer linear programming, formulated as a two-stage stochastic programming model. Ref. [13] assesses the ability of a VPP to decrease the imbalance error of renewable generators. The VPP operator bids electricity

into the day-ahead market using the forecast for solar irradiation and for the thermal demand. During the actual day, the imbalance due to deviations between the forecasted electricity delivered, and the real output has to be settled in the balancing market. Thus, in order to compensate these errors and possible economic drawbacks, the operation of the combined heat and power system is adjusted periodically by rescheduling. To implement the optimal dispatch of DGs in the VPP, a distributed optimal dispatch method is proposed in [14]. The joint distribution of maximum available outputs of multiple wind turbines in the VPP is modeled. Furthermore, a VPP optimal dispatch model is formulated to achieve maximum utilization of renewable energy generation, which takes into account the constraints of power network and DGs. A modeling approach for power-to-heat systems as a component of VPPs with a high share of renewable energies is presented in [15]. The operation strategies are evaluated with respect to economic and technical aspects and uncertainties in generation and load. The operation strategies are shown considering to market integration of renewable energies within the VPP and the provision of ancillary services. Ref. [16] treats the techno-economic impact of the integration of small generators and demands into VPPs both on the system functioning and on the outcome of demands and generators within these VPPs. In [17], a distributed optimization algorithm is projected to solve VPP bi-level optimal dispatch considering the uncertain agents number. In [18], a decision tree based method is presented that prepares to dispatch the power equivalent to the possible loss of the highest injection of one of the sources of the VPP to the rest of its sources, on an hour-ahead horizon. This allows VPP operators to provide capacity and participate effectively in the energy market. A methodology is developed in [19] to control the emissions from a group of generators aggregated in a VPP. A multi-agent system is designed, and simulations are performed. The operation of the system is demonstrated experimentally using generation sources installed in laboratories. In [20], a combined wind and pumped-storage VPP is presented that constitutes a realistic option to reach high penetrations, provided that their components are properly sized. In this reference, the optimum sizing is performed for operating in an island system. The VPPs studied in [21,22] includes distributed generation, energy storage and interruptible loads. In [21] the weekly planning of a VPP consisting of intermittent renewable sources, storage system, and a traditional power plant is considered. On the one hand, the VPPs need to complete their long-term bilateral contracts; while, on the other hand, they try to maximize their total profit. The optimal distribution problem is formulated as a stochastic mixed integer linear programming model that the weekly profit of VPP is maximized with regard to contracts and technical constraints. The uncertainty of wind power and solar power generation is resolved by employing hydroelectric pumped storage in order to provide flexible operation with a traditional power plant as a backup. Ref. [22] introduces a VPP that purchases and sells the power in both of day-ahead and balancing markets, and looks to maximize the expected profits. In the model presented, unknown parameters, including output power of intermittent resource and market prices are modeled via scenarios based on historical data. Refs. [23–25] have proposed a probabilistic price based on unit commitment method for a VPP to model the uncertainty of the market price and generation resources as well as to optimize offer in the electricity market. In [23], this has been made by employing the point estimation method. Moreover, the uncertainty of DG generations is solved by increasing the requirement reserve. In [24,25], a VPP bidding strategy is provided to participate in energy and spinning reserve markets. The proposed strategy is an unbalanced model based on the definite price-based unit commitment that

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

supply and demand balance constraints as well as VPP security restrictions have been considered. In [26], a method is presented to solve the large-scale integration of distributed resources using standard-based power system connections; a modeling application based on event-driven data services, and VPP optimized control algorithms are also proposed. Ref. [27] has developed a virtual model of the electricity market in order to investigate the strategic behavior and market player’s collusion. In this paper, a virtual electricity market model is proposed to consider the behavior of the electricity market from the regulation point of view. Refs. [28– 30] have proposed a modeling for interactions between market provisions and aggregators behavior of the electric vehicles in the virtual electricity market. In [28], the effect of changes in market conditions on the behavior of electric vehicle owners and their aggregators is studied. Also, a hybrid approach is presented to simulate the behavior of market players from both the viewpoints of regulator and aggregator. In [29], VPP is introduced as a coalition of wind generators and electric vehicles in which the wind generators use the electric vehicles as a mechanism to overcome their uncertainty. In [30], the cost and emission effects of VPP are investigated with the penetration of electric vehicles in the network. In this paper, an energy management model is presented for VPPs and the cost and emission effects of VPPs formation and electric vehicle penetration is analyzed. In [31], a method is proposed for reliability assessment of active distribution systems with several microgrid based on Monte Carlo simulation. All the above models focus on the VPP scheduling problem, while none of them has considered generation scheduling to supply industrial loads at the transmission level. In addition, none of the reviewed literatures have considered the behavior of industrial load type and interactions of DRL programs in a scheduling problem. 1.3. Contributions and paper layout The absence of VPP performance evaluation, especially a VPP containing industrial loads in a stochastic environment is observable in the papers reviewed. Therefore, this paper focuses on the definition of a VPP in a transmission power system that can manage aggregated generations spread in a distribution system. One of these VPPs is IVPP, which can manage an industrial microgrid containing some relevant loads and generations. Our main focus is on industrial environments such as steel companies and iron melting factories. To schedule enough generation in this microgrid for important industrial loads under a marketing competition, a suitable formulation is proposed here. In the system, there are wind generations; therefore, this power has uncertain behavior that is considered. Also, the day-ahead market and spot market prices have been considered to be stochastic. In the proposed formulation, a new DRL program selection scheme is presented in a stochastic environment. In addition, a test network is examined and the results are presented. To evaluate the performance of the proposed modeling, an evaluation index is also used, and the results are provided to select the suitable DRL program. The rest of this paper is organized as follows: In Section 2, the VPP concept in a transmission power system and the definition of IVPP are presented. In Sections 3 and 4, the proposed formulation for the generation of the scheduling problem and the solving method are stated, respectively. Case study and its evaluation are presented in Section 5. Finally, conclusions and contributions are mentioned in Section 6. 2. Virtual power plant definition Distributed Generations (DGs) are classified according to the two features of size and technology. The first classification is based

593

on the capacity of the unit which can be categorized into four classes of very small (1 W to 5 kW), small (5 kW to 5 MW), medium (5 MW to 50 MW), and large (50 MW to 300 MW). The second classification is based on technologies to generate electrical energy. Different technologies such as gas- and micro-turbines, wind turbines, solar cells, fuel cells, etc. can be used as DG [32]. As mentioned, the VPP concept can be used for the aggregated participation of DGs and DRLs in a power market. Here, the class of large DGs is considered for the proposed strategy. This paper focuses on the problem of scheduling in an industrial environment. Therefore, given that these loads are usually heavy, then the way of using the VPP in a transmission network seems a significant and relevant concept. This is managed by a specific REC to attract maximum aggregated power from other organized VPPs in the network or different generation companies (GENCOs). 2.1. Aggregated generation as VPP The VPPs taken into account here have been formed from DGs and DRLs in distribution and sub-transmission subnets of a specific REC. In this paper, the formation of the VPP is identified so that the industrial loads and their special generations in an industrial microgrid are organized as an IVPP. Then, according to different levels of generation and consumption, other VPPs can also be established that can work in both centralized and decentralized management as well as in control and operation states. In our network, GENCOs are traditionally managed as a specialized operation company where there are not any aggregated interruptible loads with them. 2.2. Industrial VPP As mentioned in the previous subsection, IVPP comprises industrial loads. Some of the loads, including factories and industrial parks with a variety of heavy loads specifically have electric generation units. It is noteworthy to mention that the details related to the scheduling of participation in the electricity market for this type of VPP are important. Scheduling of the IVPP is included in both normal operation mode and crisis condition of the system where the load shedding is applied. In this paper, the normal operating mode of the system is performed by the short-term dayahead scheduling. However, in emergency situations when the Independent System Operator (ISO) tries to keep the security aspects and takes into account the load shedding action, the application of an optimal scheduling is considered to cooperate with the IVPP in the balancing market. Naturally, the IVPP purchases the power at a price higher than that of the day-ahead energy market in this situation. This can be done by concluding a contract between the IVPP and other agents (other VPPs, GENCOs or other RECs). This requires a suitable formulation to have access to an optimal solution with a minimal cost and load shedding in the system. 2.3. DRL programs The analysis and implementation of DRL have been dedicated to the United States of America based on the strategic plan of International Energy Agency [33]. Federal Energy Regulatory Commission reported the results of DRL investigations to US utilities and power markets [34]. In this report, DRL programs are divided into two basic categories, namely time-based programs, and incentivebased programs. Each of them included some programs as illustrated in Fig. 1. In time-based programs such as Time of Use (TOU), Real-Time Pricing (RTP), and Critical Peak Pricing (CPP), the price of electricity varies according to the supply cost of electricity for different time

594

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

DRL Programs

Incentive Based Programs

Classic Programs

Time Based Programs

Market Based Programs Critical Peak Pricing (CPP) Program

Real Time Pricing (RTP) Program Interruptible/ Curtailable (I/C) Service

Time-of-Use (TOU) Programs

Direct Load Control (DLC)

Ancillary Service (A/S) Market

Capacity Market Program (CAP)

Emergency Demand Response Program (EDRP)

Demand Bidding/ Buy Back (DB)

Fig. 1. Classified DRL programs.

periods; for example, a high price in a peak-load period; a medium price in an off-peak-load period; and a low-price in a low-load period. In this kind of DRL program, there isn’t any incentive or penalty. TOU rates establish two or more daily periods; i.e. those reflecting hours when the system load is higher (peak) or lower (off peak), and charging a higher rate during peak hours. RTP rates vary continuously during the day reflecting the wholesale price of electricity. CPP is an overlay on either TOU or flat pricing. CPP uses real-time prices at times of extreme system peak. Incentive-based programs are included in Direct Load Control (DLC), Interruptible/Curtailable (I/C), Emergency Demand Response Program (EDRP), Capacity Market Program (CAP), Demand Bidding (DB), and Ancillary Service (A/S) programs. In DLC and EDRP programs, there are voluntary options and if customers do not interrupt their consumption, they are not penalized. I/C and CAP are mandatory programs, and the participating customers have to pay penalties if they do not curtail when directed. DB program persuades customers to provide load reductions at a price at which they are willing to be curtailed or to identify how much load they would be willing to curtail at posted prices. A/S programs allow customers to bid load interruptions in electricity markets as operational reserves. DLC refers to a program in which a utility or system operator remotely shuts down or cycles a customer’s electrical equipment on short notice to address system or local reliability contingencies in exchange for an incentive payment or bill credit. Customers on I/ C service rates receive a rate discount or bill credit in exchange for agreeing to reduce the load during system contingencies. If customers do not curtail, they can be penalized. DB program encourages a great number of customers to offer load reductions at a price at which they are willing to be curtailed, or to identify how much load they would be willing to curtail at posted prices. EDRP provides incentive payments to customers for reducing their loads during reliability triggered events, but curtailment is voluntary. In CAP, customers commit to provide pre-specified load reductions during system contingencies and are subject to penalties if they do not curtail consumption when directed. A/S program allows customers to bid load curtailments in ISO markets as operating

reserves. If their bids are accepted, they are paid the market price for committing to be on standby. If their load curtailments are needed, they are called by ISO and may be paid the spot market electricity price. More details on DRL programs can be found in [35]. In this paper, the programs of TOU, RTP, CPP, DLC, I/C, EDRP, CAP, and their compositions such as TOU+CPP, CPP+EDRP, and RTP +CAP are used. This utilization is based on the above-mentioned explanations. 3. VPP scheduling formulation 3.1. The proposed modeling A generation scheduling problem in a VPP can be performed by the proposed modeling. In the presented formula, the aim is to maximize the profit for VPPs. This is shown in (1) defined by the total income minus total cost for kth VPP. The total income includes the incomes from DRLs and DGs in a VPP and the total cost includes the costs of the participant loads, DGs, and load shedding in a VPP.

fMax:

X ProfitVPPk k

!

¼ Max:

" X

IncomeVPPk  CostVPPk



#

ð1Þ

k

where

IncomeVPP  CostVPP ¼ IncomeDRLs þ IncomeDGs  Cost Loads  Cost DGs  Cost Lshed The proposed scheduling modeling is a stochastic one. The behavior of wind turbine output power, day-ahead market price, and spot market price are considered to be uncertain. The introduced incomes and costs are defined in (2), (6)–(8) and (10).
Income of DRLs: In (2), the income of DRLs in a VPP is introduced. This includes the revenue of the customer during tth hour for using LðtÞ kWh of electricity and the revenue of customer when an incentive value is considered to contribute to a DRL program.

595

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

IncomeDRLs ¼

Nsp Nt X X

 Np j Nw X X X RevðLjwpsp ðtÞÞ csp bp aw N

t¼1 sp¼1

p¼1

w¼1

 þRevðDLjwp ðtÞÞ ¼

Nsp Nt X X

VPP k

N

program.
Income of DGs: The income of DGs included the conventional generators and the wind power is considered as follows:

p¼1

w¼1



VPP k

j¼1

þCn ðtÞ  IVðtÞ  Ljwp ðtÞ  L0j ðtÞ ¼

and L0jðBaseÞ ðtÞ is the base load before implementing the DRL

j¼1

 Np j Nw X X X csp bp aw RevðLjwpsp ðtÞÞ

t¼1 sp¼1

Nsp Nt X X

resents the maximum deferrable loads during the peak hours

VPPk

IncomeDGs



t¼1 p¼1

t¼1 sp¼1

p¼1

h

w¼1

VPPk

t¼1 p¼1

VPP k

i

ð2Þ

shows the number of jth load in kth VPP.

L0j ðtÞ (initial value) to Lj ðtÞ. This can be done on the basis of the value considered for the incentive and the penalty stated in the contract. In this paper, the linear function of the demand curve (i.e. LðtÞ ¼ apðtÞ þ b) is considered. Hence, the self-elasticity of demand can be represented as:

pp ðtÞ Lj ðtÞ



@Lj ðtÞ aLT  pp ðtÞ ¼ @ pp ðtÞ aLT  pp ðtÞ þ bLT

ð3Þ

where the self-elasticity is stochastic and depends on price LT

uncertainty. Factors aLT and b depend on the load type (residential, commercial, and industrial) and can be varied. Considering the revenue in the fifth line, if IV(t) $ is paid as an incentive to the customer in tth hour for each kWh load reduction, the total incentive for participating in incentive-based   programs will be IVðtÞ  Lj ðtÞ  L0j ðtÞ . Also CðtÞ is the demand ratio introduced to determine the value of the incentive and the penalty at each hour of the scheduling period as follows:

L0j ðtÞ n o; CðtÞ ¼ Max L0j ðsÞ

s 2 f1; 2; . . . ; t; . . . ; Nt g

ð4Þ

In (2), n is performed to show the effect of incentives in DRL programs. L0j ðtÞ can be defined as follows:

L0j ðtÞ ¼ uT gL L0jðBaseÞ ðtÞ

ð6Þ

i¼1

k tively. Also, N VPP shows the number of the gth generation in g

As it is shown in the fourth and the fifth lines of (2), the revenue obtained from the customer during tth hour for using LðtÞ kWh of electricity and the revenue of customer when an incentive value is considered to contribute to a DRL program are extended. The first part of extended revenue in the fourth line is the revenue obtained from costumer participation in spot market that psp ðtÞ is the stochastic price of the spot market. The second part of the revenue function in the fourth line, most often used, is the quadratic one and can be extended and extracted by the function introduced in [36]. Here, the customer changes the demand from

eLT p ðtÞ ¼

w¼1

where aw and bp are the factors used for the scenarios considered for the wind power and day-ahead market price, respec-

j¼1

L0j ðtÞ

where aw ; bp , and csp are factors used to consider scenarios of wind power, day-ahead market price, and spot market price, respectively. Also, N j

i¼1

Np Nt X Nw  i X X Xh ¼ bp aw pp ðtÞ  Piw p ðtÞ þ PWT wp ðtÞ

VPP k

þpp ðtÞ  Ljwp ðtÞ  ( ) Ljwp ðtÞ  L0j ðtÞ  1þ þ Cn ðtÞ  IVðtÞ 0 ðtÞ  L ðtÞ 2eLT p j   0  Ljwp ðtÞ  Lj ðtÞ

w¼1

Ng

 Np j Nw X X X csp bp aw psp ðtÞ  L0j ðtÞ N

Ng Np Nt X Nw X X X ¼ bp aw Revwp ðPi ðtÞÞ

ð5Þ

where uT is a number within the range of [0, 1]; the larger uT means that customers have more tendency to choose the shifting consumption from the peak hours to off-peak hours. gL rep-

the kth VPP. Here, the extended revenue obtained from the conventional and wind generators are shown in the second line of (6). As it is shown, the uncertain day-ahead market price is multiplied by the powers generated from mentioned generators.
Cost of loads: In (7), the cost of interruptible loads and penalty cost for customers who decide to contribute to a DRL program and do not feel obligated to the commitments according to the contract is presented. N

CostLoads

VPPk

Np j Nt X Nw X X X  ¼ bp aw Cost L ðtÞ  Ljwp ðtÞ t¼1 p¼1

w¼1

j¼1

þPenaltywp ðDLj ðtÞÞ N

VPPk

Np Nt X j Nw X X X  bp aw Cost L ðtÞ  Ljwp ðtÞ ¼ t¼1 p¼1

w¼1

j¼1

n h ioi þC ðtÞ  PVðtÞ  CDRðtÞ  L0j ðtÞ  Ljwp ðtÞ m

ð7Þ

where aw and bp are factors used for the scenarios considered for the wind power and day-ahead market price, respectively. As it can be seen, the first part of this cost function is the cost of interruptible loads. As a result, the cost of interruption ðCost L ðtÞÞ is multiplied by the load value. The second part of this function is the penalty cost for DRLs. Therefore, if the contract level for the tth hour and the penalty for that period are denoted by CDR(t) and PV(t), respectively, then the total penalty will be as the defined term in the third line of (7). Here m is performed to show the effect of penalties in DRL programs.
Cost of DGs: The costs of the purchased power from the spot market, startup, and the shutdown of conventional generators as well as the power generated from conventional generators and wind turbines are considered in (8).

CostDGs ¼

N sp Nt X X

csp

t¼1 sp¼1 VPPk

Xh

Ng

þ

Np Nw X X bp aw S:P:Pwpsp ðtÞ p¼1

w¼1

1 i C SUC iwp þ SDC iwp þ ki Piwp ðtÞ þ kw PWT wp ðtÞ A

ð8Þ

i¼1

where the purchased power from the spot market is as (9). In this function, P sp wp is the amount of power purchased from the spot market in each scenario.

S:P:Pwpsp ðtÞ ¼ psp ðtÞ  Psp wp ðtÞ

ð9Þ

Also, in the second line of (8), the terms are the startup cost, shutdown cost, the generation cost of conventional units and the generation cost of wind power units, respectively.

596

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606


Cost of load shedding: The cost of load shedding has been considered in (10). In this segment of the costs, the value of the lost load varies for different load types (residential, commercial, and industrial), which means a f factor can be considered to have different values for different load types. N

CostLshed:

VPPk

Np j Nt X Nw X X X Shed ¼ bp aw fLT j  VOLL  Ljwp ðtÞ t¼1 p¼1

w¼1

ð10Þ

j¼1

where fLT j is a factor defined to consider the different priorities of load shedding for different load types. VOLL is the value of the lost load that is constant. LShed jwp ðtÞ is the amount of the required load shedding for different scenarios in the scheduling problem. 3.2. Industrial load consideration One of the main contributions of this paper is to consider industrial loads in the form of IVPP. As it was described in the previous subsection, Eqs. (3) and (10) have been used to take these loads into account. With regard to the load type in (3) (residential, commercial, and industrial), different values can be set for the factor of the demand curve. Here, it is supposed that the industrial loads have less interaction versus the market price, i.e. the values of factors ‘‘a” and ‘‘b” are less and more than those of other factors, respectively (residential and commercial loads). Also, it is supposed in (10) that the industrial loads become the first choice for load shedding from the ISO side. Here, f factor is introduced, that its value for industrial loads is less than other loads (residential and commercial loads).

P WT;min ðtÞuWT ðtÞ 6 PWT ðtÞ 6 PWT;max ðtÞuWT ðtÞ 8WT; 8t

where uDG and uWT are the binary variables equal to 1 if the DG i units and the wind power are scheduled to be committed to time t, respectively.
Startup and shutdown constraints: the constraint of the unit startup and shutdown costs recalculated on the basis of the following relationships while considering kSU i , the startup cost and lSD , the shutdown cost for each unit. Hence: i DG DG SUC i ðtÞ P kSU 8i; 8t i ðui ðtÞ  ui ðt  1ÞÞ

ð15Þ

SUC i ðtÞ P 0 8i; 8t

ð16Þ

DG DG SDC i ðtÞ P lSD 8i; 8t i ðui ðt  1Þ  ui ðtÞÞ

ð17Þ

3.3.3. Load constraints
IVPP load detailed constraints: Each IVPP constraint including equilibrium of the generated, purchased, and consumed power is considered to have an independent performance in each IVPP consisting of industrial loads. Here, the industrial loads are the steel and iron melting companies. These factories consist of different main loads such as Electric Arc Furnace (EAF), induction motors, ventilation devices, and rolling mills. Accordingly, with this explanation, constraint (18) can show IVPP load in detail. NL X EAF X Inductionj X LIVPP ðtÞ ¼ PL i ðtÞ þ PL ðtÞ j j¼1

3.3. Constraints for the problem

3.3.1. Market constraints
Market equilibrium: the total power generated by different sources must be equal to the power consumed by the system loads. Therefore: Ng NWT X X Piwpsp ðtÞ þ PWT wpsp ðtÞ  f nr ðtÞ þ S:P:P wpsp ðtÞ WT¼1

i¼1

Xh Nj

¼

Lj ðtÞ  Ljwp ðtÞ  LShed jwpsp ðtÞ

i

8t; 8w; 8p; 8sp; 8n; 8r

ð11Þ

j¼1


Spot market power: here, it is supposed that the required power purchased from spot market at any time during the day has a maximum value, i.e. the difference between the total maximum generation capacity and the power generated.

06

P sp wp ðtÞ

6

"N g X i¼1

ðPMax Þ i



i

j

X Ventilation X Rolling k þ PL ðtÞ þ PL

Ng X 

Piwp ðtÞ

# 

ð12Þ

3.3.2. Constraints of the generation units
Unit limits: conventional units and wind power generation limits can be expressed as follows:

ð13Þ

ðtÞ

X others PL ðtÞ

ð18Þ

Also, the IVPP load can vary between the minimum and maximum values as in (19). Because of the existence of different industrial loads in an IVPP, the ramping up and down constraints are considered as (20) and (21).

Lmin ðtÞ 6 LIVPP ðtÞ 6 Lmax ðtÞ j j j

ð19Þ

ðt  1Þ  LIVPP ðtÞ 6 Lramp LIVPP j j j

down

ðtÞ  LIVPP ðt  1Þ 6 Lramp LIVPP j j j

up

t ¼ 1; 2; . . . ; T t ¼ 1; 2; . . . ; T

ð20Þ ð21Þ

The consumed energy can also be expressed as (22) at time t.

j k EL ðtÞ ¼ LIVPP ðt  1Þ þ LIVPP ðtÞ =2 ðMw=hÞ j j

ð22Þ

Here, the EAF is the most important load in an IVPP. Because of its nature for melting, this load cannot be on or off at each time; it then needs a minimum on and off time as in (23) and (24).

h

i¼1

max Pmin ðtÞuDG ðtÞuDG 8i; 8t i ðtÞ 6 P i ðtÞ 6 P i i ðtÞ i

þ

Millm

m

k

Due to the necessity for the constraints used for the definition of the mentioned objective function, the constraints related to each section of the system are described as follows.

ð14Þ

h

i





sjEAFðonÞ ðtÞ  T on  v j ðt  1Þ  v j ðtÞ P 0 j i





sjEAFðoff Þ ðt  1Þ  T off  v j ðt  1Þ  v j ðtÞ P 0 j

ð23Þ ð24Þ


Load shedding constraints: the load shedding amount is determined on the basis of the value of the lost load and the operating costs. Accordingly, the following equation must be met for each case.

0 6 Lshed ðtÞ 6 LSj ðtÞ 8j; 8t j

ð25Þ

597

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

3.3.4. Network constraints

3.4. Stochastic wind power and market prices


DC power flow considering power losses:

f nr ðtÞ ¼ Ploss 8t; 8n; 8r nr ðtÞ=2 þ Bnr ðdn ðtÞ  dr ðtÞÞ

ð26Þ

A detailed explanation about the linear approximation of losses and its modeling used in this paper is provided in [3].
Transmission line capacity constraint: max

max

f nr 6 f nr ðtÞ 6 f nr

8t; 8n; 8r

ð27Þ


Power angle constraints:

p 6 dn ðtÞ 6 p;

dref ¼ 0

ð28Þ

Wind power, day-ahead market price, and spot market price values are considered to be stochastic in the modeling presented. To model such behaviors, Weibull and Normal probability distribution functions utilizing Monte Carlo simulation [37] have been used to generate a number of scenarios for wind power and market prices (day-ahead and spot market prices), respectively. In this paper, this model is assumed to generate 200 scenarios for each parameter. To minimize the computation cost of the proposed scheduling procedure, k-means classification method [13] is used to reduce the number of applied scenarios. The explanation of scenario generation and reduction processes is beyond the scope of this paper.

Start

Input Data of the Understudy System

Stage 1: Data Receiving

Determine VPPs and IVPPs in a REC Power System

Stage 2: Formation of VPPs in the system

Main Problem

Scenario Generation for Market Prices and Wind Power Stage 3: Scenario Generation and Reduction

Scenario Number Reduction

Sub-Problem

Stage 4: Extraction of VPPs Profit Using Proposed Formulation

Extraction of VPPs Profit Based on Flowchart in Fig. 3

Select the Best DRLP from the VPP Point of View Using the NIPS Index

Offer the Best DRLP and Generation Programs to DRLs and DG units

Purchase S.P.P. Power from Spot Market (Increase Supply Power in IVPP)

Identification of the System Contingency and ISO Decision for Load Shedding

No

Stage 5: Selection of the Best DRL Program

Stage 6: Consideration of Minimum Load Shedding and Power Purchasing From Spot Market

Lshed
End Fig. 2. Flowchart of the proposed methodology.

Stage 7: Output Results

598

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

3.5. Evaluation strategy

4. Solving approach flowchart

To evaluate the performance of the proposed modeling, Evaluation Strategies (ES) such as revenue and billing cost are considered here. These are from the VPP point of view. To prepare this evaluation and select the best DRL program, a NIPS (Normalized Index of Program Selection) index is presented as follows [38]:

Fig. 2 illustrates the flowchart of the proposed method for the solution of the VPPs scheduling problem in a power system. This flowchart has 7 steps including data receiving; formation of VPPs and IVPPs in a REC system; scenario generation and reduction process for stochastic parameters; extraction of VPPs profit; selection of the best DRL program; consideration of the minimum load shedding; and the output results.

 P24  VPP ðtÞ t¼1 ESi ðtÞ  Profit n o  100 %NIPS ¼ VPP 24  Max ESi ðtÞ  Profit ðtÞ

ð29Þ

VPP

where ESi ðtÞ is the ith evaluation strategy at time t and Profit ðtÞ is the profit obtained from VPP at time t. To normalize the product VPP

of ESi ðtÞ  Profit ðtÞ in 24 h, the value obtained is divided by n o VPP 24  Max ESi ðtÞ  Profit ðtÞ .

Stage 1: At this stage, various data such as load, generation, topology, and market data for the study of the system is received. Then, according to the available daily load profile, the time periods under study are formed. Stage 2: Different VPPs in a REC will be determined based on the provider’s preferences.

Start Set DRL Programs Requirements and their Maximum Number (Case no. max) Case no.=1

BaseCase : Caseno. 1

TBR :

TOU : Caseno. 2 CPP: Caseno. 3 RTP : Caseno. 4 TOU CPP: Caseno. 5

DLC: Caseno. 6 EDRP: Caseno. 7 IBP : CAP : Caseno. 8 I/C : Caseno. 9 Case no.=Case no.+1

TBR IBP :

CPP EDRP: Caseno. 10 RTP CAP : Caseno. 11

Determination of Profit Maximization for Different Producers Using the Proposed Modeling in (1) New Setting for Generation Units Based on Constraints Satisfication Are the Presented Constraints are Satisfied?

No

Yes

Extraction of VPPs Profit

No Case no.=Case no.max Yes End Fig. 3. Flowchart of the VPPs profit calculation (sub-problem part in Fig.2).

599

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

used to generate the scenarios of wind generation and market prices (day-ahead and spot market prices), respectively. Also, as it has been mentioned, k-means classification method is used to decrease the applied scenarios.

Stage 3: Because of the stochastic consideration for wind generation and market prices, some scenarios are generated and reduced at this stage. As it was defined in the previous section, Weilbull and Normal distribution functions based on Monte Carlo method have been IVPP 2 21

18

22

REC 3 17 REC 4 VPP 3 16

VPP 2

19

20

23

REC 2 15

14

IVPP 1 13

24

11

12

VPP 3

REC 1 9

3

8

10

7

6

4

5 VPP 1 1

2

Fig. 4. Modified IEEE-RTS second area diagram with different VPPs.

Table 1 Load and generation data in different classified concepts for IEEE-RTS. VPP

Generation included

name

Bus #

Total value (MW)

Load included Bus #

Total value (MW)

IVPP1 IVPP2 VPP 1 VPP 2 VPP 3

13 18 2 15,16 12,19

(197 + 197 + 197) + 300 = 891 400 (20 + 20 + 76 + 76) + 150 + 300 = 834 12 + 12 + 12 + 12 + 12 + 155 + 155 = 370 300 + 150 = 450

13 18 2 15,16 19

265 333 97 317 + 100 = 417 170

600

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

Table 2 Demand ratio values for 24 h. Hour

CðtÞ Hour

CðtÞ

1

2 0.67

13 0.95

3 0.63

14 0.95

4 0.6

5 0.59

15

16

0.93

0.94

6 0.59

17 0.99

7 0.6

8 0.74

18

19

1

1

0.86 20 0.96

9

10 0.95

21 0.91

0.96 22 0.83

11 0.96 23 0.73

12 0.95 24 0.63

5. Case study and discussion 5.1. Under-study test system

Fig. 5. Load profile of a day for IEEE-RTS second area [39].

Stage 4: This stage contains a sub-problem for the main problem (as shown in the proposed flowchart) of the proposed procedure. This stage is illustrated as a flowchart in Fig. 3. The number of understudy DRL programs ðCase no:max Þ should be specified firstly. Then, for all of the specified programs, the proposed maximization model of VPPs profit has to be run. This is done by using CPLEX program under GAMS software. Stage 5: At this stage, by extracting the VPPs profit and returning to the main problem, the best DRL program will be selected based on the maximum profit decided by the VPP operator. Finally, the best scheduling will be sent to the DGs and DRLs. Stage 6: Application of contingencies will be examined at this stage. In this situation, the VPP operator tries to consider the events. The aim of the VPP operators, especially the IVPP ones is to decrease the load shedding. If the order of ISO leads to a load shedding value more than that of the maximum considered load shedding, then the VPP operator tries to purchase power from the spot power market and send the new setting to the sub-problem level to extract the best profit-based scheduling. Stage 7: After the satisfaction of the load shedding value for a VPP, the final results of scheduling and load shedding will be obtained at this stage.

The proposed modeling is applied to the IEEE Reliability Test System (IEEE-RTS) presented in [39]. The system taken into consideration is a modified one as shown in Fig. 4. This system includes 24 buses, 32 conventional generating units, 7 wind farms, 17 demands, and 38 lines. The generation units are classified into 3 types of production concepts of IVPP, VPP, and GENCO. The load and the generation data in classified IVPP as well as the VPP producers are presented in Table 1. Two heavy industrial loads are supposed to be in 13 and 18 buses. Because of that, IVPP is also determined in these buses. These loads are two steel companies whose main electrical parts are EAF, Induction Motors, Ventilations and Rolling Mill sections. Load and generation in different classified VPP concepts are shown in Table 1. Also, the demand ratio and the profile for a day are shown in Table 2 and Fig. 5, respectively. As it was mentioned before, there are different DRL programs that can be used for the participation of interruptible loads in the scheduling problem. In this paper, 10 programs are used for this purpose. Based on this, 11 cases (base case and 10 DRL programs) are considered to be examined in the proposed modeling. These are shown in Table 3. For these programs, uT and gL are equal to 0.7 and 0.1, respectively. As mentioned before, Weibull and Normal distribution functions utilizing Monte Carlo method have been used for the scenario generation of stochastic elements. Then, using this method, 200 scenarios are generated and after that by using the k-means classification method, they are reduced to 20 scenarios. The probabilities of scenarios are the same and equal to 0.05. As it can be seen in Fig. 6(a)–(c), different generated scenarios for the wind turbines, day-ahead market price and spot market price are illustrated, respectively. With regard to the load type, the three elements in the proposed scheduling formulation can be varied. These are the factor LT

LT of load shedding ðfLT and b ). j Þ, and factors in load model (a The values for these factors are shown in Table 4 with regard to three types of loads.

Table 3 Different DRL programs considered for scheduling application. Case no. 1 2 3 4 5 6 7 8 9 10 11

DRL program type (uT ¼ 0:7; gL ¼ 0:1)

Market price ($/MW h)

Base case TOU

Scenario based on 60 $/MW h flat rate Scenario based on 15, 60, 150 $/MWh at 3 periods valley, off peak and peak respectively Scenario based on 180 $/MW h at 18 to 19 Scenario based on Fig. 6(b) Scenario based on 15, 60, 150 $/MW h at 3 periods and 180 at 18 to 19 Scenario based on 60 $/MWh flat rate Scenario based on 60 $/MWh flat rate Scenario based on 60 $/MWh flat rate Scenario based on 60 $/MWh flat rate Scenario based on 180 $/MW h at 18 to 19 and 60 $/MW h at others Scenario based on Fig. 6(b)

CPP RTP TOU + CPP DLC EDRP CAP I/C CPP + EDRP RTP + CAP

Incentive Value (IV) ($/ MW h)

Penalty Value (PV) ($/ MW h)

0 0

0 0

0 0 0 75 150 32 75 150 32

0 0 0 0 0 16 32 0 16

601

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

Produced Power by Wind Turbine (MW)

(a) 120

Scen. 1 Scen. 2 Scen. 3 Scen. 4 Scen. 5 Scen. 6 Scen. 7 Scen. 8 Scen. 9 Scen. 10 Scen. 11 Scen. 12 Scen. 13 Scen. 14 Scen. 15 Scen. 16 Scen. 17 Scen. 18 Scen. 19 Scen. 20

100 80 60 40 20 0

0

5

10

15

20

25

15

20

25

15

20

25

Time (Hour)

(b) Day-ahead market prices ($/MWh)

120

Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen. Scen.

100 80 60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

40 20 0

0

5

10

Time (Hour)

(c) Spot market prices ($/MWh)

200

Scen. 1 Scen. 2 Scen. 3 Scen. 4 Scen. 5 Scen. 6 Scen. 7 Scen. 8 Scen. 9 Scen. 10 Scen. 11 Scen. 12 Scen. 13 Scen. 14 Scen. 15 Scen. 16 Scen. 17 Scen. 18 Scen. 19 Scen. 20

180 160 140 120 100 80 60 40 20

0

5

10

Time (Hour) Fig. 6. Scenarios for (a) wind power generation, (b) day-ahead market price, (c) spot market price.

5.2. Scheduling results using the proposed method As it was stated in Section 4, the proposed modeling can be applied to the system prepared with new types of generations. Using the obtained MINLP optimization problem in (1), the scheduling problem can be solved. The model was implemented in the GAMS software [40] environment and solved by CPLEX 12.1 on an Intel Core i5, 2.5 GHz processor with 6 GB of RAM memory. In normal conditions, the VPPs want to participate in the electrical market and prepare a day-ahead plan to supply the required power. The maximum profit obtained for IVPPs using the proposed modeling by the best DRL program selection is shown in Fig. 7. The best DRL program is shown on top of each bar to obtain the maximum profit for each hour of the day. As it can be seen, for

IVPP1 and IVPP2, case 3 is the best that can be used for 12 h in a day. This takes place because a Critical Peak Pricing (CPP) DRL program uses the real-time prices at times of extreme system peak, and CPP can be employed to have the maximum profit for the IVPP operator compared to others in the industrial environment. Since the market price suggestion based on Table 3 in the CPP program at the peak hours of 18 and 19 in a day is 180 $/MWh, then the industrial customer prefers to curtail its load and earn some profit. This is anticipated because CPP rates include a pre-specified high rate for usage designated by the utility to be a critical peak period. CPP events may be triggered by system contingencies or high prices faced by the utility in procuring power in the wholesale market depending on the program design. Also, after case 3, cases 10 and 11 which are composed of DRL program can be used more to obtain more profit. For IVPP1, sometimes such as hours 3 and 8;

602

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

Table 4 Factors of load shedding and load model for different load types. Load Type (LT) fLT j LT a

LT

b

Residential 1 5 10,000

Commercial 0.5 3 10,000

Industrial 0.2 2 20,000

and for IVPP2, sometimes such as hours 3, 4, and 8; case 1 (the base case) can be used. This means that DRL program is not suitable for the mentioned hours to be run. Furthermore, as it is shown in Fig. 8, the profit of different VPPs obtained in each DRL program case is shown daily. This clarification concerns loads or especially factories that have to select one DRL program for their day-ahead scheduling and cannot choose another program based on the processes which are working in their properties. Thus, by using these figures, it can be found that the best DRL program for achieving the maximum profit in a day can be obtained. Considering the IVPPs profit in a day, it is obvious that cases 3, 5, and 2 are the most suitable programs if an industrial load wants to gain more profit, but in VPPs, composite programs such as case 10 are more appropriate for the operator to contribute to a DRL program. These are shown in Table 5 and the value of DRL participation in each VPP is also given. As it can be seen, IVPPs actively participate in DRL strategies originated from scheduled and suitable curtailment of industrial loads to achieve the most profit.

With regard to Table 5, it can be concluded that in this understudy system, CPP and EDRP programs are the best programs for IVPP1, IVPP2, VPP1, and VPP3. But in VPP2, the time-based programs are not attractive for loads, because the generation and consumption in this VPP are so close together from the view point of distance and value. However, VPP2 can contribute to DRL program remarkably by using the proposed modeling and procedure. 5.3. Method proposed for performance evaluation As it was pointed out in Section 3, the NIPS index was used to evaluate the performance of the proposed modeling. In this index, two strategies, i.e. the revenue and billing cost are evaluated from the VPPs’ point of view. The results obtained from this evaluation are shown in Table 6. Also, to arrive at a better conclusion and to draw a suitable priority selection, the performance is illustrated in Fig. 9. With regard to Table 6, the percentage of the mentioned index as defined by (30) is given for each DRL program case. The values for the two strategies mentioned are shown and their prioritization can be achieved by considering the VPP stakeholders’ views. With regard to NIPS percentages based on revenue for IVPP1 in Table 6, cases 3, 5, and 2 have the highest values, respectively compared with other cases. Also, with regard to NIPS percentages based on the revenue for IVPP2, cases 5, 3, and 2 have the highest values, respectively compared with other cases. Cases 2, 3 and 5 are TOU, CPP, and CPP+TOU DRL programs. It is concluded that the best evaluation of revenue can be achieved by using the

Fig. 7. The maximum profit of IVPPs in 24 h using the best DRL program: (a) IVPP1, (b) IVPP2.

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

603

Fig. 8. The profit in a day obtained in each DRL program case: (a) IVPP1, (b) IVPP2, (c) VPP1, (d) VPP2, (e) VPP3.

Table 5 The best DRL program selected and its participation for different VPPs. Type of generation

Best DRL program selected

DRL participation (MW)

IVPP1 IVPP2 VPP 1 VPP 2 VPP 3

CPP CPP CPP + EDRP Except TOU and TOU + CPP CPP + EDRP

354.61 526.68 130.47 275.61 231.59

above-mentioned programs in industrial environments, because of their load types and their feedback in the peak hour to obtain more revenue. Furthermore, the best NIPS percentages based on billing cost for IVPP1 are achieved in cases 3, 10, and 5, respectively and the best percentages for IVPP2 are achieved in cases 3, 10, and 9, respectively. As a result, cases 3 and 10 are common in this strategy for IVPPs indicating that if the operator only uses CPP program or as a composite program, he/she can obtain the best reaction while considering the billing cost of customers. The priorities from the VPPs stakeholder’s point of view are illustrated in Fig. 9. The VPPs stakeholders choose a relevant strategy according to their policies based on the results of the program analysis as indicated in Fig. 9. Examination of these figures reveals

that the priorities of DRL program cases for different VPPs stakeholders depend on different decision signals like the electricity price, participation level of customers, incentive, and the penalty values determined for DRL programs. Actually, when some restrictions exist for the implementation of certain DRL program with higher priority, a VPP stakeholder can choose another program with lower priority. Therefore, as a conclusion for real application, since the main focus of this paper is on industrial environments (especially on steel companies and iron melting factories), it can contribute to the power market in the form of an IVPP. In a real application, some industrial factories, steel companies and iron melting factories can be aggregated with some generations and constitute an IVPP to participate in the power market, and with selection of the best DRL program based on the proposed procedure can obtain maximum profit and minimum load shedding cost. 5.4. Comparison of approaches To show the effectiveness of the proposed methodology for scheduling, a beneficial comparison is prepared in this subsection.

604

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

Table 6 NIPS index value from VPPs view point (bold values show the DRL program cases with %100 value for NIPS index). Case no.

E.S. % NIPS based on revenue

1 2 3 4 5 6 7 8 9 10 11

% NIPS based on billing cost

IVPP1

IVPP2

VPP1

VPP2

VPP3

IVPP1

IVPP2

VPP1

VPP2

VPP3

65.08 95.92 100.00 83.37 98.60 54.16 77.32 58.38 63.90 86.08 80.63

83.72 94.37 98.01 85.25 100.00 76.58 75.32 69.66 63.64 95.50 89.19

65.75 92.35 85.44 100.00 87.08 76.93 61.21 72.00 76.91 94.16 83.72

69.53 72.76 98.85 92.34 96.54 83.33 80.71 62.00 59.14 100.00 83.08

65.17 86.09 93.31 75.01 52.21 51.67 48.12 47.32 52.08 73.47 100.00

76.40 73.28 100.00 70.54 83.69 63.72 59.03 68.01 63.51 99.30 80.14

75.00 58.63 100.00 58.40 43.33 87.07 74.23 74.18 93.30 98.20 63.89

80.03 73.68 79.49 76.97 63.00 95.03 99.41 58.79 83.55 100.00 61.18

98.47 58.93 85.17 84.69 46.50 93.80 100.00 72.24 63.04 79.08 87.63

58.91 66.09 66.53 62.00 51.23 88.02 99.82 76.11 95.51 100.00 82.63

Fig. 9. Priority selection using the NIPS index for different VPPs stakeholders: (a) revenue strategy, (b) billing cost strategy.

605

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606 Table 7 Comparison of approaches in different items. Model

Based on presented model in [41] Based on presented model in [42] Based on proposed model

Compared item Whole system generation cost for a day scheduling ($)

DRL program participation (MW)

Load shedding by ISO (MW)

4859367.55 5338291.92 4548689.72

185.47 214.39 452.84

– 255.91 102.59

For this purpose, Refs. [41,42] have been selected. A formulation for scheduling procedure is presented for each of them. The models proposed in these papers support wind generation and demand response program as it is done in this paper. Also, the prepared understudy system is the IEEE-RTS test system. To compare the performance of these models with the methodology proposed in this paper, all conditions are considered to be the same. According to Table 7, three factors are selected to compare the effectiveness of the proposed model with other models presented in [41,42]. The DRL program in case 10 is selected for all of them to have a suitable and similar condition. The reason for this selection is to have a complex DRL program composited from timebased and incentive-based programs. As a result of using the proposed model, the cost of generation is lower than that of other models resulting from VPPs strategies. Also, the DRL participation in the proposed method is more than that of others because of the aggregation scheme of DRLs in the form of VPPs. The load shedding applied by ISO in the scheduling procedure presented by the proposed model is lower than that of the model presented in [42]; because, the proposed formulation and model considered the IVPPs and took the industrial loads into account. As it was mentioned before, in a real power system, ISO tries to react against the system security and market power balance, so it is a right choice to first apply load shedding to the industrial loads. Thus, by using the proposed strategy, IVPPs can manage the minimum load shedding and gain more power to supply their loads. 6. Conclusion In this paper, a new procedure to manage VPPs especially IVPPs for scheduling issue has been considered. Firstly, with regard to a REC, different types of VPPs are organized. Then, a new formulation to plan a day-ahead scheduling of VPPs is proposed. The model is presented as a stochastic MINLP optimization problem with regard to different generation, load, market, and system constraints. The objective of the problem is to maximize the profit of VPP and minimize the load shedding in the scheduling plan in different conditions. This objective can be obtained by selection of the best DRL programs from different points of view. The IEEE-RTS test system is used to apply the proposed procedure and evaluate the effectiveness of the presented modeling. The obtained results show that the proposed modeling can be an appropriate way to have access to the maximum profit for VPPs with different DRL plans to avoid high load shedding which can lead to lower cost of load shedding for IVPP operator. References [1] Tajeddini MA, Rahimi-Kian A, Soroudi A. Risk averse optimal operation of a virtual power plant using two stage stochastic programming. Energy 2014;73:958–67. [2] Dabbagh SR, Sheikh-El-Eslami MK. Risk-based profit allocation to DERs integrated with a virtual power plant using cooperative Game theory. Electric Power Syst Res 2015;121:368–78. [3] Motto AL, Galiana FD, Conejo AJ, Arroyo JM. Network-constrained multiperiod auction for a pool-based electricity market. Power Eng Rev, IEEE 2002;22:58.

[4] Pielow A, Sioshansi R, Roberts MC. Modeling short-run electricity demand with long-term growth rates and consumer price elasticity in commercial and industrial sectors. Energy 2012;46:533–40. [5] Asmus P. Microgrids, virtual power plants and our distributed energy future. Electricity J 2010;23:72–82. [6] Pedrasa MAA, Spooner TD, MacGill IF. A novel energy service model and optimal scheduling algorithm for residential distributed energy resources. Electric Power Syst Res 2011;81:2155–63. [7] Shabanzadeh M, Sheikh-El-Eslami M-K, Haghifam M-R. The design of a riskhedging tool for virtual power plants via robust optimization approach. Appl Energy 2015;155:766–77. [8] Thavlov A, Bindner HW. Utilization of flexible demand in a virtual power plant set-up. IEEE Trans Smart Grid 2015;6:640–7. [9] Yun L, Huanhai X, Zhen W, Deqiang G. Control of virtual power plant in microgrids: a coordinated approach based on photovoltaic systems and controllable loads. Gener Transmission Distrib, IET 2015;9:921–8. [10] Mnatsakanyan A, Kennedy SW. A novel demand response model with an application for a virtual power plant. IEEE Trans Smart Grid 2015;6: 230–7. [11] Tascikaraoglu A, Erdinc O, Uzunoglu M, Karakas A. An adaptive load dispatching and forecasting strategy for a virtual power plant including renewable energy conversion units. Appl Energy 2014;119:445–53. [12] Moghaddam IG, Nick M, Fallahi F, Sanei M, Mortazavi S. Risk-averse profitbased optimal operation strategy of a combined wind farm–cascade hydro system in an electricity market. Renew Energy 2013;55:252–9. [13] Zapata J, Vandewalle J, D’Haeseleer W. A comparative study of imbalance reduction strategies for virtual power plant operation. Appl Therm Eng 2014;71:847–57. [14] Yang H, Yi D, Zhao J, Luo F, Dong Z. Distributed optimal dispatch of virtual power plant based on ELM transformation. Indust Management Optim 2014;10:1297–318. [15] Sowa T, Krengel S, Koopmann S, Nowak J. Multi-criteria operation strategies of power-to-heat-systems in virtual power plants with a high penetration of renewable energies. Energy Proc 2014;46:237–45. [16] Dietrich K, Latorre JM, Olmos L, Ramos A. Modelling and assessing the impacts of self supply and market-revenue driven virtual power plants. Electric Power Syst Res 2015;119:462–70. [17] Yu J, Jiao Y, Wang X, Cao J, Fei S. Bi-level optimal dispatch in the Virtual Power Plant considering uncertain agents number. Neurocomputing 2015;167:551–7. [18] Moutis P, Hatziargyriou ND. Decision trees aided scheduling for firm power capacity provision by virtual power plants. Int J Electr Power Energy Syst 2014;63:730–9. [19] Skarvelis-Kazakos S, Rikos E, Kolentini E, Cipcigan LM, Jenkins N. Implementing agent-based emissions trading for controlling virtual power plant emissions. Electric Power Syst Res 2013;102:1–7. [20] Papaefthymiou SV, Papathanassiou SA. Optimum sizing of wind-pumpedstorage hybrid power stations in island systems. Renew Energy 2014;64:187–96. [21] Pandzˇic´ H, Kuzle I, Capuder T. Virtual power plant mid-term dispatch optimization. Appl Energy 2013;101:134–41. [22] Pandzˇic´ H, Morales JM, Conejo AJ, Kuzle I. Offering model for a virtual power plant based on stochastic programming. Appl Energy 2013;105:282–92. [23] Peik-Herfeh M, Seifi H, Sheikh-El-Eslami MK. Decision making of a virtual power plant under uncertainties for bidding in a day-ahead market using point estimate method. Int J Electr Power Energy Syst 2013;44:88–98. [24] Mashhour E, Moghaddas-Tafreshi SM. Bidding strategy of virtual power plant for participating in energy and spinning reserve markets-Part I: Problem formulation. IEEE Trans Power Syst 2011;26:949–56. [25] Mashhour E, Moghaddas-Tafreshi SM. Bidding strategy of virtual power plant for participating in energy and spinning reserve markets-Part II: Numerical analysis. IEEE Trans Power Syst 2011;26:957–64. [26] Sucˇic´ S, Dragicˇevic´ T, Capuder T, Delimar M. Economic dispatch of virtual power plants in an event-driven service-oriented framework using standardsbased communications. Electric Power Syst Res 2011;81:2108–19. [27] Shafie-khah M, Parsa Moghaddam M, Sheikh-El-Eslami MK. Development of a virtual power market model to investigate strategic and collusive behavior of market players. Energy Policy 2013;61:717–28. [28] Shafie-khah M, Parsa Moghaddam M, Sheikh-El-Eslami MK, Rahmani-Andebili M. Modeling of interactions between market regulations and behavior of plugin electric vehicle agregators in a virtual power market environment. Energy 2012;40:139–50.

606

S.M. Nosratabadi et al. / Applied Energy 164 (2016) 590–606

[29] Vasirani M, Kota R, Cavalcante RLG, Ossowski S, Jennings NR. An agent-based approach to virtual power plants of wind power generators and electric vehicles. IEEE Trans Smart Grid 2013;4:1314–22. [30] Arslan O, Karasan OE. Cost and emission impacts of virtual power plant formation in plug-in hybrid electric vehicle penetrated networks. Energy 2013;60:116–24. [31] Zhaohong B, Peng Z, Gengfeng L, Bowen H, Meehan M, Xifan W. Reliability evaluation of active distribution systems including microgrids. IEEE Trans Power Syst 2012;27:2342–50. [32] IRENA. Renewable energy technologies: cost analysis series; 2012. . [33] IEA. Strategic plan for the IEA demand-side management program; 2004– 2009. . [34] FERC. Assessment of demand response and advanced metering; 2006. . [35] Aalami HA, Moghaddam MP, Yousefi GR. Demand response modeling considering interruptible/curtailable loads and capacity market programs. Appl Energy 2010;87:243–50. [36] Schweppe FC, Caramanis MC, Tabors RD, Bohn RE. Spot pricing of electricity. Kluwer Academic Publishers; 1989.

[37] Hemmati R, Hooshmand R-A, Khodabakhshian A. Reliability constrained generation expansion planning with consideration of wind farms uncertainties in deregulated electricity market. Energy Convers Management 2013;76:517–26. [38] Valero S, Ortiz M, Senabre C, Alvarez C, Franco FJG, Gabaldon A. Methods for customer and demand response policies selection in new electricity markets. Gener Transmission Distrib, IET 2007;1:104–10. [39] Wong P, Albrecht P, Allan R, Billinton R, Chen Q, Fong C, et al. The IEEE reliability test system-1996. A report prepared by the reliability test system task force of the application of probability methods subcommittee. IEEE Trans Power Syst 1999;14:1010–20. [40] GAMS. A user’s guide. . [41] Parvania M, Fotuhi-Firuzabad M. Integrating load reduction into wholesale energy market with application to wind power integration. Syst J, IEEE 2012;6:35–45. [42] Morales JM, Conejo AJ, Perez-Ruiz J. Economic valuation of reserves in power systems with high penetration of wind power. IEEE Trans Power Syst 2009;24:900–10.