Quantitative flexibility assessment of a comprehensive set of demand response programs

Electrical Power and Energy Systems 116 (2020) 105562

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Quantitative flexibility assessment of a comprehensive set of demand response programs E. Heydarian-Forushani, M.E.H. Golshan

T

⁎

Department of Electrical and Computer Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Demand response programs Electricity market Flexibility Wind generation

Providing additional required flexibility as a consequence of variable wind generation is an essential challenge in future power grids. Demand Response (DR) is a relatively economic tool which can create considerable flexibility by motivating the customers to change their typical consumption patterns. This paper aims at quantitative evaluation of flexibility level of a comprehensive set of DR programs in power grid with significant amounts of wind generation through an applicable metric. The employed metric determines the flexibility of different DR programs based on their impacts on releasing technical constraints of conventional generation units which are restricted flexibility amount including minimum stable generation level, operating range, minimum up/down times and ramp up/down capability. To this end, a comprehensive portfolio of DR programs consists of tariffbased, incentive-based, and combinational DR programs have been modeled considering the customer’s benefit function based on price elasticity concept. The paper concludes with applicable guidelines for power system operators to design and implement an appropriate DR program from both the flexibility and economic aspects in wind integrated power grids.

1. Introduction 1.1. Motivation Accounting for increased uncertainty of the power grid according to the stochastic nature of growing renewable energy resources, particularly wind generation, the system operators are faced with several challenges to ensure additional required flexibility in order to not only retain load-generation balance but also facilitate wind power integration [1]. The conventional generation units cannot provide such additional flexibility due to the fact that achieving additional flexibility from thermal generation units may result in their cycling increment, efficiency reduction and even revenue loss due to more frequent startups or ramping of such units [2]. Therefore, it is essential for power system operators to use other potential flexible tools such as Demand Response Programs (DRPs). Incorporation of DRPs not only leads to flexibility promotion, but also facilitates more reliable, efficient, costeffective and environmentally friendly power system operation [3]. There are many different DRPs which can motivate the consumers to change their typical consumption pattern with respect to electricity tariff changes, incentives as well as penalties. Due to the fact that the system operators are responsible for design and implementation of DRPs, it is an important issue for them to evaluate the quantitative ⁎

flexibility level of various DRPs in order to choose an appropriate program. Due to our best knowledge, a quantitative flexibility index which determines the flexibility level of DRPs has not been addressed so far. Therefore, this paper aims to propose a novel applicable index in order to evaluate the quantitative flexibility of a comprehensive portfolio of DRPs based on merging technical and economic aspects of DR implementation on generation dispatch. 1.2. Literature review Wind generation is known as one of the fastest developing renewable energy resources that changes the way that power systems are planned and operated due to its intermittent nature. In this light, a growing amount of flexibility will be needed. The authors in [4] divided the power system flexibility into three main categories including generation side, grid side, and demand side. The flexibility of a system has been linked to flexibility options as well as flexibility enablers in [5]. The flexibility options are demand side, energy storage and new flexible supply alternatives that must be completed by the flexibility enablers, i.e. grid and market structure and policies. DR is known as one of the powerful options of delivering flexibility in energy markets due to its potential in providing valuable services such as congestion management, peak-load shaving, and load-

Corresponding author at: Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran. E-mail address: [email protected] (M.E.H. Golshan).

https://doi.org/10.1016/j.ijepes.2019.105562 Received 26 April 2019; Received in revised form 15 September 2019; Accepted 20 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

WP ,max Pwf ,t dtini dtContract Inct / Pent

Nomenclatures Indices

b, b′ i j l wf t, t′ w m

index index index index index index index index

of of of of of of of of

system buses b = 1, ...,NB conventional units i = 1, ...,NG loads j = 1, ...,NJ transmission lines l = 1, ...,L wind farms wf = 1, ...,NWF time periods t = 1, ...,NT scenarios w = 1, ...,NW segment for linearized fuel cost m = 1, ...,NM

λtini Et , t ′ Voll j, t ρw

forecasted wind generation of wind farms (MWh) initial electricity demand before DR (MW) contracted amounts of load reduction (MW) incentive/penalty values in incentive-based ($/MWh) initial electricity price before DR ($/MWh) price elasticity of demand value of lost load j ($/MWh) probability of scenario w

DRPs

Variables

SUCi, t Ui, t Pie, t , m

Parameters

CiG, t ,_mEng offered cost of energy for generating units ($/MWh) CiG, t _UC / DC offered cost of up/down capacity reserve for generating units ($/MW) CiG, t _UE / DE offered cost of up/down deployed reserve of generating units ($/MWh) WP _spill Cwf cost of wind spillage ($/MWh) start-up cost of unit i ($) SCi MUTi / MDTi minimum up/down time (h) Pimin/ Pimax minimum/maximum output of units (MW) RUi/ RDi ramp up/down limits of units (MW/h) W actual wind generation of wind farms (MWh) Pwf , w, t

RiG, t _UC / DC Fl0, t Fl, w, t LSj, w, t WP _spill Pwf , w, t riG, t ,_wup / dn Pi, w, t

start-up cost of conventional units ($) binary on/off status indicator of generation units generation of segment m in linearized fuel cost curve (MWh) scheduled up/down reserve capacity of generating units (MW) power flow through line l at the base case (MW) power flow through line l (MW) load shedding of load j (MWh) wind power spillage of wind farms (MWh) deployed up/down spinning reserve of generating units (MWh) actual power generation of generation units (MW)

electric vehicles has been studied in [18]. An interactive framework for local flexibility trading has been suggested in [19] that permits market players to reflect their flexibility requirements and to make a profit from flexibility services in a competitive environment. Demand-side flexibility has been enabled through a dynamic time-variant pricing scheme to meet the need for greater flexibility as a consequence of both variable wind generation and network equipment contingencies in [20]. Although the above literature is not lacking in qualitative analysis concerning the contribution of DR in providing operational flexibility, a dedicated quantitative assessment of different DRPs is of greatest importance in order to determine the amount of flexibility each DRP provides in generation scheduling. This may help the system operators to select the most effective DRP with application to guarantee the flexibility adequacy in their decisions. Motivated by this issue, a number of studies have developed various flexibility metrics. It is noteworthy that most of the flexibility metrics with regard to power system operation focus on conventional generation units without consideration of demand-side flexibility. For instance, a flexibility index borrowed from the process control literature has been developed in [21] with the aim of assessing the effectiveness of a balancing reserve strategy to cope with variable wind generation. In [22], an off-line flexibility index has been presented using the average value of the Ramp Up/Down (RU/RD) rates along with the Operating Range (OR) of generators. The authors in [23] visualized the operational flexibility taking into account three flexibility characteristics of generation units comprises capacity, ramp rate, and energy. The constructed flexibility index in [24] is similar to [23] whereas magnitude, ramp rate, and ramp duration of net load deviations are considered as flexibility criteria. An assessment methodology to monitor and compare the readiness of power system flexibility in the presence of a high share of renewable generation has been developed in [25]. The approach is based on a set of 80 key performance indicators across 14 flexibility domains, and permits to compare progress across different power systems. A systematic approach has been developed in [26] with the aim of evaluating the flexibility level of power system including fast-ramping units,

generation balancing [6]. The authors in [7] presented a noncooperative Stackelberg game model with application to solving power system dispatch as well as executing DR considering multiple entities which have conflict in their interests. Also, the long-term load scheduling of users has been developed using the Markov perfect equilibrium of a fully observable stochastic game with incomplete information under real-time pricing DR program in [8]. A stochastic network-constrained unit commitment associated with DR has been presented in [9] in order to investigate the role of various DRPs on providing flexible load and facilitating wind power integration. A robust framework has been developed to coordinate DR and bulk energy storages with the aim of deriving an optimal unit commitment decision in the presence of wind power [10]. The value of demand flexibility on spot and reserve markets has been analyzed in Germany in 2030 under different scenarios in [11]. The obtained results confirm that the demand flexibility can support the integration of a higher share of renewable generation. The revenues that can be captured by a flexible resource in the face of the day-ahead and intraday price variations are compared in [12]. The authors in [13–15] look at the problem from microgrid operator point of view with the aim of maximizing the expected profit of microgrid operator while minimizing the energy payments of customers with regard to voltage and frequency security constraints under real‐time pricing program. However, the current paper looks at the problem from independent system operator viewpoint in a wind-integrated transmission network with various power generation technologies. Also, the authors in [13–15] just considered real-time pricing DRP, whereas a comprehensive set DRPs have been modeled in the current paper. In addition, the authors in [new4new6] investigated the effects of DR on power system security, while the current paper evaluates and compares the impacts of various DRPs on power system flexibility through a novel quantitative metric. A stochastic bi-level programming approach has been developed for decision making of a retailer and an electric vehicle aggregator in a competitive market under a number of uncertainties in [16] and [17], respectively. Moreover, the effect of various time-based rate DRPs on the stochastic day-ahead energy and reserve scheduling in residential islanded microgrids in presence of renewable energy resources and 2

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

reflect the influence of different DRPs on generation dispatch flexibility. To this end, RU, RD, MSG, OR, MUT, and MDT are considered as six TFCs of a generation unit [28]. It is notable that the measurement units of various TFCs are different. In order to normalize all the TFCs, the min-max normalization approach has been adopted as shown in Eq. (1) [28]. In (1), the actual and normalized values of the technical flexibility characteristic c for generation unit i are depicted through tfci, c and TFCi, c , separately. Also, the mini (tfci, c ) and maxi (tfci, c ) devote to the minimum and maximum amounts of the technical flexibility characteristic c among all generation units, respectively.

hourly DR and energy storages. Moreover, an online index is defined to compare the technical capability of the mentioned flexible resources. A composite flexibility metric has been developed in [27] considering eight technical features of a generation unit including RU, RD, Minimum Stable Generation (MSG), OR, start-up and shut-down times, and Minimum Up/Down Times (MUT/MDT) without paying attention to actual operational status of generators. This index is further extended in [28] by merging technical and economic characteristics of each individual unit based on the actual operational state of generators. Hereafter, a metric so-called available generation dispatch flexibility is developed and incorporated into the day-ahead market clearing procedure through a multi-objective decision making model. Note that the implementation of only one typical tariff-based DRP has been discussed in the mentioned study. In [29], a comprehensive set of DRPs has been prioritized considering general criteria including total operation cost, total required ramp, and total emission of generation dispatch in a 24hour time horizon as economic, technical, and environmental flexibility indicators. However, the paper does not deal with detail analyses of DRPs according to the Technical Flexibility Characteristics (TFCs) of generation units. It is an important issue due to the fact that DR is displaced with a number of generation units so that some generation units are forced to shut down and also the operating points of others changed subsequently. In such a situation, a number of technical constraints related to flexibility of generation units are released according to the implementing DRP. This is the main motivation of the current paper that has not been addressed so far.

TFCi, c =

tfci, c − mini (tfci, c ) max i (tfci, c ) − mini (tfci, c )

(1)

The impression of each TFC on flexibility limitation is quantified using Flexibility Affect Factor (FAF) coefficient. To find the FAF coefficient related to each TFC, a complete unit commitment problem must be run by relaxing just the relevant constraint associates with that specific TFC. The change in total operating cost in comparison with other TFCs is considered here as a criterion to reflect the relative weight of a particular TFC. It is worth to note that if a TFC imposes a higher cost to the system operation, it has, therefore, a higher influence on limiting the power system flexibility. The mathematical representation of FAF is given in Eq. (2) [28].

FAFi, c =

opci, c − mini (opci, c ) max i (opci, c ) − mini (opci, c )

(2)

Note that FAFi, c devotes to the flexibility affect factor which represents the flexibility restriction as a result of satisfying the technical flexibility characteristic c for generation unit i. Moreover, opci, c illustrates the new system operation cost as a consequence of relaxing technical flexibility characteristic c for generation unit i. The FAFi, c is also a normalized value between 0 and 1 so that it’s lower value means that the related TFC is more rigid and consequently decreases the available flexibility more than the other ones and vice versa. A linear summation form has been selected to merge the aforementioned normalized factors in order to calculate the flexibility of a generation unit as observed in Eq. (3). It should be mentioned that a set of TFCs such as MSG, MUT, and MDT have a negative correlation with flexibility, while the other ones such as OR, RU, and RD are positively correlated with flexibility. This issue has been accounted in Eq. (3) through cp and cn sets which exhibit positive and negative correlations with flexibility, respectively [28].

1.3. Contributions This paper has remarkable contributions in different aspects. Firstly, the problem that has been raised is completely new since there is no previous published paper which evaluated the quantitative flexibility of such a comprehensive DR portfolio so far. To this end, a comprehensive DR portfolio including tariff-based, incentive-based and combinational DRPs has been modeled based on price elasticity and customer benefit function. Secondly, the applied procedure to calculate the flexibility of DRPs is another real novelty due to the fact that the proposed model extract the provided flexibility of each DRP as a consequence of its impacts on releasing technical flexibility characteristics of conventional units which has been not addressed until now. In this regard, six technical flexibility associated constraints of a generation unit including RU, RD, MSG, OR, MUT, and MDT are taken into account. Thirdly, the obtained results are very applicable for independent system operators who are responsible for designing and implementing appropriate DRPs considering their required flexibility level and economic restrictions.

Flex i =

∑ FAFi,c × TFCi,c + ∑ c ∈ cp

FAFi, c × (1 − TFCi, c )

c ∈ cn

(3)

The provided flexibility of conventional generation units in generation dispatch is formulated as given in Eq. (4). As mentioned before, DR is displaced with conventional generating units due to its economic and technical preferences. Therefore, the difference between the available flexibility of generation dispatch in two manners, i.e. with and without DR, is considered here as DR contribution in generation dispatch flexibility as shown in Eq. (5).

1.4. Paper organization The rest of the paper is continued as follows. Section 2 introduces the proposed DR flexibility metric in details. Section 3 is devoted to the model of DR portfolio. The stochastic day-ahead energy and reserve markets clearing formulation is presented in Section 4. The main simulation results are depicted and discussed in Section 5. Final remarks are concluded in Section 6.

NT NG

FLEXGen =

∑ ∑ Flexi Ui,t t=1 i=1

2. DR flexibility metric calculation

Flex _DR = FLEXGen |No DR − FLEXGen |DR

The flexibility of generation dispatch to cope with wind power variability depends on technical characteristics as well as the operating status of generation units. In addition, DR reshapes the load profile and consequently changes the initial generation dispatch so that the marginal generating units are shut down in particular hours and the output power of other generators may experience essential changes. Therefore, it is necessary to incorporate the technical features of conventional generation units in the proposed flexibility metric in order to precisely

(4) (5)

3. Model of DR portfolio DR is one of the flexibility alternatives obtained from changing the typical consumption pattern of end-users with respect to dynamic electricity tariffs or a specified given incentive/penalty. Time of Use (TOU), Real-Time Pricing (RTP), and Critical Peak Pricing (CPP) are in the category of tariff-based DRPs which persuade the customers to 3

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

4. Stochastic day-ahead energy and reserve markets clearing formulation incorporating DR

decrease or shift their demand in response to time-variant electricity tariffs, whereas Emergency Demand Response Program (EDRP), Direct Load Control (DLC), Interruptible/Curtailable Services (I/C), Ancillary Services Market (A/S), Capacity Market (CAP) and Demand Bidding (DB) are in the category of incentive-based DRPs which motivate the customers with incentive/penalty payments [30]. The load reduction, shift in energy consumption or both depending on the customer’s price elasticity of demand. Elasticity quantifies the sensitivity of customer’s demand to electricity price changes. Note that the higher values of elasticity lead to more dramatic changes in consumption pattern. In addition, there are several models such as linear, exponential, logarithmic, and power functions to demonstrate the relationship between electricity price and demand based on the price elasticity of demand concept [31]. Developing a model that properly represents the customer’s behavior is the main challenge of DR implementation which needs remarkable field researches. Investigating the performance of different DR models is a separate work which has been addressed previously in [31,32]. Without loss of generality and according to the fact that the proposed framework is a mixed-integer linear programming problem, the linear model of responsive loads is used in the current paper which has been extracted from [33]. The net benefit of customers when participate in DRPs can be calculated as formulated in Eq. (6).

A two-stage stochastic programming approach has been exerted here which explicitly incorporates uncertainty in wind power generation. The objective function is the expected system operation cost which should be minimized while meeting several constraints from the system operator point of view as given in (10).

Minimize : NT

NT

NT

⎣

+ Et , t

NT t ′= 1

)

The above objective function consists of two parts so that the first line devotes to the energy and reserve capacity market decisions, whilst the second line is related to the actual operation of the power system due to the realization of wind power generation. The operation cost resulted from start-up, minimum production, piecewise linear fuel and up/down capacity reserve of generation units as well as cost/income associates with incentive/penalty payments of DRPs are formulated in the first line, subsequently. Note that the incentive is paid to customers who successfully response to incentive-based DRPs, while the penalty is received from customers who refuse to reduce their demand due to the contract. Therefore, the decision variables that do not depend on scenario realization are commitment status, scheduled power of generation units in energy and up/down reserve capacity markets and the load changes as a consequence of DR implementation. The second line pertains to the costs of the up/down deployed reserves of generation units, involuntary load shedding, and wind power spillage, respectively. On this basis, the decision variables pertaining to each particular scenario are up/down deployed spinning reserves, involuntarily load shedding and wind power spillages. The objective function must be minimized while satisfying several constraints. The power balance equation between load and generation is declared in Eq. (11). In Eq. (11), Pi, t approximates the energy offer cost function of generating unit i in period t by blocks as expressed in (12). Also, dj, t assigns to the modified demand of load j in period t after DR implementation as formulated before in (9). Moreover, the DC power flow equation and transmission line flow limitations are formulated in Eqs. (13) and (14), respectively.

(7)

∑ Et,t′

NWF

(10)

∑

Pi, t +

i ∈ Gb

∑

WP , S Pwf ,t −

wf ∈ WFb

(8)

∑ dj,t = ∑ Fl0,t j ∈ Jb

l ∈ Lb

(11)

NM

Pi, t =

The single period model must be extended to multi period model due to the fact that electricity tariff changes or incentive/penalty payments in one period can affect consumption in the other periods. In addition, the total load must assigned to relevant load points. Therefore, the generic representation of load profile after DR implementation has been depicted in (9). ini ⎧ dj, t = (1 − ηDR) dini j, t + ηDR d j, t 1 + ⎨ ⎩

NG

NJ

Here, a quadratic customer’s utility function has been considered to model the customer’s utility as a consequence of consuming electricity as in [33]. Eq. (8) shows the single period model of responsive loads which can be obtained by differentiating the mentioned quadratic customer’s utility function and replacing the result in (7).

dt =

NW

WP _spill WP _spill Pwf , w, t + ∑ j = 1 Voll j, t LSj, w, t + ∑wf = 1 Cwf

The first term in the right hand side of Eq. (6) depicts customer’s utility as a result of consuming dt at hour t. The second term indicates the cost of customer’s electricity consumption at hour t. Moreover, the income as a result of incentive payment and the penalty cost for customers who avoid to reduce their consumption according to the contract have been formulated through the third and fourth terms, respectively. In order to find the optimal consumption pattern from the customer’s viewpoint, we must differentiate from both sides of Eq. (6) with respect to dt and then put it equal to zero as shown in Eq. (7).

(λt − λtini + Inct + Pent ) ⎤ ⎥ λtini ⎦

NJ

+ ∑t = 1 ∑w = 1 ρw (∑i = 1 (CiG, t _UE riG, t ,_wup − CiG, t _DE riG, t ,_wdn )

(6)

dtini ⎡1 ⎢

NM

+ CiG, t _DC RiG, t _DC ) + ∑t = 1 ∑ j = 1 (Inct Δdj, t − Pent (djcontract − Δdj, t )) ,t

Bt = Uti (dt ) − dt λt + Inct (dtini − dt ) − Pent (dtContract − (dtini − dt ))

∂Bt ∂Uti = − λt − Inct − Pent = 0 ∂dt ∂dt

NG

∑t = 1 ∑i = 1 (SUCi, t + MPCi Ui, t + ∑m = 1 (Pie, t , m CiG, t ,_mEng ) + CiG, t _UC RiG, t _UC

∑ Pie,t,m,

0 ⩽ Pie, t , m ⩽ Pimax ,m

m=1

Fl0, t

(12)

δb0′, t )/ Xl

(13)

− Flmax ⩽ Fl0, t ⩽ Flmax

(14)

=

(δb0, t

−

The allowable output power bounds of generation units considering their participation in energy and reserve markets are shown in (15) and (16). Up and down reserve capacities of generation units are limited according to ramp rates as expressed in (17) and (18). Also, the start-up cost of generation units is formulated in (19). Minimum up and down time of generation units are modeled through (20) and (21), respectively. Note that, the scheduled power of wind farms is restricted due to its forecasted amount in (22).

[λ t ′ − λ tini ′ + Inc t ′ + Pent ′ ] ⎫ ⎬ λ tini ′ ⎭ (9)

The first part of Eq. (9) devotes to non-responsive loads, while the second part associated with the responsive loads. In this regard, ηDR represents the percentage of customer’s responsiveness which is a constant parameter. Note that the amount of changes in consumption depends on electricity tariffs, incentive or penalty payments, and elasticity values. 4

Pi, t + RiG, t _UC ⩽ Pimax Ui, t

(15)

Pi, t − RiG, t _DC ⩾ Pimin Ui, t

(16)

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

0 ⩽ RiG, t _UC ⩽ RUi

(17)

Pi, w, t − 1 − Pi, w, t ⩽ RDi Ui, t − 1 + SDRi (1 − Ui, t )

(29)

0 ⩽ RiG, t _DC ⩽ RDi

(18)

0 ⩽ LSj, w, t ⩽ dj, t

(30)

SUCi, t ⩾ SCi (Ui, t − Ui, t − 1), SUCi, t ⩾ 0

(19)

WP _spill W 0 ⩽ Pwf ⩽ Pwf , w, t , w, t

(31)

t + MUTi

∑

(1 − Ui, t ′) + MUTi (Ui, t − Ui, t − 1) ⩽ MUTi

5. Simulation results

(20)

t ′= t + 2

Numerical simulations to investigate the performance of the presented model are performed on the modified IEEE Reliability Test System (RTS 24-bus) [34]. The install capacity of conventional units is 3105 MW whereas the system peak load is 2850 MW. The offered costs of generation units for participation in energy and reserve markets have been directly obtained from [35] as shown in Table 1. Also, the technical flexibility features of generation units have been listed in Table 2. Moreover, six hydro units which were on bus 22 are excluded and instead of them, six 200 MW wind farms are integrated at buses 1, 4, 6, 18, 21, and 22. The assumed wind power capacity reflects the uncertainty of future power grids. The South East and North of South Australia wind speed data have been used for wind speed scenarios generation applying An Autoregressive Moving Average (ARMA) method [36]. Afterward, the K-means clustering approach has been adopted to extract ten scenarios for each wind farm [37]. The reduced wind speed scenarios have been converted to wind generation scenarios through the Vestas 3 MW wind turbine characteristics. In addition, the load shedding and wind spillage costs are considered to be 200 and 40 $/MWh, respectively [29]. This is due to the fact that the system operators perform a number of corrective actions in the face of occurring deviation in real-time stage including adjustment of up/down deployed reserve through conventional generation units, partial wind power spillage, and customer’s load shedding in emergency circumstances in order of preferences. It is assumed that only 20% of the customers at each load point are responsive to dynamic tariffs or incentive/penalty payments. Moreover, the flat rate before DR implementation is considered to be 15 $/MWh and the price elasticity values are extracted from [33]. A comprehensive set of well-known DRPs has been considered including tariff-based, incentive-based, and combinational programs as it can be observed in Table 3. Note that, DR modeling methodology as well as all the assumed DR parameters such as electricity tariffs, incentive or penalty payments, elasticity values, customer’s participation level, initial electricity tariff, and initial electricity consumption may affect the obtained results. The DR portfolio including considered DRPs, tariffs, and incentive/penalty payments has been directly extracted from [29]. The proposed model is a mixed-integer linear programming problem which has been solved using CPLEX in GAMS software environment. In order to assess the quantitative flexibility that each DRP provides in

t + MDTi

∑

Ui, t ′ + MDTi (Ui, t − 1 − Ui, t ) ⩽ MDTi

t ′= t + 2

(21)

WP , S WP ,max 0 ⩽ Pwf , t ⩽ Pwf , t

(22)

The aforementioned constraints pertain to the electricity markets, however, there are a number of scenario dependent constraints that must be met for each scenario realization. Deviations coming from variability of wind power generation is justified by the deployed up/ down reserve of generation units, wind power spillage, and involuntary load shedding in actual system operation as expressed in (23). The deployed up and down reserves must be less than the scheduled reserve capacities enforced by the market clearing procedure as shown in (24) and (25), respectively. An auxiliary variable is defined in Eq. (26) in order to represent the net output power of generation units. Also, the net output power limitations are given in Eq. (27). The constraints associated with ramp up and ramp down rates of generation units are modeled in (28) and (29), respectively. The involuntary load shedding and wind power spillage limits are given as formulated subsequently in (30) and (31). Note that, the mathematical formulation of the constraints such as DC power flow and bounds on transmission lines have been also taken into account for different scenarios realization, even if their mathematical formulations are eliminated here for the sake of conciseness.

∑

G _dn (riG, w_,up t − ri, w, t ) +

i ∈ Gb

=

∑

WP _spill W WP , S (Pwf , w, t − Pwf , t − Pwf , w, t ) +

wf ∈ WFb

∑ LSj,w,t j ∈ Jb

∑ Fl,w,t − Fl0,t (23)

l ∈ Lb

G _UC 0 ⩽ riG, w_,up t ⩽ R i, t

(24)

G _DC 0 ⩽ riG, w_,dn t ⩽ R i, t

(25)

G _dn Pi, w, t = Pi, t + riG, w_,up t − ri, w, t

(26)

Pimin Ui, t ⩽ Pi, w, t ⩽ Pimax Ui, t

(27)

Pi, w, t − Pi, w, t − 1 ⩽ RUi Ui, t + SURi (1 − Ui, t − 1)

(28)

Table 1 Generation units cost data [35]. Generation unit No. i1-i5

i6-i9

i10-i13

i14-i16

i17-i20

i21-i23

i24

i25-i26

87.4 5.2 23.4

15.0 5.0 29.6

715.2 7.5 11.5

575 8.5 18.6

312 6.2 9.9

1018.9 15.0 19.2

2298 20.0 10.1

0 0 5.3

CiG, t _,2Eng ($/MWh)

23.8

30.4

12.0

20

10.2

20.3

10.7

5.4

CiG, t _,3Eng ($/MWh)

26.8

42.8

13.9

21.9

10.7

21.2

11.1

5.5

CiG, t _,4Eng ($/MWh) CiG, t _UC ($/MW) CiG, t _DC ($/MW) CiG, t _UE ($/MWh) CiG, t _DE ($/MWh)

30.4

43.3

15.9

22.7

11.3

22.1

11.7

5.7

10.4

14.6

5.3

8.3

4.2

8.3

4.3

2.2

10.4

14.6

5.3

8.3

4.2

8.3

4.3

2.2

26.1

36.5

13.3

20.8

10.5

20.7

10.9

5.5

26.1

36.5

13.3

20.8

10.5

20.7

10.9

5.5

SCi ($) MPCi ($) CiG, t _,1Eng ($/MWh)

5

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Table 2 Technical flexibility characteristics of generation units in IEEE RTS 24-bus [27]. Generation unit No.

Size (MW)

MSG (MW)

OR (MW)

MUT (h)

MDT (h)

RU (MW/h)

RD (MW/h)

i1-i5 i6-i9 i10-i13 i14-i16 i17-i20 i21-i23 i24 i25-i26

12 20 76 100 155 197 350 400

2.4 15.8 15.2 25 54.25 68.95 140 100

9.6 4.2 60.8 75 100.75 128.05 210 300

0 0 3 4 5 5 8 8

0 0 2 4 3 6 5 5

9.6 16 38.5 51 55 55 70 50.5

9.6 16 60.8 74 78 99 120 100

Table 3 Statements of portfolio of DRPs [29]. DR Type

Case No.

Programs

Electricity price ($/MWh)

Incentive value at peak ($/MWh)

Penalty value at peak ($/MWh)

Base

C1

Initial load

15 flat rate

0

0

Tariff-based

C2 C3

TOU RTP

0 0

0 0

C4

CPP

7.5, 15, 30 at low-load, off-peak, and peak periods, respectively 12, 10.7, 10.2, 5.7, 5.4, 5.4, 5.5, 5.7, 11.1, 13.9, 15, 20.3, 20.3, 20.1, 20.3, 19.1, 20.6, 22.1, 22.1, 22.1, 21.9, 21.2, 20.3, 13.8 at 1–24 h 30 at peak period and otherwise 15

0

0

Incentive-based

C5 C6

EDRP I/C

15 flat rate 15 flat rate

5 2.5

0 1.25

Combinational

C7 C8

TOU + EDRP RTP + EDRP

5 5

0 0

C9 C10

TOU + I/C RTP + I/C

7.5, 15, 30 at low-load, off-peak, and peak periods, respectively 12, 10.7, 10.2, 5.7, 5.4, 5.4, 5.5, 5.7, 11.1, 13.9, 15, 20.3, 20.3, 20.1, 20.3, 19.1, 20.6, 22.1, 22.1, 22.1, 21.9, 21.2, 20.3, 13.8 at 1–24 h 7.5, 15, 30 at low-load, off-peak, and peak periods, respectively 12, 10.7, 10.2, 5.7, 5.4, 5.4, 5.5, 5.7, 11.1, 13.9, 15, 20.3, 20.3, 20.1, 20.3, 19.1, 20.6, 22.1, 22.1, 22.1, 21.9, 21.2, 20.3, 13.8 at 1–24 h

2.5 2.5

1.25 1.25

Fig. 1. Flexibility score of conventional generation units.

base-case, when there is no DR. The obtained flexibility value of each DRP and its associated system operation cost is illustrated in Fig. 3. As observed in Fig. 3, the highest flexibility can be obtained in case C7 (TOU + EDRP), whilst the lowest flexibility devotes to case C6 (I/C). Moreover, it is obvious that the tariff-based DRPs can provide more flexibility in comparison with incentive-based DRPs. Note that, although the incentive-based DRPs (C5 and C6) have low flexibility and high cost, however, their combination with TOU program (C7 and C9) may lead to significant flexibility with low operation cost. The commitment status of generation units has been compared for cases C7 (highest flexibility) and C6 (lowest flexibility) with case C1 as the benchmark in Table 4. According to Table 4, the implemented DRP in case C7 not only has been replaced with units i10-i13 at hours 23:00 to 24:00, but also leads to avoid commitment of i14 and i16 between hours 12:00 to 23:00. On this basis, the implemented DRP in case C7 could provide more flexibility so that the calculated Flex_DR metric for case C7 is 21.6, while it is equal to 3.7 for case C6. The flexibility

generation dispatch, it is essential to calculate the flexibility score of conventional generation units as explained in Section 2. Fig. 1 compares the flexibility score of different generation units. As observed in Fig. 1, the minimum flexibility score is assigned to i25-i26 which are the base-load nuclear units, while the maximum flexibility value pertains to i6-i9 which are peak-load units with Oil/CT technology. Before assessing the quantitative flexibility of each DRP, it is important to investigate the impact of the aforementioned DRPs on initial load curve of the system as shown in Fig. 2. As observed, the tariffbased DRPs, particularly TOU program persuades the customers to shift their loads to off-peak period, while the incentive-based DRPs, especially EDRP motivates the customers to decrease their consumption at peak-load period. Note that the combinational DRPs include both of the objectives, i.e. peak shaving as well as load shifting. In order to quantify the flexibility of various DRPs, the DRPs are incorporated to stochastic market clearing procedure one by one and the available flexibility of generation dispatch is compared with the

6

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

Fig. 2. Impact of given DRPs on initial load curve.

Fig. 3. Flexibility of different DR programs vs. operation cost.

the wind spillage amount in cases C5 and C6 is substantial. On the other hand, the Flex_DR metric for cases C7 to C10 is high and hence, the associated wind power spillage in the mentioned cases is relatively low. The changes in Flex_DR metric for each DRP as a result of customer participation level variations are reported in Table 5. The obtained results reveal that the Flex_DR metric is increased when customers participate in DRPs more. However, the changes in flexibility values are non-linear so that cases such as C5 and C6 experience negligible changes, whereas the changes for cases such as C4 are remarkable. It is notable that DR depends on not only the customer’s

enhancement in case C7 leads to more than 8% operation cost reduction in comparison with case C6. In addition, a comparison of the amount of integrated wind power in the two mentioned cases reveals that wind integration has been grown approximately 51%. The detail analysis of DRP’s flexibility value and its relevant impact on wind power integration is shown in Fig. 4. The point that must be mentioned is that the amount of wind power spillage is completely in correlation with the flexibility of DR so that the cases with higher flexibility have less wind power spillage and vice versa. For instance, the Flex_DR metric for cases C5 and C6 is negligible and consequently, 7

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

Table 4 Unit commitment status for cases C6 and C7.

Table 5 Impact of customer’s participation level on DR flexibility in given cases. DR Type

Case No.

Programs

Participation level (%)

Flex_DR

Base

C1

Initial load

–

–

Tariff-based

C2

TOU

C3

RTP

C4

CPP

10 20 30 10 20 30 10 20 30

10.7 18.9 21.5 6.4 12.9 13.2 4.3 11.9 22.9

C5

EDRP

C6

I/C

10 20 30 10 20 30

3.2 3.7 4.3 3.2 3.7 4.3

C7

TOU + EDRP

C8

RTP + EDRP

C9

TOU + I/C

C10

RTP + I/C

10 20 30 10 20 30 10 20 30 10 20 30

16.6 21.6 23.2 7.1 16.6 17.2 10.7 21.1 23.2 6.4 16.6 16.9

Incentive-based

Combinational

C4. Therefore, it can be concluded that although the lowest flexibility is pertained to C6 (I/C), however, it is less sensitive to DR parameters and can be considered as a relatively robust DRP in comparison with other programs. It is noteworthy that although a higher number of scenarios results in a more accurate modeling of the uncertainties, however, it yields some computational burden difficulties. In order to indicate the effect of wind farm scenario numbers on solving procedure, the computation time and other optimization statistics of the model are reported in Table 6 for two different manners. Note that a 64-bit Intel core i5 laptop is employed as the platform with 4 GB DDR3 of RAM and 2.3 GHz processors to accomplish aforementioned cases. Comparing the optimization statistics of Table 6 reveal that although the number of scenarios have been increased 3 times, however, the solution times is almost 7.5 times greater than the case with 10 scenarios. Moreover, the number of equations, variables, and iterations have been increased, significantly. Here, the IEEE RTS 24-bus has been used for simulations, whereas the real transmission networks have huge size which may create some additional computational burden

participation level but also the customer’s elasticity. In this regard, the mentioned factors may affect the provided flexibility of DRPs and consequently the Flex_DR metric. On this basis, it is necessary for the system operators to calculate the sensitivity of various DRPs to DR parameters in order to choose and implement an appropriate DR program. For this purpose, the price elasticity values extracted from [33] are multiplied by coefficients change from 0 to 2 in ten equal steps. Also, the customer’s participation level is changed from 0 to 40% in a similar way. The average standard deviation of variations in Flex_DR metric in response to changes of elasticity and participation level is shown in Fig. 5. Due to Fig. 5, case C6 has the lowest standard deviation while the highest standard deviation of Flex_DR metric devotes to case

Fig. 4. Flexibility of different DR programs vs. wind power spillage. 8

Electrical Power and Energy Systems 116 (2020) 105562

E. Heydarian-Forushani and M.E.H. Golshan

Fig. 5. Average standard deviation of Flex_DR with respect to elasticity and participation level in the given cases. Table 6 Optimization statistics for two given scenario numbers. No. of scenarios

No. of single constraints

No. of single variables

No. of discrete variables

No. of iterations

Solution times (s)

10 30

101,601 281,601

65,361 175,281

1824 1872

56,090 182,126

36.1 270.4

Declaration of Competing Interest

difficulties as the number of scenarios increases. It is noteworthy that the proposed flexibility metric considers the impacts of net load (i.e. actual load power minus renewables output power) variations due to the fact that it depends on actual operational state of generators which are affected by net load changes. The authors would like to emphasis that accurate estimation of customer baseline load is a necessity for evaluating the flexibility level of different DRPs. In this regard, the behind the meter distributed photovoltaic systems could create significant error in customer baseline load estimation since only the net load data is metered [38]. To tackle such a problem, an approach based on support vector machine with customer net load curve features to predict the capacity of distributed photovoltaic systems has been presented in [39]. Moreover, a synchronous pattern matching principle-based baseline load estimation approach has been proposed in [40]. Also, a distributed real-time DR strategy and a multiagent structure in order to obtain an accurate customer baseline load have been addressed in [41] and [42], respectively.

There is no conflict of interest. Acknowledgements This work was supported by Iran National Science Foundation (INSF) under grant agreement no. 96017036. References [1] Troy N, Denny E, O'Malley M. Base-load cycling on a system with significant wind penetration. IEEE Trans Power Syst 2010;25(2):1088–97. [2] Troy N, Flynn D, Milligan M, O'Malley M. Unit commitment with dynamic cycling costs. IEEE Trans Power Syst 2012;27(4):2196–205. [3] Liu G, Tomsovic K. A full demand response model in co-optimized energy and reserve market. Electr Power Syst Res 2014;111:62–70. [4] Li J, Liu F, Li Z, Shao C, Liu X. Grid-side flexibility of power systems in integrating large-scale renewable generations: a critical review on concepts, formulations and solution approaches. Renew Sustain Energy Rev 2018;93:272–84. [5] Papaefthymiou G, Dragoon K. Towards 100% renewable energy systems. Uncapping power system flexibility. Energy Policy 2016;92:69–82. [6] Cruz MR, Fitiwi DZ, Santos SF, Catalão JPS. A comprehensive survey of flexibility options for supporting the low-carbon energy future. Renew Sustain Energy Rev 2018;97:338–53. [7] Mohammadi A, Rabinia S. A comprehensive study of game theory applications for smart grids, demand side management programs and transportation networks. In: Smart Microgrids 2019, Springer, Cham. p. 57–64. [8] Bahrami S, Wong VW, Huang J. An online learning algorithm for demand response in smart grid. IEEE Trans Smart Grid 2017;9(5):4712–25. [9] Heydarian-Forushani E, Moghaddam MP, Sheikh-El-Eslami MK, Shafie-khah M, Catalão JPS. A stochastic framework for the grid integration of wind power using flexible load approach. Energy Convers Manage 2014;88:985–98. [10] Heydarian-Forushani E, Golshan MEH, Moghaddam MP, Shafie-khah M, Catalão JPS. Robust scheduling of variable wind generation by coordination of bulk energy storages and demand response. Energy Convers Manage 2016;106:941–50. [11] Roos A, Bolkesjø TF. Value of demand flexibility on spot and reserve electricity markets in future power system with increased shares of variable renewable energy. Energy 2018;144:207–17. [12] Goutte S, Vassilopoulos P. The value of flexibility in power markets. Energy Policy 2019;125:347–57. [13] Vahedipour-Dahraei M, Najafi HR, Anvari-Moghaddam A, Guerrero JM. Securityconstrained unit commitment in AC microgrids considering stochastic price-based demand response and renewable generation. Int Trans Electr Energy Syst 2018;28:2596. [14] Vahedipour-Dahraie M, Reza Najafi H, Anvari-Moghaddam A, Guerrero JM. Optimal scheduling of distributed energy resources and responsive loads in islanded microgrids considering voltage and frequency security constraints. J Renew Sustain Energy 2018;10:25903.

6. Conclusions This paper proposed a new flexibility metric to determine the provided flexibility of various DRPs in the day-ahead market clearing procedure. The proposed metric has been developed based on the impacts of each DRP on releasing technical constraints of conventional generation units which are associated with flexibility. To this end, six technical flexibility characteristics of conventional generation units including MSG, OR, MUT, MDT, RU, and RD have chosen to compose the flexibility metric. In addition, a comprehensive set of DRPs modeled and incorporated to day-ahead stochastic energy and reserve market clearing problem in the presence of wind power generation. Simulation results show that the highest flexibility pertains to TOU + EDRP, whilst the lowest flexibility devotes to I/C program which imposes more than 8% additional operation cost. Comparing wind power integration in the two mentioned cases demonstrate that wind power spillage has been reduced by about 58% in the case of TOU + EDRP with higher flexibility measure. The sensitivity analysis also shows that the flexibility metric significantly depends on customer’s behavior including participation level as well as demand elasticity. In this respect, although the lowest flexibility pertained to I/C program, however, it is less sensitive to customer’s behavior. 9

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