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Impact of Microgrid Aggregator on Joint Energy and Reserve Market Based on Pure Strategy Nash Equilibrium
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Energy (2019) 000–000 142–147 EnergyProcedia Procedia159 00 (2017) www.elsevier.com/locate/procedia
Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018, 29–30 September 2018, Rhodes, Greece
Impact of Aggregator Joint Heating Energy Reserve TheMicrogrid 15th International Symposium on on District andand Cooling Market Based on Pure Strategy Nash Equilibrium Assessing the feasibility of using the heat demand-outdoor b Liua, Zhaohong Biea*, Jiangfeng Jianga,heat Ke Wang temperatureFan function for a long-term district demand forecast a State
State Key Laboratory of Electrical Insulation and Power Equipment, Smart Grid Key Laboratory of Shaanxi Province, Xi’an Jiaotong a,b,c a a b c c University, Xi’an 710049, China b China Southern Power Grid Dispatching Control Center, Guangzhou 510663, China a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Abstract
With the coordination of various distributed energy resources, microgrid has the capability to participate energy and reserve market Abstract simultaneously via a microgrid aggregator (MGA). The profit-maximizing offering problem of MGA satisfying a pure strategy Nash equilibrium (NE) is modelled in the paper as a bi-level programming to analyze the impact of MGA on the market equilibrium. heating networks are strategy commonly the literature one the most effective solutions for decreasinginto the ADistrict linearization method for pure NE addressed conditionsin is proposed, and as then theofbi-level problem is equivalently transformed gas emissions from the building systems require high(KKT) investments whichand are returned through the heat mixed integer linear programming (MILP)sector. basedThese on Karush-Kuhn-Tucher conditions strong duality theorem. a greenhouse sales. Dueresults to the changed climate conditionsof and building renovation policies, the futurebycould decrease, the effectiveness proposed method and present marketheat NE demand prices areininfluenced the scalability Numerical demonstrate prolonging the investment return period. and location of integrated MGA. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand ©forecast. 2019 The Authors. Published Ltd. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Copyright © 2018 Elsevier Ltd. by AllElsevier rights reserved. This is an open accessinarticle under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) buildings that vary both construction period andthetypology. weatherofscenarios (low,Energy medium, high) and and threeForum, district Selection and peer-review under responsibility of scientificThree committee the Applied Symposium Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Renewable Energy Integration with REM 2018. Renewable Energy Integration withMini/Microgrids, Mini/Microgrids, REM 2018. compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showedaggregator; that whenJoint only weather changemarket; is considered, the Nash margin of error could beoffering; acceptable for some applications Microgrid energy and reserve Pure strategy equilibrium; Strategic Bi-level programming Keywords: (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.The Introduction decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Microgrid (MG) has been well developed as an important part of Smart Grid and effectively integrates distributed coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and energy resources (DERs), energy storage system and flexible loads to improve efficiency, economics, and resiliency. improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-29-8266-8655; fax: +86-29-8266-5489. E-mail address: [email protected] Keywords: Heat demand; Forecast; Climate change
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 10.1016/j.egypro.2018.12.032
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Fan Liu et al. / Energy Procedia 159 (2019) 142–147 Fan Liu, Zhaohong Bie, et al. / Energy Procedia 00 (2018) 000–000
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The major power supply of MG is distributed generation including renewable energy resources with advantages of low cost, low voltage and low emission. Considering the feasibility of islanded mode and renewable uncertainties, MG is generally deployed with more generation capacity than its average consumption [1], creating an opportunity to trade the energy surplus at a lower price in grid-connected mode. Moreover, with the use of fast-responsive resources such as micro turbines, fuel cells, energy storage and demand response, MG also has great potential for providing ancillary services to the utility grid [2]. However, the direct involvement of individual MGs in the prevailing electricity market is impracticable due to the scalability problem, and MG aggregator (MGA) is introduced in [3] to coordinate the MGs within the distribution networks and facilitate their market participation. As an emerging marketer, MGA has aroused a great concern from researchers and stakeholders, especially for its strategic behavior. A risk-constrained stochastic programming was proposed in [4] to maximize the profit of MGA with demand response where MGA was assumed as a price-taker for which only the hourly power bid quantities were optimally determined. Nevertheless, MGA can further play a more active role in the electricity market by the optimal offering strategy. Based on the concept of MGA, a two-stage market framework to involve MGs in real-time power transaction was introduced in [5] and a robust bidding strategy for MGA was presented to guarantee the profits of both MGA and individual MG. [6] modelled a two-stage Stackelberg game for the market where MG transacted power via MGA and showed the dependence of MGA’s profit on the cost function of MGs. While early researches addressed the MGA integration in a single energy market, there is no prior effort on the strategic offering of MGA in the joint energy and reserve market which is beneficial for minimizing overall cost and strengthening system reliability [7]. In [8], the strategic behavior of a distribution company to manage DERs was formulated as a bi-level optimization problem, which is helpful for MGA modelling. Besides, previous researches mainly focused on strategic offering from MGA’s perspective which also affects the electricity market Nash equilibrium (NE) and needs to be further considered. In this paper, a profit-maximizing offering problem of MGA based on a pure strategy NE is proposed to analyze the impact of MGA on the joint energy and reserve market. The main contributions are threefold: 1) modelling a bilevel programming for the strategic offering of MGA which can trade both energy and ancillary services; 2) improving the pure strategy NE conditions described in [9] to satisfy the pricing mechanism of joint energy and reserve market with a novel linearization method; 3) evaluating the impact of MGA on market equilibrium from perspectives of different scalabilities and locations. The rest of the paper is organized as following: Section 2 presents the problem formulation subject to the introduced market rules and assumptions; Section 3 proposes the solution methodology; numerical cases and conclusions are drawn in Section 4 and Section 5, respectively. Nomenclature
bMGA,e , bMGA, r
energy and reserve offer prices of block b for MGA awarded power and reserve of block b for MGA PbMGA , RbMGA Pi ,Gb , RiG,b awarded power and reserve of block b for generator i MGA ,e , MGA ,r locational marginal price (LMP) of energy and market clearing price (MCP) of reserve for MGA X , H Market , G Market primal variables, equality constraints and inequality constraints of the market clearing problem , dual variables of equality constraints and inequality constraints binary variables x, y ciG,b,e , ciG , r energy marginal cost of block b and reserve marginal cost for generator i energy and reserve marginal cost of block b for MGA cbMGA,e , cbMGA,r price caps of energy and reserve e, r load at bus n, system reserve capacity requirement, ramp rate of generator i Ln , D r , riG Pi G , Pi G , Pi ,Gb min and max power capacity of generator i, max power capacity of block b for generator i P MGA , PbMGA , RbMGA max power capacity of MGA, max power and reserve capacity of block b for MGA min and max power flow of transmission line k Fk , Fk T power transmission distribution factor (PTDF) matrix 2. Mathematical Formulation Before formulating the proposed problem, the market rules and assumptions are introduced. The joint energy and
Fan Liu et al. / Energy Procedia 159 (2019) 142–147 Fan Liu, Zhaohong Bie, et al. / Energy Procedia 00 (2018) 000–000
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3
reserve market with MGA integration is designed based on the settlement mechanism of locational marginal price (LMP) for energy and uniform market clearing price (MCP) for reserve. Generators are conventional market players and required to submit multi-block energy offers and single-block reserve offers. MGA is an emerging player to connect MGs and the wholesale market. Generally, MGs submit their surplus capacity of energy and reserve with marginal costs or power demand to MGA while MGA coordinates the various resources of MGs, gives a priority to meet MGs’ demand and generate its multi-block supply functions of both energy and reserve. The main assumptions are as follows: 1) the demand is known and inelastic; 2) the DC power flow is adopted with the neglect of power loss and voltage limits; 3) MGA is gaming in the wholesale market, and operational constraints of MGs and relevant distribution network are ignored; 4) spinning reserve is typically concerned in this paper. 2.1. Modelling the clearing problem of joint energy and reserve market Energy and reserve are procured simultaneously and the objective function of market clearing problem in (1) is to minimize the total cost of energy and reserve based on their offer prices. To analyze the impact of integrated MGA on market equilibrium, all generators are assumed not strategic and submit offers based on their true marginal costs. The active power balance and system reserve requirement are satisfied in (2). The capacity limits of generators are presented in (3)-(4) where the awarded reserve is limited by its ramping capability within 10-min response time. Similarly, the capacity limits of awarded energy and reserve for MGA are described in (5)-(6). The power flow of transmission lines is bounded by their finite capacities in (7).
min
PbMGA , RbMGA , PiG,b , RiG
s.t.
n
QMarket
b
bMGA,e PbMGA b bMGA,r RbMGA i b ciG,b,e Pi G,b i ciG,r RiG
G G Ln b PbMGA i b Pi 0 ( e ); D r b RbMGA i Ri 0 ( r ) ,b
Pi G b Pi ,Gb , i ( iG );
0 P P , i, b (
,
G i ,b
b
G i ,b
G ,e i ,b
b
(2)
Pi ,Gb RiG Pi G , i ( iG )
G ,e i ,b
(3)
); 0 R 10 ri , i ( G i
G
G,r i
,
G,r i
(4)
)
PbMGA b RbMGA P MGA ( MGA, sum ) MGA b
0P
MGA b
P
, b (
MGA, e b
Fk i b T P b T G G ki i , b
,
MGA, e b
MGA MGA k b
P
(1)
(5) MGA b
); 0 R
MGA b
R
, b (
MGA, r b
,
MGA, r b
)
n Tkn Ln Fk , k ( k , k )
(6) (7)
2.2. Modelling the strategic offering problem of MGA MGA participates in the energy and reserve market jointly and tries to achieve the maximum profit by its strategic offers. The profit-maximizing objective function of MGA is shown in (8) where the first two terms are the revenue of awarded energy and reserve and the last two terms are the energy and reserve cost related to MGs’ resources within the MGA. The number of blocks and the power quantity of each block for MGA are fixed while offer prices of energy and reserve are decision variables which are monotonically non-decreasing for multiple blocks shown in (9). Moreover, offer prices are considered not less than their marginal costs and not more than the price cap in (10). The strategic offering problem of MGA in (8)-(10) depends on the LMP and MCP defined in (11), which are dual variables of the market clearing problem in (1)-(7) while the market clearing problem depends on the offer prices of MGA, which are primal variables of the strategic offering problem. Thus, a typical bi-level programming is modelled where strategic offering problem of MGA is the upper-level problem and market clearing problem is the lower-level problem. max
bMGA,e , bMGA,r , PbMGA , RbMGA
QMGA b MGA,e PbMGA +b MGA,r RbMGA b cbMGA,e PbMGA b cbMGA,r RbMGA
,e ,r s.t. bMGA,e bMGA , b 2; bMGA, r bMGA , b 2 1 1 MGA, e b
c
MGA, e
MGA, e b
, b; c e
k k H e
MGA, r b
MGA k
MGA, r b
k k H
MGA k
(9)
, b
;
r
MGA, r
(8)
(10) r
(11)
4
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2.3. Modelling the necessary conditions of pure strategy Nash equilibrium When market players game through a multi-block supply function, a pure strategy NE is existing with some necessary conditions. The pure strategy NE offers of a single player was proposed in [9] for energy market cleared by MCP, and then we develop necessary conditions of the pure strategy NE to be suitable for joint energy and reserve market cleared by LMP and MCP, respectively. To analyze the impact of MGA on the market equilibrium satisfying a pure strategy NE, the block offers of MGA are decided according to the following strategy (12).
bMGA,e
MGA cbMGA,e , PbMGA P cbMGA, r , RbMGA RbMGA b c MGA,e , P MGA 0 and MGA,e c MGA,e c MGA, r , R MGA 0 and MGA, r c MGA, r MGA, r b b b b b b ; MGA, r b MGA, r MGA, r ,b MGA, e MGA MGA, e MGA, e MGA P c R , 0 and , 0 an d c b b b b MGA, r MGA, e , 0 PbMGA PbMGA , 0 RbMGA RbMGA
(12)
3. Solution Methodology 3.1. Linearization of the bi-level programming The lower-level market clearing problem is formulated linearly, so it is equivalently replaced by its Karush-KuhnTucher (KKT) optimality conditions to transform the bi-level problem into a mathematical program with equilibrium constraints (MPEC) [10]. The Lagrangian function of market clearing problem is formulated in (13) with its KKT conditions (14)-(17) including first order derivatives of (13) with respect to its primal decision variables in (14), primal equality constraints (15), primal inequality constraints (16) and complementarity conditions (17). Complementarity conditions are nonlinear and constraints (16)-(17) can be reformulated into the linear forms of (18) by the use of Big M method and introduced binary variables x. The first two terms of profit-maximizing objective function (8) are other nonlinear components of MPEC. Based on complementarity conditions (17) and strong duality theorem, the nonlinear equation (8) can be equivalently linearized as (19).
LMarket QMarket ( X ) λT H Market ( X ) μT G Market ( X )
(13)
Market
L / X 0 H Market ( X ) 0
(14) (15)
G Market ( X ) 0
(16)
0 μ G
Market
M x G
( X ) 0, μ 0 X 0, 0 μ M 1 x , x 0,1
(17)
Market
(18)
Q MGA i b ciG,b,e Pi ,Gb i ciG , r RiG + n Ln e D r r i Pi G iG i Pi G iG i b Pi ,Gb iG,b,e
i 10 riG iG , r k Fk + n Tkn Ln k k Fk + n Tkn Ln k b cbMGA,e PbMGA b cbMGA, r RbMGA
(19)
3.2. Linearization of the pure strategy NE conditions The complementarity constraints of (6) are linearized as (18) and explicitly presented in (20)-(21) where the binary variables xbMGA reflect whether the block b is marginal or non-marginal. If xbMGA 0 and xbMGA 1 , X bMGA X bMGA (nonmarginal block); if xbMGA 1 and xbMGA 0 , X bMGA 0 (non-marginal block); if xbMGA 1 and xbMGA 1 , 0 X bMGA X bMGA (marginal block). Since one player may own a single marginal block or all non-marginal blocks, binary variables xbMGA are constrained in (22) where Nb is the number of blocks. Hence, MGA offers based on the pure strategy NE conditions in (12) are reformulated into linear constraints (23)-(26) according to Big M method and binary variables ybMGA which are introduced to compare the values of marginal costs and market prices for both energy and reserve.
M xbMGA X bMGA 0,0 bMGA M 1 xbMGA , X bMGA {PbMGA , RbMGA }, bMGA {bMGA.e , bMGA,r }, b
(20)
Fan Liu et al. / Energy Procedia 159 (2019) 142–147 Fan Liu, Zhaohong Bie, et al. / Energy Procedia 00 (2018) 000–000
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5
M xbMGA X bMGA X bMGA 0, 0 bMGA M 1 xbMGA , bMGA {bMGA,e , bMGA, r }, b
(21)
(22)
b
MGA b
x
0
MGA b
b x
MGA b
c
MGA b
M y
MGA b
Nb 1 MGA b
M x
MGA
MGA b
c
,
MGA b
{
MGA, e b
MGA b
M (1 y
),
c M (1 y ), MGA MGA MGA MGA b M (2 xb xb ), b MGA b
MGA b
MGA b
MGA b
,
MGA
MGA, r b
MGA
MGA b
}, c
{
MGA,e
MGA b
My
MGA, e b
{c ,
MGA,e
MGA b
,y
MGA, r b
,c
MGA b
}, y
(23)
}, b
(24)
{0,1}, b
(25)
{0,1}, b
(26)
Consequently, the MPEC for profit-maximizing problem of MGA supported by the pure strategy NE is finally transformed into an equivalent MILP as following: max QMGA presented in (19) s.t. constraints (9)-(10), (14)-(15), (18), (22)-(26) 4. Numerical Cases The optimal offering of MGA based on the pure strategy NE in joint energy and reserve market is analyzed on an IEEE 30-bus power system with 6 generators and 1 MGA to demonstrate the effectiveness of proposed MILP model. The system load is 189.2 MW and the reserve requirement is set as 8% system load. Energy and reserve offers of generators are shown in Table 1, including the capacity limits, ramp rates and marginal costs. The multi-block supply functions of MGA are derived from MGs’ resources and presented as [6, 8, 6] MW energy blocks with marginal costs of [0, 12, 18] $/MWh and [4, 4, 2] MW reserve blocks with marginal costs of [4.7, 5.5, 7] $/MW. Several cases are designed to evaluate the impact of MGA as following: 1) non-strategic MGA integrated at bus 7 with base quantity of blocks; 2) strategic MGA at bus 7 with base quantity; 3) strategic MGA at bus 7 with half quantity; 4) strategic MGA at bus 7 with twice quantity; 5) strategic MGA at bus 30 with twice quantity. Table 1. Energy and reserve offers of generators. Generator no.
Min (MW)
Max (MW)
Ramp rate (MW/min)
G1 (at bus 01) G2 (at bus 02) G3 (at bus 22) G4 (at bus 27) G5 (at bus 17) G6 (at bus 13)
0 0 0 0 0 0
80 80 50 55 30 40
4 4 2.5 2.5 1.5 1.5
Energy offer Block 1 Cost ($/MWh) 12 13 15 16 17 19
Max (MW) 40 45 30 35 20 25
Block 2 Cost ($/MWh) 21 22 23 24 27 28
Reserve offer Max (MW) 40 35 20 20 10 15
Cost ($/MW) 5.5 5 6.5 6 9 10
Table 2. Strategic offers and market clearing results of MGA. Case no. Case 1 Case 2 Case 3 Case 4 Case 5
Energy offer ($/MWh) [0, 12, 18] [0, 12, 19] [0, 12, 18] [0, 12, 18] [0, 12, 18]
LMP ($/MWh) 18.3 19 19 17 16
Awarded energy (MWh) 19.2 19.2 10 28 28
Energy profit ($) 351.36 364.8 190 476 448
Reserve offer ($/MW) [4.7, 5.5, 7] [5, 5.5, 7] [5, 5.5, 7] [4.7, 5.5, 7] [4.7, 5.5, 7]
MCP ($/MW) 5 5 5 5 5
Awarded reserve (MW) 0.8 0.8 0 8 8
Reserve profit ($) 4 4 0 40 40
Strategic offers and market clearing results of MGA are shown in Table 2 and energy clearing results of generators in Table 3 where Energya refers to awarded energy. The awarded reserve of generators for Cases 1-5 are fully procured from G2 as [14.336, 14.336, 15.136, 7.136, 7.136] MW. In Case 1, MGA participates the joint energy and reserve market by the non-strategic offers of marginal costs and the capacity is fully scheduled. The opportunity cost 0.3 $/MW is incurred to MGA for providing reserve which equals to the LMP minus MGA’s energy offer of the last block. Compared to Case 1, the energy offers of MGA in Case 2 are strategically decided as [0, 12, 19] $/MWh, leading to a higher LMP with a greater energy profit. For Cases 3, 2, and 4, the capacity scale of MGA is sequentially increasing and presents different impacts on market equilibrium. The smaller-scale MGA in Case 3 offers at marginal costs and has no capability to influence the market NE energy price because the marginal generator is G6. The larger-scale
6
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147
MGA in Case 4 also offers at marginal costs, but it effectively decreases the market NE energy price due to sufficient capacity of cheaper energy. For Cases 2-4, block quantity of cheaper reserve at 4.7 $/MW is inadequate to meet the system reserve requirement, so MGA cannot change the market NE reserve price by its strategic offers. When MGA is integrated in bus 7, LMPs of different buses are identical due to uncongested transmission shown in Cases 1-4. However, for Case 5, transmission congestion is caused by the location of MGA integrated in bus 30, which leads to a limited dispatch of cheaper G4 and a lower LMP for MGA. Table 3. Energy clearing results of generators. Generator no. G1 G2 G3 G4 G5 G6
Case 1 Energya (MWh) 40 45 30 35 20 0
LMP ($/MWh) 18.3 18.3 18.3 18.3 18.3 18.3
Case2 Energya (MWh) 40 45 30 35 20 0
LMP ($/MWh) 19 19 19 19 19 19
Case 3 Energya (MWh) 40 45 30 35 20 9.2
LMP ($/MWh) 19 19 19 19 19 19
Case 4 Energya (MWh) 40 45 30 35 11.2 0
LMP ($/MWh) 17 17 17 17 17 17
Case 5 Energya (MWh) 40 45 30 19.2 20 7
LMP ($/MWh) 18.47 18.46 19.33 16 19.52 19
5. Conclusion The strategic offering of MGA satisfying the pure strategy NE was modelled in the joint energy and reserve market which was a bi-level programming. The lower-level market clearing problem was replaced by its KKT optimality conditions to transform the bi-level model into a MPEC. Considering the settlement mechanism of LMP for energy and MCP for reserve, the pure strategy NE conditions were improved and a linearization approach was proposed to address the nonconvexity. Then, the MPEC was equivalently reformulated as a MILP based on Big M method and strong duality theorem. The proposed model was performed on an IEEE 30-bus power system and the impacts of MGA on the joint energy and reserve market were concluded as following: 1) MGA effectively raised its profit by the use of strategic offers; 2) when the capacity scale is small, MGA had no influence on market NE prices and acted as a price-taker; 3) with the increasing scalability, MGA presented the capability to change market NE prices; 4) market NE prices are sensitive to the location of MGA due to the potential transmission congestion. Acknowledgements This work was supported by National Key Research and Development Program of China (2016YFB0901900) and National Natural Science Foundation of China (51637008). References [1]
Yazdani-Damavandi M, Neyestani N, Shafie-Khah M, et al. Strategic behavior of multi-energy players in electricity markets as aggregators of demand side resources using a bi-level approach. J IEEE Trans. Power Syst. 2018; 33(1): 397-411. [2] Majzoobi A, Khodaei A. Application of microgrids in providing ancillary services to the utility grid. J Energy. 2017; 123: 555-63. [3] Sardou I G, Khodayar M E, Khaledian K, et al. Energy and reserve market clearing with microgrid aggregators. J IEEE Trans. Smart Grid. 2016; 7(6): 2703-12. [4] Nguyen D T, Le L B. Risk-constrained profit maximization for microgrid aggregators with demand response. J IEEE Trans. Smart Grid. 2015; 6(1): 135-46. [5] Pei W, Du Y, Deng W, et al. Optimal bidding strategy and intramarket mechanism of microgrid aggregator in real-time balancing market. J IEEE Trans. Ind. Informat. 2016; 12(2): 587-96. [6] Kim H, Thottan M. A two-stage market model for microgrid power transactions via aggregators. J Bell Labs Tech J. 2011; 16(3): 101-8. [7] Wu T, Rothleder M, Alaywan Z, et al. Pricing energy and ancillary services in integrated market systems by an optimal power flow. J IEEE Trans. Power Syst. 2004; 19(1): 339-47. [8] Bahramara S, Yazdani-Damavandi M, Contreras J, et al. Modeling the strategic behavior of a distribution company in wholesale energy and reserve markets. J IEEE Trans. Smart Grid. 2018; 9(4): 3857-70. [9] Hasan E, Galiana F D, Conejo A J. Electricity markets cleared by merit order—Part I: Finding the market outcomes supported by pure strategy Nash equilibria. J IEEE Trans. Power Syst. 2008, 23(2): 361-71. [10] Gabriel S A, Conejo A J, Fuller J D, et al. Complementarity Modeling in Energy Markets. New York: Springer; 2013.
ScienceDirect Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2018) 000–000
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www.elsevier.com/locate/procedia
Energy (2019) 000–000 142–147 EnergyProcedia Procedia159 00 (2017) www.elsevier.com/locate/procedia
Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018, 29–30 September 2018, Rhodes, Greece
Impact of Aggregator Joint Heating Energy Reserve TheMicrogrid 15th International Symposium on on District andand Cooling Market Based on Pure Strategy Nash Equilibrium Assessing the feasibility of using the heat demand-outdoor b Liua, Zhaohong Biea*, Jiangfeng Jianga,heat Ke Wang temperatureFan function for a long-term district demand forecast a State
State Key Laboratory of Electrical Insulation and Power Equipment, Smart Grid Key Laboratory of Shaanxi Province, Xi’an Jiaotong a,b,c a a b c c University, Xi’an 710049, China b China Southern Power Grid Dispatching Control Center, Guangzhou 510663, China a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Abstract
With the coordination of various distributed energy resources, microgrid has the capability to participate energy and reserve market Abstract simultaneously via a microgrid aggregator (MGA). The profit-maximizing offering problem of MGA satisfying a pure strategy Nash equilibrium (NE) is modelled in the paper as a bi-level programming to analyze the impact of MGA on the market equilibrium. heating networks are strategy commonly the literature one the most effective solutions for decreasinginto the ADistrict linearization method for pure NE addressed conditionsin is proposed, and as then theofbi-level problem is equivalently transformed gas emissions from the building systems require high(KKT) investments whichand are returned through the heat mixed integer linear programming (MILP)sector. basedThese on Karush-Kuhn-Tucher conditions strong duality theorem. a greenhouse sales. Dueresults to the changed climate conditionsof and building renovation policies, the futurebycould decrease, the effectiveness proposed method and present marketheat NE demand prices areininfluenced the scalability Numerical demonstrate prolonging the investment return period. and location of integrated MGA. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand ©forecast. 2019 The Authors. Published Ltd. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Copyright © 2018 Elsevier Ltd. by AllElsevier rights reserved. This is an open accessinarticle under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) buildings that vary both construction period andthetypology. weatherofscenarios (low,Energy medium, high) and and threeForum, district Selection and peer-review under responsibility of scientificThree committee the Applied Symposium Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Renewable Energy Integration with REM 2018. Renewable Energy Integration withMini/Microgrids, Mini/Microgrids, REM 2018. compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showedaggregator; that whenJoint only weather changemarket; is considered, the Nash margin of error could beoffering; acceptable for some applications Microgrid energy and reserve Pure strategy equilibrium; Strategic Bi-level programming Keywords: (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.The Introduction decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Microgrid (MG) has been well developed as an important part of Smart Grid and effectively integrates distributed coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and energy resources (DERs), energy storage system and flexible loads to improve efficiency, economics, and resiliency. improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-29-8266-8655; fax: +86-29-8266-5489. E-mail address: [email protected] Keywords: Heat demand; Forecast; Climate change
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 10.1016/j.egypro.2018.12.032
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The major power supply of MG is distributed generation including renewable energy resources with advantages of low cost, low voltage and low emission. Considering the feasibility of islanded mode and renewable uncertainties, MG is generally deployed with more generation capacity than its average consumption [1], creating an opportunity to trade the energy surplus at a lower price in grid-connected mode. Moreover, with the use of fast-responsive resources such as micro turbines, fuel cells, energy storage and demand response, MG also has great potential for providing ancillary services to the utility grid [2]. However, the direct involvement of individual MGs in the prevailing electricity market is impracticable due to the scalability problem, and MG aggregator (MGA) is introduced in [3] to coordinate the MGs within the distribution networks and facilitate their market participation. As an emerging marketer, MGA has aroused a great concern from researchers and stakeholders, especially for its strategic behavior. A risk-constrained stochastic programming was proposed in [4] to maximize the profit of MGA with demand response where MGA was assumed as a price-taker for which only the hourly power bid quantities were optimally determined. Nevertheless, MGA can further play a more active role in the electricity market by the optimal offering strategy. Based on the concept of MGA, a two-stage market framework to involve MGs in real-time power transaction was introduced in [5] and a robust bidding strategy for MGA was presented to guarantee the profits of both MGA and individual MG. [6] modelled a two-stage Stackelberg game for the market where MG transacted power via MGA and showed the dependence of MGA’s profit on the cost function of MGs. While early researches addressed the MGA integration in a single energy market, there is no prior effort on the strategic offering of MGA in the joint energy and reserve market which is beneficial for minimizing overall cost and strengthening system reliability [7]. In [8], the strategic behavior of a distribution company to manage DERs was formulated as a bi-level optimization problem, which is helpful for MGA modelling. Besides, previous researches mainly focused on strategic offering from MGA’s perspective which also affects the electricity market Nash equilibrium (NE) and needs to be further considered. In this paper, a profit-maximizing offering problem of MGA based on a pure strategy NE is proposed to analyze the impact of MGA on the joint energy and reserve market. The main contributions are threefold: 1) modelling a bilevel programming for the strategic offering of MGA which can trade both energy and ancillary services; 2) improving the pure strategy NE conditions described in [9] to satisfy the pricing mechanism of joint energy and reserve market with a novel linearization method; 3) evaluating the impact of MGA on market equilibrium from perspectives of different scalabilities and locations. The rest of the paper is organized as following: Section 2 presents the problem formulation subject to the introduced market rules and assumptions; Section 3 proposes the solution methodology; numerical cases and conclusions are drawn in Section 4 and Section 5, respectively. Nomenclature
bMGA,e , bMGA, r
energy and reserve offer prices of block b for MGA awarded power and reserve of block b for MGA PbMGA , RbMGA Pi ,Gb , RiG,b awarded power and reserve of block b for generator i MGA ,e , MGA ,r locational marginal price (LMP) of energy and market clearing price (MCP) of reserve for MGA X , H Market , G Market primal variables, equality constraints and inequality constraints of the market clearing problem , dual variables of equality constraints and inequality constraints binary variables x, y ciG,b,e , ciG , r energy marginal cost of block b and reserve marginal cost for generator i energy and reserve marginal cost of block b for MGA cbMGA,e , cbMGA,r price caps of energy and reserve e, r load at bus n, system reserve capacity requirement, ramp rate of generator i Ln , D r , riG Pi G , Pi G , Pi ,Gb min and max power capacity of generator i, max power capacity of block b for generator i P MGA , PbMGA , RbMGA max power capacity of MGA, max power and reserve capacity of block b for MGA min and max power flow of transmission line k Fk , Fk T power transmission distribution factor (PTDF) matrix 2. Mathematical Formulation Before formulating the proposed problem, the market rules and assumptions are introduced. The joint energy and
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3
reserve market with MGA integration is designed based on the settlement mechanism of locational marginal price (LMP) for energy and uniform market clearing price (MCP) for reserve. Generators are conventional market players and required to submit multi-block energy offers and single-block reserve offers. MGA is an emerging player to connect MGs and the wholesale market. Generally, MGs submit their surplus capacity of energy and reserve with marginal costs or power demand to MGA while MGA coordinates the various resources of MGs, gives a priority to meet MGs’ demand and generate its multi-block supply functions of both energy and reserve. The main assumptions are as follows: 1) the demand is known and inelastic; 2) the DC power flow is adopted with the neglect of power loss and voltage limits; 3) MGA is gaming in the wholesale market, and operational constraints of MGs and relevant distribution network are ignored; 4) spinning reserve is typically concerned in this paper. 2.1. Modelling the clearing problem of joint energy and reserve market Energy and reserve are procured simultaneously and the objective function of market clearing problem in (1) is to minimize the total cost of energy and reserve based on their offer prices. To analyze the impact of integrated MGA on market equilibrium, all generators are assumed not strategic and submit offers based on their true marginal costs. The active power balance and system reserve requirement are satisfied in (2). The capacity limits of generators are presented in (3)-(4) where the awarded reserve is limited by its ramping capability within 10-min response time. Similarly, the capacity limits of awarded energy and reserve for MGA are described in (5)-(6). The power flow of transmission lines is bounded by their finite capacities in (7).
min
PbMGA , RbMGA , PiG,b , RiG
s.t.
n
QMarket
b
bMGA,e PbMGA b bMGA,r RbMGA i b ciG,b,e Pi G,b i ciG,r RiG
G G Ln b PbMGA i b Pi 0 ( e ); D r b RbMGA i Ri 0 ( r ) ,b
Pi G b Pi ,Gb , i ( iG );
0 P P , i, b (
,
G i ,b
b
G i ,b
G ,e i ,b
b
(2)
Pi ,Gb RiG Pi G , i ( iG )
G ,e i ,b
(3)
); 0 R 10 ri , i ( G i
G
G,r i
,
G,r i
(4)
)
PbMGA b RbMGA P MGA ( MGA, sum ) MGA b
0P
MGA b
P
, b (
MGA, e b
Fk i b T P b T G G ki i , b
,
MGA, e b
MGA MGA k b
P
(1)
(5) MGA b
); 0 R
MGA b
R
, b (
MGA, r b
,
MGA, r b
)
n Tkn Ln Fk , k ( k , k )
(6) (7)
2.2. Modelling the strategic offering problem of MGA MGA participates in the energy and reserve market jointly and tries to achieve the maximum profit by its strategic offers. The profit-maximizing objective function of MGA is shown in (8) where the first two terms are the revenue of awarded energy and reserve and the last two terms are the energy and reserve cost related to MGs’ resources within the MGA. The number of blocks and the power quantity of each block for MGA are fixed while offer prices of energy and reserve are decision variables which are monotonically non-decreasing for multiple blocks shown in (9). Moreover, offer prices are considered not less than their marginal costs and not more than the price cap in (10). The strategic offering problem of MGA in (8)-(10) depends on the LMP and MCP defined in (11), which are dual variables of the market clearing problem in (1)-(7) while the market clearing problem depends on the offer prices of MGA, which are primal variables of the strategic offering problem. Thus, a typical bi-level programming is modelled where strategic offering problem of MGA is the upper-level problem and market clearing problem is the lower-level problem. max
bMGA,e , bMGA,r , PbMGA , RbMGA
QMGA b MGA,e PbMGA +b MGA,r RbMGA b cbMGA,e PbMGA b cbMGA,r RbMGA
,e ,r s.t. bMGA,e bMGA , b 2; bMGA, r bMGA , b 2 1 1 MGA, e b
c
MGA, e
MGA, e b
, b; c e
k k H e
MGA, r b
MGA k
MGA, r b
k k H
MGA k
(9)
, b
;
r
MGA, r
(8)
(10) r
(11)
4
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2.3. Modelling the necessary conditions of pure strategy Nash equilibrium When market players game through a multi-block supply function, a pure strategy NE is existing with some necessary conditions. The pure strategy NE offers of a single player was proposed in [9] for energy market cleared by MCP, and then we develop necessary conditions of the pure strategy NE to be suitable for joint energy and reserve market cleared by LMP and MCP, respectively. To analyze the impact of MGA on the market equilibrium satisfying a pure strategy NE, the block offers of MGA are decided according to the following strategy (12).
bMGA,e
MGA cbMGA,e , PbMGA P cbMGA, r , RbMGA RbMGA b c MGA,e , P MGA 0 and MGA,e c MGA,e c MGA, r , R MGA 0 and MGA, r c MGA, r MGA, r b b b b b b ; MGA, r b MGA, r MGA, r ,b MGA, e MGA MGA, e MGA, e MGA P c R , 0 and , 0 an d c b b b b MGA, r MGA, e , 0 PbMGA PbMGA , 0 RbMGA RbMGA
(12)
3. Solution Methodology 3.1. Linearization of the bi-level programming The lower-level market clearing problem is formulated linearly, so it is equivalently replaced by its Karush-KuhnTucher (KKT) optimality conditions to transform the bi-level problem into a mathematical program with equilibrium constraints (MPEC) [10]. The Lagrangian function of market clearing problem is formulated in (13) with its KKT conditions (14)-(17) including first order derivatives of (13) with respect to its primal decision variables in (14), primal equality constraints (15), primal inequality constraints (16) and complementarity conditions (17). Complementarity conditions are nonlinear and constraints (16)-(17) can be reformulated into the linear forms of (18) by the use of Big M method and introduced binary variables x. The first two terms of profit-maximizing objective function (8) are other nonlinear components of MPEC. Based on complementarity conditions (17) and strong duality theorem, the nonlinear equation (8) can be equivalently linearized as (19).
LMarket QMarket ( X ) λT H Market ( X ) μT G Market ( X )
(13)
Market
L / X 0 H Market ( X ) 0
(14) (15)
G Market ( X ) 0
(16)
0 μ G
Market
M x G
( X ) 0, μ 0 X 0, 0 μ M 1 x , x 0,1
(17)
Market
(18)
Q MGA i b ciG,b,e Pi ,Gb i ciG , r RiG + n Ln e D r r i Pi G iG i Pi G iG i b Pi ,Gb iG,b,e
i 10 riG iG , r k Fk + n Tkn Ln k k Fk + n Tkn Ln k b cbMGA,e PbMGA b cbMGA, r RbMGA
(19)
3.2. Linearization of the pure strategy NE conditions The complementarity constraints of (6) are linearized as (18) and explicitly presented in (20)-(21) where the binary variables xbMGA reflect whether the block b is marginal or non-marginal. If xbMGA 0 and xbMGA 1 , X bMGA X bMGA (nonmarginal block); if xbMGA 1 and xbMGA 0 , X bMGA 0 (non-marginal block); if xbMGA 1 and xbMGA 1 , 0 X bMGA X bMGA (marginal block). Since one player may own a single marginal block or all non-marginal blocks, binary variables xbMGA are constrained in (22) where Nb is the number of blocks. Hence, MGA offers based on the pure strategy NE conditions in (12) are reformulated into linear constraints (23)-(26) according to Big M method and binary variables ybMGA which are introduced to compare the values of marginal costs and market prices for both energy and reserve.
M xbMGA X bMGA 0,0 bMGA M 1 xbMGA , X bMGA {PbMGA , RbMGA }, bMGA {bMGA.e , bMGA,r }, b
(20)
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M xbMGA X bMGA X bMGA 0, 0 bMGA M 1 xbMGA , bMGA {bMGA,e , bMGA, r }, b
(21)
(22)
b
MGA b
x
0
MGA b
b x
MGA b
c
MGA b
M y
MGA b
Nb 1 MGA b
M x
MGA
MGA b
c
,
MGA b
{
MGA, e b
MGA b
M (1 y
),
c M (1 y ), MGA MGA MGA MGA b M (2 xb xb ), b MGA b
MGA b
MGA b
MGA b
,
MGA
MGA, r b
MGA
MGA b
}, c
{
MGA,e
MGA b
My
MGA, e b
{c ,
MGA,e
MGA b
,y
MGA, r b
,c
MGA b
}, y
(23)
}, b
(24)
{0,1}, b
(25)
{0,1}, b
(26)
Consequently, the MPEC for profit-maximizing problem of MGA supported by the pure strategy NE is finally transformed into an equivalent MILP as following: max QMGA presented in (19) s.t. constraints (9)-(10), (14)-(15), (18), (22)-(26) 4. Numerical Cases The optimal offering of MGA based on the pure strategy NE in joint energy and reserve market is analyzed on an IEEE 30-bus power system with 6 generators and 1 MGA to demonstrate the effectiveness of proposed MILP model. The system load is 189.2 MW and the reserve requirement is set as 8% system load. Energy and reserve offers of generators are shown in Table 1, including the capacity limits, ramp rates and marginal costs. The multi-block supply functions of MGA are derived from MGs’ resources and presented as [6, 8, 6] MW energy blocks with marginal costs of [0, 12, 18] $/MWh and [4, 4, 2] MW reserve blocks with marginal costs of [4.7, 5.5, 7] $/MW. Several cases are designed to evaluate the impact of MGA as following: 1) non-strategic MGA integrated at bus 7 with base quantity of blocks; 2) strategic MGA at bus 7 with base quantity; 3) strategic MGA at bus 7 with half quantity; 4) strategic MGA at bus 7 with twice quantity; 5) strategic MGA at bus 30 with twice quantity. Table 1. Energy and reserve offers of generators. Generator no.
Min (MW)
Max (MW)
Ramp rate (MW/min)
G1 (at bus 01) G2 (at bus 02) G3 (at bus 22) G4 (at bus 27) G5 (at bus 17) G6 (at bus 13)
0 0 0 0 0 0
80 80 50 55 30 40
4 4 2.5 2.5 1.5 1.5
Energy offer Block 1 Cost ($/MWh) 12 13 15 16 17 19
Max (MW) 40 45 30 35 20 25
Block 2 Cost ($/MWh) 21 22 23 24 27 28
Reserve offer Max (MW) 40 35 20 20 10 15
Cost ($/MW) 5.5 5 6.5 6 9 10
Table 2. Strategic offers and market clearing results of MGA. Case no. Case 1 Case 2 Case 3 Case 4 Case 5
Energy offer ($/MWh) [0, 12, 18] [0, 12, 19] [0, 12, 18] [0, 12, 18] [0, 12, 18]
LMP ($/MWh) 18.3 19 19 17 16
Awarded energy (MWh) 19.2 19.2 10 28 28
Energy profit ($) 351.36 364.8 190 476 448
Reserve offer ($/MW) [4.7, 5.5, 7] [5, 5.5, 7] [5, 5.5, 7] [4.7, 5.5, 7] [4.7, 5.5, 7]
MCP ($/MW) 5 5 5 5 5
Awarded reserve (MW) 0.8 0.8 0 8 8
Reserve profit ($) 4 4 0 40 40
Strategic offers and market clearing results of MGA are shown in Table 2 and energy clearing results of generators in Table 3 where Energya refers to awarded energy. The awarded reserve of generators for Cases 1-5 are fully procured from G2 as [14.336, 14.336, 15.136, 7.136, 7.136] MW. In Case 1, MGA participates the joint energy and reserve market by the non-strategic offers of marginal costs and the capacity is fully scheduled. The opportunity cost 0.3 $/MW is incurred to MGA for providing reserve which equals to the LMP minus MGA’s energy offer of the last block. Compared to Case 1, the energy offers of MGA in Case 2 are strategically decided as [0, 12, 19] $/MWh, leading to a higher LMP with a greater energy profit. For Cases 3, 2, and 4, the capacity scale of MGA is sequentially increasing and presents different impacts on market equilibrium. The smaller-scale MGA in Case 3 offers at marginal costs and has no capability to influence the market NE energy price because the marginal generator is G6. The larger-scale
6
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MGA in Case 4 also offers at marginal costs, but it effectively decreases the market NE energy price due to sufficient capacity of cheaper energy. For Cases 2-4, block quantity of cheaper reserve at 4.7 $/MW is inadequate to meet the system reserve requirement, so MGA cannot change the market NE reserve price by its strategic offers. When MGA is integrated in bus 7, LMPs of different buses are identical due to uncongested transmission shown in Cases 1-4. However, for Case 5, transmission congestion is caused by the location of MGA integrated in bus 30, which leads to a limited dispatch of cheaper G4 and a lower LMP for MGA. Table 3. Energy clearing results of generators. Generator no. G1 G2 G3 G4 G5 G6
Case 1 Energya (MWh) 40 45 30 35 20 0
LMP ($/MWh) 18.3 18.3 18.3 18.3 18.3 18.3
Case2 Energya (MWh) 40 45 30 35 20 0
LMP ($/MWh) 19 19 19 19 19 19
Case 3 Energya (MWh) 40 45 30 35 20 9.2
LMP ($/MWh) 19 19 19 19 19 19
Case 4 Energya (MWh) 40 45 30 35 11.2 0
LMP ($/MWh) 17 17 17 17 17 17
Case 5 Energya (MWh) 40 45 30 19.2 20 7
LMP ($/MWh) 18.47 18.46 19.33 16 19.52 19
5. Conclusion The strategic offering of MGA satisfying the pure strategy NE was modelled in the joint energy and reserve market which was a bi-level programming. The lower-level market clearing problem was replaced by its KKT optimality conditions to transform the bi-level model into a MPEC. Considering the settlement mechanism of LMP for energy and MCP for reserve, the pure strategy NE conditions were improved and a linearization approach was proposed to address the nonconvexity. Then, the MPEC was equivalently reformulated as a MILP based on Big M method and strong duality theorem. The proposed model was performed on an IEEE 30-bus power system and the impacts of MGA on the joint energy and reserve market were concluded as following: 1) MGA effectively raised its profit by the use of strategic offers; 2) when the capacity scale is small, MGA had no influence on market NE prices and acted as a price-taker; 3) with the increasing scalability, MGA presented the capability to change market NE prices; 4) market NE prices are sensitive to the location of MGA due to the potential transmission congestion. Acknowledgements This work was supported by National Key Research and Development Program of China (2016YFB0901900) and National Natural Science Foundation of China (51637008). References [1]
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