GraphVPP: Enabling Optimal Bidding Strategy of VirtualPower Plants in Graph Computing FrameworksLongfei Weia, Guangyi Liua, Jun Tana, Renchang Daia, Jianqi Zhoub, Zhiwei Wanga

aGlobal Energy Interconnection Research Institute North America, San Jose, CA, USAbState Grid Jiaxing Power Supply Company, Jiaxing, Zhejiang, China

{longfei.wei, guangyi.liu}@geirina.net

Abstract—This paper proposes the GraphVPP, a graph com-puting framework for developing the optimal bidding strategyof virtual power plants (VPPs) participating in the wholesaleelectricity market. Compared with existing literature that onlyposition the VPP as a commercial unit, GraphVPP considersboth the economic operation of distributed energy resources(DERs) within the VPP and their technical impacts towards thenetwork security of transmission and distribution systems. First,GraphVPP stores the power grid data and market information ina graph structure, and then formulates a two-stage optimizationproblem for deriving the market clearing results including localmarginal prices (LMPs) and generation dispatches. To ensure thepower grid’s stability under the scheduled generation dispatches,a graph based power flow algorithm is introduced for thetransmission and distribution network security analysis. Once thenetwork security check approved, a profit-maximization biddingdecision model is introduced for each VPP to derive the optimalbidding strategy. Finally, case study compares different types ofVPPs within the wholesale market to demonstrate the feasibilityand validity of the proposed GraphVPP.

Index Terms—bidding strategy, decision model, wholesale mar-ket, graph computing, local marginal price

I. INTRODUCTIONDuring the last few years, the penetration of distributed

energy resources (DERs) within the power grid has increasedsignificantly to reduce greenhouse gas (GHG) emissions andmeet clean energy requirements. Due to the limited capacityand flexibility of independent DERs, they typically participatein the retail electricity market and help lower the electriccustomers’ costs. With the advance of information and com-munication technologies (ICTs), DERs currently can be aggre-gated through a control center, referred to as the virtual powerplant (VPP), to simultaneously take part into the wholesaleelectricity market and provide grid services such as energycapacity and ramp rate smoothing. As a novel industry term,the VPP could harness the value from heterogeneous DERsincluding distributed generation (DG) units, energy storagesystems (ESSs), controllable loads (CLs), and electric vehicles(EVs), and act as a unified unit for energy trading in thewholesale market. Compared with a stand-alone DER, theVPP normally could achieve a better market performance bycooperatively compromising the strengths and weaknesses ofdifferent DER devices.

Generally, the objective of VPP is to analyze the economicoperation schedules of its DER devices and determine theoptimal bidding strategy to maximize its expected profits from

This work was supported by state grid corporation technology project5455HJ180018.

energy trading in the wholesale market. Despite there havebeen a rich of research on deriving the VPPs’ optimal biddingstrategy [1]–[4], most of the works treated the VPP as a price-taker and assumed that its bidding strategies have no influenceon the market clearing prices and other market participants’strategies. However, the impacts of VPP towards the marketshould be considered with its increasing size and capacity. In[5], the VPP was first treated as a price-maker, and a bi-leveloptimization model was proposed for deriving its optimal day-ahead bidding strategy. Similarly, a two-stage VPP biddingstrategy optimization framework considering demand responsemechanisms and uncertainties of DG units was introduced in[6]. In addition, a distributed algorithm towards multi-players’strategy optimization was introduced in [7] to accelerate theconvergence of bidding procedure. Compared with traditionalstochastic methods, a chance-constrained two-stage optimiza-tion model was presented in [8] to achieve the optimal biddingstrategy for maximizing the micro-VPP’s daily profits.

In all above works, the VPP is considered to be a commer-cial unit, but the power grid operation constraints, such as linecongestion, voltage regulation, and different bus connectionsfor various VPPs, are ignored. Given the wide breadth ofDER integration, the operation changes within the VPP mightlead to the rippling effects throughout the rest of the powergrid. With the emergence of graph computing technologies, thegraph based power flow algorithms provide an opportunity foranalyzing the technical impacts of VPPs in a hybrid powergrid. Our previous works [9], [10] respectively proposed thegraph based power flow algorithms for the transmission anddistribution network security analysis.

This paper proposes GraphVPP, a graph computing frame-work for developing the VPP’s optimal bidding strategy con-sidering both the economic operation of its DER devicesand their technical impacts towards the transmission anddistribution network security. GraphVPP is comprised of twomain parts including graph database and graph computingtechnologies. Graph database employs semantic queries withan ordered pair of vertices and edges to store power systemdata and electricity market information in a graph structure,and graph computing technologies are implemented for theVPP bidding strategy derivation and network security analysis.The main contributions of this paper are listed as follows:

1) The VPP optimal bidding strategy problem is abstractedinto a graph structure;

2) Based on the information stored in the graph’s attributes,

Fig. 1. ISO wholesale electricity market ranging from VPP elements to transmission and distribution networks and corresponding graph modelling.

a two-stage optimization model is formulated to derivethe market clearing results including local marginalprices (LMPs) and generation dispatches;

3) To analyze the network security under the scheduledgeneration dispatches, a graph based power flow algo-rithm is proposed for the network security analysis ofthe hybrid power grid integrating both transmission anddistribution networks;

4) Once the network security check approved, a profit-maximization optimization model considering both thecooperation between different DER devices and distribu-tion network security is developed for the VPP to derivethe optimal bidding strategy;

5) Simulation results based on a modified IEEE 118-bussystem integrated with four VPPs are introduced to il-lustrate the applicability and effectiveness of GraphVPP.

II. PROBLEM STATEMENT AND GRAPH MODELLING

This paper considers the VPP consisting of different typesof DERs including DG units (wind farms and solar PVs)and ESSs. The VPP is granted to operate and control allDERs included in its domain based on the entire portfo-lio’s operational requirements and network constraints. Asa result, the VPP acts as an aggregator that participates inthe wholesale market by submitting a bidding curve to theindependent system operator (ISO) and fulfilling the loaddemand of local electric customers. Assume that the VPPi’s bidding curve for time t ∈ T is m-part piecewisefunction determined by the price-quantity pair: πi(t) =[(λi,1(t), Pi,1(t)), ..., (λi,m(t), Pi,m(t))]T , where λi,j(t) is thebid price ($/MW), Pi,j(t) is the bid quantity (MW), j =1, ...,m. Then, the optimal VPP bidding problem can beclassified as the following four stages as shown in Fig. 1:

1) Bid Submission Stage: Competing with conventionalpower plants (CPPs), each VPP submits its biddingcurve π to the ISO based on its DG forecasts and loaddemand forecasts before the market gate closure.

2) Market Clearing Stage: After the gate closure, theISO derives the day-ahead (DA) market clearing resultsincluding LMPs and generation dispatches based onCPPs and VPPs’ bidding curves and system network

constraints. Mathematically, the ISO market clearingproblem can be formulated as a two-stage optimizationmodel, which is comprised of a bid-based securityconstraint unit commitment (SCUC) problem (ProblemP1) for determining the DA generation schedules and asecurity constrained economic dispatch (SCED) problem(Problem P2) for calculating the LMPs.

3) Network Security Analysis Stage: After the announce-ment of market clearing results, a graph based powerflow algorithm is implemented for the network securitycheck. If the check fails, the corresponding networkconstraints are first added into Problem P2. If the currentgeneration schedules cannot fulfill the constraints, theconstraints should be added to Problem P1. Then repeatstage 2 until network security constraints are satisfied.

4) VPP Optimization Stage: Once the network securitycheck approved, the VPP could optimize its biddingcurve π, allocate the generation dispatches to the DGunits, and adjust the operation of its facilities such asESSs based on the market clearing results, which math-ematically can be formulated as a profit-maximizationbidding strategy optimization problem (Problem P3).

To solve the optimal VPP bidding problem in graph com-puting frameworks, GraphVPP abstracts the wholesale mar-ket as a graph of an ordered pair of vertices and edges,G = {V, E}, which contains three subgraphs including trans-mission network subgraph GT, distribution network subgraphGD, and electricity market subgraph GEM. Especially, due tothe loop nature for the transmission network, GT is definedas a directed, cyclic graph using bus-branch model, wherea bus is represented by a vertex, a branch is expressed asan edge, and bus and branch parameters, such as powergeneration, load demand, and bus voltage, are represented byattributes associated with vertices and edges. Compared withGT, GD is represented as a directed, acyclic graph with radialnetworks, which comprises of multiple VPP subgraphs GVPP.GEM is represented as a directed, connected graph, where thevertex set contains the market information, such as biddingcurves and LMPs, where the bidding curve vertices are fullyconnected with the generation vertices in GT and the VPPcontrol center vertices in GVPP, and the LMP vertices are fully

connected with the bus vertices in GT.Graph computing technologies can be realized using the

graph data structure G, where each vertex/edge is a storage andcomputing unit. The calculation of the optimal VPP biddingproblem can be applied on each vertex/edge independently andin parallel. Therefore, GraphVPP integrated with graph parallelcalculation algorithms enable the fast Problem 1-3 solving andnetwork security analysis.

III. MATHEMATICAL FORMULATION

A. Market Clearing (Problem 1 & 2)In the DA electricity market, the main objective of ISO mar-

ket clearing is to determine the DA generation dispatches andcalculate the LMPs, which mathematically can be formulatedas a two-stage optimization model including SCUC (Problem1) and SCED (Problem 2). Based on CPPs and VPPs’ biddingcurves, the objective of Problem 1 is to determine an optimalunit commitment (UC) for minimizing the energy supply cost:

min∑t∈T

{ ∑i∈GCPP

[ m∑k=1

λi,k(t)Pi,k(t)Ii(t) + γSUi (t)Wi(t)

+ γSDi (t)Yi(t)

]+∑

j∈GVPP

m∑k=1

λj,k(t)Pj,k(t)Ij(t)

} (1)

where (λi,k(t), Pi,k(t)) and (λj,k(t), Pj,k(t)), k = 1, ...,m,respectively denote the k-part bidding price-quantity pair forCPP i and VPP j at time t, i ∈ GCPP, j ∈ GVPP, t ∈ T ; Ii(t)and Ij(t) separately represent the binary indicator for CPP iand VPP j’s on/off status at time t; γSD

i (t)(γSDi (t)) denotes

the start-up (shut-down) cost of CPP i at time t; Wi(t)(Yi(t))is the start-up (shut-down) binary indicator for CPP i.

Problem 1 is subject to the following constraints, ∀t ∈ T :m∑

k=1

( ∑i∈GCPP

Pi,k(t)Ii(t) +∑

j∈GVPP

Pj,k(t)Ij(t))

= DTA(t) (2)

0 ≤ Pi,k(t) ≤ Pmaxi,k Ii(t),∀i ∈ GCPP, k = 1, ...,m (3)

−PRmaxi ≤

m∑k=1

(Pi,k(t)− Pi,k(t− 1)) ≤ PRmaxi ,∀i ∈ GCPP

(4)Pr{Pmin

j Ij(t) ≤m∑

k=1

Pj,k(t) ≤ Pmaxj Ij(t)} ≥ ε,∀j ∈ GVPP

(5)|

∑i∈GCPP∪GVPP

Pi,l(t)| ≤ Pmaxl ,∀l ∈ ET (6)

Constraint (2) represents the system balance between powergeneration and load demand, and DTA(t) denotes the systemload demand at time t. Constraint (3) provides the maximumpower generation Pmax

i,k for CPP i at the k-part of biddingcurves. Constraint (4) presents the ramp rate limit PRmax

i forCPP i. Due to the stochastic nature of DG units within theVPP, constraint (5) ensures that VPP j’s power generationstays within [Pmin

j , Pmaxj ] with probability more than ε. For

transmission line l ∈ ET , constraint (6) guarantees the totalpower flow at l is not greater than the threshold Pmax

l , andPi,l(t) denotes the power flow at l injected from unit i.

Problem 1 can be reformulated as a mixed integer linearprogramming (MILP) problem by measuring constraint (5)using the value-at-risk (VaR) and linearizing constraint (6)using generation shift factor GSF i,l from unit i to line l:

Pminj Ij(t) ≤ VaR(

m∑k=1

Pj,k(t); ε) ≤ Pmaxj Ij(t) (7)

∑i∈GCPP∪GVPP

m∑k=1

GSF i,l(Pi,k(t)− P ∗i,k(t)) ≤ Pmaxl − P ∗l (t)

(8)where VaR(

∑mk=1 Pj,k(t); ε) = inf{γ|Pr{

∑mk=1 Pj,k(t) ≤

γ} ≥ ε} is the VaR function of random variable∑m

k=1 Pj,k(t);power generation P ∗i,k(t) and line power flow P ∗l are derivedby the power flow aglorithm, i ∈ GCPP ∪ GVPP, ∀l ∈ ET .

Based on UC plans derived by Problem 1, Problem 2 aims todetermine the specific generation dispatches for both CPPs andVPPs and LMPs at each time t ∈ T . The objective functionof SCED for time t then can be defined:

min

m∑k=1

[ ∑i∈GCPP

λi,k(t)Pi,k(t) +∑

j∈GVPP

λj,k(t)Pj,k(t)]

(9)

Similar with Problem 1, this problem is subject to constraints(2)-(4), (7), and (8) for time t.

Then, the LMP λi at each bus i can be derived by solvingProblem 2, which can be categorized into three parts: energycomponent, congestion component, and loss component.λi(t) = λ(t) +

∑l∈ET

(GSF i,l × µl(t)) + (DF i − 1)λ(t) (10)

where λ(t) is the shadow price of constraint (2) for theenergy component;

∑l∈ET (GSF i,l×µl(t)) represents for the

congestion component, where µl(t) denotes for the shadowprice of line l’s transmission constraint (6); (DF i − 1)λ(t) isthe loss component, where DF i denotes the delivery factorrepresenting that how much power to be delivered to thereference bus if additional one MW is injected at bus i.B. Network Security Analysis

To derive transmission line l’s power flow P ∗l , ∀l ∈ ET , anddistribution network voltages for the network security analysis,a graph based power flow algorithm (Algorithm 1) is proposedfor the hybrid power grid. As the load demand of each VPPwithin GD is varying with the substation voltage VVPP [11],[12], the hybrid power flow problem needs to be solved inan iterative process to find the actual load demand of eachVPP. First, define the rated load demand as initial load at eachsubstation node in GT . Then, the graph based fast decoupledpower flow (FDPF) algorithm is performed for GT to derive thevoltage at each bus. Thus, VVPP for each VPP in GD is updatedand the graph based forward-backward sweep (FBS) algorithmis used for solving the power flow problem for each VPPand updating the load demand in GT . This iterative processcontinues until the bus voltages in GT converge to a steadystate and power flow for the hybrid network is solved.

Based on the graph computing frameworks, this processfor solving the power flow of VPPs can be paralleled byusing the sub-query technical. The power flow for the VPPscan be carried out as sub-queries in the FDPF algorithm for

Algorithm 1 Graph based Power Flow Algorithm1: Set the rated load demand as initial load for GT ;2: while |∆VVPP| ≥ εTOTAL do3: procedure FAST DECOUPLED POWER FLOW (FDPF)4: V,B′, B′′, InsertLU ← GT ;5: if InsertLU = ∅ then LU factorization;6: ∆P , ∆Q← Initial Values;7: while max |∆P + j∆Q| ≥ εFDPF do8: traversal process for vertex/edge in GT .9: procedure FORWARD-BACKWARD SWEEP (FBS)

10: each VPP substation voltage VVPP ← GT ;11: compute node current Ii, ∀i ∈ VVPP;12: Backward: compute branch current Il, ∀l ∈ EVPP;13: Forward: update VVPP based on Il, ∀l ∈ EVPP.

return P ∗l , VVPP, ∀l ∈ ET .

calculating the power flow of GT . Thus, the power flow for allVPPs are calculated in a paralleled process and computationalspeed can be significantly improved.

C. VPP Optimization (Problem 3)By integrating the DG units, the VPP could participate in

the wholesale market bidding. However, due to uncertainties ofDG units, when the real power generation is greater/less thanthe bidding quantity, the VPP needs to dispatch the greaterpower output or buy the less power from the real-time market,otherwise it will be punished by the market operator. Withthe integration of ESSs, the VPP could implement the ESSdevices such as batteries to be in charging/discharging statusto minimize the difference between the real power generationand the bid quantity to smooth the uncertainties of DG powergenerations. In summary, the VPP’s profit can be described asthe following objective function:

max∑i∈GDG

{∑t∈T

m∑k=1

(λi(t)Pi,k(t)− γi(t)P cosi,k (t))−

[∑t∈T

λi(t)(ωeci (t)µec

i (t)P eci (t) + ωbli(t)µbl

i (t)P bli (t)

)]}(11)

where [(γi,1(t), P cosi,1 (t)), ..., (γi,m(t), P cos

i,m(t))]T is the m-partpiecewise operation cost function of DG unit i within theVPP; µec

i (t) and µbli (t) are both binary indicators for the

real power generation P reali (t) is greater/less than the bidding

quantity∑m

k=1 Pi,k(t) at time t, respectively. ωeci (t) and

ωbli (t) represent the system punishment price when the power

generation is greater/less than the bidding quantity at timet, respectively. Given that P cha

i (t) and P disi (t) represent the

ESS device charging/discharging power at time t, P eci (t) and

P bli (t)

(= −P ec

i (t))

satisfy:

P eci (t) = P real

i (t)−m∑

k=1

Pi,k(t) + P chai (t)− P dis

i (t) (12)

Problem 3 is subject to the following constraints, ∀t ∈ T :

Pmini (t) ≤ VaR(

m∑k=1

Pi,k(t); ε) ≤ Pmaxi (t) (13)

Ci(t) = Ci(t− 1) + P chai (t)ηcha − P dis

i (t)ηdis (14)Cmax

i ≤ Ci(t) ≤ Cmaxi (15)

Fig. 2. The flowchart of deriving the VPP optimal bidding strategy.

Fig. 3. The modified IEEE 118-bus system with 50 CPPs and 4 VPPs.TABLE I

VPP WIND FARM, SOLAR PV AND ESS SPECIFICATIONS

VPP Wind Farm Solar PV EESNo. Buses No. Buses No. Buses

1 3 21, 57, 108 3 25, 40, 105 3 13, 54, 1012 3 21, 57, 108 — — 3 13, 54, 1013 — — 3 25, 40, 105 3 13, 54, 1014 4 21, 25, 57, 108 4 25, 50, 55, 105 4 13, 54, 56, 101

P chai,min(P dis

i,min) ≤ P chai (t)(P dis

i (t)) ≤ P chai,max(P dis

i,max) (16)VVPP ≤ V Threshold

VPP (17)Constraint (13) ensures that DG unit i’s power generation stayswithin [Pmin

i , Pmaxj ] at time t; constraint (14) represents the en-

ergy balance constraint of ESS installed with DG unit i, whereCi(t) is the capacity of EES device i at time t, ηcha and ηdis areits charging and discharging efficiency, respectively; constraint(15) is the ESS energy constraint; constraint (16) providesthe charging/discharging capacity constraint; constraint (17)represents the substation voltage threshold for the VPP.

The flowchart of deriving the VPP’s optimal bidding strat-egy is shown in Fig. 2. First, the system measurements andinitial CPP and VPP bidding curves stored at G are providedas inputs of Problems 1 and 2 for the market clearing. Then,Algorithm 1 (graph based power flow algorithm) is introducedfor analyzing the network security of both transmission anddistribution networks. Once the network security approved,an updated VPP bidding curve could be derived by solvingProblem 3, which will replace the initial bidding curves storedat G. Then, repeat the above Problems 1-3 calculation until theVPP’s optimal bidding curve is derived.

IV. CASE STUDY AND TEST RESULTS

In this paper, a modified IEEE 118-bus system (Fig. 3) isused as the test system for evaluating the proposed GraphVPP.

(a) Power & Load Forecasts and Bid Quantity for VPP1 (b) Power & Load Forecasts and Bid Quantity for VPP2

(c) Power & Load Forecasts and Bid Quantity for VPP3 (d) Power & Load Forecasts and Bid Quantity for VPP4

Fig. 4. The power & load forecasts (MW) and optimal bid quantity (MW) of four VPPs for each hour in one market operating day.

The test system is connected with 50 CPPs and 4 VPPs, whereeach VPP is model as a IEEE 123-bus distribution system.The DER specifications and connected buses of four VPPs arelisted in Table I, where VPP1 connects with 3 wind farms, 3solar PVs and 3 ESSs, VPP2 integrates with 3 wind farms and3 ESSs, VPP3 aggregates with 3 solar PVs and 3 ESSs, andVPP4 with 4 wind farms, 4 solar PVs and 4 ESSs.

Fig. 4 presents four VPPs’ hourly power & load forecastsand bid quantity in one market operating day, respectivelyVPP1 for (a), VPP2 for (b), VPP3 for (c), and VPP4 for(d). Green line denotes the total power generation forecastsby aggregating all DG units, and red line represents the totalload demand by integrating all customers. Blue bar providesthe 24-hour bidding quantities for the market operating day,where the negative values denote that the VPP need to buythe energy from the main grid and the positive values meanthat the VPP could provide the energy to the main grid. Fromthis figure, we could find that the 24-hour bidding quantitiesfor VPP4 are all negative, since the power generation is lowerthan the load demand, and all power generation is used forthe local customers’ loads. In addition, assume that VPP1’sbiding curve to be a 3-piecewise function, its optimal biddingcurve for each hour of the operating day is listed in Table II.

V. CONCLUSION

This paper establishes GraphVPP, a graph computing basedVPP decision-making framework considering both networksecurity and uncertainties of its DERs, where the operationschedules of DER devices within the VPP are determined bythe LMPs. In the market operating day, when the LMP isrelatively low, the VPP tends to purchase energy from themain grid and charge the ESSs. When the LMP is relativelyhigh, the VPP tends to sell energy to the main grid anddischarge the ESSs. In addition, the VPP’s optimal biddingcurve is determined by its DER devices’ capacity, aiming tosatisfy that the real generation output fulfills the bid quantitywith probability more than 90%. At the same time, the VPP’s

TABLE IIVPP1 BID CURVE IN NEXT 24 HOURS

Hour λ1($/MWh) P1(MW) λ2($/MWh) P2(MW) λ3($/MWh) P3(MW)

3 5 5.0039 19.48 0.556 38.96 0.5565 5 2.8524 17.32 0.3169 34.64 0.31696 5 17.3612 19.6 1.929 39.2 1.9297 5 23.4755 23.41 2.6084 46.82 2.608414 5 15.6496 25.12 1.7388 50.24 1.738815 5 32.8136 31.36 3.646 62.72 3.64616 5 30.7386 31.94 3.4154 63.88 3.415417 5 5.4004 29.08 0.6 58.16 0.622 5 0.8357 31.94 0.0929 63.88 0.092924 5 16.4917 27.51 1.8324 55.02 1.8324

bidding curve is influenced by the competition from CPPs andother VPPs. REFERENCES

[1] H. T. Nguyen, L. B. Le, and Z. Wang, “A bidding strategy for virtualpower plants with the intraday demand response exchange marketusing the stochastic programming,” IEEE Transactions on IndustryApplications, vol. 54, no. 4, pp. 3044–3055, July 2018.

[2] D. Yang, S. He, Q. Chen, D. Li, and H. Pandzic, “Bidding strategyof a virtual power plant considering carbon-electricity trading,” CSEEJournal of Power and Energy Systems, vol. 5, no. 3, 2019.

[3] E. Mashhour and S. M. Moghaddas-Tafreshi, “Bidding strategy ofvirtual power plant for participating in energy and spinning reservemarkets—part i: Problem formulation,” IEEE Transactions on PowerSystems, vol. 26, no. 2, pp. 949–956, May 2011.

[4] Q. Zhao, Y. Shen, and M. Li, “Control and bidding strategy forvirtual power plants with renewable generation and inelastic demand inelectricity markets,” IEEE Transactions on Sustainable Energy, vol. 7,no. 2, pp. 562–575, April 2016.

[5] E. G. Kardakos, C. K. Simoglou, and A. G. Bakirtzis, “Optimal offeringstrategy of a virtual power plant: A stochastic bi-level approach,” IEEETransactions on Smart Grid, vol. 7, no. 2, pp. 794–806, March 2016.

[6] Y. Wang, X. Ai, Z. Tan, L. Yan, and S. Liu, “Interactive dispatch modesand bidding strategy of multiple virtual power plants based on demandresponse and game theory,” IEEE Transactions on Smart Grid, vol. 7,no. 1, pp. 510–519, Jan 2016.

[7] G. Zhang, C. Jiang, X. Wang, B. Li, and H. Zhu, “Bidding strategyanalysis of virtual power plant considering demand response and uncer-tainty of renewable energy,” IET Generation, Transmission Distribution,vol. 11, no. 13, pp. 3268–3277, 2017.

[8] H. Fu, Z. Wu, X. Zhang, and J. Brandt, “Contributing to dso’s energy-reserve pool: A chance-constrained two-stage µ vpp bidding strategy,”IEEE Power and Energy Technology Systems Journal, vol. 4, no. 4, pp.94–105, Dec 2017.

[9] G. Liu, C. Yuan, X. Chen, J. Wu, R. Dai, and Z. Wang, “A high-performance energy management system based on evolving graph,”IEEE Trans. on Circuits and Systems II: Express Briefs, pp. 1–1, 2019.

[10] R. Dai, G. Liu, Z. Wang, B. Kan, and C. Yuan, “A novel graph-basedenergy management system,” IEEE Trans. on Smart Grid, pp. 1–1, 2019.

[11] L. Wei, A. I. Sarwat, W. Saad, and S. Biswas, “Stochastic games forpower grid protection against coordinated cyber-physical attacks,” IEEETransactions on Smart Grid, vol. 9, no. 2, pp. 684–694, March 2018.

[12] Y. Tang, C. Ten, C. Wang, and G. Parker, “Extraction of energy infor-mation from analog meters using image processing,” IEEE Transactionson Smart Grid, vol. 6, no. 4, pp. 2032–2040, July 2015.