Deregulated Electricity Market for Smart Grid: A Network Economic Approach

Transcription

1 Deregulated Electricity Market for Smart Grid: A Network Economic Approach Chenye Wu Institute for Interdisciplinary Information Sciences (IIIS) Tsinghua University Chenye Wu (IIIS) Network Economic Approach May 28, / 43

2 Key Challenges to Smart Grid If centralized control were feasible, then everything is straightforward. However,... From demand side Electric vehicles are owned by their owners Industrial loads are controlled by each company From supply side Renewables are uncontrollable Hence, a centralized control may not be feasible. A promising alternative is to use market - deregulated electricity market. This motivates us to take a network economic approach to understand the market. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

3 Efficiency and Fairness: Key to a Successful Market Part I: Efficiency: Goal: to provide adequate incentives to each entity to stabilize the power system Primary market: to constantly balance the active power Ancillary service market: to enhance the stability of the power system Part II: Fairness: Goal: to identify and assess the market power in deregulated electricity market Serving as guidance for the market design (e.g., where to install renewables, how to build more transmission lines to mitigate the existing market power) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

4 Ancillary Service Market and V2G Techonology 1 1 Chenyw Wu, Hamed Mohsenian-Rad, Jianwei Huang, PEV-based Reactive Power Compensation for Wind DG Units: A Stackelberg Game Approach, In Proc. of IEEE SmartGridComm 12, pp , Tainan, Taiwan, Nov Chenye Wu (IIIS) Network Economic Approach May 28, / 43

5 Challenges to Integrate Wind Power No long term wind power prediction method. Researchers implement various demand side management scheme. Compensate the reactive power for each wind DG unit. Shunt or switchable capacitors, static var compensators (SVCs). STATCOM with faster response time. PEV charger/inverter may help. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

6 Reactive Power Compensation with AC-DC inverters Recent studies have shown that the power electronics AC-DC inverter circuits (e.g., used for charging PEVs) can potentially contribute to reactive power compensation using appropriate P-Q control. Cvetkovic 09: energy resource system using PEVs to perform frequency and voltage regulation. Turitsyn 11: reactive power control by distributed photovoltaic generators. Farag 12: two-way communication distributed control scheme for voltage regulation in distribution feeders. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

7 System Model Power Grid Wind DG Unit Shunt & Switchable Capacitors Loads Vacant Vacant Vacant Vacant Chenye Wu (IIIS) Network Economic Approach May 28, / 43

8 Key Question How can we provide incentives for PEV owners to participate in reactive power compensation in order to optimally utilize the reactive power compensation potential of the PEV AC-DC inverters? Chenye Wu (IIIS) Network Economic Approach May 28, / 43

9 Wind DG Unit Model Q d : the wind DG unit predicts the amount of reactive power compensation that it needs. Q c C: the reactive power support from the shunt and switchable capacitors. The wind DG unit will select Q c according to the solution of the following optimization problem: minimize Q c Q d Q c subject to Q c C. (1) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

10 Wind DG Unit Model (Continued) For each PEV n N, q n denotes the amount of reactive power provided by PEV n to the wind DG unit in the current time slot. Assume PEVs use trickle chargers. As such, q max q n q max, n N. (2) When using level 1 charging, q max is 1.44 kvar and when using level 2 charging, q max is 7.68 kvar. With a selected Q c, the wind DG unit would like to select q to achieve the desirable Q d, ( g(q max, Q c ) = n N q n + Q c Q d ) 2. (3) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

11 Pricing Scheme We denote Q min as the minimal reactive power injection the wind DG unit needs, and Q max as the maximal reactive power injection the wind DG unit can handle. Higher payments correspond to higher incentives. If the total reactive power injection, Q c + n N q n, keeps the voltage profile in an acceptable range (i.e., between Q min and Q max ), then each PEV will receive a higher payment than some base price p b. However, if the total reactive power injection falls beyond the expected range, then each PEV will face a lower payment than the base price p b. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

12 Pricing Scheme (Continued) When Q d < Q c, we set the price as: ( p c (q)= p b α Q c + ) q n Q min. (4) n N α > 0 is the incentive control parameter. On the other hand, when Q d Q c, we set the price as: ( p i (q)=p b +β Q max Q c ) q n. (5) n N β > 0 is another incentive control parameter. We aim to set incentive control parameters α and β to achieve the optimal overall system performance. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

13 PEV s Model For the reactive power compensation that each PEV n provides, it receives the following payment from the wind DG unit: { p c (q)q n, if Q d < Q c, f n (q) = p(q)q n = p i (6) (q)q n, if Q d Q c, where q max q n q max, n N. (7) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

14 Stackelberg Game Formulation DG unit (leader) Stage I: DG unit determines β and Q max. PEVs (followers) Stage II: PEVs determine q n, n N, given the price. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

15 Reactive Power Compensation Subgame Players: The set N of all the PEVs; Strategies: For each PEV n N, based on the given pricing scheme set by the DG unit, it chooses its own reactive power compensation profile q n [ q max, q max ]. Payoffs: For each PEV n N, its payoff function is defined as its payment from the DG unit. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

16 Determining β and Q max in Stage I when Q d Q c If 0 Q d Q c Nq max, then the wind DG unit wants to have Each PEV s best response is Combining (8) and (9), we have qn = Q d Q c, n N, (8) N qn = p b+β(q max Q c s N \{n} q s). (9) 2β β = Np b (N + 1)Q d NQ max Q c. (10) Q max < Q d + 1 N (Q d Q c ). (11) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

17 Selecting α and Q min when Q d < Q c Analyzing the case when Nq max Q d Q c 0, we require α = Np b NQ min + Q c (N + 1)Q d, (12) and Q min > Q d + 1 N (Q d Q c ). (13) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

18 Optimality Guarantee We can show that: If (Q d Q c )/N < q max, then at Nash equilibrium of the RPC game, we have q n = q max, n N. (14) If q max (Q d Q c )/N q max, then at Nash equilibrium of the RPC game, we have q n = (Q d Q c )/N, n N. (15) If (Q d Q c )/N > q max, then at Nash equilibrium of the RPC game, we have q n = q max, n N. (16) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

19 Centralized Optimal Control ( ) 2 minimize q n + Q c Q d q n N subject to q max q n q max, n N. (17) Chenye Wu (IIIS) Network Economic Approach May 28, / 43

20 Simulation Setups Wind DG unit with 15 MW peak generation capacity and 6 MVAR peak requested reactive power, equipped with one 1 MVAR, one 2 MVAR, and one 3 MVAR switchable capacitors. Maximal Mismatch (kvar) Mismatch Variance (a) Number of PEVs in N 2 x (b) Level 1 Charging Level 2 Charging Level 1 Charging Level 2 Charging Number of PEVs in N Chenye Wu (IIIS) Network Economic Approach May 28, / 43

21 Conclusion and Future Works PEV-based Reactive Power Compensation Stackelberg Game Formulation Equilibrium Analysis Simultaneous active and reactive power compensation for the wind DG units to also tackle the fluctuations in active power generation. The stochastic availability of the PEVs when it comes to decide on optimal operation of the charging stations, and the time coupling for the set of possible amounts of reactive power shunt and switchable capacitor can provide - C. Assess the impact of PEVs on the network stresses. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

22 Unifying Functional Approach to Assessing Market Power 2 2 Chenye Wu, Subhomensh Bose, Adam Wierman, Hamed Mohsenian-Rad, A Unifying Approach to Assessing Market Power in Deregulated Electricity Markets, accepted by IEEE PES General Meeting 2013, Vancouver, BC, Canada, Jul Chenye Wu (IIIS) Network Economic Approach May 28, / 43

23 Why we care about Market Monitoring Traditionally, inelastic supply: expensive storage system, short-run capacity constraint. inelastic demand: limited price-responsive demand. What s waiting for us in the future? significant penetration of renewable energy, distributed generation, increased penetration of demand-response programs. Monitoring market power will become even more important in the coming years. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

24 Challenges to Monitor Market Power Inappropriate to naively apply standard measures of market power developed by economists. Congestion fragments the transmission system into smaller zones. Market within these zones may be highly concentrated even when the whole transmission system seems competitive. These smaller zones emerge and disappear over time. There are often internal transmission constraints that can be exploited by market players. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

25 Empirical Evidences: California energy crisis Frequent blackouts. 800% increase in wholesale prices from April to December 2000 The total extra payments as a result of market power between 1998 and 2000 in California is estimated at approximately $5.55 billion. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

26 Defining Market Power The ability to profitably alter prices away from competitive levels. In practice, researchers need to specify alter prices, competitive levels. The identification of market power requires ensuring that the manipulation was profitable, intentional. Detecting market power is a delicate task. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

27 Existing works Two main categories of market power tools and measures are in use: actual exercise of market power, mostly with empirical studies, e.g., analyzing historic market share. identifying the potential for market power prior to the market. Pivotal Supplier Index (PSI), binary indicator Residual Supply Index (RSI), TCRSI, maximal network flow, etc. These indices seem to be related, but not in a clear way. Our contribution is to provide a unifying approach to assessing the market power, which relates almost all the existing methods to some extent. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

28 Revisiting RSI Residual Supply Index RSI s = Total Generation Capacity - Generation Capacity of Generator s. Total Demand If RSI s < 1, then removing generator s will cause a shortfall of demand. Such difference can also be interpreted as the minimal generation. While RSI is efficient to identify market power in an electricity power pool, it may not work for power network model. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

29 3 node example 6 MW ~ Bus 1 Bus 3 -j / 11 MVA 11 MW -j / 1 MVA With electricity pool model, the shortfall of demand for each generator is 5 MW. However, if the transmission constraints are taken into consideration, 6 MW ~ Bus 2-2j / 11 MVA Gen 1 Gen 2 Shortfall 9 MW 7 MW Minimal generation 6 MW 5 MW It is evident from this example that the impact of transmission constraints and network topology on the market power is significant. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

30 Formulations of TCRSI and TCMGI Transmission Constrained Residual Supply Index TCRSI s = maximum q,d subject to D 1 q = 1 d = D H q q H d d b 0 q i q i, i s q s = 0 0 d j d j. Transmission Constrained Minimal Generation Index TCMGI s = minimum q q s subject to 1 q 1 d = 0 H q q H d d b 0 q i q i. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

31 A Functional Unifying Approach What if generator s is not excluded but its generation is limited to ρ q s? Network-flow (NF) function NF s (ρ) = maximum q,d subject to D 1 q = 1 d = D H q q H d d b 0 q i q i, i s q s = ρ 0 d j d j. NF function properties: TCRSI s = NF s (0), and NF s (TCMGI s ) = 1 d. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

32 A Functional Unifying Approach What if we aim to support only a portion of load 1 d = D, where D 1 d? Minimal Generation (MG) function MG s (D) = minimum q,d subject to q s 1 q = 1 d = D H q q H d d b 0 q i q i 0 d j d j. MG function properties: TCMGI s = MG s (1 T d), and MG s (TCRSI s ) = 0. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

33 The Big Picture Theorem 1 For any generator s, we can show that: (a) The NF s function is continuous, piecewise linear, concave, and monotonic increasing. (b) The MG s function is continuous, piecewise linear, convex, and monotonic increasing. Theorem 2 The NF and MG functions are inverse functions of each other. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

34 The Big Picture Pivotal Supply Index Residual Supply Index TCRSI Max-Flow NF Function inverse Must Run Capacity Minimal Generation MG Function Chenye Wu (IIIS) Network Economic Approach May 28, / 43

35 NF Curves for 3-node example Node 1 (4x) Node 2 (2y) dnf + s dρ = µ = 1 γ λ Hq s = 1 γ ρ=ρ0 l h s,l q λ l Chenye Wu (IIIS) Network Economic Approach May 28, / 43

36 More Insights dnf + s dρ = µ = 1 γ λ Hq s = 1 γ ρ=ρ0 l h s,l q λ l For each generator s, the physical meaning of the summation term can be explained as follows: For any transmission line constraint l that is binding, if q s increases by one unit, then the total amount of power flow from other generators will increase by hq s,l λ l. Therefore, if a generator s has h s,l q < 0 on several congested lines l, that generator is more likely to gain market power. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

37 Firm-based Extension We can further extend the results to a scenario where a group of generators belong to the same firm. For each set S of generators that create a firm, we have: TCRSI Extension TCRSI S = maximum q,d subject to D 1 q = 1 d = D H q q H d d b 0 q i q i, i S q s = 0, s S 0 d j d j. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

38 Firm-based Extension We can further extend the results to a scenario where a group of generators belong to the same firm. For each set S of generators that create a firm, we have: NF function Extension NF S (ρ) = maximum q,d subject to D 1 q = 1 d = D H q q H d d b 0 q i q i q s = ρ s S 0 d j d j, Chenye Wu (IIIS) Network Economic Approach May 28, / 43

39 Firm-based Extension Similarly, we can define: TCMGI Extension TCMGI S = minimum q,d subject to s S q s 1 q = 1 d H q q H d d b 0 q i q i 0 d j d j. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

40 Firm-based Extension Similarly, we can define: MG function Extension MG S (D) = minimum q,d subject to s S q s 1 q = 1 d = D H q q H d d b 0 q i q i 0 d j d j, Chenye Wu (IIIS) Network Economic Approach May 28, / 43

41 Superadditive Nature of MG function Theorem 3 For a given D and two disjoint sets of generators A and B, we can show that MG A (D) + MG B (D) MG A B (D). Example of superadditive indices combining the advantages of NF function (TCRSI) and MG function (TCMGI): ( D TCRSI S ) TCMGI S ; TCMGIS 0 ( D NF S (ρ))dρ. Chenye Wu (IIIS) Network Economic Approach May 28, / 43

42 Conclusion and Future Works Review the existing indices to assess the potential of market power and propose a functional unifying approach to better evaluate the market power issues in the power system. Using the superadditive nature of MG function, we can define a family of superadditive market power index. Though the focus of this paper is on the long term market power analysis, it is possible to generalize our functional approach to the short term market power analysis by incorporating some particular classes of cost function, e.g., linear and quadratic. How to incorporate strategic behavior and consider the stochastic brought by the renewable energies? Chenye Wu (IIIS) Network Economic Approach May 28, / 43

43 Contact Chenye Wu Chenye Wu (IIIS) Network Economic Approach May 28, / 43