Electricity Market for Distribution Networks Na (Lina) Li Electrical Engineering & Applied Mathematics Harvard University University of Maryland, College Park Oct. 17 th , 2016
Electricity Grid 1.0 Power plant Transmission Distribution Users Supply = Demand Unresponsive Predictable Energy Time 12 AM 12 AM
Electricity Grid 1.0 Power plant Transmission Distribution Users Supply = Demand Controllable Unresponsive Predictable
Transmission market Power plant Transmission Distribution Users Supply = Demand A Monthly Trans. Market Controllable Unresponsive Bill Predictable Forward Energy Market e.g., Day ‐ ahead market (one day forward); Real ‐ time Energy Market e.g., Every five minutes in PJM; Ancillary service market e.g., Spinning reserve market; (short ‐ term, unexpected changes)
Transmission market Power plant Transmission Distribution Users Supply = Demand Market Controllable Unresponsive Predictable Forward Energy Market e.g., Day ‐ ahead market (one day forward); Real ‐ time Energy Market e.g., Every five minutes in PJM; Ancillary service market e.g., Spinning reserve market; (short ‐ term, unexpected changes)
www.dsireusa.org/ March2015 Renew able energy
Random and intermittent Real power output (MW) 4 3 2 1 0 0 2000 4000 6000 Seconds since start of day Source: Rosa Yang, EPRI
• Small CHP (Combined Heat & Power) More distributed • Large CHP (Combined Heat & Power) • Wind Denmark’s progress over the past decades
Tomorrow’s Grid 2.0 Power plant Transmission Distribution Users Supply = Demand Less controllable Responsive Unresponsive Highly uncertain Distributed Large scale
Tomorrow’s Grid 2.0 Power plant Transmission Distribution Users DR appliances Storage EV Supply = Demand Less controllable Responsive Highly uncertain Distributed Large scale Distributed Smart appliances Solar PVs Energy Storage Wind turbines Resources Electric vehicles
Transforming Electricity Grid: DER
Debate over solar rates simmers in the Nevada desert February 27, 2016 Sources: PBS
Electricity Market for Distribution Netw orks: Challenges Power Engineering: Power flow, system dynamics, operation constraints Human Incentive: Strategic behavior, self-interested, market power Uncertainties: Renewable energy, user’s behavior, emergency
Electricity Market for Distribution Netw orks: Challenges Power Engineering: Power flow, system dynamics, operation constraints Human Incentive: Strategic behavior, self-interested, market power Uncertainties: Renewable energy, user’s behavior, emergency
Transmit and Distribute Pow er Kirchhoff’s law
Transmit and Distribute Pow er: Kirchhoff’s Law Capacity constraint on any line or node limit the entire flow
Challenges: An Example 2 2 2 25 1 3 1 3 1 3 50 100 100 150 150 150 Transaction 2 3 alleviates Line 1 ‐ 2 capacity: 25 congestions on line 1 ‐ 2 1, 2: generation nodes/buses; 3: load bus (two users)
How much to pay for public distribution service? Social Welfare Benefit Cost Physical Constraints
How much to pay for public distribution service? Social Welfare Individual ( d, g ) price How to set the price?
How to choose the prices? Social Welfare Given an convex problem, duality of the optimization provide efficient prices, p *
Challenges: Nonconvexity Nonconvex Optimal Power Flow 2 min + | | C P U p r I 0 , , j i i i j i j c g s s (0, ) , j i i j j j : : over : ( , , , , ) s p iq S P iQ x S v p q j j j j j j 2 2 : | | , 2 : | | s. t. I S v Nonconvex v V , ij i j ij ij i i i 2 * 2 Re , Branch flow model v v z S z j i ij ij ij ij , S z S s ij ij ij jk j i j j k Convexification gives , v v v i i i exact solutions , q q q i i [Lavaei 2011, Li 2012, Gan i , p p p 2012, 2013] i i i Baran & Wu 1989, Chiang & Baran 1990
Efficient Prices: Market Equilibrium (d * , g * , p * ) * p 1 Utility Company * p 2 * p 3 Social Welfare Individual ( d * , g * )
A Distributed Algorithm to Reach the Equilibrium Utility Company Utility company gathers requests MOPF : No info about individuals’ Privacy for costs and benefits function individuals Utility company updates price g p n d p 1 1 n Individual i receives the price User i optimizes max ( ) B d p d d i i i i i Individual i updates its request max - ( ) p g C g g i i i i i Theorem [Li et al. 2012, 2014] : The distributed algorithm converges to market equilibrium over a radial distribution network. Recent work : Distributed algorithms with limited communication . [2015, 2016]
Case studies Substation 45 Schematic Diagram of a South California Edison distribution System
Real power calculated by the user ( MW ) 0.06 bus 3 bus 6 0.05 bus 14 bus 54 0.04 0.03 0 10 20 30 40 50 60 Iteration Real power calculated by the utility company ( MW ) 2 1 0 bus 3 bus 6 -1 bus 14 Zoom in bus 54 -2 0.05 0.03 bus 3 bus 6 0.01 bus 14 bus 5 0 -0.01 0 10 20 30 40 50 60 Iterations
How about decentralized market? Bilateral Transaction? Decentralized? Challenge: Externality: Any local change induces a (complicated) global change! Delivery Service (in distribution networks) • Voltage support (constraint): v v v i i i • Power loss
Market rule [ , ] [ , ] [ , ] v v v v v v v v v j j j k k k i i i Line loss Line loss Bus i Bus j Bus k Buy voltage right at each bus Pay for line loss rent Each Bilateral Transaction Buy voltage right (constraint) at each bus Pays for line loss rent of each line Q: Budget balance on the voltage right and also the power loss? Voltage right at each bus = Σ i voltage right bought by transaction i Power losses at each line = Σ i Losses paid by transaction i
Market Prices and Equilibrium [ , ] [ , ] [ , ] v v v v v v v v v j j j k k k i i i Line loss Line loss rent rent Bus i Bus j Bus k Electricity price Electricity price Electricity price Voltage right price Voltage right price Buy voltage right at each bus Pay for line loss rent Each user/generator maximizes net benefit/profit given elec. prices
Market Prices and Equilibrium [ , ] [ , ] [ , ] v v v v v v v v v j j j k k k i i i Line loss Line loss rent rent Bus i Bus j Bus k Electricity price Electricity price Electricity price Voltage right price Voltage right price Buy voltage right at each bus Pay for line loss rent Each user/generator maximizes net benefit/profit given elec. price For each unit transaction between any two node i and k Elec. Price i = Elec Price j + Sum(Voltage right price*Quantity 1 ) + Sum (Line loss rent * Quantity 2 ) Voltage right price is 0 if there is excess voltage capacity supply Question: How to determine Quantity 1 ,Quantity 2 ?
How to determine the quantities? Duality of the Social Welfare Maximization Quantity 1 Quantity 2 Prices Budget Balance Constraints on Voltage Right and Line Losses For each unit transaction between any two node i and k Price i = Price j + Sum(Voltage right price*Quantity 1 ) + Sum (Line loss rent * Quantity 2 )
How to determine the quantities? One Allocation Rule for Voltage Right and Line Losses Quantity 1 : R: resistance V: voltage Quantity 2 : p: power injection P,Q: real/reactive power flow L: line losses For each unit transaction between any two node i and k Price i = Price j + Sum(Voltage right price*Quantity 1 ) + Sum (Line loss rent * Quantity 2 )
Competitive Market Equilibrium [ , ] [ , ] [ , ] v v v v v v v v v j j j k k k i i i User i User j User k Voltage right price Voltage right price Voltage right price Electricity price Electricity price Buy voltage rights at each bus Pay for line loss rent Theorem (Li 2015): Under the designed market rule, there exists a competitive market equilibrium that is socially optimal.
So far... Utility Scheme 1: Company Markets are efficient Scheme 2: Bilateral Transaction? Decentralized?
Electricity Market for Distribution Netw orks: Power Engineering: Power flow, system dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions) Human Incentive: Strategic behavior, self-interested, market power Uncertainties: Renewable energy, user’s behavior, emergency
Electricity Market for Distribution Netw orks: Power Engineering: Power flow, system dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions) Human Incentive: Strategic behavior, self-interested, market power Uncertainties: Renewable energy, user’s behavior, emergency
Recall… Utility Company Social Welfare Individuals need to report info. What if they DON’T report true info.?
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