Na (Lina) Li Electrical Engineering & Applied Mathematics - PowerPoint PPT Presentation

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.?