distribution networks: control and pricing
DESCRIPTION
Distribution Networks: control and pricing. Desmond Cai Caltech (CS) John LedyardCaltech ( Ec ) Steven Low Caltech (CS and EE) With a lot of help from others at Caltech and Southern California Edison. The Problem. - PowerPoint PPT PresentationTRANSCRIPT
Distribution Networks:control and pricing
Desmond Cai Caltech (CS)John Ledyard Caltech (Ec)Steven Low Caltech (CS and EE)
With a lot of help from others at Caltech and Southern California Edison
U of FL 2
The Problem• Increasing DER adoption implies difficulties for
frequency and voltage control– Especially if economical storage is slow to come
online
• Control of the wholesale side is not enough.
• Need to integrate distribution networks (retail) into the management of the grid.
3/28/14
U of FL 3
A Distribution Network:Today
3/28/14
ISO
DistributionNetwork
Control
DevicesHVAC
EVPool pump
Etc….
Customer preferences
PV
L,G
P
C-P
external
control
U of FL 4
A Distribution Network:Adding Demand Response
3/28/14
ISO
DistributionNetwork
Control
DevicesHVAC
EVPool pump
Etc….
Customer preferences
PV
L,G
P
C-P
external
control
U of FL 5
A Distribution Network:Adding Demand Response
3/28/14
ISO
DistributionNetwork
Control
DevicesHVAC
EVPool pump
Etc….
Customer preferences
PV
L,G
P
C-P
external
control
This is not enough!
U of FL 6
A Distribution Network:Adding Responsive Demand
3/28/14
ISO
DistributionNetwork
VolVar Control or “Market”
DevicesHVAC
EVPool pump
Etc….
Customer preferences
PV
L,G
P
C-P
PricesBids
external
control
U of FL 7
How should we do this?
• Engineers – Give us control– Implementable but not optimal
• Economists – Let there be markets– Optimal but not implementable
• There is a way that is both implementable and optimal – Smart (economic?) control
3/28/14
U of FL 8
Outline
• Optimal Distribution Network Operation
• Theory– Direct control– Markets– Smart Control
• Simulations
We focus on Vol/Var control in 5 min increments– Principles would apply to frequency regulation, etc.
3/28/14
U of FL 9
A Model of the DN: the network
3/28/14
U of FL 10
A Model of the DN: the consumer
3/28/14
U of FL 11
The Goal is Socially Optimal Management
Maximize Consumers’ welfare + Producer’s welfare subject tothe Laws of Physics and Laws of Economics
For now we assume there is only one producer on the network – the Distribution Network Operator.– Assumed to be regulated and willing to follow rules.– Allows us to focus on consumer responses.
3/28/14
U of FL 12
Socially Optimal Vol/Var control
3/28/14
Ignores the effect of variance and peak-levels of P on capital costs and depreciation of equipment. (Easily added)
Is neutral on distributional effects.
U of FL 13
3 difficulties in solving the optimal VVC
• Computation– NP hard
• Non-convexities in the Vol/Var control network– Time scale – We do 5 minute intervals
• Is every every 5 minutes enough? • Is every 5 minutes even possible?
– Time correlation• Pool pumps, EV,…
• Information– The DNO does not know the consumers’ utility functions.
• Incentive compatibility– Getting the consumer to “do the right thing”
3/28/14
U of FL 14
The engineers’ solution:Let me control everything
• Give the DNO access to the consumers’ devices.– Both controls and information.
• Minimize a weighted average of Cost of power (from ISO)
+ Load Volatility + Peak Power
+ line/transformer loading subject to the laws of physics.
• Maintain standard regulatory average cost pricing policy with payments for access.
3/28/14
U of FL 16
The engineers’ solution:let me control everything
3/28/14
U of FL 20
The Problem with the engineers’ solution
• Not optimal– Completely ignores consumer preferences– Doesn’t use the full range of potential consumer
responses.
• Computation is not easy– Will assume it is computable so we can concentrate on
the economics.– In simulations this will have to be dealt with.– Open question: Can economics help the computation?
3/28/14
U of FL 21
The economists’ solution:Let there be markets
• A 5 minute market for power at each node.– Centralized, bi-lateral, brokered, an auction … ?
• Given prices, consumers maximize utility.• Given prices, the DNO maximizes net receipts
from power.• Prices are set so that:
consumers’ demands = DNO supply.– Who sets the prices?
3/28/14
U of FL 24
The Problem with the economists’ solution
• Optimal only if voltage is not a choice variable.– The equilibrium solves the optimal VVC only if dF/dV = 0.
• Markets do not equilibrate instantaneously.– Requires simultaneous solution by consumers and DNO and
price setter, but…– No one has the information needed to equlibrate in one shot.
• Iteration to equilibrium is infeasible.– If information and calculation are iterated, computational
constraints require time to overcome. Not enough time.
• Temporary solution is not feasible during iteration.3/28/14
U of FL 25
Other market-like options• Bidding into the wholesale market
– Too intensive cognitively and computationally for retail consumers
• Priority pricing– Requires service contracts contingent on external temperatures.– Too intensive cognitively and computationally for anyone.
• Prices to devices– Might work.– Let’s analyze in context of distribution networks.
3/28/14
U of FL 26
Optimality of Prices to devices• Given c, the DNO minimizes the cost of power acquired from
ISO.
• That power demand generates a substation LMP from the ISO. Which determines a local LMP price for each consumer.
• Given that price, each consumer chooses c to maximize their utility minus their cost of power.
• In equilibrium, this solves the optimal VVC problem.
3/28/14
U of FL 39
Stability of Prices to Devices
• Prices to Devices is more likely to be unstable– The more consumers are using the service– The more responsive consumers are to prices– The closer to capacity the ISO is
• Paradox: We need consumers to be responsive but if they are too responsive this policy won’t work.
3/28/14
U of FL 42
Summary to here
• The Economists’ solution is efficient but not implementable.
• The Engineers’ solution is implementable but not efficient.
• But , there is an integration that is optimal and implementable – Smart Control
3/28/14
U of FL 43
Smart Control• The consumer “reports” to the DNO.• The DNO solves the Optimal VVC with that .
3/28/14
U of FL 44
Smart Control
• Each consumer pays their local LMP price.
3/28/14
U of FL 45
Smart Control
• If this is compatible with communication limits, incentives, and computational limits then we will get the optimal VVC solution.
• Three issues– Communication: Will the consumer be able to describe their
utility function?– Incentives: Will the consumer report the true utility function?– Computation: Will the DNO be able to solve the Optimal VVC
with the utility functions in it?
3/28/14
U of FL 46
Will the consumer be able to describe their utility function?
• Consider an approximation around the consumer’s ideal setting c*.– The ideal setting is what the consumer would choose if power were free. uc(c*) =0.
• The consumer “reports” only two numbers: c*, ucc(c*). – Now a thermostat records a set-point, c*, and reports a temperature, c.– Here a thermostat also records a strength of preference, ucc(c*), and reports a
charge,
The answer is yes. 3/28/14
U of FL 47
Today’s simple thermostat
3/28/14
48
Tomorrow’s thermostat
3/28/14U of FL
Inside Temp
Cool ideal
setting
7472
System
Cool
Fan
Auto
Strength of preference setting
150
Average $/kwh
$2.50Energy cost
$20.50Time period
Last 24 hours
Currentsetting
74
U of FL 49
Will the consumer report their true utility function?
3/28/14
The answer is yes, subject to local network effects.
U of FL 50
Can the DNO solve the Optimal VVC with the utility functions?
• Use the quadratic approximation with information from the consumer.
• Can ignore constant term in the optimization.• We are adding quadratic terms to something that is
already quadratic.• This problem is no harder than
the control-only problem.
3/28/14
U of FL 52
Simulations
• Description
• Methodology
• Results
3/28/14
Simulated networkSCE Rossi circuit
– #houses: 1,407– #commercial/industrial: 131– #transformers: 422– #lines: 2,064 (multiphase, inc. transfomers)– peak load: 3 – 6 MW
Simulation scenarios– 2012, 2016, 30%PV– Baseline scenario– Optimal scenario
Simulated networkDER adoption (only residential houses)
– 2012• PV: 16, EV: 7, both: 3• PV: 2.4%, EV: 1.5% (cap wrt peak load)
– 2016 • PV: 135, EV:79, both: 15• PV: 19%, EV: 11%
– 30%PV• PV: 200, EV: 119, both: 24• PV: 28%, EV: 19%
AssumptionsControllable devices
– HVAC (through thermostat setpoint)– Plug-in electric vehicle – Pool pumps– Inverters for PV– Adjust control every 5 mins
Voltage dependent loads– HVAC, pool pumps, baseload– Parameters from GridLab-D– Implication: drives CVR optimization
• Voltage tolerance– + or – 5% of nominal– Implication: set bounds on possible results
AssumptionsPower loss on Rossi is small– kW losses: 0.84%– kVAR losses: 3.90% – kVA losses: 1.21%
• Implies: A linearized branch flow model is accurate– Assumes no losses on lines– Unlike DC model, does not assume V=1.– Unbalanced
Methodology
baseline scheduling OPF
simulations & optimizations
DER adoption network models
modeling & data
power flows cost benefits
analysis
network statistics
visualization
market control comm
design
databaseestimation & validation
user behavior parameter
baseline scheduling OPF
simulations & optimizations
DER adoption network models
modeling & data
power flows cost benefits
analysis
network statistics
visualization
market control comm
design
databaseestimation & validation
user behavior parameter• SCE Rossi circuit model – Primary and secondary circuits
• GRIDLab-D simulation model• Caltech PV adoption model– Using SCE customer data
• SCE EV adoption data and arrival/charge stats• SCE LMP for Rossi circuit• Public data on solar irradiance • Centrally recorded weather data
baseline scheduling OPF
simulations & optimizations
DER adoption network models
modeling & data
power flows cost benefits
analysis
network statistics
visualization
market control comm
design
databaseestimation & validation
user behavior parameter
All modeling and GridLab-D simulation data converted into MySQL
Issues w/GridLab-DVoltages
All house voltages 120V - zero anglesSubstation current injection
All constant over timeHouse temperatures
No heating modeled, temp goes to 60FCapacitor schedule
Inconsistent with power flow solutionCommercial load
1 zero load; 1 zero reactive powerPool pump
Zero reactive power
DER adoption network models
modeling & data
market control comm
design
databaseestimation & validation
user behavior parameter
Use GridLab-D to estimate u and F
– User utility– Pool pump reqs– EV behavior
Partially validated– to be continued
U of FL 62
Inferring F – HVAC only(voltage constant)
• Estimate from 2012 GridLab-D output– Don’t know what’s inside– Separate estimate for each house, office, etc.
• Why not
– Fits well if not cycling.
• In the steady state (e and c constant)
• What about V?3/28/14
U of FL 63
Inferring F – HVAC only
• Again use 2012 Gridlab-D output to estimate– Separate estimate for each house, office, etc
3/28/14
U of FL 64
Inferring u – HVAC only• Approximate around 2012 GridLab-D setpoint.• Assume consumer is maximizing u– Given F– Given the regulated price (constant)
3/28/14
U of FL 65
Inferring u – HVAC only• We use demand elasticity estimates from Riess-White (20..)
– Estimates are by device– They use monthly demand data
3/28/14
baseline scheduling OPF
simulations & optimizations
DER adoption network models
modeling & data
power flows cost benefits
analysis
network statistics
visualization
market control comm
design
databaseestimation & validation
user behavior parameter
Baseline Multiphase unbalanced BFM; forward-backward sweep
Optimal scenario Linearized multiphase unbalanced BFM; Second Order Cone Use 2 stage optimization procedure:
(1) fix V*, optimize w.r.t c,P,… (2) optimize w.r.t V
U of FL 67
Objective Functions
• We use …. different objective functions
• The Engineer’s
• Smart Control
3/28/14
baseline scheduling OPF
simulations & optimizations
DER adoption network models
modeling & data
power flows cost benefits
analysis
network statistics
visualization
market control comm
design
databaseestimation & validation
user behavior parameter
Simulation Results
Caveat: These results provide upper bounds on potential savings
They are preliminary and subject to revision with more validation and
simulations
U of FL 70
Change in Social Payoff
3/28/14
15-Jul 16-Jul 17-Jul 18-Jul 19-Jul 20-Jul 21-Jul0
100
200
300
400
500
600
700
800
900
change in utility minus energy costs
2012201630%
$
22-Feb 23-Feb 24-Feb 25-Feb 26-Feb 27-Feb 28-Feb0
50
100
150
200
change in utlity minus energy costs
2012201630%
$
Savings seem big:mainly on peak days
Savings increase withDER adoption
PV 2012: 16, 2.4% 2016: 135, 19% 30%PV: 200, 28%EV: 2012: 7, 1.5% 2016: 79, 11% 30%PV: 119, 19%
U of FL 71
Weekly Total Change in Social Payoff
3/28/14
2012 2016 0.30
500
1000
1500
2000
2500
3000
3500
weekly total - peak week
DRCVRDR + CVR
2012 2016 0.30
200
400
600
800
weekly total - off peak week
DRCVRDR + CVR
Per unit: 2012 2016 30% 2012 2016 30% (per day) $0.23 $0.26 $0.27 $0.05 $0.06 $0.06
Questions: - Are there significant savings
in fixed costs (time scale years)?- Are there significant savings
in reductions in reserve requirements?
U of FL 72
DR (demand response) vs CVR(conservation voltage reduction)?
3/28/14
2012 2016 0.30
100200300400500600700800
weekly total - off peak week
DRCVRDR + CVR
2012 2016 0.30
500
1000
1500
2000
2500
3000
3500
weekly total - peak week
DRCVRDR + CVR
DR more important asDER adoption increases.
CVR gives 25-30% of the saving.
U of FL 73
Changes in week’s energy costs and utility
3/28/14
peak utility peak energy off peak utility off peak energy
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2012201630%
U of FL 74
Changes in the Week’s Volatility and Max Peak
3/28/14
2012 2016 0.3
-5
0
5
10
15
20
peak max peakoff peak max peak
The base for the peak peak is 2,090, off-peak is 909.
The change is insignificant, even at 30% penetration .
U of FL 75
Volatility and Week’s Max Peak
3/28/14
2012 2016 0.30
500
1000
1500
2000
2500
3000
3500
peak volatilityoff peak volatility
Need volatility to get energy cost savings. Doesn’t violate constraints.
Question: How to account in VVC problem (5 minute time scale) for fixed cost increases (years time scale) due to volatility and peak change?
- Add in line constraints.
U of FL 76
Smart Control vs Engineer
3/28/14
2012 2016 0.30
500
1000
1500
2000
2500
3000
3500
Smart Control Volatility Changes
peak volatilityoff peak volatility
2012 2016 0.3
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Engineer Volatility Changes
peak volatilityoff peak volatility
U of FL 77
Smart Control vs Engineer
3/28/14
2012 2016 0.30
500
1000
1500
2000
2500
3000
3500
Smart Control Volatility Changes
peak volatilityoff peak volatility
2012 2016 0.3
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Engineer Volatility Changes
peak volatilityoff peak volatility
2012 2016 0.3
-5
0
5
10
15
20
Smart Control Peak Load Changes
peak max peakoff peak max peak
2012 2016 0.3
-25
-20
-15
-10
-5
0
Engineer Peak Load Changes
peak max peakoff peak max peak
U of FL 78
Smart Control vs Engineer
3/28/14
2012 2016 0.3
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
Smart Control Social Payoff - Peak
utilityenergy costtotal
2012 2016 0.3
-40000
-35000
-30000
-25000
-20000
-15000
-10000
-5000
0
Engineer Social Payoff - Peak
utilityenergytotal
U of FL 79
Smart Control vs Engineer
3/28/14
2012 2016 0.3
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
Smart Control Social Payoff - Peak
utilityenergy costtotal
2012 2016 0.3
-40000
-35000
-30000
-25000
-20000
-15000
-10000
-5000
0
Engineer Social Payoff - Peak
utilityenergytotal
2012 2016 0.3
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
Engineer Social Payoff - Off peak
utilityenergytotal
2012 2016 0.3
-1500
-1000
-500
0
500
1000
1500
Smart Control Social Payoff - Off peak
utilityenergy costtotal
Simulation Results
Caveat: These results are preliminary and subject to revision with more
validation and simulations
U of FL 81
Recap• Increasing DER adoption requires integration of distribution
networks grid management.
• The Engineers’ solution is implementable but not efficient.
• The Economists’ solution is efficient but not implementable.
• Smart Control is both optimal and implementable.– 1 more “dial” on the thermostat– PV metered separately– DNO able to read 2 numbers and set 1 on the thermostat– The DNO to know F.
• Preliminary simulations provide some support for this.3/28/14
U of FL 82
With a lot of help from
• Steven Low’s group– Changhong Zhao– Qiuyu Peng– Lingwen Gan– Anish Agarwal– Michael Lauria
• My group– Marcello Fernandez– Jin Huang
• Southern California Edison– Sunil Shah– Robert Sherick
3/28/14