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

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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