employing distributed resources in smart grids smart...

Employing Distributed Resources in Smart Grids

Smart & Cool project

Morten Juelsgaard,Rafael Wisniewski, Jan Bendtsen,

Palle Andersen, Christoffer Sloth, Jayakrishnan Pillai

Dept. of Automation and Control, Aalborg University

ACL presentation, KTH, 16/09/2013

Who am I

◮ Ph.d. student at Aalborg University,Dept. of Automation and Control

◮ Employed at the project called ’Smart and Cool’

◮ Project period: 15/8/11 - 14/8/14

◮ Visiting researcher at ACL during 1/9-20/12 under strictsupervision of prof. Mikael Johansson

2 of 255

Where is Aalborg

3

Some background: Tendencies

◮ Decreasing use of fossil fuels, both with respect to energyproduction and -consumption

◮ Production: Wind, solar, hydro etc. are promoted over oil,gas and coal

◮ Consumption: electric vehicles (EVs), electric heatpumps (EHPs), etc., are preferred over traditionalcombustion engines and oil-fired boilers

4

Some background: Consequences

◮ Production: Decreasing controllability, increasing volatilityand uncertainty,

◮ Consumption: Increased load, increased risk of congestion,increasing losses

Emerging problems:

How to maintain balance, security of supply, satisfactory grid

operation, etc. during and after this shifting paradigm

5

Some background: Suggested solution

◮ It has been suggested that part of the solution may bederived from smart grids

◮ By smart grid we mean a future electric grid, with advancedinfrastructure for metering and control:

◮ Near real-time measurements of consumption◮ Control rights for various classes of consumers◮ Advanced communication structure to support the above

◮ This allows demand management

◮ The underlying existence of a smart grid, is the vantagepoint of our work

6

This talk

◮ Some of the problems we have been working on:

1. Distributed energy balancing2. Consumption coordination for loss minimization3. Voltage control through consumption coordination

◮ Some initial thoughts on what I will be doing here

7

1. Distributed balancing

◮ We consider a portfolio operator, managing a number ofpower production and consumption units

◮ The portfolio should collectively obey a predeterminedoperating schedule

◮ Imbalances can be eliminated by adjusting either productionor (flexible) consumption

◮ Each unit presents individual operating costs, and-constraints

Type 1Type 2

Consumers

External actors

Grid

Σ

8


The overall problem is:

minimize∑

i

fi (xi )

subject to xi ∈ Xi∑

i

xi = d

The solution must be ob-tained distributed:

x1

x2

x3

x4

x5

x6

xn

9


Dual decomposition:

Obtain:x⋆i = arg inf

xi∈Xi

(fi (xi ) +λT xi ), ∀i

Update Lagrange variables:λ := λ+ α(

∑

i x⋆

i − d)

Lagrange update may beformed from average.

The solution must be ob-tained distributed:

x1

x2

x3

x4

x5

x6

xn

10

2. Coordination for loss minimization

We consider a community of households in the low-voltagedistribution grid:

r1

r2

rm

PCC

Grid

tie-connection

All households are characterized by both flexible (controllable)and inflexible consumption, and some further represent localpower production

11


The task is to schedule flexible consumption such as to

◮ Minimize local objectives on cost and comfort

◮ Obey local constraints

◮ Minimize joint objective on cost of losses

◮ Obey grid capacity constraints

The goal is to efficiently utilize the grid, while increasing thepossible installation of e.g. EVs and solar panels

12


The task is to schedule flexible consumption such as to

minimize∑

i

fi(xi ) + l(x1, . . . , xn)

subject to xi ∈ Xi , ∀i

|∑

i∈rj

xi | ≤ ν j , ∀j

13


The cost of losses is a joint objective for the community, and weuse this for coordination:

◮ Coordination among consumers

◮ Coordination between consumptionand local production

14


A centralized coordination scheme requires

◮ Knowledge about each individual control objectives

◮ Access to all dynamic models

◮ Knowledge about local constraints

unlikely that one entity will be able to collect all this

15


We enforce a distributed approach, using ADMM∗ iterations

◮ each consumer optimizes own objective, subject to localconstraints

◮ coordination is conducted by iteratively updating anddistributing tariff functions

◮ this task may be performed by the distribution systemoperator

Distribution System

Consumers

OperatorUpdate tariff, basedon local results

Local optimizationincluding tariff

∗Alternating Direction Method of Multipliers16

3. Voltage control through coordination

We consider again the low voltage distribution grid:

us

z1

i1

ppv,1q̃pv,1

p1,

q1

p̃ev,1

un

zm−1

in

ppv,nq̃pv,n

pn,

qn

p̃ev,n

zm

u1

z2

q̃ev,1 q̃ev,n

(pi , qi): inflexible consumption , (p̃i , q̃i ): inflexible consumption(ppv,i , q̃pv,i): local photo voltaic production, zi : grid impedances

17


Massive installation of EVs and photo-voltaics (PVs), may carryundesired scenarios:

|u(h)|

[pu]

Distance to transformer (h) [-]

0 10 20 30 40 50

0.9

1

1.1

1.2

18


The task is again utilize flexibility such as to

◮ Minimize local objectives on cost and comfort

◮ Obey local constraints

◮ Minimize joint objective on cost of losses

◮ Obey constraints on voltage variation

The goal is to efficiently utilize the grid, while increasing thepossible installation of e.g. EVs and solar panels

19


Consumer modeling:

◮ Consider the set of consumers H = {1, . . . , n}, over thetime period T = {1, . . . ,T}

◮ Consumer flexibility is given by EV charging and PVreactive capabilities

◮ We let Hev ⊆ H and Hpv ⊆ H denote households with EVsand and solar panels installed, respectively

20


Consumer modeling:

◮ Let Eev,h(t) denote EV state of charge (SOC):

Eev,h(t) = Eev,h(tev,h) +

t∑

τ=tev,h

Ts p̃ev,i (τ), ∀h ∈ Hev,

where tev,h denotes time of plug-in, and Eev,h(tev,h) denotesplug-in SOC.

◮ EV charging is flexible within the constraints:

Eev,h(T ) = Edem,h, Emin,h ≤ Eev,h(t) ≤ Emax,h,

pmin,h ≤ p̃ev,h(t) ≤ pmax,h, q̃ev,h(t) = p̃ev,h(t) tan(acos(ψh)),

21


Consumer modeling:

◮ Solar panel active power output is defined by weatherconditions

◮ Reactive power is controllable with the constraint:

|q̃pv,h(t)| ≤√

s2max,h − p2pv,h(t), ∀t ∈ T

where smax,h is the inverter apparent power limit.

22


Consumer modeling:

◮ For each h ∈ H and t ∈ T , the active and reactive power is

ph(t) = ph(t) + p̃ev,h(t)− ppv,h(t),

qh(t) = qh(t) + q̃ev,h(t)− q̃pv,h(t).

◮ Current drawn by each consumer is

ih(t) = f (ph(t), qh(t), uh(t)) =

(

ph(t) + jqh(t)

uh(t)

)†

, ∀t ∈ T ,

◮ We let

i(t) = (i1(t), . . . , in(t)) ∈ Cn, u(t) = (u1(t), . . . , un(t)) ∈ Cn,

23


Grid modeling:

◮ We consider grids,represented as trees:

z1

z2

us

z4

z5

z3

z6

z7

i1(t) i2(t) i3(t) i4(t)

◮ Here zi = ri + jxi denotes gridimpedance

◮ For h ∈ H, let Zh denote theimpedance indices on theunique simple path between thetransformer and consumer h

◮ Define matrix J ∈ Cn×n

[Jx,y ] =

∑

h∈Zx

zh, x = y

∑

h∈Zx∩Zy

zh, x 6= y ,

24


Grid modeling:

◮ Let Jr = Re(J), then total active losses are

∑

t∈T

i(t)†Jri(t) > 0.

◮ Voltage throughout is

u(t) = us − Ji(t), ∀t ∈ T .

◮ Voltage is constrained by

umin ≤ |u(t)| ≤ umax, ∀t ∈ T

with | · | denoting element wise complex magnitude

25


Centralized problem formulation:Given:sets: H,Hev,Hpv, signals: ph(t), ppv,h(t), qh(t) ∀ h ∈ H, t ∈ T ,matrices: J, Jr , values: ψh, tev,h for each h ∈ Hev,

solve

minimizep̃ev,h(t), q̃pv,h(t)

T∑

t=1

i(t)†Jri(t)

subject to umin ≤ |u(t)| ≤ umax,

Eev,h(T ) = Edem,h,

Emin,h ≤ Eev,h(t) ≤ Emax,h,

pmin,h ≤ p̃ev,h(t) ≤ pmax,h

q̃pv,k(t) ≤√

s2max,k − p2pv,k(t),

ij(t) = f (pj(t), qj(t), uj(t)),

for all t ∈ T , j ∈ H, h ∈ Hev and k ∈ Hpv.

26


Simplified problem formulation:

◮ We have considered only the centralized case

◮ Our approach so far:◮ Convexify main problem, by e.g. linear approximations◮ Employ sequential convex programming with iterative

update of convexifications

27


Numerical Example: A feeder from Aasted in Northern Jutland

z1

z6

z7 z11z15 z21

z20

z19

z32

z33

z41

us

z2

z5

z14

z12

z10

z8

z18

z16 z22

z23

z31

z29

z28

z26

z25

z24

z38

z34

z40

z39

z45

z42

14

57

810

11

13

14

15

16

18

19

21

22

23

24

28

29

30

31

34

28


Numerical Example: Provided datappv(t)[pu]

t

13:56 18:58 24:00 04:52 09:540

2

4

6

8

ph(t)[pu]

t

13:56 18:58 24:00 04:52 09:540.2

0.3

0.4

0.5

29


Numerical Example: Setup

◮ 34 households, 21 hrs, 10 min. sample intervals

◮ 3 cases to be examined

A. Flexibility only from EVsB. Flexibility only from PVsC. Flexibility from mixture of EVs and PVs

◮ Comparison to the current situation, where flexibility is notutilized

30


Numerical Example: ResultsBenchmark; HA

ev = {30 − 34}, HBev = {1− 7, 29 − 34}

uh(t)[pu]

t

uh(t)[pu]

13:56 18:58 24:00 04:52 09:54

0.9

1

1.1

0.9

1

1.1

31


Numerical Example: ResultsCoordinated; HA

ev = {1− 34}, HBev = {1− 7, 29 − 34}

uh(t)[pu]

t

uh(t)[pu]

13:56 18:58 24:00 04:52 09:54

0.9

1

1.1

0.9

1

1.1

32


Numerical Example: ResultsCoordinated; HA

ev = {1− 34}, HBev = {1− 7, 29 − 34}

uh(t)[pu]

t

uh(t)[pu]

13:56 18:58 24:00 04:52 09:54

0.9

1

1.1

0.9

1

1.1

33


Numerical Example: Results, mixed example

|uh(t)|

[pu]

t

pev,h(t)[kW

]

Bench.Opt.

ph(t)[kW

]

13:56 18:58 24:00 04:52 09:54

0.9

1

1.1

0

5

10

−10

0

10

34

4. Pending work

◮ Distributing the voltage coordination algorithm

◮ Communication structure should be neighbor-to-neighbor

35

4. Pending work

Simplified problem sketch:

us

r1 rmr2

xc1

x i1 xo1

l1(x i1, xo1 )

f1(xc1 )

u1

xc2

x i2 xo2

l2(x i2, xo2 )

f2(xc2 )

u2

xcm

x im xom

lm(x im, xom)

fm(xcm)

um

x i , xo : Power entering and leaving each cable section,xc consumed power, l : power losses in each cable section,f : cost function of each consumer, r : cable resistance,u: connection point voltage

36

4. Pending work

The simplified problem may be formulated as

minimizem∑

j=1

(fj(xcj ) + lj(x

ij , x

oj ))

subject to xcj ∈ Xj ,

x ij + xoj + lj(xij , x

oj ) = 0

x ij + xcj + xoj+1 = 0

u = us − Ax i

umin ≤ u ≤ umax

for j = 1, . . . ,m, where u = (u1, . . . , um), xi = (x i1, . . . , x

im) and

A ∼

r1r1 r2...

.... . .

r1 r2 · · · rm

37

4. Pending work

◮ Optimization of grid sections and consumers, are decoupled

◮ Couplings introduced through nodal and voltage constraints

38

4. Pending work

A first approach could be ADDM:

minimizem∑

j=1

(f +j (xcj ) + l+j (x ij , xoj )) + g+(z i , zo , zc)

subject to x i = z i , xo = zo , xc = zc

with superscript + denoting extended value function, and:

g+(z i , zo , zc) =

0, if z ij + zcj + zoj+1 = 0 ∀j ∧

umin ≤ us − Az i ≤ umax

∞, otherwise

39

4. Pending work

◮ The x-updates can now be run in parallel

◮ However, the z-update does not decompose well on accountvoltage coupling across entire line

◮ Current suggestion involves an axillary variable y , andreformulating constraints:

umin ≤ y ≤ umax, y = us − Axi = e1 − Cy − Dxi

with e1 = (1, 0, . . . , 0)T and

C =

[

0T 0I 0

]

D =

r1. . .

rm

40

4. Pending work

This allows a reformulation of the ADDM problem

minimize

m∑

j=1

(f +j (xcj ) + l+j (x ij , xoj )) + g+(z i , zo , zc , y)

subject to x i = z i , xo = zo , xc = zc

now with:

g+(z i , zo , zc , y) =

0, if: z ij + zcj + zoj+1 = 0 ∀j ∧

y = ei − Cy − Dz i ∧

umin ≤ y ≤ umax

∞, otherwise

here, there is still coupling across the line, but the coupling isnow reduced so that it is between neighbors only.

41

Thank you

In summary:

◮ We have discussed issues related to future smart grids

◮ We have seen how many of these naturally form distributedcontrol and optimization problems

◮ I have outlined some of the approaches we have employedso far, and presented a few of our results

42

employing distributed resources in smart grids smart...

Documents