Tackling Dynamics in Grid Integration of Wind Energy:
Modeling, Multi-scale Scheduling and Pricing
Junshan Zhang
School of ECEE, Arizona State University
http://informationnet.asu.edu
1
State-of the-Art of Power Grid
“If Alexander Graham Bell were somehow transported to the 21st century, he
would not begin to recognize the components of modern telephony – cell
phones, texting, cell towers, PDAs, etc; while Thomas Edison, one of the
grid’s key early architects, would be totally familiar with the grid.''
[ “Final report on smart grid," Dept of Energy Report, Dec. 2008]
2
Smart Grid in the Making
The many meanings of “smart”:
– Generation: renewable energy integration …
– Transmission: enhanced situational awareness …
– Distribution: demand response, micro-grid, …
– End-user: smart metering, smart appliances…
Multi-scale Power System Dynamics and
Operation Functions
4
Multi-scale Nature of Wind Energy
5
Growing Wind Generation Capacity
WIND GENERATION CAPACITY IN THE BPA BALANCING AUTHORITY AREA
MW
Sequential Increases in Capacity, Based on Date When Actual Generation First Exceeded 50% of Nameplate
3750
3522 MW
2/11/11
3500
12/1/10
11/29/10
11/15/10
8/11/10
6/6/10
3250
10/24/10
10/8/10
3000
8/11/10
6/30/10
1/15/10
2750
1/1/10
12/16/09
11/30/09
2500
9/21/09
8/6/09
5/1/09
1/27/09
1/1/09
12/7/08
6/6/08
11/17/07
2000
3/22/09
2/12/09
11/26/07
2250
1750
1500
5/10/08
4/29/08
1250
10/15/07
1000
10/5/07
750
10/4/06
8/10/06
500
11/25/05
6/28/05
12/31/2011
7/2/2011
12/31/2010
7/2/2010
12/31/2009
7/1/2009
12/31/2008
7/1/2008
1/1/2008
7/2/2007
12/31/2006
7/2/2006
12/31/2005
7/2/2005
12/31/2004
7/1/2004
1/1/2004
0
7/2/2003
1/1/2003
7/2/2002
6/18/02
1/16/02
12/31/2001
7/2/2001
12/31/2000
7/2/2000
1/1/2000
7/2/1999
1/1/1999
7/2/1998
1/1/1998
250
12/18/01
10/25/98
6
Part I
• Multi-scale Scheduling and Pricing in Smart Grids with
Wind Generation Integration [INFOCOM’11]
7
Wind Generation Integration
• Challenge: Integrating wind generation into bulk power grid is
challenging for generation planning and reliability guarantees
 Wind generation is non-dispatchable and volatile
 Reliability: balance between supply and demand all the time
• Traditional approach: ISOs and utilities rely on operating
reserves
 Operating reserve: additional generation capacity (spinning or nonspinning); more expensive than base generation
 Reserve amount (and hence the cost) monotonically increases with
the penetration level of wind energy
8
Motivation
• Supply-side management: multiple timescale scheduling for
generation planning to address supply uncertainty of wind
generation
• Demand side management: a supply-following load solution
to reduce the cost of operating reserves
– Demand response of opportunistic energy users
– Real-time pricing based on energy availability
Technical difficulty: Coupling between sequential decisions
on scheduling and pricing across multiple timescales
9
Two-settlement Electricity Market

T1
Day d-1
T2
t
Day d
T2
T2
Day-ahead Market
for Day d
Energy
Procurement
T2
T2
T2
t
Real-time Market
for Day d
– Day-ahead market (forward market)
• Unit commitment: base-load generators (hydro, thermal, nuclear,
etc.) have start time and ramp rate limits
• Schedules generations based on day-ahead forecasting of load
– Real-time market (spot market)
• Close the gap between supply and demand in spot-market
• If necessary, utilizes fast-start generators (e.g., gas turbine)
10
Opportunistic Energy Users
• A “smart” class of energy users: Opportunistic energy users
are emerging as a result of end-user technologies (programcontrolled smart appliances, smart metering, and real-time retail pricing)
[Newman 08]: 10% daily energy consumption in United States is from the
household appliances such as water heater, AC, washer & dryers, and
dish washers
• Opportunistic energy users behave different from traditional
energy users:
– Respond to price signal on a much finer timescale (minutes)
– Opportunistic access to the energy system
– Load profiles are bursty, and can be either inelastic or elastic
11
Basic Setting
• Two categories of energy resources: 1) controllable conventional energy
generation (base-load and fast-start), and 2) volatile wind generation
• Two classes of energy users: conventional and opportunistic
• Two-stage schedule at different timescales ( T1 and T2 periods for dayahead and real-time, resp.)
12
Basic Setting (2)
• Day-ahead scheduling
•
•
•
Statistical information on wind generation and demand from traditional energy users
Energy procurement from base-load generation
Day-ahead prices are announced to traditional energy users
• Real-time scheduling
•
•
•
Realizations of wind generation and demand from traditional energy users
Real-time retail prices are announced to opportunistic energy users
Fast-start generation is used, as needed, to close gap between demand and supply
13
Energy Supply Model
• Conventional energy generation
– base-load generation and peaking generation, have generation
cost c1 and c2 per unit (c2 > c1 ), resp.
– cost of base-load generation includes the start-up cost
( cP <
cP
c1)
• Non-stationary wind generation [Bouffard08]
the wind generation amount in (k,m)th slot is given by:
– Statistical information of wind generation is commonly provided
by commercial entities, and available one day ahead, to the
day-ahead scheduler
14
Energy Demand Model
• Demand of traditional energy users [Fleten 05]:
Dt  E  Dt    t
with
E  Dt   t u t
– Price elasticity:
u dE  Dt 
t 
E  Dt  du
• Demand of opportunistic energy users
Assumption: opportunistic energy users respond to real-time pricing;
– Arrive according to a Poisson process with rate0
– Accept or reject the announced real-time price v by comparing with a
price acceptance level Vi , which is random, i.i.d. across users
– Incur a energy consumption of E0
15
Problem Formulation
• Objective: maximize the overall expected profit
M
P : max  Rmu  

m 1
R     E l Rkl ,m  kl ,m ,  
k ,m
k 1
where
K
u
m
Policy dictates the energy
procurement s, day-ahead price
u for each T1 slot, and real-time
price v for each T2 slot
–
Rkl ,m  kl ,m ,  : expected net profit in the (k,m)th slot
–
 kl ,m: the system state in the (k,m)th slot
16
Non-persistent Response Model
• Non-persistent response: an opportunistic energy user leaves
the system if the current real-time price is unacceptable
• Coupling between the multiple timescale schedules
– Energy procurement S and retail price in day-ahead schedule have
significant impact on the real-time price
– Real-time price , in turn, affects the optimization of the day-ahead
schedule ( S , u )
– Joint optimization of the day-ahead and real-time schedules is needed
• A two-stage approach
– First solve the real-time scheduling problem conditioned on the dayahead decisions ( S , u )
– Then consider the day-ahead scheduling problem by making use of
the real-time scheduling policy
17
Two-stage View
• Real-time Scheduling
the expected net profit in a T2-slot:
with
• Day-ahead Scheduling
18
Approximate Solution
• Condition A:
– Wind generation is not sufficient to meet total demand
– The variance of wind generation is much larger than that of the
demand from opportunistic energy users
• Proposition I. Suppose condition A holds.
– Case I: opportunistic energy users are elastic (
):
• If energy surplus is relatively high (
• If energy surplus is relatively low (
)
)
• Otherwise
where
, and
is the expected demand from
opportunistic energy users at price
19
Approximate Solution (2)
• Proposition I (contd.)
– Case II, opportunistic energy users are inelastic (
• Proposition II. The optimal decision of
):
is given by
20
Persistent Response Model
• Persistent response: opportunistic energy users wait in the
system until the real-time price is acceptable (respond by
load-shifting)
– Opportunistic demand has memory
– Opportunistic energy users are persistent across both timescales
• A Multi-timescale Markov decision process (MMDP) formulation
– Day-ahead decisions affect real-time decision process
– Real-time decisions affect the day-ahead decisions
– Unique characteristics:
• non-overlapping horizons between day-ahead and real-time schedules
• day-ahead decisions are made solely based on distributional
understanding of the lower-level process
21
Transform to a MDP Problem
• A stationary real-time pricing policy in a T1 slot:
• Proposition III. With appropriately defined immediate reward
and action space, the two-level scheduling problem can be
written as a classic MDP at the slower time-scale, as below:
with
22
Numerical Results
• Profit margin monotonically increases with the penetration level of
wind energy
• Profit margin is higher when real-time pricing is employed with
elastic opportunistic energy users
• The amount and the elasticity of opportunistic energy users also
impact the profit margin
23
Part II
• Finite State Markov Chain Model for Wind Generation
Forecast: A Data-driven Spatiotemporal Approach [ISGT’12]
25
Wind Farm Spatial Dynamics
• A vast majority of forecasting models focus on wind speed
forecast and directly map it to wind power using turbine
power curves
• Wind farms exhibit special spatial dynamics often ignored
– Wind farms can be made of heterogeneous turbines,
from different manufacturer classes with different power
curves
– Power outputs from turbines can be unequal (and
random) even if they are identical and co-located
Distribution Forecasts
• Sophisticated stochastic design paradigms, e.g., demand
response, multi-scale pricing, are on a rise
• Critical to have a distribution forecast of wind power in
contrast to a simple ‘point-forecast,’ for efficient integration
• Continuous state space distribution forecasts may suffer
from computational complexity due to dimensionality
• Our approach:
– Finite state space Markov chain based forecast models strike a
balance between complexity and accuracy;
– Based on data from a real wind farm in western USA
Spatio-Temporal Analysis
• Use tools in graph theory and time-series analysis to
characterize probability distribution of farm aggregate
power output
– The procedure takes into account spatial dynamics of
the power output from individual turbines across the
farm, often overlooked in literature
• Using regression analysis tools, characterize temporal
dynamics of the aggregate power output of the farm, taking
into account diurnal non-stationarity and wind seasonality.
• Building on these spatial and temporal characterizations,
develop a finite state Markov chain model for forecasting
the aggregate wind power, in a rigorous optimization
framework
Minimum Spanning Tree for Wind Turbines
29
An Outline of Spatial Analysis
•
Using graph tools, identify ‘parent-child’ turbine pairs across the farm,
develop linear model for ‘parent-child’ turbine power, and analyze the
aggregate power
•
Based on spatial analysis, characterize steady state distribution of the
aggregate power output from the farm, by quantifying the power output
as a function of wind speed of a ‘root turbine’
Further Comments on Spatial Analysis
• Classic central limit theorem (CLT) cannot be applied to
characterize the distribution of aggregate wind farm output.
– Due to the correlation structure between the power output from
individual turbines;
– Due to strong correlation, even ‘CLT under weak dependence’ cannot
be applied, despite the fact that the correlation between turbine power
outputs weakens with distance between them (‘mixing distance’).
– Marginal distribution is not Gaussian or even stable laws; it is non31
stationary in general.
An Outline of Temporal Analysis
• Level crossing (LC) rate of a random process: for a given
level, the average number of times, per unit time, that the
random process crosses that level
• Using tools from auto-regression analysis, characterized
the LC rate of the aggregate
power output from the farm
• The LC rate is crucial in the
design of the Markov chain
forecast model
Characteristics of Markov Forecast Model
• Use the results from spatio-temporal analysis to design a
Markov chain forecast model for aggregate power output,
with following implementation friendly characteristics:
– 1) The Markov chain is defined on a discrete time and is of
order one
– 2) State transitions occur mostly between adjacent states
Design approach:
• Property 1: via a careful choice of the discrete time axis
resolution
• Property 2: via a careful choice of Markov state space; a
simple uniform quantization of the power output would be
insufficient
Markov State Space Design
• For any state in the state space, define the average segment
length (Tavg) as the average length of contiguous time the
power output process stays in that state
• Characterize Tavg as a function of the steady state distribution
and level crossing rates derived in spatiotemporal analysis
• Carefully choose the state space such that, for each state in
the state space,
– Tavg is close to an integer multiple of the discrete time axis
slot length
– This reduces in-slot state transitions and increases
likelihood of adjacent-states-only transitions across slots
Markov State Space Design – An Example
•
•
•
For the data at hand, more dense states around the extremes and sporadic
around the mid ranges
Fig. 1 compares Tavg for uniform and optimized state space designs
Fig. 2 demonstrates high incidence of adjacent-state-only transitions for the
non-uniform state space compared to that of uniform state space
Utilization of Wind Forecast Model:
Reserve, Demand Response and Tradeoffs
• Reserve: standby generation to address contingencies;
higher cost.
• Demand response: flexible loads that ‘follow’ available
supply;
– paradigm shift from ‘load-following supply’ to ‘supplyfollowing load’
– Consumer flexibility may be constrained
• The finite state Markov chain model for wind forecast
can facilitate demand response and reserve planning
Two Timescale Scheduling Model
• Wind energy assumed to evolve across the T2 slots
according to the finite state Markov chain forecast model
Demand Response Model
• Deferrable load contract
– Loads arrive in each mini-slot (real-time scheduling slot)
– Each arriving load can be deferred for a few mini-slots
– Number of loads that can be deferred is constrained
– If a load cannot be deferred or served, it must be dropped
with penalty proportional to the amount of dropped load
•
Number of deferrals allowed is a resource that must be
judiciously utilized, with the help of wind forecast, to minimize
average penalty
Scheduling as MDP
• Objective: to minimize average total penalty, for given
reserve and base-load generation schedules
• Define
•
- optimal average total penalty from slot t till
horizon
•
- immediate penalty in slot t
• Bellman Equation (assuming deferrable slot equal to 1)
MDP formulation (continued)
•
- current state
•
- wind realized in slot t
•
- Load arriving in slot t (perfectly forecast)
•
- Load deferred from previous slot
•
- Remaining number of loads that can
be deferred until horizon
•
- Indicator functions for various
energy surplus/deficit events
Case Study – No Deferrable Load Contract
• Consider a sample path of wind energy production,
constant load
• Without deferrable load contracts, load dropped during
energy deficits (penalties) and energy spilled during
surpluses (wastage)
Case Study – With Deferrable Load Contract,
No Wind Forecast
• Assume only one deferral opportunity allowed by the
contract
• Without wind forecast, this opportunity is used greedily in
the very first slot
Case Study – With Deferrable Load Contract,
Markov Wind Forecast
• With Markov wind forecast, the deferral
opportunity is (stochastically) judiciously used in
the third slot, saving the larger load in slot 3 and
utilizing the excess energy in slot 4
Reserve vs. Average Penalty
• The higher the reserve,
the lower the average
penalty (dropped load)
• For fixed average penalty,
lesser reserve required
with more flexible contract
• Effective integration of
deferrable contract made
possible by Markov
wind forecast model
Engineering Implication
• With integrated wind energy, if only reserve is used, higher
reserve levels are required to guarantee reliability
• ‘supply following’ demand response, along with good wind
forecast models, can be envisioned as the load-side dual of
reserves in countering wind energy volatility
• Deferrable contracts, together with Markov wind forecast
model, is shown to effectively counter wind volatility and
lower reserve level requirements
Robust CPS Inter-networking Architecture
46
CPS - Two Interacting Networks
cross-networks support
physical system
(e.g. power grid)
cyber network
(e.g. Internet)
Networked systems: modern world consists of an intricate web of
Interconnected infrastructure systems.
Interdependence: Operation of one network depends heavily on the
functioning of the other network
Vulnerability to cascading failures: node failures in one network may
trigger a cascade of failures in both networks, and overall damage on
cyber-physical systems can be catastrophic since the affected area is
much greater than that affected in a single network alone.
47
Robust Inter-networking Architecture:
Interconnecting Edge Allocation
Q) How to improve robustness against cascading failures, under constraint of
average inter-edges per node
•
•
Allocation without intra-degree information
• Random vs. Uniform allocation
• Unidirectional edges vs. bi-directional edges
Allocation with intra-degree information
• Preferential allocation
• Ranking based allocation
• Approach: compute ultimate fractions of functioning giant components, and critical
threshold pc; the lower pc the more robust
[TPDS'11]
48
Conclusions
• Modeling, scheduling and pricing for grid integration of wind energy.
• Other issues smart grid we have looked into: robust CPS architecture, data
processing (decision tree for contingency analysis; fault diagnosis based
on Markov random field model of PMU data).
•
Our research on wireless networks: cognitive radio, wireless scheduling
with hard deadlines, network optimization, information theory …
• Many emerging research problems need “marriage” of
expertise: (renewable energy, power system, social networks)
+ (communication, control, computing) …
49
• Backup slides
50
Conclusion for Part II
• The often overlooked spatial dynamics between turbine
power outputs is studied using graph theoretical tools, and
the steady state distribution of the farm aggregate power
output is analytically characterized
• The temporal dynamics of the aggregate power is studied
using auto-regression analysis tools and analytical level
crossing rates are derived
• Based on the spatial and temporal characterizations, a
realistic Markov chain model to forecast aggregate power
output is developed.
Uniform Allocation of B-directional Edges (Cont’d)
Stage 3: Network A’s further fragmentation due to B-node failures
inter-edge can be disconnected w.p. 1-PB(p’B2)
The remaining fraction of A1: 1-(1-PB(p’B2))k
For A, the joint effect of Stage 1&3 on A equals
the node failures in A with fraction
Key step: further node failures
in A1 at Stage 3 has the same
1-p’A3=1- p+p(1-PB(p’B2))k
effect as taking out equivalent
fraction of nodes in A
functioning giant component A3
pA3=p’A3PA(p’A3)
54
Uniform Allocation of Bi-directional Edges (Cont’d)
functioning giant component size in the dynamics of cascading failures
Stage 1
network A
network B
pA1=pPA(p)
pB2=p’B2PB(p’B2)
Stage 3 pA3=p’A3PA(p’A3)
Stage 2
Stage 4
pB4=p’B2PA(p’B2)
….
….
 The recursive process reaches an equilibrium point
 By calculating the equilibrium point, we can get the ultimate giant component
size and critical threshold
55