Industrial Demand Response by Steel Plants with
Spinning Reserve Provision
Xiao Zhang† , Gabriela Hug† , Zico Kolter‡ , and Iiro Harjunkoski§† Electrical and Computer Engineering, Carnegie Mellon University, USA‡ Computer Science, Carnegie Mellon University, USA§ ABB Corporate Research, Ladenburg, Germany

Abstract—Demand response has gained significant attention
in recent years as it demonstrates potentials to enhance thepower system’s operational flexibility in a cost-effective way.
Industrial loads such as steel manufacturing plants consume large
amounts of electric energy, and their electricity bills account for aremarkable percentage of their total operation cost. Meanwhile,lots of industrial loads are very flexible in terms of adjusting theirpower consumption rate, e.g. through switching the transformer
tap position. Hence, industrial loads such as the steel plants haveboth the motivation and the ability to support power system
operation through demand response. In this paper, we focus on
the steel plant and optimize its scheduling to maximize its profits
from both the energy and the spinning reserve markets.
Index Terms—Demand response, spinning reserve, industrial
load, resource-task network (RTN), steel plant.

I. I NTRODUCTION
Increased operational flexibility is an inherent characteristicof what is commonly referred to as the smart grid. This isbecause a large share of renewable generation resources suchas wind and solar generation are expected to be deployed toenable a sustainable energy future. However, the power outputof these renewable resources is intermittent and uncertain
which requires significant amounts of balancing resources toincrease the operational flexibility of the grid. Traditionally,
the power system relies on generators to provide such flexibility, but it is not economical for generators to frequently change
their output. Hence, demand response has gained significant
attention in recent years as it demonstrates potentials toenhance the power system’s operational flexibility in a costeffective way [1]–[3]. There have been intensive discussions
and promising solutions for demand response provided bybuildings [4], storage [5], data centers [6], [7], residential
areas [8], as well as industrial loads [9]–[11].
Within the realm of demand response, industrial loads havethe following advantages [12], [13]: the magnitude of power
consumption by an industrial manufacturing plant and thechange in power it can provide are generally very large;
besides, the industrial plants usually already have the infrastructures for control, communication and market participation,
which enables the provision of demand response; moreover,
The authors would like to acknowledge the financial support by ABB.

some industrial plants are able to offer fast and accurate adjustments in their power consumption [9], [14]. Among these industrial loads, steel manufacturing is a highly energy-intensive
process and also has the required consumption flexibility. A
steel plant with electric arc furnaces has a limited capability
to schedule its production activities to follow a desired energy
consumption profile over time. A steel plant can reduce its
loading level drastically by controlling the transformers that
supply power for its equipment, which enables the provisionof spinning reserves.
Besides their capability, industrial plants also have the incentive to actively contribute to the electricity markets throughdemand response programs. Nowadays, with the needs forindustrial materials slowing down, and the competition fromall over the world, industrial plants such as aluminum smeltersand steel manufacturing plants have experienced a hard timein recent years, especially in developed countries [15], [16].
Demand response could be an opportunity for these industrial
plants to make use of their assets and increase their profits.
For instance, the industrial plants can move the most energyintensive activities to off-peak hours thereby reducing theirelectricity bills; in addition, they can also sell ancillary services to the electricity markets by effectively utilizing theiroperational flexibility.
In this paper, we study the participation of the steel plants
in demand response. The steel plant is assumed to be aparticipant in the day-ahead electricity markets, both energy
and spinning reserve markets, and we want to optimize itsscheduling of production activities to maximize its revenues
from the electricity markets. The remaining of the paper isorganized as follows: Section II introduces the schedulingproblem that we are interested in; Section III explains theresource task network approach that we use to model thesteel plant scheduling problem; in Section IV, the optimalscheduling model is proposed and described; the case study ofa typical steel plant is discussed in Section V, based on which
the conclusions are drawn in Section VI.
II. P ROBLEM S TATEMENT
The considered steel production process is illustrated inFig. 1. There are four stages in the production. In the firststage, the solid metal scrap (e.g. recycled from abandonedcars) is transformed to molten metal in the electric arc furnaces

(EAF); then, the impurities in the molten steel such as carbon
elements are extracted by the argon oxygen decarburization(AOD) units in the second stage; in the ladle furnaces (LF)stage, the molten metal gets refined and the quality of themetal is further improved; and finally, the molten metal iscasted into slabs by the continuous casters (CC). The slabs
are the final products of the melt-shop production, and they
can be classified into different categories according to theirsteel grade, slab width, slab thickness and so on.
For the first three stages, the equipment processes a particular amount of metal at one time. That particular amount
depends on the size of the equipment units, e.g. the volume of
the furnace. Each such amount of metal is termed as a heat.
Using the definition of heats, we can quantify the throughputof the steel plant, e.g. a medium-sized steel plant produces
around 20 heats a day. For the fourth stage, the casters operatecontinuously but subject to certain critical constraints: thecasters are only allowed to process a limited number of heats
after which they need maintenance (e.g. changing the castermold and tundish). Usually a campaign of several heats sharing
the same or very similar features such as steel grade andslab shape are casted together as a campaign group, and thecasters can be maintained between these campaign groups.
The casting order for the heats within one group should follow
certain rules and the casting sequence must not be interrupted.
The power consumption rate of the EAFs can be adjusted
very quickly by switching the on-load tap changers (OLTCs)of the transformers which supply power to the EAFs. Thisqualifies the steel plant to be a valid demand response resourcefor providing spinning reserve. The amount of spinning reserve
it can provide depends on the melting power profile, i.e.
the power consumption rate of the melting process, and thesustaining (minimal) power the furnace requires to keep themolten metal from solidification.
The payment structures for spinning reserve are different
across different electricity markets. In most North American
electricity markets, e.g. the Midwest Independent System Operator (MISO) where demand response is actively encouraged
and where an aluminum smelter (Alcoa’s Warrick Operation)
has participated as a regulation provider for the first time,
spinning reserve is compensated by both reserve capacity
and actual allocation. In other words, the spinning reserve
provider gets paid for the capacity it has committed to provide
independent of if this reserve capacity is dispatched or not; andif it does get dispatched, it receives an additional payment as
the allocation compensation. However, the actual dispatch ofspinning reserve is very rare. According to Alcoa’s Warrick

Fig. 1: Production process of steel manufacturing [17]Operation, the regulation provider we previously mentioned
who is also offering spinning reserve to MISO, their socalled interruptible load (i.e. spinning reserve) only gets 55
deployments annually with an average length of 42 minutes,
resulting in an actual dispatch rate of only around 0.44% [14].
Even if the capacity payment rate is fairly low, the spinningreserve providers still find it profitable as they earn money
simply by standing by and waiting.
In this paper, we consider the participation of the steel plantin a day-ahead electricity market, from the perspective of thesteel plant scheduling. The scheduling horizon is one day. The
daily production activities, i.e. the heats to produce, are known
ahead according to the business contracts and the long-termscheduling. The hourly prices of the day, both energy andspinning reserve, are assumed to be known ahead: these prices
may be part of a given demand response program contract orthey could also be obtained by prediction techniques. Given
the production activities and their power profile, the steel plant
optimizes the scheduling to minimize its net cost - the costof electric energy minus the revenue from spinning reserve
provision. Of course, the steel plant endures other aspects ofcost such as labor, metal scraps, chemical ingredients and soon. But all these costs are fixed in the daily operation andtherefore we do not take them into account in the operation optimization process. Furthermore, the impact of actual dispatchof spinning reserve is not considered in this daily schedulingproblem, as the dispatch rate is very low and it should betaken into account in a longer term, e.g. weekly or monthly,
optimization problem.
III. R ESOURCE TASK N ETWORK M ODELING
We model the steel plant and its production activities
through a resource task network (RTN) approach. Figure 2
provides an illustration of the RTN of a steel plant. The
circles represent resources such as equipment units used indifferent stages, intermediate and final products for different
heats, electric energy usage and spinning reserve provision.
As intermediate products are transferred from one stage to thenext, they are super-indexed with s or d to specify their current
locations (start or destination, respectively). For example, EAdh
represents the intermediate product between stage EAF andAOD that has already been transferred to the AOD stage
and is waiting to be processed. The RTN modeling in thispaper also employs resources of electric energy (EN) andspinning reserve (SP) to help accumulate the plant’s energy
usage and reserve provision. The set of resources in the steel
plant is denoted by S, i.e. S = {EAF, AOD, LF, CC} ∪{EAsh , EAdh , ALsh , ALdh , LCsh , LCdh , Hh |h ∈ H}∪{EN,SP} with
H as the set of heats to produce. We use a matrix Y ∈ R|S|×T
to denote the amount of each resource available at all timeslots, in which |S| is the size of S; we use a discrete time gridwith uniform time slot width of t0 , and T is the total numberof time slots. Each element of Y is a continuous variable,
ys,t , which stands for the available amount of resource s attime t. For example, yEAF,t = 2 means there are two furnaces
available at time slot t; yEAdh ,t = 0 means either intermediate
product EAdh has not been transported to AOD yet or has

Fig. 2: Resource task network for a steel plant.
already been processed by AOD, while yEAdh ,t = 1 means EAdh
is there waiting to be processed; yEN,t = 100 MWh means thesteel plant uses 100 MWh electric energy during time slot t;
ySP,t = 50 MW means the plant provides 50 MW of spinningreserve to the power system. Actually, most ys,t can only takediscrete values such as 0, 1, or 2. However, we model them as
continuous variables for computational considerations, but as
discussed later the constraints in the optimization model will
enforce them to take discrete values.
The tasks are denoted by rectangles in Fig. 2. There are
two types of tasks: the operational tasks at each of the fourstages and the transfer tasks between the stages. There is
one task for every heat h for each type of operation andtransfers except for the casting; these tasks are denoted by
the task type sub-indexed with the corresponding heat, e.g.
Eh stands for the melting of heat h in the EAF stage, andEAh (without super-index s or d) denotes the transfer of heath between stage EAF and AOD. Unlike the first three stages
where parallel units are not distinguished, we treat the casters
individually because different casters are designed for casting
different slabs. Besides, as mentioned before, the tasks in the
CC stage are executed by group instead of by heat. Therefore,
the casting task is denoted by Cg,u which corresponds to thecasting of group g by caster unit u. Note that Cg1 ,u1 is different
from Cg1 ,u2 . For example, their casting durations might bedifferent due to the different casters. Of course, only one of
Cg1 ,u1 and Cg1 ,u2 will actually take place as group g1 should
be casted exactly once. We use K to denote the set of tasks,
i.e. K = {Eh , EAh , Ah , ALh , Lh , LCh |h ∈ H} ∪ {Cg,u |g ∈G, u ∈ CC}, with G and CC as the set of casting campaign
groups and available casters, respectively.
A |K|-by-T binary matrix X is used to denote the startingtimes of tasks, in which |K| is the size of K. Each element of
X is a binary variable xk,t that denotes whether task k starts attime slot t. For instance, xEh ,t denotes whether the processing(melting) of heat h in stage EAF starts at time slot t or not.
Hence, only one out of xEh ,t , t = {1, . . . , T } is non-zero.

Fig. 3: Illustration of interaction parameters for a melting task.
In Fig. 2, the networks are represented by arrows whichindicate how each task interacts with each resource. For eachtask k ∈ K whose duration is τk time slots, the interaction
parameter ∆k is a |S|-by-(τk + 1) matrix that quantifies how
much task k consumes or generates of each of the resources
as it proceeds. For instance, its element ∆ks,1 quantifies theinteraction between task k and resource s at the beginningof the first time slot during this task, and ∆ks,τk +1 quantifies
the interaction at the end of the last time slot. ∆k is very
sparse and a zero element means that there is no interaction.
The interaction parameters for a melting task are illustrated
in Fig. 3. The time slot width in Fig. 3 is t0 = 15 minutes.
The duration of the melting task is 45 minutes. Therefore, themelting spans 3 time slots. This task interacts with resources
EAF, EN, SP and EAsh , and its interaction parameter matrix
only has four rows with nonzero elements. At the very
beginning, the task reduces EAF by one as it uses one furnace.
After the completion of the melting process, EAF is increased
by one as that furnace is freed up. Also, EAsh is increased by
one to promote the execution of the following transfer. The

melting task consumes electric energy continuously during its
entire duration. The sustaining power is assumed to be 48 MW,
hence, it can provide 32 MW spinning reserve for each timeslot.

2) Task Execution: We use the following constraints tomake sure that the tasks are executed the proper number oftimes, as in
XK¬CC 1T = 1(4)
10 XCu 1T = 1 ∀u ∈ CC

IV. O PTIMAL S CHEDULING

in which XK¬CC denotes X without the rows involving thecasting tasks; XCu denotes the rows of X corresponding tocasting tasks by caster u; 1T means a vector of 1s with length
T and 1 stand for vectors of 1s with appropriate lengths. The
above constraints ensure that each heat is processed exactly
once by all types of tasks within the scheduling horizon.
3) Waiting Time: In steel plant operations, it is common to
enforce the transfer task to be executed immediately after thecompletion of its preceding processing task. This requirement
is reflected by enforcing

The scheduling model in this section is based on the
Aggregated Equipment Resource and Simple Transfer Tasks
model from [17], and has been updated to incorporate spinningreserve provision. As discussed in Section II, the following
scheduling model does not consider the impact of actual
dispatch of spinning reserve, as the actual dispatch is veryrare and we assume that there is no actual dispatch in thescheduling horizon.

YEAs = 0

A. Constraints
1) Resource Balance: Resource evolution over the time
horizon is managed by the resource balance equation, as in
ys,t = ys,t−1 +τkXX∆ks,θ · xk,t−θ ∀s ∈ S¬{EN,SP } , ∀t (1)k∈K θ=0in which the value of resource s at time step t is equal toits previous value at t − 1 adjusted by the amounts generated/consumed by all the tasks. Only nonzero ∆ks,θ implies
actual interaction and the interaction only occurs when task k
is proceeding, i.e., the interaction occurs at time slot t only
if task k starts θ earlier than t (xk,t−θ = 1) and ∆ks,θ 6= 0.
S¬{EN,SP} stands for the set of all the resources except EN
and SP. For any resource s ∈ S¬{EN,SP } , its initial value
is integer: the initial value is zero for any intermediate or
final product, and the initial value for any equipment equals
to the number of units available in the steel plant. Since theinteraction parameters ∆ks,θ for these resources are integers
and xk,t−θ are binary variables, the ys,t can only take integer
values due to constraint (1). As mentioned before, even thoughys,t only take integer values, we model them as continuous
variables to reduce the computation burden for this mixed
integer programming problem.
The electric energy usage of the steel plant is calculated as
yEN,t =

τkXX

in which YEAs stands for the rows of Y corresponding to
the intermediate products EAs ; 0 is a zero matrix with thesame dimensions as YEAs . Similar constraints apply for theintermediate products ALs and LCs .
The transfer time of the intermediate products, wEA , wAL ,and wLC , are assumed to be independent of the specific heats
and the exact locations of the units. We use w̄EA , w̄AL , andw̄LC to denote the maximum allowable transportation times
that ensure that the intermediate products are processed by
the next stage in time before the cooling effects adversely
affect the product quality. Therefore, the maximum waitingtime constraint for intermediate products should be satisfied,
YEAdh 1T ≤(w̄EA − wEA )
1
t0

∀t

(2)

k∈K θ=0

where ∆kEN,θ is the electricity used by task k at the θ-thtime slot duration of its execution. We assume that only the
EAF can provide spinning reserve, and the provided spinningreserve should be upper bounded by its availability, as given
by
τk
X
X
ySP,t ≤∆kSP,θ · xk,t−θ∀t(3)k∈{Eh |h∈H} θ=0with ∆kSP,θ denoting the available spinning reserve.

(6)

in which YEAd stands for the rows of Y corresponding tointermediate products EAd before the transfer. The left sideof the constraint corresponds to the number of time slots
during which the intermediate product is waiting before being
processed. Similar constraints apply for intermediate products
ALd and LCd .
4) Product Delivery: The final products should be available
at the end of the time horizon, which is enforced by
yHh ,T = 1∆kEN,θ · xk,t−θ

(5)

∀h

(7)

in which yHh ,T stands for the availability of the final productfor heat h at the end of the scheduling horizon.
5) Spinning Reserve Provision: Spinning reserve is tradedhourly in most electricity markets. The time slot width in thediscrete time formulation is usually smaller than the trading
window. Once the reserve provider has committed to themarket an hourly quantity, it is obligated to guarantee thatamount of reserve for any time slot in that hour. In otherwords, the time slots belonging to the same hour (Thr ) should
provide the same amount of spinning reserve, as enforced by
ySP,t − ySP,t0 = 0∀t, t0 ∈ Thr(8)

TABLE III. Nominal processing times [min] [17]
heats
60

Price [$/MW]

EnergyPrice
ReservePrice
40

20

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour

H1 −H4H5 −H6H7 −H8H9 −H12H13 −H14
H15 −H16
H17
H18
H19
H20
H21 −H22
H23 −H24

EAF1 EAF2 AOD1 AOD2 LF1 LF2 CC1 CC2
80
85
85
90
85
85
80
80
80
80
80
80

80
85
85
90
85
85
80
80
80
80
80
80

75
80
80
95
85
85
85
95
95
95
80
80

75
80
80
95
85
85
85
95
95
95
80
80

35
40
20
45
25
25
25
45
45
30
30
30

35
40
20
45
25
25
25
45
45
30
30
30

50
60
55
60
70
75
75
60
70
70
50
50

50
60
55
60
70
75
75
60
70
70
50
60

Fig. 4: MISO hourly prices on 02/06/2014.

B. Objective Function
The objective of the scheduling is to minimize the net costof the steel production, i.e. the electric energy cost minus
the spinning reserve revenue. Given the energy and spinningreserve price vectors λEN , λSP ∈ RT , the overall optimization
problem is formulated asminimizeX

YEN λEN − YSP λSP

subject to (1) − (8)xs,t ∈ {0, 1}, ys,t ∈ [0, ȳs ], ∀s, ∀t
in which ȳs is the upper bound for the available amount of
resource s. For example, ȳEAF equals to the number of EAF
furnaces and ȳEN equals to the summation of energy usage by
all the equipment units in one time slot.
V. C ASE S TUDY
In this section, we present the study of the daily schedulingfor a typical steel plant to demonstrate the effectiveness of the
optimal scheduling model.
A. Problem Parameters
The hourly energy and spinning reserve prices for the casestudy are taken from MISO, as displayed in Fig 4. Note that the
spinning reserve (capacity) prices follow the trend of energy
prices, but are much lower. In practice, the hourly prices are
obtained either from demand response contracts, e.g. timeof-use pricing programs, or price prediction techniques. For
the latter case, the prices are uncertain and are decided by
the markets, and we have to rely on price prediction tools.
We could simply use the point-wise price prediction or the
expected price if its distribution is available. Note that theconstraints in Section IV do not involve any price information.
The steel plant layout and parameters are taken from thetypical scheduling example in [17] and are restated here. There
are two parallel units for each of the four stages, and the
TABLE I. Nominal power consumptions [MW] [17]equipment EAF1 EAF2 AOD1 AOD2 LF1 LF2 CC1 CC2
power
85
85
2
2
2
2
7
7

TABLE II. Steel heat/group correspondence [17]
group
G1
G2
G3
G4
G5
G6
heats H1 −H4 H5 −H8 H9 −H12 H13 −H17 H18 −H20 H21 −H24

nominal power consumption rates of the units are given in
Table I. The group correspondences of the heats to produce are
given in Table II, and their nominal processing times are shownin Table III. It can be observed from these tables that the EAF
is the most energy-intensive process stage. The transfer times
wEA , wAL , and wLC are 10, 4, and 10 minutes respectively, andthe maximum waiting times w̄EA , w̄AL , and w̄LC are 240, 240,
and 120 minutes. The caster setup times are 70 minutes forCC1 and 50 minutes for CC2, which are the times needed forequipment maintenance between casting two groups of heats.
The sustaining power needed for spinning reserve provision isassumed to be 60% of the nominal EAF melting power.
B. Scheduling Results
The optimal scheduling results of the model in Section IV
are given in Table IV, in which t0 is set as 15 minutes. The
four rows correspond to different scenarios with respect to how
many and which groups are being scheduled and processedin the simulation. The column Groups gives the campaign
groups to produce, e.g. the first row denotes scheduling group1, 2, and 3 with the heats as indicated in Table II; w/o
SP stands for the scheduling model without spinning reserve
provision, which corresponds to the above model but without
the resource SP and only minimizing electric energy cost;with SP is the scheduling model described in Section IV
including spinning reserve; the column Obj represents the final
objective value of the optimization problem; the column EN
stands for the electric energy cost while the SP represents
the spinning reserve revenue. All these optimization problems
are mixed integer linear programming problems and we solve
them in MATLAB by TOMLAB/CPLEX on a linux 64 bit
machine. The relative optimality tolerance is set as 10−6 , andall these optimization problems are solved to optimality within
three minutes. With spinning reserve participation, the electricenergy cost increases a little bit, but the net cost of the steel
plant operation is reduced because of the spinning reserve
revenues. The decrease for the case studies here are around1%.
We also set t0 as 10 minutes to study the scheduling witha finer time grid. The optimal scheduling results are listed inTable V. The time limit for CPLEX is set to 2 hours. Forscheduling groups 1-5 under both w/o SP and with SP, therelative objective gap between the best integer objective (by afeasible solution) and the best bound remaining in the iteration
process are 0.02%. Compared with the results in Table IV, thefinal objective values in Table V are slightly improved because
the rounding error due to discrete-time formulation is reduced

80

w/o SP

with SPGroupsObj(k$)

Obj(k$)EN Cost(k$)

SP Revenue(k$)

1-3
1-4
1-5
1-6

39.30757.82469.73186.34639.00257.35769.15785.50839.32157.86469.89786.474

0.319
0.507
0.741
0.966

TABLE V. Optimization results with t0 = 10min
w/o SP

with SPGroupsObj(k$)CPU Time(s)EObj(k$)CPU Time(s)

1-3
1-4
1-5
1-6

39.04157.51769.16285.228397.7
637.8
7200.0916.038.65157.00968.46884.164739.7
1094.77200
3569.7by using a finer time grid. However, the computation time in
Table V grows drastically as the number of variables (bothinteger and continuous) increases by a factor of 1.5.
The equipment assignment chart for scheduling 24 heatswith spinning reserve provision is displayed in Fig. 5. The
rectangles denote the tasks. Different heats are represented
by different colors. From Fig. 5 we can observe that thescheduling solution is valid: each heat is processed sequentially by each stage; each campaign group of heats are casted
together without any interruption, and there is enough time forcaster maintenance between each two campaign groups on thesame caster; for any time slot, each equipment is occupied
by one single task and there is no conflict in equipment
assignment. Figure 5 also shows that the RTN model is able
to generate detailed and practical schedules that can be easily
understood by the steel plant operators. The corresponding
spinning reserve provision schedule is displayed in Fig. 6.
The maximum spinning reserve provided is around 70 MW.
The spinning reserve provision cannot always stay at the
maximum value due to constraint (8). The hourly spinningreserve provision should be less or equal to the available
spinning reserve in any time slot of that hour.
VI. C ONCLUSIONThe RTN-based scheduling model for the steel plant is able
to optimize the steel plant’s production activities such that it
can benefit the most from electricity markets. The steel plant isable to make use of the electric arc furnaces to offer spinningreserve services to the electricity markets and earn revenues.
With the provision of spinning reserve, the steel plant could
further lower its operation net cost. The proposed schedulingFig. 5: Equipment assignment for scheduling 24 heats.

Spinng reserve [MW]TABLE IV. Optimization results with t0 = 15min

SP provision

60
40
20
0
1

5

9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 9396
Time slot [15 min]Fig. 6: Spinning reserve provision from scheduling 24 heats.
model is computationally effective and can generate detailed
and practical production schedules.
ACKNOWLEDGMENT
We gratefully acknowledge the discussions with Marjia
Zima and Xiaoming Feng from ABB and Dragoljub Gajic
from ThyssenKrupp Acciai Speciali Terni Steel Plant.
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