1Model Predictive Control of Industrial Loads andEnergy Storage for Demand Response
Xiao Zhang∗ , Gabriela Hug† , J. Zico Kolter‡ , and Iiro Harjunkoski§∗ Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, USA† Information Technology and Electrical Engineering, ETH Zurich, Switzerland‡ Computer Science, Carnegie Mellon University, Pittsburgh, USA§ ABB Corporate Research, Ladenburg, Germany

Abstract—With the potential to enhance the power system’s
operational flexibility in a cost-effective way, demand response isgaining increased attention worldwide. Industrial loads such as
cement crushing plants consume large amounts of electric energy
and therefore are prime candidates for the provision of significant
amounts of demand response. They have the capability to turnon/off an arbitrary number of their crushers thereby adjusting
their electric power consumption. However, the change in power
consumption by cement crushing plants and also other industrial
loads are often not granular enough to provide valuable ancillary
services such as regulation and load following. In this paper, we
propose a coordination method based on model predictive control
to overcome the granularity restriction with the help of an energy
storage.
Index Terms—Demand response, industrial loads, model predictive control, ARMA prediction, regulation, load following.

I. I NTRODUCTION
Renewable generation resources such as wind turbines andsolar panels are expected to be widely deployed in the future toenable a sustainable energy future. However, the intermittent
and uncertain nature of power output from these renewable resources imposes challenges on power system operation, which
requires large amounts of balancing resources to enhance theoperational flexibility of the grid. According to the Federal
Energy Regulatory Commission, “effective demand response
can help reduce electric price volatility, mitigate generation
market power, and enhance reliability” [1]. Demand response
is gaining increased popularity all over the world, as it demonstrates potentials to enhance the power system’s operational
flexibility in a cost-effective way [2]–[5]. Moreover, demand
response has been one of the key components in the Smart
Grid R&D program, as stated by the US Department ofEnergy: “One of the goals of the Smart Grid R&D Programis to develop grid modernization technologies, tools, andtechniques for demand response” [6]. In recent years, there
have emerged a number of studies and projects on demand
response, provided by residential, commercial, or industrial
loads, e.g. by electric vehicles [7], residential areas [8]–[10],buildings [11], aluminum smelters [12], [13], air separation
units [14], as well as steel plants [15], [16].
Within the realm of demand response, industrial loads
have the following advantages [17], [18]: most industrial
loads have already installed the infrastructures for control,
measurement, and communications which are necessary for
demand response; the adjustments of the power consumption
The authors would like to acknowledge the financial support by ABB.

from many industrial loads can be very large, fast, andaccurate; the industrial loads are also strongly motivated toparticipate in demand response programs even at the costof increasing their operation complexity, as making profitsis their primary concern. Industrial loads that can support
the power system operation through demand response include
aluminum smelting pots, steel melting furnaces, fans, freezers,
pumps, mills, crushers, etc. The industrial demand response
resources are not only participating in the energy markets
through programs like load shifting, they are also actively
providing ancillary services such as spinning reserve, load
following, and regulation. For instance, in previous work
we have studied the regulation provision and load following
by aluminum smelters [12], developed an offering strategy
for spinning reserve by aluminum smelters [13], and use a
resource-task network framework to enable the steel plant
scheduling with spinning reserve provision [15].
Different from spinning reserve which only involves the
reduction of power consumption, regulation and load following
require a much faster response of power change, both up anddown, and hence are much more valuable in the ancillary
service markets. Lots of industrial loads are able to provide
very fast change of power in both directions, qualifying themfor regulation and load following. For example, the crushers
or mills in the cement industry can be switched on and offvery rapidly [19], [20]. However, most of these industrial
loads can only provide power changes in a discrete manner,e.g. the power change is several MWs at a time. This coarse
granularity hinders those industrial loads from providing themost valuable ancillary services, as the regulation and load
following in the current electricity markets require a continuous change of power. Consequently, these balancing resources
with fast consumption changing capability are not utilized to
the full extent.
In this paper, we intend to overcome the granularity restriction for those industrial loads discussed above. We propose acoordination framework in which the industrial loads provide
the regulation or load following services with the help froman on-site energy storage: the industrial loads provide a large
but discrete power change which constitutes as the main bodyfor the service, while the energy storage provides a fine andcontinuous power change which ensures that the combinationof the two accurately follows the desired power signal. These
two parts are coordinated by a model predictive control (MPC)
approach which incorporates the prediction of the upcoming
signals of the services into the decision making. As seen in

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the case study, the combination of the industrial loads and theenergy storage is able to accurately follow the regulation orload following command in a very wide range.
The key contribution of this work is the proposed coordination method for providing ancillary services such as regulationand load following by a combination of a storage device andan industrial plant capable of adjusting its power consumption
in large discrete steps. We demonstrate that the whole isgreater than the sum of its parts. The remaining of the paper
is organized as follows: Section II describes the considered
problem. Section III presents the coordination method byMPC, in which the prediction method is introduced in Section
III-A and the optimization at each MPC step is explained in
Section III-B. The case study for the cement crushers andenergy storage is discussed in Section IV to demonstrate theeffectiveness of the proposed approaches, based on which theconclusions are drawn in Section V.
II. P ROBLEM S TATEMENT
A variety of industrial loads can be switched on andoff very rapidly, which enables them to change the power
consumption rate fast and frequently, e.g. the crushers (mills)
in the cement crushing industry [19] and the crushers in thethermal mechanical paper & pulp industry [21]. In this paper,
we want to investigate and provide the mechanisms to use
these industrial loads for the provision of regulation service.
However, the proposed method can also be employed to enableload following. For simplicity, we assume there are n machines
which can be switched on and off rapidly, and each machine
has a power consumption rate of ρ MW. Note that in practice
the power consumption rates for different machines may not
be the same, yet the proposed method can be easily extended
to consider this deviation from our assumption.
The regulation signal of PJM (currently the largest competitive wholesale electricity market in the US) is published in[22], in which the RegD dynamic regulation signal is designed
for fast-responding resources. We will use this RegD signal
for our study. The accurate prediction of the regulation signal
is impossible over a long time period, e.g. several minutes.
However, predictions with reasonable accuracy for a horizonof around 1 minute are possible by using autoregressivemoving-average (ARMA) models. As demonstrated later, thisprediction is good enough for the coordination of the industrial
loads and the energy storage. The regulation signal is in
per unit value and it ranges between -1.0 and 1.0. Thissignal multiplied by the regulation capacity R MW plus theregulation baseline B MW is the regulation command for theindustrial plant, i.e. the targeted power consumption rate in
MW.
The industrial loads are switched on/off or adjusted tofollow the regulation command with the support of an onsite energy storage. It has been demonstrated that stand alone
storage has significant potentials to support the power system
operation [23], [24], whereas in this paper the flexible charging
power of the storage helps the industrial loads to overcome
the granularity restriction. We assume that the storage has amaximum energy capacity of E MWh and its charging power

Fig. 1. MPC coordination framework.

is bounded by −P and P MW. To simplify the problem, we
further assume that there is no energy loss associated with the
charging and discharging processes. Note that the energy loss
can be considered easily by extending the formulations. The
industrial loads and the energy storage are coordinated by the
MPC method, which is presented in the following section.
III. C OORDINATION BY M ODEL P REDICTIVE C ONTROLThe coordination framework is illustrated in Fig. 1. At eachstep t, the ARMA predictor outputs the regulation prediction
for the next H steps, based on historical regulation commands;
then the optimal controller optimizes over the number of active
machines xi and the storage charging power yi for each timei = t, · · · , t + H in the MPC horizon, based on the regulation
prediction and previous operation record of the machines; after
obtaining the optimization results, only the optimal decisions
for the current time step t is applied to the industrial loads
and the energy storage.
A. Prediction
We have trained different ARMA models by the Time Series
Analysis package in Python (statsmodels.tsa). For different
training data sets [22], the ARMA(2,1) model resulted in thebest performance, in terms of Akaike information criterion(AIC) scores. The ARMA (2,1) model is described by:ωt = φ1 ωt−1 + φ2 ωt−2 + θ1 t−1 + t
in which ωt stands for the regulation signal, t stands forthe white noise. The auto-regressive parameters φ1 , φ2 andmoving-average parameters θ1 are trained and obtained by
the Python package statsmodels.tsa. The regulation prediction
mean squared errors by ARMA(2,1) for different prediction
horizons are plotted in Fig. 2 and compared to the Persistence
Model and the Mean Prediction approach. The Persistence
Model uses the latest available observation as prediction and
the Mean Prediction uses the average from all available observations as prediction. According to Fig. 2, the ARMA(2,1)
model results in a good performance up to horizons of around
1 minute by ARMA(2,1). The Python implementation for theprediction is available online1 .
B. Optimal Control
The objective of the optimal control is to provide high quality regulation service at low cost. The decision variables for
1 https://github.com/xxxzhang/Reg

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actions in the objective function. The number of switch actions
st+i at the i-th step is defined as:si ≥ |xt+i − xt+i−1 |∀i ∈ H(3)

in which the right side represents the change in the numberof active machines between time steps.
4) Storage Level Deviation: Another objective is to control
the final energy level in the storage for each MPC horizon.
Otherwise, if the energy level is near its full capacity, thenthere is little room for the storage to contribute to the provisionof regulation. This deviation is defined asd ≥ |et+H − e|in which e is the targeted storage level. We usually set e equal
to 50% of its energy capacity.
5) Storage Energy Balance: The energy balance for the
storage describes the relationship between stored energy andits charging power, as given by:

Fig. 2. Prediction mean squared errors.

et+i − et+i−1 = yt+i δ
the optimal control are the number of active machines and thecharging power for the storage. In this paper, we assume thatthe regulation capacity and the regulation baseline are fixedin advance and they are denoted as R (MW) and B (MW),respectively; how to optimally choose these values is part of
future research. Note that the average power consumption of
the industrial machines is therefore B MW, as the regulation
signal is balanced, i.e. the integral over time is zero; thisindicates that the plant throughput, which is proportional tothe energy (MWh) it consumes, is close to the base load,as the energy level in the storage changes very little. The
optimization formulations for the optimal control are statedas follows.
1) Objective: In the optimization objective, we penalize
the regulation violation vi , the number of machines switchingaction si , and the deviation d of the final storage energy levelfrom the targeted level, as in:Xminimize(αvi + βsi ) + γd(1)i∈Hin which α, β, γ are the penalty parameters. Different valuesof the penalty parameters indicate different preferences for the
regulation provision. Details of the impact of these parameters
are discussed in the case study.
2) Regulation Violation: The regulation signal prediction
for step i within the optimization horizon is denoted as ω
bt+i .
According to the regulation prediction, the regulation violation
vt+i at the i-th step is defined as:
vt+i ≥ |B + Rb
ωt+i − Pm xt+i − yt+i |(4)∀i ∈ H(2)

in which the first two terms on the right side correspond to
the regulation command and the last two terms correspond to
the plant power consumption rate. Since we penalize vt+i in
the objective function, the above constraint can be formulated
as two linear inequality constraints.
3) Machine Switching: Too much switching of the machines potentially increases degradation and may even damage
the machines; that is why we penalize the number of switch∀h ∈ H(5)

where δ is the length of one time step. In addition, the energy
in the storage is constrained by the storage capacity.
6) Switching Limitation: In practice, the industrial machines cannot be switched on/off without causing inconvenience. For example, the machines cannot be switched too
frequently, otherwise the machines could get damaged. Hence,
we restrict the number of switch actions to be no more than s̄
for every successive L steps (typically, L > H) for each MPC
step t and each time i in the MPC horizon, as given by:
t−1
X
j=t+i−L

sej +

t+i
X

sj ≤ s̄ ∀i ∈ H

(6)

j=t

in which the first term corresponds to the summation of switch
actions that already took place before i, and the second term
stands for the possible number of switch actions that may
take place from i to the end of this MPC horizon. Notethat the above constraint applies to each step i within the
MPC time horizon, as we require the switching to not violate
the bound on number of switchings for every successive L
steps. Consider an example where H is 10 steps and L
corresponds to 100 steps, if there are s̄ times of switching
between t-100 and t-90, then the first 10 steps within this MPC
horizon cannot allow for any switching. Other constraints
on switching limitation can be considered in a similar way,e.g. the minimum energy consumption requirement of themachines for successive time durations.
7) Variable Ranges: The decision variables can take values
within the following bounds:
xt+i ∈ {0, 1, ..., n} and − Ps ≤ yt+i ≤ Ps∀i ∈ H(7)

in which xt+i is an integer variable while yt+i is a continuous
variable.
To sum up, the MPC recedes forward and at each time step t,
it first predicts the upcoming regulation signals, then optimizes(1) subject to constraints (2)-(7), but only applies the optimal
decisions at time step t. The resulting optimization problem
is a mixed integer linear programming problem, which can besolved by CPLEX very quickly as the problem size is small.

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Fig. 3. Regulation signal (AGC) over one hour and its prediction.
Fig. 4. MPC simulation results.

IV. C ASE S TUDY
A. Parameters
For the case study, we consider a cement plant with n = 4
crushing machines which can be switched on and off rapidly.
The power consumption rate of each machine is Pm = 2
MW when it is on. The on-site energy storage has E = 1
MWh energy capacity and its maximum charging/discharging
power is Ps = 3 MW [25]. In the following simulations, thecement plant provides R = 6 MW regulation at a baselineof B = 4 MW. In other words, the regulation command
ranges between -2 MW and 10 MW. Note that the range of theregulation command is 12 MW, which is much higher than thatof the energy storage. The one hour regulation signal for thesimulation is plotted in Fig 3, together with the ARMA(2,1)
prediction at a few distinct time instances. The length of thetime step is δ = 2 seconds.
B. Simulation Results
The MPC simulation results over the hour are plotted inFig. 4, in which the prediction horizon is H = 15 steps, thepenalties α, β, γ are all taken as 10, the targeted final energy
is ē = 0.5 MWh, and we require the maximum number ofswitch actions to be s̄ = 10 times for every successive 5
minutes, i.e. L = 150 steps. According to the simulation in
Fig. 4, the integral of regulation violation over the hour is only
0.01 MWh, the total number of switch actions is 21 times, andthe storage energy level at the end of the hour is 0.6 MWh, i.e
the energy deviation is 0.1 MWh. In the second plot in Fig. 4,
the dashed lines are the bounds for the charging/discharging
power of the storage. The simulation results demonstrate thatthe coordination method proposed in this paper is able toutilize the advantages from both the industrial loads and theenergy storage, and provides high-quality regulation service tosupport the power system operation.
The impacts of the penalties are investigated by simulations
with different penalty values. First of all, if we increase
the penalty on switch actions β, the total number of switch
actions is expected to decrease. For example, increasing β to
200 while keeping all other parameters the same as before
yields to the simulation results in Fig. 5, in which the total
number of switches decreases to 12 times but the regulation
violation increases to 0.12 MWh. Secondly, if we increase

Fig. 5. Simulation results with increased penalty on switch actions.

the penalty on the energy level deviation γ, then we cando better at stabilizing the energy level in the storage. For
instance, the simulation results for increasing γ to 1000 while
keeping all other parameters unchanged at 10 are displayedin Fig. 6, in which the energy level in the storage is very
stable, however, there are as many as 34 switching actions.
Thirdly, if we impose a stronger switch limitation constraint,
e.g. requiring the maximum number of switches to be 4 forevery successive 5 minutes, then the switch frequency will
decrease, as demonstrated by the simulation results in Fig. 7.
However, there is more regulation violation and the storage
energy level varies dramatically.
In practice, we suggest to the plant operators to choose theirown penalties according to their preferences. For example, inan electricity market where the regulation quality is highly valued, a higher regulation violation penalty α is recommended;
meanwhile, if switching the machines is very expensive, thenthe operator should use a large switching action penalty β.
V. C ONCLUSION
The key contribution of this work is the proposed coordination method for providing the most valuable ancillary services
such as regulation and load following by the combination of
the industrial loads, which can adjust their power consumption
only in large discrete steps, and the energy storage, which
provides the more granular power adjustments.

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restrictions on granularity.
R EFERENCES

Fig. 6. Simulation results with increased penalty on energy deviation.

Fig. 7. Simulation results with stronger switching limitation constraint.

Thanks to the coordination method proposed in this paper,
the industrial loads have more options in supporting the powersystem operation through demand response. The industrial
loads are able to overcome the granularity restriction andprovide regulation or load following ancillary services, withthe help of an on-site energy storage. The power change fromthe industrial loads serve as the main contributor in the service,while the charging power from the storage is responsible for
eliminating the mismatches. Note that the method proposedin this paper applies to a variety of industries, e.g. cement
crushing, paper milling, and steel melting, and applies toboth load following and regulation service. The proposed
framework also has other potential applications outside of
demand response, e.g. the coordination among fast and slow
generators and energy storage.
Additional future work includes how to optimally decide theregulation capacity and baseline for the combination of industrial loads and energy storage, and how to schedule the entire
industrial plant such that providing regulation will not interrupt
the processing flows within the plant. Some practical concerns
also need to be addressed such as the charging/discharging
loss in the energy storage and the mileage compensation inproviding the regulation or load following service. Besides,
the method proposed here intends to provides a solution to
the problem that the current electricity markets cannot fully
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