1

Achieving the Dispatchability of DistributionFeeders through Prosumers Data Driven Forecasting

and Model Predictive Control of ElectrochemicalStorage

Fabrizio Sossan, Member, IEEE, Emil Namor, Student Member, IEEE, Rachid Cherkaoui, Senior Member, IEEE,Mario Paolone, Senior Member, IEEE.

Abstract—We propose and experimentally validate a controlstrategy to dispatch the operation of a distribution feederinterfacing heterogeneous prosumers by using a grid-connectedbattery energy storage system (BESS) as a controllable elementcoupled with a minimally invasive monitoring infrastructure. Itconsists in a two-stage procedure: day-ahead dispatch planning,where the feeder 5-minute average power consumption trajectoryfor the next day of operation (called dispatch plan) is determined,and intra-day/real-time operation, where the mismatch withrespect to the dispatch plan is corrected by applying recedinghorizon model predictive control (MPC) to decide the BESScharging/discharging profile while accounting for operationalconstraints. The consumption forecast necessary to compute thedispatch plan and the battery model for the MPC algorithmare built by applying adaptive data driven methodologies. Thediscussed control framework currently operates on a daily basisto dispatch the operation of a 20 kV feeder of the EPFL universitycampus using a 750 kW/500 kWh lithium titanate BESS.

Index Terms—Battery storage plants, Optimal control, Mod-eling.

I. INTRODUCTION

THE progressive displacement of conventional generationin favor of renewables requires to restore an adequate

capacity of regulating power to assure reliable power systemoperation. An emerging concept to tackle this problem consistsin achieving the controllability of portions of distributionnetworks by exploiting controllable distributed energy re-sources (DERs), such as flexible loads and battery energystorage systems (BESSs), and dispatching local generation.This paradigm can be traced in a number of frameworks,such as virtual power plants (VPPs) and microgrids which, inbroad terms, consist in operating aggregates of heterogeneousDERs to provide ancillary services to an upper grid later, e.g.dispatchable power for primary/secondary frequency/voltagesupport and energy management (e.g. [1]–[3]). In general,solutions based on aggregating the capability of DERs requirean extended ICT infrastructure and an efficient control policyto harvest flexibility until LV distribution level [4]–[6]. As amatter of fact, these solutions are of difficult integration in

The authors are with the Distributed Electrical Systems Laboratory,Ecole Polytechnique Federale de Lausanne, Switzerland (EPFL), e-mail:{fabrizio.sossan, emil.namor, rachid.cherkaoui, mario.paolone}@epfl.ch.

This research received funding from the Swiss Competence Center forEnergy Research (FURIES) and Swiss Vaud Canton within the initiative “100millions pour les energies renouvelables et l’efficacite energetique”.

the existing grid because: (i) they might not offer the samereliability level as conventional generation, (ii) they are notalways compatible with current regulation schemes, and (iii)their technical requirements are not met. An essential aspect toenable the transition towards a smarter grid is the availabilityof plug-and-play solutions, namely solutions that can provideancillary services to the grid in the current operational and reg-ulatory framework with a reduced set of technical requirementswith minimal complexity level. In this paper, we propose andexperimentally validate a control framework that achieves todispatch the operation of a medium voltage (20 kV) distribu-tion feeder by using a BESS. It is implemented as a two-stageprocedure: day-ahead scheduling, where the feeder dispatchplan is determined, and an intra-day stage where the mismatchis tracked to zero by adjusting the BESS power injectionsby using model predictive control (MPC). In comparison toconventional closed loop controllers, integrating the BESSmodels into the MPC framework improves the awareness ofthe control action thanks to an efficient handling of the BESSconstraints and the possibility of integrating predictions atdifferent time scale. Both battery and consumption forecastingmodels (the latter is used during day-ahead operation) areidentified and estimated from measurements (data-driven) andrelies on a minimally invasive monitoring infrastructure.

EPFL sub-transmission grid

Primary Substation50/20 kV20 MVA

P (aggregated consumption)

L (feeder consumption)

Office buildingswith PV injections(300 kWp)

20/0.17 kV0.75 MW

B (BESS injection)

Lithium Titanate BESS500 kWh/750 kW

Dispatched feeder. Known power flows.

Fig. 1. The experimental setup: a MV distribution feeder of the EPFL campusequipped with an utility-scale BESS. The only requirement for dispatching thefeeder is knowing the power flow at the GCP and the BESS power injection.Measurements are provided by a PMU placed at the beginning of the feederand the battery management system (BMS). The feeder consumption L isestimated from the other two measurements.

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The experimental validation is performed on a distributionfeeder supplying five buildings with photovoltaic generation(300 kWp), using a grid connected 750 kW/500 kWh lithiumtitanate BESS. The paper is organized as follows: Section IIstates the problem, III presents the two-stage control strategy,IV discusses the models that were identified and their inte-gration in the MPC strategy, V summarizes the experimentalsetup, VI presents the experimental results and VII draws theconclusions.

II. PROBLEM STATEMENT

We consider a distribution network populated by an un-known mix of electric loads, possibly distributed generationtoo, and equipped with a BESS. The power transit at thegrid connection point (GCP) and BESS power injection areknown from measurements, which are respectively providedby a remote terminal unit (RTU) or a phasor measurementunit (PMU) installed at the root of the feeder and the batterymanagement system (BMS). An example of the setup is givenby our experimental configuration, depicted in Fig. 1. Fig. 1also introduces the notation for the power flows: P is theaggregated consumption as seen at the GCP, B is the BESSinjection (positive when discharging and viceversa) and L isthe feeder consumption, that, by ignoring transmission lossesbetween the BESS and GCP, is estimated as L = P −B. Theproblem is given by dispatching the feeder according to a 5-minute average power consumption profile, called feeder dis-patch plan, that is determined the day before operation. Sim-ilarly to the conventional power system operational paradigmbased on day-ahead scheduling and intra-day balancing, thecontrol strategy consists in a two-stage structure (see Fig. 2).• Day-before operation: the feeder dispatch plan is de-

termined based on consumption forecasts and used todispatch the operation of the feeder;

• Intra-day/real-time operation: the BESS power injectionis controlled in order to compensate from any deviationsfrom the dispatch plan (that are likely to occur due toprediction errors) using a MPC action to account forBESS operation constraints.

The choice of the 5 minute dispatch interval is according to theenvisaged trend for real-time electricity markets. Although notspecifically discussed in this work, this formulation potentiallyallows for day-ahead scheduling considering also dynamicelectricity prices, in a similar way as done in [7]–[9].

Time (hours before the beginning of the day of operation)

TSO Dispatchable feeder operator BESS

The feeder dispatch plan on a5-minute basis is determined.

-12

0

The feeder is dispatched accord-ing to the dispatch plan.

Tracking of the dispatch plan.

24

Receding horizon MPC tocontrol BESS injections.

Day-ahead scheduling Intra-day and real time operation

Fig. 2. One hour before operation, the dispacth plan is sent to the grid balanceresponsible, e.g. transmission system operator (TSO). At the beginning ofthe day of operation, the feeder is dispatched, and a receding horizon MPCdetermines the battery charge/discharge power set-point in order to correctthe load mismatch with respect to the dispacth plan.

There are two motivations underlying the willingness ofdispatching the feeder:

1) it is a bottom-up solution to decrease the amount ofregulating power capacity required to operate the grid, awell known issue related to operating the grid at a largeproportion of production from intermittent renewablegeneration. The amount of regulating power, that couldbe potentially saved on a large scale might be indeedused to schedule additional renewable generation too.

2) the feeder dispatch plan is built in order to respect thepower flow constraints at the GCP, therefore implicitlyaccomplishing congestion management in this point al-lowing the integration of non-dispatchable generation.

The control strategy is passive, in the sense that its objectiveis strictly local and does not require exchange of informationwith other parts of the grid. Moreover, the fact of relying on aminimally invasive monitoring infrastructure (only the powertransit at the GCP is required) makes this strategy an eligiblesolution for DSOs who might install utility scale BESSs inprimary substations to provide ancillary services to the gridand manage local congestions.

III. METHODS

A. Day-ahead scheduling

The objective is to determine the feeder dispatch plan,namely the average power consumption profile on a 5-minutebasis that the feeder should follow the day-after. We denotethe feeder dispatch plan as the sequence P0, P1, . . . , PN−1 ofN = 288 (number of 5-minute intervals in 24 hours) averagepower consumption values. The feeder dispatch plan is as:

Pt = Lt − Bot , t = 0, . . . , N − 1, (1)

namely, the difference between the predicted power con-sumption profile L and the BESS demand Bo necessary tobring the battery state-of-charge (SOC) to a predefined targetvalue, denoted as SOC∗. The reason of the latter contributeis promptly explained: at the end of the day of operation,the BESS SOC is likely different than e.g. 50%, that is theoptimal level to compensate for unbiased (i.e. with nonzeromean error) consumption forecast. Indeed, including in thedispatch plan the battery charge/discharge demand to restoreand adequate charge level for the coming day of operationnaturally allows to ensure continuity of operation and optimalfeeder dispatchability. A similar solution is also envisaged in[10], whereas it is normally disregarded in dispatch strategiesfor PV installations, which normally assume that the batterycan be charged during overnight [11]–[13].

1) Computation of L (day-ahead consumption forecasting):The feeder consumption is only known in terms of aggregatedpower consumption (type and consumption and individualloads are unknown). Therefore, we approach the forecastingproblem applying a simple black-box, data driven methodbased on vector autoregression (VAR). The forecasting proce-dure is as follows. First, the vectors are obtained by splittingthe time series of the historical power consumption measure-ments with 5 minutes resolution in 1-day long sequences (inour study, 1.5 year of data were considered). Vectors are

3

grouped into two sets, according to if they refer to nationalholidays or not. The consumption forecast for a given dayis determined by selecting the right set of vectors (holiday ornon-holiday) and then averaging the p most recent vectors thatrefer to the same day of week (Monday, Tuesday, . . . ), wherep is a design parameter (in our case is empirically chosenas 3). It is noteworthy that the formulation of the proposedcontrol strategy is independent of the forecasting tool used atthis stage.

2) Computation of Bo (BESS demand): The BESS demandprofile is with the objective of achieving the target BESSSOC∗. Additionally, it should be such to peak shave the ag-gregated power consumption to respect power flow constraintsat the GCP. These requirements are modelled by the followingconvex optimization problem:

Bo0 , . . . , B

oN−1 = arg min

B0,...,BN−1

N−1∑t=0

(SOC∗ − SOCt)2 (2)

subject to:

SOCt+1 = SOCt + ηBt

Enom· 60 · 53600

, t = 0, . . . , 1− 2 (3)

0 ≤ SOCt ≤ 1, t = 0, . . . , N − 1 (4)

|Bt| ≤ Bnom, t = 0, . . . , N − 1 (5)

Pt = Lt + Bt, t = 0, . . . , N − 1 (6)

|Pt| ≤ Snom · PF, t = 0, . . . , N − 1 (7)

where Enom is the BESS nominal energy capacity in kWh,η and Bnom the efficiency and nominal power of the BESSconverter, Snom the nominal apparent flow of the substation,and PF the power factor of the substation power transit.Although the BESS converter is four-quadrant and the reactivepower can be easily included as control objective in theproposed formulation, at this stage we only focus on theactive power (we assume PF=1). Since day-ahead procedure isperformed one hour before operation, SOC0 (the initial BESSSOC) is still unknown and, therefore, needs to be estimated. Inthis case we use a simply persistent predictor, namely SOC0 asthe current SOC. If available, one might consider to use short-term consumption forecast (e.g. one-hour-ahead) to improvethe SOC0 estimate.

B. Intra-day/real-time operation

At the beginning of the day of operation, the feeder isdispatched according to the dispatch plan. During operation,the consumption will likely differ from it because forecastingerrors: the objective of intra-day operation is to control theBESS power injection in order to compensate for deviationswith respect to the dispatch plan. The decision process isimplemented using MPC, that is applied in a receding horizonfashion once each 15 seconds with updated measurements.Before proceeding further with the formulation, we introducethe following notation (that is also exemplified in Fig. 3):• double index subscripting, like (t, k), denotes quantities

with 15 seconds resolution: indexes respectively refers tothe 5 minutes interval and 15 seconds subinterval. E.g.

Lt0 is the measured power consumption of the feeder,averaged over the first 15 seconds of the 5-minute intervalwith index t.

• Ltk denote power consumption measurements, that pro-gressively become available in real-time. Bo

tk is the BESSpower injection set-point on the AC side calculated by theMPC strategy (superscript o stands for “optimal”).

In the following, we will introduce two MPC formulation inincreasing order of complexity.

Interval index

Subinterval index

Lt0 Lt1

Bot2

Pt: average powerconsumption to achieve

Current time instant (t, 2)

t t + 1

0 1 2 3 4 5 6 . . . 18 19 0

Bot0 Bo

t1

Fig. 3. The main interval is divided into 20 subintervals: double indexsubscripting denotes quantity sampled at 15 s. Lt0, Lt1, . . . are averagepower consumption measurements which are progressively available. At thebeginning of each subinterval, the BESS power injections Bo

t0, Bot1, . . . are

computed by the MPC. Here, it is sketched the situation at time (t, 2), wherethe consumption measurements from the previous subintervals are known, andBt2 is determine.

1) MPC: Formulation A (MPC-A): Say being at time (t, k),the dispatch plan error is defined as:

etk =

0, k = 0

Pt −1

k

k−1∑j=0

(Ltj +Btj) , k > 0, (8)

e.g. at (t, 2) as in Fig. 3, it is the sum of known terms

et2 = Pt − (Lt0 +Bt0 + Lt1 +Bt1) /2 (9)

if et2 = 0, we would have that

Pt = (Lt0 +Bt0 + Lt1 +Bt1)/2 (10)

namely, the average power consumption in the time frame(t, 0) to (t, 2) equals Pt, exactly the (partial) fulfillment ofthe intra-day operation objective. The target of MPC is todetermine, at each subinterval, a suitable discrete controlaction to perform zero-tracking of (8) using the BESS. Thedispatch plan error (8) corrected accounting for the currentcontrol action Btk is:

Pt −1

k

k−1∑j=0

(Ltj +Btj) +Btk

= etk −1

kBtk (11)

We seek for the control action Botk that minimizes the squared

value of (11) while respecting BESS constraints, formally:

Botk = arg min

Btk∈R(etk − 1/k Btk)

2 (12)

subject to

Bmin ≤ Btk ≤ Bmax (13)vmax ≤ vtk+1 ≤ vmax (14)0 ≤ SOCtk+1 ≤ 1 (15)vtk+1 = f(Btk, SOCtk) (16)SOCtk+1 = g(Btk, SOCtk) (17)

4

The constraints (13)-(15) are to respect BESS converter nom-inal power, battery DC nominal voltage and SOC limits. Notrespecting those might result in anomalous BESS conditions,which are eventually conducive to disruptive general systemfailures, like converter tripping. Clearly, system failures arehighly undesirable because they imply the complete loss ofcontrollability. In this respect, MPC allows to handle systemconstraints more efficiently than conventional close-loop con-trol strategies. Expressions (16)-(17) specify that voltage andSOC predictions are determined by the prediction models fand g, which will be presented in Section IV. In order toretain a convex formulation of the optimization problem, fand g will be linear functions of the decision variable. Weexplicitly seek for convexity because it allows for an efficientcomputation of the solution of the problem (if exists) withguaranteed convergence.

2) MPC: Formulation B (MPC-B): It can be noted fromFig. 3 that at time t(t+1, 0) it not possible to compensate forthe events at the previous subinterval (Lt19) because they referto two different dispatching periods. In order to compensatein advance for the next power consumption realization, weintroduce the concept of short-term consumption forecast.Being at time (t, k), the predicted dispatch plan error is as:

etk+1 = Pt −1

k + 1

k−1∑j=0

(Ltj +Btj) + Ltk +Btk

(18)

where Ltk denotes the power consumption for the incomingsubinterval period, that is calculated as the average of the pre-vious three power consumption realizations (with respect to thepersistent predictor, normally used for short-term consumptionprediction at high level of disaggregation e.g. [14], this allowsa smoothing effect). We reformulate (18) as:

etk+1 = e−tk+1 −1

k + 1Btk, (19)

e−tk+1 = Pt −1

k + 1

k−1∑j=0

(Ltj +Btj) + Ltk

. (20)

The objective of this MPC is to find the value of Btk thatminimizes the squared value of (19). Formally, it is as:

Botk = arg min

Btk∈R

(e−tk+1 −

1

k + 1Btk

)2

(21)

subject to the same constraints (13)-(17) as the previous MPCformulation.

IV. PREDICTION MODELS FOR BESS AND THEIRINTEGRATION INTO MPC

A. Grey-box dynamic voltage models

Battery models for control applications are normally tothe purpose of predicting the terminal voltage as a functionof the charge/discharge current or power and trade detailedmodelling of electrochemical reactions for an increased levelof tractability, as e.g. in [15]–[17]. In this work, the purposeof this section is to formalize the constraints (13)-(17). Systemidentification of voltage dynamics is carried out by applying

grey-box modelling, a framework that allows to identify avalidated model incorporating available physical knowledgetogether with measurements from a real device [18], [19].In our specific case, it consisted in: (1) model formula-tion, (2) estimation of model parameters from experimentalmeasurements (BESS voltage and charge/discharge current)using maximum likelihood estimation (MLE) and (3) modelvalidation through checking for residual correlations in theone-step-ahead prediction errors (residual analysis). If theresidual analysis is satisfactory the model is retained (4),otherwise a new model is formulated (adding for examplea state) and the procedure above is repeated. In order toachieve an efficient identification of the system dynamicsout of the BESS voltage measurements, we performed aspecific experimental session where we controlled the BESScharge/discharge power according to a nearly pseudo-random-binary-signal (PRBS), a signal with two states (±200 kW),constant period and random, uniformly distributed duty cycles.The general model structure is from existing literature andconsists in a voltage generator with a series resistance andmultiple RC-branches, until accomplishing the criteria (4)specified above. To capture the dependency of the modelparameters with respect to the BESS SOC, we estimated fivesets of parameters by feeding MLE with the identificationsignal performed at five different level of BESS SOC (10,30, 50, 70 and 90%): during operation, the right set ofparameters is selected according to the current BESS SOC(model scheduling)1. Models are formulated using continuous-time, stochastic state-space representation:

dx = Ac(θ)xdt+ Bc(θ)udt+Kc(θ)dω (22)

vtk = CTxtk +DT (θ)utk + qetk (23)

where x ∈ Rn is the system state vector, A ∈ Rn×n,B ∈Rn×2, C,D ∈ Rn are the state-space matrices, ω is a standardn-dimension Wiener process, θ a vector of p parameters toestimate and ek a white noise process with variance q2

1) Model Selection and Formulation: It was found thatthe third order model shown in Fig. 4 was able to satisfythe residual analysis for all the SOC ranges. The modelis formalized as in (22)-(23) with the following state-spacematrices, state vector and inputs:

Ac =

−1R1C1

0 0

0−1R2C2

0

0 0−1R3C3

,Bc =1/C1 01/C2 01/C3 0

(24)

Kc = diag(k1, k2, k3), C =[1 1 1

]T,D =

[Rs E

]T(25)

x =[vC1

vC2vC3

], utk =

[itk 1

]T(26)

where the estimated model parameters are shown in Table I.The residual analysis of the selected model in the case of

1It is known from the literature that parameters of equivalent circuit modelsalso depend on temperature and C-rate [15]: at the current stage, thesedependencies are not included in the models and will be the focus of futureinvestigations

5

50% SOC is shown Fig. 5: vertical lines denotes the auto-correlaction function of the model one-step-ahead predictionerrors (using the training data set), while the horizontal linesare the limits of the autocorrelation function (ACF) of whitenoise (uncorrelated by definition) at 95% confidence level.The lasts should be considered as the thresholds above/belowwhich the model residuals are correlated in time. Fig. 5denotes that the model structure together with the identifiedparameters was able to capture all the dynamics contained inthe measurements data set. This condition was also satisfiedfor the other combinations of parameters of Table I. Modelsare characterized by a fast time constant (few seconds) andtwo slower (minutes). Since the MPC is applied once every30 and that the fastest dynamic of the system correspond toa real eigenvalue, it is computationally convenient to drop itand replace it with an algebraic relationship.

TABLE IEXPERIMENTALLY ESTIMATED MODEL PARAMETERS ACCORDING TO

THE BESS STATE-OF-CHARGE

SOC 0.1 0.3 0.5 0.7 0.9E 592.2 625.0 652.9 680.2 733.2Rs 0.029 0.021 0.015 0.014 0.013R1 0.095 0.075 0.090 0.079 0.199C1 8930 9809 13996 9499 11234R2 0.04 0.009 0.009 0.009 0.010C2 909 2139 2482 2190 2505R3 2.5e-3 4.9e-5 2.4e-4 6.8e-4 6.0e-4C3 544.2 789.0 2959.7 100.2 6177.3k1 0.639 0.677 0.617 0.547 0.795k2 -5.31 -0.22 -0.36 -0.28 0.077k3 5.41 40 0.40 2.83 -0.24

−+

E i

Rs

R1

C1

+vC1

−

R1

C1

+vC2

−

R1

C1

+vC3

− v

Fig. 4. Equivalent circuit of the BESS voltage model. The quantities vand i are respectively the BESS terminal voltage and DC current, whilevC1

, vC2, vC3

denote the states of the state-space model.

0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

1

Lag

AC

F

Fig. 5. ACF of model residuals (full line) and white noise (horizontal lines)at 95% confidence level.

2) Implementation of voltage models in the MPC: Theobjective is to determine the voltage evolution as a linearfunction f of the BESS power injection Btk. We denote thediscretized voltage models as:

xtk+1 = Axtkdt+ Butk +Kω. (27)

Combining this with (23), yields:

vtk+1 = CAxtk + CButk +Dutk (28)

By partitioning the input vector and matrices as

B =[B0 B1

], D =

[D0 D1

], (29)

the expression (28) can be written as:

vtk+1 = α+ βitk,

α = CAxtk + CB1 +D1, β = CB0 +D0.(30)

The average BESS power injection during the time interval(t, k) to (t, k+1) is approximated by the product between theDC current, average DC voltage and converter efficiency η:

Btk = itk · η(vtk+1 + vtk)/2 (31)

Multiplying both sides of (30) by η(vtk+1 + vtk)/2 and usingthe expression above for Btk leads to:

v2tk+1 + (vtk − α)vtk+1 − (αvtk + 2/η · βBtk) = 0. (32)

Solving for vtk+1 and considering only the physically mean-ingful solution, i.e. positive voltage:

vtk+1 = h(Btk) =

= −vtk − α2

+

((vtk − α)2

4+ αvtk +

2

ηβBtk

)1/2

. (33)

The function h(Btk) above is the BESS voltage evolution asa function of the AC injected power. The linearization withrespect to Btk is given by its first order Taylor approximation:

vtk+1 ≈ h(Bx) +dh

dBtk

∣∣∣∣Btk=Bx

(Btk −Bx), (34)

where Bx is the linearization point. Our choice for Bx is zero2.In (34), the first derivative of h with respect to Btk is:

dh

dBtk=β

η

((vtk − α)2

4+ αvtk +

2

ηβBtk

)−1/2. (35)

Summarizing, the linear relationship between the BESS volt-age and power is

vtk+1 ≈ f(Btk) = h(0) + dh/dBtk

∣∣Btk=0

Btk. (36)

3) State estimation: In state-space battery voltage models,the full information on the state vector x (necessary in (30)to compute the system evolution) is not available becauseindividual state components are a modelling abstraction anddo not correspond to measurable quantities. Rather, theircontributions are lumped into the measurement of the batteryterminal voltage v, normally available from the BMS. Sincethe residual analysis of the previous section indicated overallsatisfactory performance, state estimation is performed withKalman filtering (KF, [20]) that is known to provide bestestimates in hypothesis of i.i.d. system and measurementnoise. KF consists in a two-stage procedure, repeated at eachdiscrete time interval: a prediction step to determine the system

2If available, one might choose a more suitable value for Bx to obtain abetter approximation of the voltage estimate; e.g. if the battery is due toabsorb power (i.e. the dispatch plan is biased in the positive direction), Bx

could be as −Bnom/2.

6

evolution (state expected value and covariance matrix P )solely on the basis of the knowledge on the system

xk|k−1 = Axk−1|k−1 + Buk−1 (37)

Pk|k−1 = APk−1|k−1AT +KKT , (38)

and an update stage, where the predicted state is correctedaccounting for the last measurement yk

xk|k = xk|k−1 +G(yk − Cxk|k−1) (39)

Pk|k =(P−1k|k−1 + C

T v−1C)−1

. (40)

where G is the Kalman gain:

G = Pk|k−1CT(CPk|k−1CT + v2

)−1, (41)

where v is the measurement noise (also known from theparameters estimation). KF requires full system observability,that in our case is enforced by construction since the modelis estimated from measurements. It is noteworthy that whencomputing (37), there are two possible choices for the inputsignal u: the battery power, known since it is the control set-point, or the average DC current, that is normally known fromthe BMS at the next discrete time interval. We use the latterbecause it allows to retain a linear formulation of the problem(the former would require extended KF).

B. State of charge model

1) Model Formulation: The one-step-ahead prediction ofthe BESS SOC is as:

SOCtk+1 = SOCtk + γitk (42)

where the coefficient γ = Ts/Cnom is the ratio between thesubinterval duration and the BESS nominal capacity Cnom, andSOCtk is known from the BMS.

2) Linearization of SOC constraints: The objective is todetermine the evolution of the BESS SOC as a function glinear in the BESS power injection Btk. Multiplying both sidesof (42) by η(vtk+1 + vtk)/2 and rearranging yields:

(SOCtk+1 − SOCtk) η(vtk+1 + vtk) = 2γBtk, (43)

that by using (36) to approximate vtk+1 and reorganizing is:

SOCtk+1 ≈ l(Btk) = SOCtk +2γ

η

Btk

mBtk + b+ vtk. (44)

As for the voltage, the linearization of the BESS SOC withrespect to Btk is obtained by a first order Taylor approximationaround Btk = 0:

SOCtk+1 ≈ g(Btk) = l(0) + dl/dBtk

∣∣Btk=0

Btk (45)

where

dl/dBtk = (b+ vtk)/(mBtk + b+ vtk)2. (46)

V. EXPERIMENTAL SETUP

The setup used for the experimental validation of the pro-posed control strategy (shown in Fig. 1) consists in a mediumvoltage (20 kV) distribution feeder that serves five office build-ings of the EPFL campus and equipped with a grid-connected750 kW/500 kWh BESS (Fig. 6). Office buildings embed300 kWp of non dispatchable PV generation. The BESS isbased on the lithium titanate technology and can performup to 20 thousand cycles without noticeable capacity fading.Although the feeder under consideration is completely instru-mented with a real-time, PMU-based monitoring infrastructure(see [21]), the control algorithm only relies on the aggregatedpower consumption measurements at the GCP. Fig. 7 showsthe information flow during operation: PMU measurements areused to compute average power consumption values on a 1-second period. These are timestamped, saved in a time seriesdatabase and processed by a MATLAB script that computes inreal-time the BESS set-point according to the feeder dispatchplan, that was determined the day before by a second script.Set-points are finally actuated by the BESS converter. Thecontrol strategy currently operates on a daily basis in a rollingtime fashion to dispatch the operation of the feeder.

Fig. 6. A view of the 500 kWh/750 kW Lithium Titanate-based BESS usedin this work. The system, developed by Swiss company Leclanche, includesa four-quadrant fully controllable DC/AC converter and a 0.3/20 kV step-uptransformer. It is hosted in a temperature controlled container (picture of AlainHerzog, EPFL).

Measurements Server(InfluxDB on Debian)

Controller(MATLAB)

PMU

BMS

Converter

Dispatch plan,Measurements.

Syncrophasor measurementsat the GCP to compute the

aggregated PQ injections (50 Hz).

Battery state, alarms,PQ injections,

DC voltage and current (1 Hz).

Battery active power set-point(piecewise constant at 0.1 Hz).

PQ set-point (1 Hz).

Fig. 7. Architecture of the control and acquisition system: components andinformation flow. Measurement refresh rates are reported in parenthesis. Dataare exchanged over an IP network, using UDP, in the case of of PMUmeasurements, and TCP, for the other measurements.

VI. RESULTS AND DISCUSSION

In this section, we analyze the experimental results obtainedby applying the algorithm detailed in sections III and IV todispatch the operation of the MV feeder described in the pre-vious section. The discussion encompasses the analysis of twoday scenarios, denoted as day senario 0 and day scenario 1which respectively show the operation of MPC-A and MPC-B. The analysis concerns two main aspects: the first is to

7

0 5 10 15 200

50

100

150

Time (Hour of day)

Rea

lpo

wer

(kW

)

Consumption forecastBattery demandDispatch plan

(a) Day-ahead operation: computation of the dispatch plan.

0 5 10 15 2040

60

80

100

120

140

160

180

Time (Hour of day)

Rea

lpo

wer

(kW

)

ConsumptionConsumption and BESSDispatch plan

(b) Intra-day operation: real-time dispatch plan tracking.

0 5 10 15 20−100

−50

0

50

100

150

Time (Hour of day)

DC

Cur

rent

(A)

0 5 10 15 2050

60

70

80

90

100B

ESS

stat

e-of

-cha

rge

(%)

(c) Intra-day operation: BESS current and SOC (30 s resolution).

Fig. 8. Experimental results during day scenario 0 with MPC-A.

exemplify the operation of the control strategy and the secondis a quantitative assessment of the performance of the twoMPC controllers.

A. Experimental operation of the control strategy

Fig. 8 shows the operation of MPC-A during the experimen-tal day scenario 0. Fig. 8a shows the elaboration performedin the day-ahead stage: the dispatch plan P (denoted by theyellow dashed profile) is computed according to Eq. (1) asthe difference between the consumption forecast L (blue) andthe BESS demand Bo (orange). Recalling from III-A, thedispatch plan includes the BESS demand in order to bringthe BESS SOC to 50%, namely with at the largest capacity tocompensate for unbiased electricity consumption forecast. Theeffect of incorporating the BESS demand into the dispatch planis well visible if observing the first hours of intra-day/real-time operation. In particular from Fig. 8c, it can be seenthat the BESS is close to be fully charged at the beginningof the day of operation: a positive Bo causes the dispatchplan to underestimate the real consumption (Fig. 8b). Thisrequires the BESS to inject power in order to compensatefor it, finally inducing its SOC to decrease close to its targetlevel at around five in the morning (57% vs 50%, Fig. 8c).There are two sources of uncertainty in the dispatch plan thatprevent the BESS SOC to exactly reach the half level: first,Bo is determined without knowing the real BESS SOC at the

0 5 10 15 20

0

50

100

150

Time (Hour of day)

Rea

lpo

wer

(kW

)

Consumption forecastBattery demandDispatch Plan

(a) Day-ahead operation: computation of the dispatch plan.

0 5 10 15 2060

80

100

120

140

160

180

200

Time (Hour of day)

Rea

lpo

wer

(kW

)

ConsumptionCorrected consumptionDispatch Plan

(b) Intra-day operation: real-time dispatch plan tracking.

0 5 10 15 20−150

−100

−500

50

100

150

Time (Hour of day)

Cur

rent

(A)

0 5 10 15 2040

45

50

55

60

65

70

BE

SSst

ate-

of-c

harg

e(%

)

(c) Intra-day operation: BESS current and SOC (30 s resolution).

Fig. 9. Experimental results during day scenario 1 with MPC-B.

beginning of the day of operation (as discussed in III-A2);second, an unforeseen BESS activity in the time frame frommidnight to five in the morning due to imprecise consumptionforecast L included in the dispatch plan.

Similar considerations apply to day scenario 1 in Fig. 9,unless that, in this case, the BESS needs to be charged at thebeginning of the day of operation.

B. Performance assessment of the MPC controllers

To evaluate the ability of the MPC strategies to track thedispatch plan, we introduce the relative error sequence

e ={(Pt − Pt)/Pt, t = 0, . . . , N − 1

}(47)

that is determined for each day of operation and used tocompute the statistics shown in Table II. The data in Table IIrefer to two experimental day scenarios and are to compare theeffect of applying MPC with respect to respective base-case(as if the BESS injection was 0). The former is obtained bycalculating the relative error (47) using the actual power transitat the GCP, whereas, in the latter, the BESS contribute (thatis known from the BMS) is subtracted from the the actualconsumption; moreover, in the base-case, also the batterycharging demand Bt is ignored (in other words, Pt = Lt

and Pt = Lt, t = 0, . . . , N − 1). Numerical results inTable II show that both MPC-A and MPC-B accomplishesa fairly accurate tracking the of the feeder dispatch plan,

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with the RMS and mean metrics that are well below 1%and substantially lower than their respective base-case. Al-though MPC-B achieves better performance (lower RMS,lower median, reduced skewness, lower extreme values), itis noteworthy that, at this stage, it is not possible to operatea fair comparison since the base-cases are different. This isbecause they refer to two different experimental day-scenarios,and clearly the stochasticity inherent the real consumptionprofile cannot be replicated from one day to another. In thisrespect, a quantitative assessment of the different performancesof the two MPC controllers should be performed using a largerdataset covering different seasons corresponding to differentprosumers behaviours (i.e., loads and PV production).

TABLE IIPERFORMANCE METRICS FOR TWO EXPERIMENTAL DAY-SCENARIOS

(IN PERCENTAGE)

Day Scenario 0 Day Scenario 1

Metric (%) Base-case(no MPC) MPC-A Base-case

(no MPC) MPC-B

RMS(e) 11.44 0.46 9.57 0.29mean(e) 0.1 -0.07 2.36 -0.08median(e) -3.97 -0.1 1.73 -0.07max(e) 39.85 1.01 22.4 0.77min(e) -21.68 -2.08 -28.96 -0.77

VII. CONCLUSIONS AND PERSPECTIVES

Motivated by the objective of reducing the amount ofregulating power required to operate the grid to achieve alarger proportion of production from renewables, we haveproposed and experimentally validated on a realistic scale acontrol framework that achieves to dispatch the operation of aMV distribution feeder by controlling the operation of a grid-connected BESS. The proposed approach relies on a minimallyinvasive monitoring infrastructure and is suggested as a poten-tial solution for DSO to deploy utility-scale BESS. The controlstrategy consisted in following a consumption profile with 5minute resolution (called dispatch plan and determined the daybefore operation) by adjusting the BESS charging/dischargingset-points. The real-time tracking problem was accomplishedby applying receding horizon model predictive control (MPC),that was formulated as a convex optimization problem. Themodels implemented in the MPC were estimated from mea-surements applying the greybox modelling methodology, al-lowing for robust BESS operation thanks to implementingpredictive voltage and SOC constraints. The experimentalvalidation consisted in dispatching the operation of a 20 kVdistribution feeder of the EPFL university campus by using a750 kW/500 kWh lithium titanate BESS. Experimental resultsshow that the proposed control framework is able to trackthe dispatch plan precisely, with a RMS error below 0.5%.The MPC strategy was proven to be a flexible framework,allowing for an efficient integation of BESS constraints aswell consumption forecast at different time scale that weredeveloped using data-driven methodology, fully exploiting theavailability of local measurements. Further investigations willbe devoted to the implementation of more complete BESSmodels, possibly including the effect of ageing.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support Mr. MarcoPignati and Dr. Paolo Romano.

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