On Development and Optimization of Energy Management System (EMS) for Battery Energy Storage System (BESS) -Providing Ancillary Services

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IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2020,

On Development and Optimization of Energy Management System (EMS) for Battery Energy Storage System (BESS) -

Providing Ancillary Services

HAMZA SHAFIQUE

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

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On Development and Optimization of Energy Management System (EMS) for Battery Energy Storage System (BESS) - Providing Ancillary Services

HAMZA SHAFIQUE

EIT InnoEnergy Master’s Program in Renewable Energy Master in Energy Innovation (TIETM)

School of Electrical Engineering and Computer Science, KTH Host Company: CheckWatt

Company Supervisor: Dan-Eric Archer & Samuel Wingstedt Supervisor: Lina Bertling Tjernberg & Yared Bekele

Examiner: Lina Bertling Tjernberg

Date: October 15

^th

, 2020

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Abstract

The battery energy storage systems (BESS) installed standalone and with solar photovoltaic installations can be used beyond just storing excess generated electricity from the solar panels. The BESS can be intelligently managed by an Energy Management System (EMS) that uses the BESS resource for multiple ancillary services. The hypothesis in this study is that by optimizing the distribution of BESS resource between peak shaving of local load and providing frequency regulation service through the reserve market additional value can be generated from the already present resource. The EMS designed during the course of this thesis consists of two main parts, first the Prognosis Module that forecasts and makes recommendation for the delivery of hourly service from the BESS with quantified uncertainty and, second the Realtime Operation Module that takes the recommendations from the Prognosis Module and dispatches the necessary service meanwhile correcting for the uncertainty from the Prognosis Module. The Prognosis Module of the EMS is tested through the Öckero Ice Rink case study. In the case study local peak shaving saves 9.5% of the monthly power tariff by reducing its demand component through shaving the peak power of the test day by 21%. The EMS also allows for profit generation by frequency regulation through reserving capacity for three hourly slots within the test day on the reserve market.

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Sammanfattning

Ett batterilager installerat separat eller tillsammans med en solelanläggning kan användas för mer än att öka egenanvändning av solel. Smart styrning med ett Energy Management System (EMS) möjliggör leverans av systemtjänster från batterilagret till elnätet. Hypotesen i denna studie innefattar att optimering av distributionen av ett energilagers kapacitet mellan kapning av effekttoppar och leverans av systemtjänsten frekvensreglering innebär en ökning av resursens värde. EMS som designats under detta projekt består av två delar; dels en prognosmodul som prognostiserar energianvändning för att ge rekommendationer för distribuering av kapacitet, dels en modul som i realtid styr batteriet baserat på prognosmodulens rekommendationer och uppmätt data.

Prognosmodulen har testats i en fallstudie av Öckerö Ishall. Fallstudiens resultat visar att EMS som konstruerats reducerar nätavgiften med 9,5% genom att minska dagens högsta effekttopp med 21%. Resultatet visar även att frekvensreglering kunde levereras under tre timmar samma dag, vilket skulle generera ytterligare intäkter.

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Acknowledgement

I would like to extend my gratitude to Dan-Eric Archer at CheckWatt AB, who presented me with the great opportunity of perusing this project and trusted me to create the complete system from scratch. Without his critical foresight of the work it would not have been possible to design the EMS at its present state-of-art. I am also indebted to Samuel Wignstedt for his open-mindedness and ever so perceptive critique of this work which helped me navigate my way through difficult problems. Finally, I cannot express enough gratitude to Professor Lina Bertling Tjernberg for being a constant mentor throughout this thesis and for her pragmatic insights helping me constantly improve my work.

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Abbreviations

aFRR: Automatic Frequency Restoration Reserve BESS: Battery Energy Storage System

BRP: Balance Responsible Party DER: Distributed Energy Resource DES: Distributed Energy Storage DSO: Distribution System Operator EMS: Energy Management System FCR: Frequency Containment Reserve

FCRN: Frequency Containment Reserve - Normal FCRD: Frequency Containment Reserve - Disturbance FFR: Fast Frequency Reserve

FR: Frequency Regulation HAP: Hourly Average Power

HPAM: Hourly Power Averaging Module mFRR: manual Frequency Restoration Reserve PIFR: Frequency Regulation Preparation Interval PIPS: Peak Shaving Preparation Interval

PS: Peak Shaving PV: Photovoltaic

RR: Restoration Reserve SOC: State of Charge

Svk: Svenska Kraftnät (Swedish National Grid) TSO: Transmission System Operator

VPP: Virtual Power Plant

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Nomenclature

𝑃_𝐿(𝑡) [kW]: Load power 𝑊_𝐿 [kWh]: Load Energy

𝑃_𝑔(𝑡) [kW]: Power supplied at grid connection

𝑊_𝑔 [kWh]: Electrical Energy supplied at grid connection 𝑃_𝑃𝑉 [kW]: Power supplied by solar PV system

𝑃_𝑇ℎ [kW]: Threshold power. Beyond which peak shaving takes place for BESS operation 𝑡_𝑝𝑠[s]: Time interval of peak shaving

𝑃_{𝑃𝑒𝑎𝑘,𝐿} [kW]: Load peak power for the present day 𝑃_{𝑃𝑒𝑎𝑘,𝑀} [kW]: Peak power for the present month 𝜆_𝑝𝑠 [EUR]: Cost saving due to peak shaving

𝜆_𝐹𝑅 [EUR]: Profit benefit due to frequency regulation 𝛿_{𝑝𝑜𝑤𝑒𝑟} [EUR/MW, month]: Monthly power grid fee 𝛿_𝑏𝑖𝑑 [EUR/MW]: Frequency reserve power bid rate

𝑊_𝑐ℎ [kWh]: Electrical energy available to charge the BESS without exceeding the P_TH. 𝑊_𝑃𝑆 [kWh]: Electrical energy needed to shave a load power peak

𝜖^𝑃𝑆: Peak Shaving safety factor 𝜖^𝑐ℎ: Charging safety factor

𝑆𝑂𝐶: State of Charge of the BESS

𝑆𝑂𝐶_𝑚𝑖𝑛: Minimum limit of state of charge of the BESS 𝑆𝑂𝐶_𝑚𝑎𝑥: Maximum limit of state of charge of the BESS 𝑆𝑂𝐶_𝑐: State of charge of BESS at the moment

𝐷𝑜𝐷: Depth of discharge = 𝑆𝑂𝐶_𝑚𝑎𝑥− 𝑆𝑂𝐶_𝑚𝑖𝑛

𝑊_{𝐵𝐸𝑆𝑆}^𝑀𝐴𝑋 [kWh]: Total energy storage capacity BESS (BESS Size)

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𝑊_{𝐵𝐸𝑆𝑆} [kWh]: Total dispatchable energy stored in the BESS (𝑊_{𝐵𝐸𝑆𝑆} = 𝑊_{𝐵𝐸𝑆𝑆}^𝑀𝐴𝑋. (𝑆𝑂𝐶_𝑚𝑎𝑥 − 𝑆𝑂𝐶_𝑚𝑖𝑛))

𝑃_{𝐵𝐸𝑆𝑆} [kW]: Total Dispatchable power in the BESS

𝑊_{𝐵𝐸𝑆𝑆}^𝐴𝑣. [kWh]: Available stored energy in the BESS (𝑊_{𝐵𝐸𝑆𝑆} = 𝑊_{𝐵𝐸𝑆𝑆}^𝑀𝐴𝑋. (𝑆𝑂𝐶_𝑐− 𝑆𝑂𝐶_𝑚𝑖𝑛))

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LIST OF FIGURES

Figure 1: Various ancillary services with their activation time (adapted from

(Svenska_Kraftnät, 2017)) ... 2

Figure 2: Illustration of Power Peak Shaving. (adapted from, (Ideal_Energy_Inc, 2020)) ... 3

Figure 3: Schematic of the system to be controlled by the EMS ... 4

Figure 4: Power Peak Shaving [adapted from (Levron & Shmilovitz, 2012)] ...10

Figure 5: Peak shaving curve with the threshold plateau [adapted from (Levron & Shmilovitz, 2012)] ...11

Figure 6: Schematic of various load condition cases ...12

Figure 7: EMS for BESS Schematic ...25

Figure 8: Complete EMS architecture ...26

Figure 9: Overview of Peak Shaving Prognosis ...29

Figure 10: Overview of Peak Shaving Preparation Interval Prognosis ...30

Figure 11: Overview of Frequency Regulation Prognosis ...30

Figure 12: Frequency Regulation Preparation Interval Prognosis Schematic ...31

Figure 13: Suboptimal consecutive power peak shaving method...32

Figure 14: Optimal consecutive power peak shaving method ...32

Figure 15: Prognosis Algorithm schematic...33

Figure 16: Graph showing the peak shaving electricity and safe peak shaving electricity prognosis ...36

Figure 17: Schematic of Realtime Peak shaving algorithm ...37

Figure 18: Graph showing Peak Shaving Preparation Interval Prognosis ...38

Figure 19: Schematic of Peak Shaving Preparation Interval Realtime Algorithm ...38

Figure 20: Realtime PI_FR method SOC correction loop ...40

Figure 21: Öckerö Ice Rink [retrieved from(Club)] ...41

Figure 22: Daily load profile for the complete month of January ...43

Figure 23: Daily load profile for the complete month of February ...44

Figure 24: Daily load profile for the complete month of March ...45

Figure 25: Daily load profile for the complete month of April ...46

Figure 26: Daily load profile for the complete month of May ...47

Figure 27: Daily load profile for the complete month of June ...48

Figure 28: Load Profile for Öckerö Ice Rink ...50

Figure 29: Prognosis Load profile for Ockero Ice Rink for 2020-06-30 ...51

Figure 30: Comparison of shaved and unshaved power peaks and the SOC of BESS ...53

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LIST OF TABLES

Table 1: Peak shaving summary ...13

Table 2: Summary of BESS dispatch between Peak Shaving and Frequency Regulation. ...16

Table 3: Summary of profit and cost benefit of the various outcomes defined by the BESS dispatch strategy ...17

Table 4: Frequency Regulation summary ...19

Table 5: Peak shaving and Frequency regulation combinations ...20

Table 6: Values of BESS Parameters...42

Table 7: Interval Identification data frame created by EMS with identified Peak Shaving (PS) and Peak Shaving Preparation Interval (PIPS) hours...52

Table 8: Hourly capacity values for Peak shaving and Peak Shaving Preparation Interval ...52

Table 9: Interval Identification data frame created by EMS with additional identification of Frequency Regulation (FR), Frequency Regulation Preparation Interval (PIFR) and the Frequency Regulation Preparation interval for SOC restoration (PIFR_SOC)...54

Table 10: BESS Schedule ...54

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1. Introduction

1.1. Background

Traditionally the electricity market has been operating with centralized generation, where the major variability in electricity balance came from the demand-side and the supply- side was relatively more stable. In recent years there has been remarkable growth in the installed renewable electricity capacity around the world, even outpacing the annual growth of conventional electricity capacity installations. Within the renewable electricity ecosystem solar PV installations have been at the forefront, with a 20% increase in the installed power capacity from 386GW in 2017 to 480GW in 2018. (IRENA, 2019). This advent of renewable energy sources is presenting new challenges in handling electricity imbalances created by higher variability of the supply-side. This changing electricity ecosystem provides opportunities to innovate by improving reliability of the electricity grid while integrating the intermittent and distributed renewable energy sources.

Forecasting the variable electricity production of non-dispatchable electricity resources that are tied to the electricity grid presents us with management challenges at the production, transmission, distribution and usage levels.

One of the ways to supplement the variability of production at a renewable electricity source is to install Battery Energy Storage Systems (BESS) alongside the renewable power generation unit. The BESS enables a smooth transition from conventional forms of power production to more novel means of production that have certain intermittency challenges.

Beyond acting as just as an auxiliary to renewable electricity installations BESS are in fact starting to become an essential part of any renewable electricity installation as they enable the Distribution System Operators (DSO) to maintain grid stability and flexibility while an increasing number of distributed renewable energy sources are added to the grid.

(EUROBAT, 2013) 1.2. The Swedish Reserve Market

In Sweden, in order to supplement this intermittency and variability in the balance between electricity generation and consumption the Transmission Service Operator (TSO) - The Swedish National Grid maintains the Reserve Market. The reserve market ensures that the grid voltage frequency is maintained as close as possible to 50Hz. This is done by balancing electric consumption and production thus ensuring a reliable supply of electricity throughout the Swedish national grid. The Swedish National Grid purchases reserve capacities from balance responsible parties (BRP) to regulate the frequency within safe limits. There are two main types of frequency reserves in Sweden, with different endurance and activation times, that are procured in order to regulate the grid frequency.

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Frequency Containment Reserves (FCR), one of these reserves, is the primary mode of frequency stabilization. It is activated automatically to handle minor fluctuations in the grid frequency. The secondary form of frequency regulation reserve is the Frequency Restoration Reserve (FRR), which are procured by the TSO, have relatively longer activation times with larger capacities. The FCR is further classified into FCR-N (Frequency Containment Reserve - Normal) and FCR-D (Frequency Containment Reserve - Disturbance) having different dispatch characteristics. FRR is also classified into two different types, aFRR (Automatic Frequency Restoration Reserve) and mFRR (manual Frequency Restoration Reserve) with the difference in activation control and capacity size. (Svenska_Kraftnät, 2020)

Besides these forms of frequency reserves that are currently in operation in Sweden there are various other types of frequency reserves including Inertia, FFR (Fast Frequency Reserve) and RR (Restoration Reserve). A summary of all types of reserves that are currently implemented in Sweden, are in plan and or can be implemented in future is shown in the Figure 1.

Figure 1: Various ancillary services with their activation time (adapted from (Svenska_Kraftnät, 2017))

1.3. Power Peak Shaving

Peak shaving involves eliminating the short-term spikes in load power in order to reduce the overall load power peak. Commercial power consumers make use of peak shaving for a number of reasons ranging from reducing the installed power production capacity to reducing their power tariff costs. In an otherwise stable load if there are a few short-term power spikes, the minimum installed load power capacity needs to be elevated to accommodate for these power spikes. An alternative solution would be to implement peak shaving and eliminate these spikes by supplementing the power from an eternal power unit.

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Various utility companies in Sweden are introducing power. Starting with commercial consumers but with plans to introduce these power tariffs for residential customers as well.

(Vattenfall_Eldistribution_AB, 2020) The component of this power tariff that will be the focus of this study is the demand side component of the Power tariff. This component charges the consumer for the power used in EUR/kW. The system in place adds the demand side component to the monthly electricity bill by using the monthly highest hourly average power value noted at the grid connection meter and charging the demand side component according to this power value and a fixed power tariff rate.

In order to avoid paying extra electricity bills due to power peaks, power peak shaving is as important for residential power consumers as it is for commercial consumers.

Figure 2 illustrates this mechanism.

Figure 2: Illustration of Power Peak Shaving. (adapted from, (Ideal_Energy_Inc, 2020))

In Figure 2 above the two peaks labeled in red are shaved to a lower level P_TH, thus reducing the incurred power tariff cost and eliminating the need to increase the power capacity for sustaining this local load just for these short-term power spikes.

1.4. Objectives

For frequency regulation, an energy resource i.e. a production unit or a unit with a controllable energy consumption, is required to provide the grid balancing service. During this thesis a system, consisting of a battery energy storage system (BESS) tied to a solar PV generation unit and the electricity grid, providing electricity for a local load will be studied. By intelligently managing the BESS it can be used as a reserve for providing ancillary services to this system and the electricity grid. An energy management system

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(EMS) that manages the BESS for performing local power peak shaving of the demand- supply balance for this system and for participation in the reserve market to provide frequency regulation and power balance services through FCR-N is economically viable and technically feasible. (Wingren & Johnsson, 2018) It will be the first version of an EMS for the BESS used for performing ancillary services, for singular systems at this point but can be updated to a Virtual Power Plant (VPP) level by integrating Distributed Energy Resource (DER) and Distributed Energy Storage (DES).

Figure 3: Schematic of the system to be controlled by the EMS

As is seen in Figure 3 the EMS is controlling the BESS which is charged through the solar installations and the grid and discharged for the two ancillary services i.e. local peak shaving and frequency regulation.

The Swedish electricity market will be considered in order to optimize the approach of battery resource dispatch distribution between the two ancillary services, such that it maximizes profits and resource efficiency while enhancing the overall system reliability of the electricity grid. The overall objectives of the thesis are summarized as follows:

x Perform a theoretical study on the components required for an EMS for a BESS to be used for ancillary services.

x Define the approach required to implement local peak shaving and frequency regulation while supplying power to the consumer.

x Perform a dynamic cost-benefit analysis on dispatch approach of the battery resource between local peak shaving and frequency regulation.

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x Implement a proof of concept for the EMS by running the algorithms for the approach that would define the EMS for the BESS.

x Validate the proof of concept by testing it through a case study.

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2. State-of-art

2.1. Overview

This state of art study aims at finding out the different approaches developed until now that can be built upon for the development of an EMS for BESS. The initial step was to review the work that has already been done at CheckWatt AB, by reviewing the works of Samuel Wingstedt and Erik Nilsson on virtual power plants (VPP). (Wingstedt & Nilsson, 2019) Through their study of the Swedish energy market and various configurations of virtual power plants it was concluded that for the utilization of distributed energy resource as a means of energy reserve it is optimal to participate through the FCR-N as an instrument of market reserve.

Having established common grounds with the current state of knowledge at CheckWatt the literature study was further developed in order to understand all the individual components required for an energy management system using distributed energy resource.

Parisio, et.al explain a Model Predictive Control (MPC) approach to energy management system for multiple residential buildings by optimally scheduling end-user appliances and services with the aim of minimizing the overall cost of the residential microgrid. (Parisio, Wiezorek, Kyntäjä, Elo, & Johansson, 2015) Asgher, et.al in their work detail out a residential load management system by incorporating renewable energy sources by considering real-time electricity price, energy demand, user preferences and renewable energy parameters as inputs. (Asgher, et al., 2019) These systems although describe nicely energy management schemes for distributed energy sources and residential use, they are lacking the major component that incorporates peak shaving and frequency regulation.

Shen et.al define a peak-time rebate scheme to perform peak shaving for a microgrid using multiple controllable loads and multiple power generation units. (Shen, Jiang, Liu, & Qian, 2016) García-Plaza et.al have created a peak shaving algorithm using dynamic minimum voltage tracking for battery energy storage systems in a microgrid application. The authors consider the overall cost of shaving peaks and the battery health in order for calculating the optimal peak shaving.

For the purposes of this project, it is required to go a step beyond generic energy management systems that are available for distributed energy sources and incorporate the components needed for the specific case of this thesis. For that a thorough study of peak shaving algorithms, frequency regulation methodologies and BESS maintenance architectures are required.

2.2. Peak Shaving

Barzkar and Hosseini have described a peak shaving algorithm using real-time battery scheduling for residential distributed energy storage systems. The authors have modeled

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peak load shaving as an objective function and tried to solve it via the optimal energy path. (Barzkar & Hosseini, 2018). The authors have used works of Levron & Shmilovitz to calculate the optimal energy path. Levron & Shmilovitz describe an analytical design method for optimal peak shaving. The authors suggest a system of peak shaving where a threshold level is created for peak shaving. This level can be dependent on the element we are trying to optimize for, as in their case its cost minimization. (Levron & Shmilovitz, 2012) This will form a crucial element of our project approach.

2.3. Frequency Regulation

A study of the Swedish and Nordic regulation for frequency regulations, particularly for FCR-N, is vital. The regulations for the activation of FCR-N and the frequency response approach is clearly described by the term of FCR by The Swedish National Grid. The reserve is activated when frequency deviates between 49.90Hz and 50.10Hz, the system should be able to activate 63% of the capacity in 60seconds and 100% capacity in 3minutes.

The maximum D-1 bid is 3 hr and the max D-2 bid is 6 hours. Where D-1 is a day before and D-2 is two days before. (Svenska_Kraftnät, 2020)

The reserve capacity is reimbursed for the power reserved through pay as bid system and the energy reimbursement is made at the Nordpool prices of the hour. (Svenska_Kraftnät, 2020)

2.4. Battery Energy Storage System (BESS)

For the optimal execution of peak shaving and frequency regulation an optimal operation of the Battery Energy Storage System (BESS) is needed. Rahmann et.al have performed economic analysis of the breakeven point of using BESS for peak shaving. What is important for this project in their work is the creation of a BESS Schedule that is created for the BESS depending on feasible energy and power pairs for eventual operation of the BESS. (Rahmann, Mac-Clure, Vittal, & Valencia, 2017) The BESS schedule will become an essential part of this study after some necessary changes done to tailor it to this system.

Zhou et.al have proposed a model that considers the effect of battery degradation cost on optimal virtual power plant (VPP) scheduling. The authors have approximated the battery degradation cost as a piecewise linear function and VPP scheduling as a two-stage stochastic mixed integer linear programing problem. (Zhou, et al., 2016) The two-stage stochastic modeling is very useful and can be adapted for this project, but instead of the VPP schedule we can use it for the BESS schedule instead. Where our first stage model is a prognosis with uncertainties involved and the second stage model is Realtime operation where we try to narrow down the uncertainties. Similar to this, Zheng et.al have proposed an optimal operation system for BESS, in order to optimize energy transaction cost. The authors show that the key issue for real-time optimal BESS operation is the

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optimization accuracy and speed. To deal with this the authors have created what they call the day-ahead operation module and the real-time operation module. The authors make full optimal operation model with multiple forecast uncertainties, i.e. load forecast, solar forecast. The authors then use this mode to create a day-ahead schedule which they use along with the real-time information like real-time load and real-time electricity price to narrow down the gap in demand and also minimize cost to have the real-time BESS operation schedule. (Zheng, et al., 2018) By quantifying the uncertainties in the day-ahead operation schedule this system allow for preparation for these uncertainties.

The BESS schedule basically involves the charging and discharging schedule. Lu et.al optimize the charging a discharging of the BESS to minimize the peak-valley difference in load and minimizing the daily load variance through peak shaving. Doing this the authors can optimally minimize the BESS capacity required for peak shaving. (Lu, Xu, Pan, &

Song, 2014) Chouhan et.al have used linear programming technique to optimize the BESS charge/discharge schedule using distributed energy resources. The authors have comprehensively outlined all the parameters that add up towards the total cost function of the BESS operation and they have outlined the linear programming formulation to minimize this cost function. (Chouhan, Tiwari, Inan, Khushalani-Solanki, & Feliachi, 2016) The parameters that the authors have used for their formulation are relevant for this project as well.

2.5. Load Prognosis

Zheng et.al have compared conventional load forecasting that forecasts the total load with a bottom up strategy that aggregates the forecasts made at the individual room or appliance level make an eventual forecast for the total load. The authors use symmetric mean absolute percentage error for the comparison. The authors have further compared a deep-learning model-based bottom up strategy with a Kalman filter based bottom up strategies. The authors have shown that their Kalman filter-based bottom-up approach reduces the error 49% more than the deep-learning model and 47% more than the conventional strategy. (Zheng, Chen, & Luo, 2019)

Considering that the bottom approach is impractical for this project we consider the works of Veit et.al. The authors have bench-marked the state-of-the-art methods for top down electricity demand forecast. The authors have used Mean Absolute Percentage Error for comparing the various models. The authors define forecasting horizon and the granularity of forecast. The authors then compare various forecasting methods including PERSIST (same as before), Autoregressive Integrated Moving Average (ARIMA) model, Exponential smoothing state space model (BATS) with Box-Cox transformation and feed- forward neural networks. The authors also define two different strategies, i.e. sliding

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window strategy where the data set is divided into smaller sets for forecast and day-type strategy where the data set is arranged with the similar day-types together. The authors conclude that longer forecasting horizons increase error and lower granularity reduces error, day-type strategy is better than sliding window strategy. The authors also concluded that without much refinement advanced prediction models like ARIMA and neural networks are not any better than PERSIST in most situations. (Veit, Goebel, Tidke, Doblander, & Jacobsen, 2014)

2.6. Optimization

After thoroughly studying the individual components of the EMS for BESS to be used for peak shaving and frequency regulation, it is important to review the literature where these the collective optimization of these components in a singular system have been studied.

In this section some of these studies will be discussed.

Lucas & Chondrogiannis have modeled the use of Vanadium Redox Flow Batteries (VRFB) for providing multi-ancillary services by simulation it over MATLAB/Simulink. The authors have chosen VRFB for its quick response time and higher rated power and discharge times. The authors show that the peak shaving and frequency regulation should not be considered independently for the optimization, because this leads to conflicts in execution. (Lucas & Chondrogiannis, 2016)

Shi et.al have considered using BESS simultaneously for peak shaving and frequency regulation in order to make joint optimization of super-linear gains. The authors consider the battery degradation cost, operational constraints and uncertainties in load and in frequency regulation signal. The authors consider the energy market in the United States and FFR as the market reserve of choice. The authors make a load prediction scenario generation feed it to a day ahead stochastic joint optimization framework that optimizes for capacity bidding and peak shaving which finally are used to define the real time battery control algorithm. The authors conclude that the saving from joint optimization in certain cases can be larger than the sum of individual savings from devoting the battery to on of the applications. (Shi, Xu, Wang, & Zhang, 2018) Zhang et.al in their paper on operation schedule for battery energy storage companies in electricity market mention that the BESS should be charged when the spot market prices are low and discharged when the prices are high. The authors have performed this analysis using the Australian energy markets as the case study within different control strategy results for different weather conditions.

(ZHANG, MISHRA, LEDWICH, & XUE, 2013) In that the authors hint at making a spot market price prognosis and optimizing based on the overall cost rather than prioritizing any one service.

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3. Theoretical Framework

3.1. Power Peak Shaving

Power peak shaving is a process by which the peak power of a load profile is reduced in order to cut down on the power costs incurred and the power supply burden on the electricity grid. This subsection is aimed at developing the correct theoretical background basis for the implementation of peak shaving.

Figure 4: Power Peak Shaving [adapted from (Levron & Shmilovitz, 2012)]

As seen in Figure 4, P_g (green curve),the power taken from the grid has been shaved from its original locus that would have followed P_L(red curve) had the peak shaving not been implemented. The extra power that is needed to supplement the power from the grid comes from a local electricity source, for example a battery energy storage system (BESS).

The BESS provides P_BESS in order to supplement P_g such that

𝑃_𝐿(𝑡) = 𝑃_𝑔(𝑡) + 𝑃_{𝐵𝐸𝑆𝑆}(𝑡) Equation 3.1

For a local system that has solar PV installed, the power balance can be written as 𝑃_𝐿(𝑡) = 𝑃_𝑔(𝑡) + 𝑃_{𝐵𝐸𝑆𝑆}(𝑡) + 𝑃_𝑃𝑉(𝑡) Equation 3.2

The BESS only operates if the load exceeds certain power threshold, P_TH. P_BESS enter the equation only if the following is true.

|𝑃_𝐿(𝑡) − 𝑃_𝑃𝑉(𝑡)| > 𝑃_𝑇𝐻 Equation 3.3

Here the quantity P_L – P_PV is termed as the power balance.

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In order to implement local peak shaving it is necessary to first define the method of implementation. In order to do that it is required that a way be found that defines the power threshold beyond which peak shaving should be implemented. The amount of power that can be shaved is highly dependent on the amount of power and energy that can be supplemented through the BESS. So, in order to determine the power threshold, it is essential to size the BESS resource available for peak shaving, i.e. P_BESS and W_BESS, the power and energy from the BESS.

The constraints on the system can be written as follows:

𝑊_𝐿(𝑡) ≤ 𝑊_𝑔(𝑡) ≤ 𝑊_𝐿(𝑡) + 𝑊_{𝐵𝐸𝑆𝑆} Equation 3.4

𝑃_𝑔(𝑡) = 𝑑

𝑑𝑡𝑊_𝑔(𝑡) Equation 3.5

In order to apply the constraints accurately an accurate load forecast is needed. Which will allow for the accurate planning of the BESS dispatch and resource allocation for peak shaving. Once an accurate load forecast is acquired, the threshold value is to be found that would work for the W_BESS to be allocated for peak shaving.

Figure 5: Peak shaving curve with the threshold plateau [adapted from (Levron & Shmilovitz, 2012)]

As can be seen in the Figure 5, the load forecast is shown as pL(t) and the source power taken from the grid is shown as pg(t). PTH, i.e. the level of threshold power plateau is yet be determined. The energy needed to shave the peak is denoted as W_PS. For the peak shaving to work the following should hold true

Using Figure 5, equations can be formulated as follows,

𝑊_𝑃𝑆 ≤ 𝑊_{𝐵𝐸𝑆𝑆} Equation 3.6

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12 𝑊_𝑃𝑆 = ∫ 𝑝^𝑡³ _𝐿(𝑡)

𝑡2

𝑑𝑡 − ∫ 𝑝^𝑡³ _𝑔(𝑡)

𝑡2

𝑑𝑡 ≤ 𝑊_{𝐵𝐸𝑆𝑆} Equation 3.7

∫ 𝑝^𝑡³ _𝐿(𝑡)

𝑡₂

𝑑𝑡 − ∫ 𝑝_𝑇𝐻

𝑡₃ 𝑡₂

𝑑𝑡 ≤ 𝑊_{𝐵𝐸𝑆𝑆} Equation 3.8

∫ 𝑝^𝑡³ _𝐿(𝑡)

𝑡2

𝑑𝑡 − 𝑊_{𝐵𝐸𝑆𝑆} ≤ 𝑝_𝑇𝐻× (𝑡₃− 𝑡₂) Equation 3.9

∫ 𝑝^𝑡³ _𝐿(𝑡)

𝑡₂

𝑑𝑡 − 𝑊_{𝐵𝐸𝑆𝑆} ≤ 𝑝_𝑇𝐻× 𝑡_𝑃𝑆 Equation 3.10

𝑝_𝑇𝐻 ≥∫ 𝑝_𝑡^𝑡³ 𝐿(𝑡)

2 𝑑𝑡 − 𝑊_{𝐵𝐸𝑆𝑆} 𝑡_𝑃𝑆

Equation 3.11

𝑡_𝑃𝑆 = (𝑡₃− 𝑡₂) Equation 3.12

The value of P_TH can be iterated for until it is accurate enough. This value is then compared with the concerned load peak power, P_peak,L and the monthly power peak, P_peak,M.There could be three possibilities to decide the extent of BESS to be dispatched,

x Case 1: PTH < P_peak,L ≤ Ppeak,M

x Case 2: PTH ≤ Ppeak,M < P_peak,L x Case 3: P_peak,M < P_TH < P_peak,L

Note that the P_TH for a certain load profile is always lower than P_peak,L of that load profile.

Figure 6: Schematic of various load condition cases

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In Case 1 there is no cost saving for allocating the battery resource for peak shaving. Even without any peak shaving there are no extra power charges incurred because P_peak,L ≤ P_peak,M.

In Case 2 there is a cost benefit to perform peak shaving because without peak shaving the current power peak would exceed the monthly power peak and this would incur higher power costs then it would originally be having. To optimize the BESS dispatch, the PTH

will be increased to equal Ppeak,M. This will ensure that unnecessary peaks are not being shaved and peak shaving is only being implemented to the extent where it is cost effective.

So peak shaving in this case would return a cost saving 𝜆_𝑝𝑠 which can be written as, 𝜆_𝑝𝑠 = (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟} Equation 3.13

Where 𝛿_{𝑝𝑜𝑤𝑒𝑟} [EUR/MW, month] is the monthly power fee.

In Case 3, P_TH > P_peak,M, the P_TH becomes the new monthly peak power. In this case peak shaving becomes essential to maximize cost saving. The cost saved in this case would be calculated as,

𝜆_𝑝𝑠 = (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟} Equation 3.14

The results of the three different cases are summarized in the Table 1.

Table 1: Peak shaving summary

Case 1

P_TH < P_peak,L ≤ Ppeak,M

Case 2

P_TH ≤ Ppeak,M < P_peak,L

Case 3

P_peak,M < P_TH < P_peak,L Peak

Shaving No Yes Yes

BESS

dispatch 0% Enough to make P_TH

equal to P_peak,M 100%

𝜆_𝑝𝑠 None (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻)

× 𝛿_{𝑝𝑜𝑤𝑒𝑟} (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟}

3.2. Frequency Regulation

The Swedish electric grid falls under the Nordic grid synchronous area. This means that the electricity transmitted throughout the Nordic transmission network has to have the same voltage frequency of 50Hz in order for the electricity system to function properly.

Variations in electricity production and consumption will make this frequency deviate from the normal. To balance out these frequency deviations the national TSO, The Swedish National Grid maintains the frequency reserve market. On this market Balancing

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Responsible Parties (BRP) can place bids for contributing to the grid voltage frequency regulation. The BRP uses an electricity resource in order to supply the balancing power needed to regulate the frequency. Herein a BESS is used to proving the balancing service needed for frequency regulation.

In order for the BRP to participate in the reserve market, it needs to have the capacity to dispatch the needed power and electricity for the time it bids for. If a BRP is to participate in FCR-N (normal Frequency containment Reserve), it needs to bid for certain number of hours to provide a given power capacity. This could be both upward or downward regulation which mean that it needs to have the capacity to take in or give out the power capacity that it bid for the hour. From a BESS standpoint, it needs to be ready for discharging in case of upward regulation and charging in case of downward regulation.

This condition then applies the following constraint on the state of charge (SOC) of the BESS,

𝑆𝑂𝐶_𝑚𝑖𝑛≤ 𝑆𝑂𝐶_𝑐 ± (𝑃_𝑏𝑖𝑑[𝑀𝑊] × 𝑡_𝑏𝑖𝑑[ℎ]

𝑊_{𝐵𝐸𝑆𝑆}^𝑀𝐴𝑋[𝑀𝑊ℎ] ) ≤ 𝑆𝑂𝐶_𝑚𝑎𝑥 Equation 3.15

Here, SOC_min and SOC_max are the minimum and maximum state of charge limits of the BESS, SOC_c is the current state of charge of the battery, P_bid and t_bid are the power and time of the capacity reserved for frequency regulation bid and 𝑊_{𝐵𝐸𝑆𝑆}^𝑀𝐴𝑋 is the total energy storage capacity of the BESS.

As described in section 3.1 there are three different cases as dictated by the local load.

With a primary analysis of the cost benefit that can be gained by performing peak shaving in the various cases, its effect on frequency regulation capacity and the alternatives that can be provided through it can be formulated.

In Case 1, no peak shaving is performed so the BESS resource can be safely dedicated for frequency regulation.

The profit that is generated as a result of bidding this power for frequency reserve is as follows,

𝜆_𝐹𝑅 = 𝑃_𝑏𝑖𝑑 × 𝛿_𝑏𝑖𝑑 Equation 3.16

𝑃_𝑏𝑖𝑑 = 𝜖 × (𝑃_{𝐵𝐸𝑆𝑆}^𝐹𝑅 ) Equation 3.17

Where 𝜆_𝐹𝑅[EUR] is the available profit; 𝑃_𝑏𝑖𝑑 [MW] is the power bid in frequency reserve market; 𝛿_𝑏𝑖𝑑 [EUR/MW] is the bid rate and 𝜖 is the safety factor incorporated while translating the power available in the BESS for bidding to the actual power bid placed in

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the reserve market. 𝑃_{𝐵𝐸𝑆𝑆}^𝐹𝑅 can easily calculated from the available 𝑊_{𝐵𝐸𝑆𝑆} by fixing a charging rate (𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 ) for the battery while dispatching for frequency reserve.

𝑃 = 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 × 𝑊 Equation 3.18

𝛿_𝑏𝑖𝑑 is needed to be estimated for Case 1 based on the calculations of the marginal operational cost (MOC) as will follow in the coming sections. Therefore, we can write the profit generated by this bid as,

𝝀_𝑭𝑹 = 𝝐 𝑪_{𝒓𝒂𝒕𝒆}^𝑭𝑹 𝜹_𝒃𝒊𝒅^𝑴𝑶𝑪 𝑾_{𝑩𝑬𝑺𝑺}^𝑭𝑹 Equation 3.19

In Case 2, the BESS resource is only partly used for peak shaving, i.e. 𝑃_{𝐵𝐸𝑆𝑆}^𝑃𝑆 , 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 . Where,

𝑊_{𝐵𝐸𝑆𝑆} = 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 + 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 Equation 3.20

𝑃_{𝐵𝐸𝑆𝑆} = 𝑃_{𝐵𝐸𝑆𝑆}^𝑃𝑆 + 𝑃_{𝐵𝐸𝑆𝑆}^𝐹𝑅 Equation 3.21

Therefore, the BRP is free to place the bid for frequency reserve services based on the available BESS resource, i.e. 𝑃_{𝐵𝐸𝑆𝑆}^𝐹𝑅 , 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 at a bid rate based on the marginal operational cost.

𝜆_𝐹𝑅¹ = 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 Equation 3.22

On top of the bid mentioned in Equation 2.2, another bid will be placed based on the resource being used for peak shaving, i.e. 𝑃_{𝐵𝐸𝑆𝑆}^𝑃𝑆 , 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 . This bid rate will be calculated in order to match the cost benefit received from peak shaving. The bid needs to be placed a day ahead of the day of execution of the bid and peak shaving, so a bid can actually be placed to match the cost benefit from peak shaving. If the bid gets rejected peak shaving can be performed as usual on the day of execution, but if the bid gets accepted the resource for frequency reserve can be dispatched to get a profit equal to or larger than the cost benefit from peak shaving depending on the bid rate set initially. There is an added advantage in this case, because there is a certain likelihood of dispatch attached with frequency reserve. The resource reserved for frequency regulation is not always dispatched.

So, the battery degradation cost can be saved and added profit can be gained in that case.

The profit from such a bid would have the following form,

𝜆²_𝐹𝑅 = 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 Equation 3.23

Where 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} [EUR/MW] is the frequency reserve bid rate based on matching the peak shaving cost benefit (PSCB). The total profit in case 2 would be a sum the two individual profits.

𝝀_𝑭𝑹 = 𝝀_𝑭𝑹^𝟏 + 𝝀_𝑭𝑹^𝟐 = 𝝐 𝑪_{𝒓𝒂𝒕𝒆}^𝑭𝑹 ( 𝜹_𝒃𝒊𝒅^𝑴𝑶𝑪 𝑾_{𝑩𝑬𝑺𝑺}^𝑭𝑹 + 𝜹_𝒃𝒊𝒅^{𝑷𝑺𝑪𝑩} 𝑾_{𝑩𝑬𝑺𝑺}^𝑷𝑺 ) Equation 3.24

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In Case 3, all the BESS resource was being dedicated to peak shaving. Therefore, a bid would be made with the TSO at a bid rate that is based on the peak shaving cost benefit and follows the procedure as described in Case 2 for 𝜆_𝐹𝑅² . The cost benefit of frequency regulation if the bid gets accepted would then be,

𝝀_𝑭𝑹 = 𝝐 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑾_{𝑩𝑬𝑺𝑺}^𝑷𝑺 Equation 3.25

In the following section a summary of the individual and joint profit and cost benefits of allocating the BESS for the two services in the different cases is presented.

3.3. Peak shaving-Frequency Regulation cost-benefit analysis dispatch optimization – Single Dispatch

In this section the BESS dispatch will be optimized between the two ancillary services.

Various profits and cost benefits will also be explored depending on whether the placed bid gets accepted by the TSO or not.

Table 2: Summary of BESS dispatch between Peak Shaving and Frequency Regulation.

Parameter

Case 1 P_TH < P_peak,L ≤

P_peak,M

Case 2

P_TH ≤ P_peak,M < P_peak,L

Case 3 P_peak,M < P_TH <

P_peak,L Peak

Shaving No Yes Yes

𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 ** 0% of 𝑊_{𝐵𝐸𝑆𝑆} ∫ 𝑝^𝑡³ _𝐿(𝑡)

𝑡₂

𝑑𝑡 − (𝑃_{𝑝𝑒𝑎𝑘,𝑇𝐻}× 𝑡_𝑃𝑆)

𝑊_{𝐵𝐸𝑆𝑆}

𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 𝑊_{𝐵𝐸𝑆𝑆} 𝑊_{𝐵𝐸𝑆𝑆}− 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 0% of 𝑊_{𝐵𝐸𝑆𝑆}

𝜆_𝑝𝑠 None (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟} (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻)

× 𝛿_{𝑝𝑜𝑤𝑒𝑟}

𝜆_𝐹𝑅* 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 ( 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 + 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 ) 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆

(*) This is the profit from frequency regulation given the bids are accepted. In the case the BESS is dispatched for frequency regulation there will be no cost benefit from peak shaving as all of the BESS is utilized for frequency regulation.

(**) In Case 2, 𝑃𝑝𝑒𝑎𝑘,𝑇𝐻= 𝑃𝑝𝑒𝑎𝑘,𝑀

Now that the available information on the profits and cost benefits have been established in cases when the BESS needs to be used partially or fully for either one of the services,

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the various possible outcomes can be analyzed and the cost benefits and profits in each of those outcomes be determined.

Table 3: Summary of profit and cost benefit of the various outcomes defined by the BESS dispatch strategy

Bid type

Case 1 P_TH < P_peak,L <

P_peak,M

Case 2

P_TH < P_peak,M < P_peak,L

Case 3 P_peak,M < P_TH <

P_peak,L PSCB

based FR Bid accepted

𝜆_𝑝𝑠

All BESS capacity bid @ 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝜆_𝐹𝑅

= 𝜖 𝐶_{𝑟𝑎𝑡𝑒} 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅

0 0

𝜆_𝐹𝑅 𝜖 𝐶_{𝑟𝑎𝑡𝑒} ( 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 + 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 ) 𝜖 𝐶_{𝑟𝑎𝑡𝑒} 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆

PSCB based FR Bid rejected

𝜆_𝑝𝑠 (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟} (𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻)

× 𝛿_{𝑝𝑜𝑤𝑒𝑟}

𝜆_𝐹𝑅 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 0

3.4. Frequency Regulation bid rates

3.4.1. Peak shaving cost benefit-based frequency regulation bid rate, (𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵})

In this section a frequency reserve bid is formulated that equals the cost benefit from peak shaving. This is done to see if the same monetary return can be gained by choosing to perform frequency regulation service instead of peak shaving. The added advantage is the likelihood that certain frequency reserve capacities would not be dispatched, and the battery degradation cost would be saved. To calculate this bid rate, the work done in section 3.2 will be used,

𝜆_𝑝𝑠 = 𝜆_𝐹𝑅² Equation 3.26

(𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟}= 𝜖 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 𝛿_𝑏𝑖𝑑^{𝑃𝑆𝐶𝐵} 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 Equation 3.27

𝜹_𝒃𝒊𝒅^{𝑷𝑺𝑪𝑩} = 𝜹_{𝒑𝒐𝒘𝒆𝒓}

𝝐 𝑪_{𝒓𝒂𝒕𝒆}^𝑭𝑹 ×(𝑷_{𝒑𝒆𝒂𝒌,𝑳}− 𝑷_𝑻𝑯) 𝑾_{𝑩𝑬𝑺𝑺}^𝑷𝑺

Equation 3.28

𝑃_𝑇𝐻== 𝑃_{𝑝𝑒𝑎𝑘,𝑀}

N.B. This method of equating the two opportunity costs is not entirely accurate because for Frequency Reserve dispatch the charge rate 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 is not constant. It gradually builds up to its value during the course of the dispatch and depending on the demand from the TSO. So, this equation shows the case where any value of 𝐶_{𝑟𝑎𝑡𝑒}^𝐹𝑅 would satisfy this equation

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and the opportunity profit from frequency regulation would always equal or exceed the opportunity cost saving from peak shaving.

3.4.2. Marginal operational cost-based frequency regulation bid rate, (𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶)

In order to calculate the marginal operational cost-based bid rate for the frequency regulation bid this method will be based on the system implemented by Zhou et.al. (Bin Zhou, 2016) . Start by defining the BESS degradation cost 𝐶_𝑑[EUR/MWh] as,

𝐶_𝑑 = 𝐶_𝑐 𝐿 . 𝑊_𝑚𝑎𝑥 . 𝐷𝑜𝐷

Equation 3.29

Where 𝐶_𝑐[EUR] is the Capital Cost of the BESS, 𝑊_𝑚𝑎𝑥 [MWh] is the maximum energy storage capacity of the BESS, 𝐷𝑜𝐷 is the limited depth of discharge of the BESS and 𝐿 is the number of lifecycles the BESS is rated to achieve given the 𝐷𝑜𝐷 as described by the battery manufacturer.

The bid rate 𝛿_𝑏𝑖𝑑^𝑀𝑂𝐶 [EUR/MW] can be defined as,

𝜹_𝒃𝒊𝒅^𝑴𝑶𝑪 = 𝑪_𝒅 . 𝑪_{𝒓𝒂𝒕𝒆}^𝑭𝑹 Equation 3.30

3.5. Peak shaving-Frequency Regulation cost-benefit analysis dispatch optimization – Simultaneous Dispatch

For the scope of this project, only single BESS dispatch action is considered at a time, i.e.

the BESS is either used a single service at a given time. This however is not the optimal solution, because this means prioritizing an action over another. This section is dedicated to exploring the theoretical framework for a simultaneous dispatch system where both peak shaving and frequency regulation are taken into consideration at the same time. This section aims to find the extent to which the BESS resource is dedicated to each of the services for a given timeslot.

As described in section 3.1, there could be three different cases concerning the local load.

The overarching aim of the BESS EMS is to reduce the overall cost of the system; therefore, the cost benefits of utilizing the BESS bidding for the frequency reserve market in the different cases should be taken into consideration. While considering the different cases in the previous section for making dispatch decisions for peak shaving, the load peaks were considered. For the purposes of deciding for frequency regulation the load levels need not be considered, instead decisions are needed to be made based on the available W_BESS and P_BESS.

x 𝐶𝑎𝑠𝑒1 ∶ 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ = 0%

x 𝐶𝑎𝑠𝑒2: 0% < 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ < 100%

x 𝐶𝑎𝑠𝑒3: 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ = 100%

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In Case1 the BESS is not being dispatched for peak shaving at all, therefore all the available BESS resource can be used for that hour and reserve it for frequency regulation.

In Case2 the BESS is partially being dispatched for peak shaving so only part of the BESS can be utilized to reserve for frequency regulation. As described in the previous section the BESS dispatch for peak shaving in Case2 is as follows,

𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 = ∫ 𝑃^𝑡¹ _𝐿− 𝑃_{𝑝𝑒𝑎𝑘,𝑀}

𝑡₀

𝑑𝑡 Equation 3.31

𝑃_{𝐵𝐸𝑆𝑆}^𝑃𝑆 = 𝑃_𝐿− 𝑃_{𝑝𝑒𝑎𝑘,𝑀} Equation 3.32

Where P_L is the current load, P_peak,M is the monthly peak power line and t0 and t1 are the intercepts of the two curves mentioned.

The BESS dispatch available for frequency regulation for the concerned hour is,

𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅 = 𝑊_{𝐵𝐸𝑆𝑆}− 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 Equation 3.33

𝑃_{𝐵𝐸𝑆𝑆}^𝐹𝑅 = 𝑃_{𝐵𝐸𝑆𝑆}− 𝑃_{𝐵𝐸𝑆𝑆}^𝑃𝑆 Equation 3.34

The profit that is generated as a result of bidding this power for frequency reserve is as follows,

𝜆_𝐹𝑅 = 𝑃_𝑏𝑖𝑑 × 𝛿_𝑏𝑖𝑑 Equation 3.35

Where 𝜆_𝐹𝑅[EUR] is the available profit; 𝑃_𝑏𝑖𝑑 [MW] is the power bid in frequency reserve market; 𝛿_𝑏𝑖𝑑 [EUR/MW] is the bid rate and 𝜖 is the safety factor incorporated while translating the power available in the BESS for bidding to the actual power bid placed in the reserve market.

In Case3, all of the BESS is being used for peak shaving therefore there is no capacity left to bid in the frequency reserve market.

Table 4: Frequency Regulation summary

Parameters Case 1

𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ = 0%

Case 2

0% < 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ < 100%

Case 3

𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ = 100%

Frequency

regulation Yes Yes No

𝑊_{𝐵𝐸𝑆𝑆}^𝐹𝑅

dispatch 100% 𝑊_{𝐵𝐸𝑆𝑆}− 𝑊_{𝐵𝐸𝑆𝑆}^𝑃𝑆 0%

𝜆_𝐹𝑅 𝑃_𝑏𝑖𝑑 × 𝛿_𝑏𝑖𝑑 𝑃_𝑏𝑖𝑑 × 𝛿_𝑏𝑖𝑑 None

(32)

20

The calculation performed above assume that it is always more valuable to perform peak shaving before dedicating the leftover capacity for frequency regulation. The decision- making process needs to be modified in a way that either it validates this assumption or eliminates the need to have this assumption.

In absence of peak shaving a cost is incurred and in absence of frequency regulation a profit loss is incurred. For the purposes of optimization, either a cost function can be minimized or using its negative, a profit function can be maximized. In the end what is being achieved is just the optimization of an objective function. To start peak shaving of the local load can be set as the reference. There will be cases where peak shaving is not required at all but given the availability of dispatchable BESS it can always be used to bid for frequency regulation. With these considerations there will be two cases,

Table 5: Peak shaving and Frequency regulation combinations

Peak shaving Frequency Regulation

Case 1 No Yes

Case 2 Yes Yes

In Case 1, P_peak,L ≤ P_peak,M,so there is no need to perform peak shaving. In this case all the BESS resource will be available for Frequency regulation.

In Case 2, P_peak,L > P_peak,M,so there is a need to perform peak shaving. There is now a need to decide how much resource should be allocated for Peak shaving and how much for frequency regulation. The resource allocation will be optimized for the maximum total value provided by performing the two ancillary services.

𝜆_{𝑇𝑜𝑡𝑎𝑙} = 𝜆_𝑃𝑆+ 𝜆_𝐹𝑅 Equation 3.37

𝜆_{𝑇𝑜𝑡𝑎𝑙} = ((𝑃_{𝑝𝑒𝑎𝑘,𝐿}− 𝑃_𝑇𝐻) × 𝛿_{𝑝𝑜𝑤𝑒𝑟}) + (𝑃_𝑏𝑖𝑑 × 𝛿_𝑏𝑖𝑑) Equation 3.38

Using limiting case of the inequality from section 3.1 for the definition of 𝑃_𝑇𝐻,

𝑝_𝑇𝐻 =∫ 𝑝_𝑡^𝑡³ _𝐿(𝑡)

2 𝑑𝑡 − 𝑊_{𝐵𝐸𝑆𝑆}

𝑡_𝑃𝑆 Equation 3.39

Using the theory developed in section 3.2 to define 𝑃_𝑏𝑖𝑑,

𝑃_𝑏𝑖𝑑 = 𝜖 × (𝑃_{𝐵𝐸𝑆𝑆}− 𝑃_{𝐵𝐸𝑆𝑆}^𝑃𝑆 ) Equation 3.41

On Development and Optimization of Energy Management System (EMS) for Battery Energy Storage System (BESS) -Providing Ancillary Services

On Development and Optimization of Energy Management System (EMS) for Battery Energy Storage System (BESS) -

Providing Ancillary Services

HAMZA SHAFIQUE

On Development and Optimization of Energy Management System (EMS) for Battery Energy Storage System (BESS) - Providing Ancillary Services

HAMZA SHAFIQUE

EIT InnoEnergy Master’s Program in Renewable Energy Master in Energy Innovation (TIETM)

School of Electrical Engineering and Computer Science, KTH Host Company: CheckWatt

Company Supervisor: Dan-Eric Archer & Samuel Wingstedt Supervisor: Lina Bertling Tjernberg & Yared Bekele

Examiner: Lina Bertling Tjernberg

Date: October 15

, 2020

Abstract

Sammanfattning

Acknowledgement

Abbreviations

Nomenclature

LIST OF FIGURES

LIST OF TABLES

Contents

1. Introduction

2. State-of-art

3. Theoretical Framework