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## Bottlenecks with energy storage: Li-Ion battery

Li-Ion battery could be used for many power system applications, however, there are various bottlenecks associated with Li-Ion battery and energy storage in general. Firstly, energy storage is a costly solution making it financially infeasible if deployed for many of the applications. Careful financial evaluation is essential. Secondly, due to energy storage parameters and chemistry batteries consume cycling losses, degrade over time and have limited life time. Furthermore, batteries require maintenance at regular intervals. Battery health and thus its life is affected by temperature, humidity, charging and discharging pattern to name a few. Thirdly, there is uncertainty in system variables based on which battery mode of operation is selected. Note that optimal storage operation of energy storage requires look-ahead in time. If the parameters based on which mode of operation of battery is decided are drastically different, then the mode decided might not be optimal. Thus due to inaccurate information the storage returns could be undermined. Forecasting is a heavily research area in power systems. However, the forecast models are not modular, i.e., a forecast model in a region could be of little use in forecasting the same parameters in a different region.

### Roles energy storage can play in a smart grid

Batteries in future smart grid will play many essential roles, such as reserves, load balancing, frequency regulation, microgrid stabilization, facilitating connection of renewable energy sources (RES) for the grid and perform load shifting, demand response and energy arbitrage for the end user. However, batteries are costly devices which consume some energy, act as inefficient buffers of energy and undergoes degradation, therefore, health of battery should be considered for maximizing operational life.

In the previous section, 2.1, we discuss the future challenges the power network will face due to growth of DGs and new loads such as EVs. In such power grids, balancing the load will be difficult. Energy storage devices act as energy buffers and can therefore be used for diversified tasks in future power grids. Batteries are an attractive solution as:

• Expected reduction in cost: The cost of batteries are expected to drop further in coming future, pertaining to the fact that intense research is going on in developing cost effective energy storage technology. Fig. 2.11 shows the decrease in storage cost, extrapolating this decrease which has a learning rate of 18%. The Li-Ion battery cost is projected to to be around $94/kWh by 2024 and $62/kWh by 2030 [103].

• New avenues: as indicated earlier, the innovative billing strategies provides energy participants with opportunity to reduce their cost of consumption by participating in grid based services. These opportunities are expected to increase for energy participants due to increased uncertainty and greater responsiveness required. For instance, the volatility of electricity price signal will increase with increased share of RES in total energy generation [185].

• For large energy participants: For big consumers or generators, the rules are well drafted by ISOs.

Such energy participants can install energy storage to ensure that the power quality and operational

norms are not violated.

Ideally, a battery which has a low cost, high energy density, high ramp rate, low maintenance, nontoxic in nature will instantly become the ultimate solution for the various storage applications in the future electricity grid. Although the research in achieving these goals are ongoing, batteries are becoming popular in smart grids. Few contemporary examples are:

• California planning billion dollar battery: “In 2013, the California Public Utilities Commission (CPUC) recognized the need to expand the role of energy storage in support of a carbon-free grid by establishing an energy storage procurement target of 1,325 megawatts for load serving entities. The investor-owned utilities, Pacific Gas and Electric Company, Southern California Edison and San Diego Gas & Electric, as well as energy service providers operating in California must procure storage resources by 2020 with installations completed by the end of 2024” [50].

• Hawaii island powered by Tesla battery and solar panels: The Kauai project consists of a 52 megawatt-hour battery installation plus a 13 megawatt SolarCity solar farm. Tesla and the Kauai Island Utility Cooperative, the power company that ordered the project, believe the project will reduce fossil fuel usage by 1.6 million gallons per year [64].

#### Fast ramping and low response time

California aims to generate 50% of retail electricity from renewable power by 2030 in order to reduce greenhouse gas emission to 1990 levels. Such goals would constitute increase in distributed generation and large scale inclusion of electric vehicles. Historically, the ISO directed controllable power plant units to track instantaneous demand. With growing penetration of renewables on the grid, there are higher levels of uncontrollable, variable generation resources. Because of that the ISO must use controllable resources to achieve a balance between both variable demand and variable supply. CAISO uses net load which is the difference between total load and renewable generation such as wind and solar. The net-load curve illustrates the variability and often referred as duck curve.

The CAISO performed an analysis on changing grid conditions by analyzing loads in past and near future [197]. With growing inverter based renewables the frequency response of the power network deteriorates.

This study identifies inclusion of specific resource operational capabilities for mitigation of [197], [322] (i) oversupply risk, (ii) short and steep ramps. In order to mitigate the possible issues, the ISO needs a resource mix that can react quickly to adjust electricity production to meet the sharp changes in electricity demand.

**Case-Study : EV Charging in Pasadena14**

Phase unbalance can be an issue behind the meter as well. In this sub-section presents a case study around phase unbalance at the Adaptive Charging Network (ACN) testbed located at Caltech in Pasadena, California.

A description of the testbed including its electrical topology and usage patterns is provided then provide examples of power unbalance between phases which occur do to usage patterns which lead to non-symmetric loading between phases. Finally a motivation is provided for the need for phase balancing techniques such as the energy storage which can account not only for instantaneous unbalances but also long term unbalances caused by differences in the total energy demand on each phase.

Electric vehicle charging EVs are expected to dominate future transportation. Charging EV batteries

can place a massive load on the local electrical infrastructure. Table 2.6 lists some EVs and their battery characteristics. The batteries can either be charged using three-phase or single-phase AC connection. In the case of AC level-2 charging, a single-phase connection is used by the AC/DC converter inside the EV. In the case of DC charging, a single-phase or three-phase connection can be used to feed an AC/DC converter outside the EV, which then feeds DC current directly to the EV’s battery. Table 2.7 lists the standard single and three-phase EVSEs (charging ports) and their rated power transfer capability. For instance, Nissan Leaf can be completely charged within 4 hours using 1-phase 32A charging EVSE. All charging points in Caltech ACN Testbed are of single phase and 32A rated type.

**Case Study 2: Quantifying length of a sub-horizon**

Identifying optimal look-ahead horizon for performing arbitrage would be essential for maximizing the gains by performing arbitrage. Prior works [251] indicate selecting a time horizon of 1 day is sensible since the electricity pattern repeats with a period of one day approximately, being high during peak consumption hours during the day and low during the night [196]. In this work we claim that the optimal control actions for energy storage device depends on electricity price and load variations in a smaller part of a larger time horizon and independent of all points in past or beyond the sub-horizon, as shown in Fig. 3.3. However, identifying this optimal look-ahead period is challenging as it is governed by variation of electricity price, load and battery parameters. Next we present a case study for understanding the influence of battery parameters on length of a sub-horizon.

**Case Study: CAISO 2017 for equal buying and selling price of electricity**

We consider 2017 electricity price for CAISO and identify the variation of sub-horizon over a year with different energy storage parameters. The variable considered here in this case study are:

• Electricity price for CAISO in 2017.

• Ramp rate of the battery: in this case study we consider 1 kWh capacity battery with 3 different ramp rates. xC-yC represents that battery takes 1/x hours to completely charge and 1/y hours to completely discharge.

• Efficiency of the battery: we consider 5 levels of efficiency (): 0.99, 0.95, 0.9, 0.8 and 0.7. Here = ch = dis.

The performance indices used in this case study are:

• Tmean: denotes the mean length of a sub-horizon over the whole year.

• T99%: denotes the 99% quartile.

• Tworst: denotes the worst case length of a sub-horizon.

**Comparing Run-Time of Algorithms**

We compare the run-time of three optimal arbitrage algorithms for a given battery and present the runtimes with different number of samples in the time horizon of optimization. The three algorithms compared here are:

(a) Proposed algorithm in this work which shows the structure of optimal arbitrage solution based on price and net-load variation.

(b) Linear Programming: We use the LP formulation proposed in Appendix B and [184]. The LP formulation is possible due to piecewise linear convex cost functions. In this formulation we consider: (i) net-metering compensation (with selling price at best equal to buying price) i.e. i 2 [0, 1], (ii) inelastic load, (iii) consumer renewable generation, (iv) storage charging and discharging losses, (v) storage ramping constraint and (vi) storage capacity constraint. Using numerical results we perform sensitivity analysis of batteries with varying ramp rates and varying ratio of selling and buying price of electricity.

(c) Convex optimization: There could be several different ways of formulating optimal arbitrage problem using convex optimization toolbox. We propose one of the many ways of solving optimal arbitrage problem with convex piecewise linear cost function using CVX. Since in the optimization formulation we do not have any binary variable, this optimization problem could be solved using the default solver, SDPT36.

The decision variable xi is fragmented into two variable given as xi = xch i − xds i , where xch i 2 [0,Xmax] and xds i 2 [0,−Xmin], denotes the charging and discharging values. For the numerical evaluation we use a battery with initial charge level, b0=500 Wh, bmax=3000 Wh, bmin=100 Wh, ch=dis=0.9 and sampling time is equal to 1 hour.

**Table of contents :**

Abstract

R´esum´e

Abbreviations

Some Notations

List of Figures

List of Tables

**1 Introduction **

1.1 Motivation

1.2 Contributions of the Thesis

1.3 Organization of the Thesis

1.3.1 Part I of the thesis: energy storage arbitrage

1.3.2 Part II of the thesis: energy storage co-optimization

1.3.3 Part III of the thesis: large-scale application

1.3.4 Conclusion and future directions

1.4 Publications

**2 Challenges and Literature Review **

2.1 Future Power System Challenges

2.1.1 Need for innovative billing

2.1.2 Need for ancillary services

2.2 Roles energy storage can play in a smart grid

2.2.1 Energy Arbitrage

2.2.2 Dynamic Regulation and Reserves

2.2.3 Peak Demand Flattening

2.2.4 Fast ramping and low response time

2.2.5 Power Quality

2.2.6 Case Study : EV Charging in Pasadena, California

2.2.7 Increasing Reliability and Inertia

2.2.8 Congestion and Voltage Support

2.2.9 Infrastructure Deferral

2.3 Bottlenecks with energy storage: Li-Ion battery

2.3.1 High Cost

2.3.2 Battery life and parameters

2.4 Uncertainty in parameters

2.4.1 AutoRegressive Forecasting and Model Predictive Control

2.5 Notation and battery model

**3 Energy Arbitrage – Net Metering 1.0 **

3.1 Introduction

3.2 Arbitrage under NEM 1.0

3.2.1 Optimal Energy Arbitrage Problem: NEM 1.0

3.2.2 Proposed Algorithm under NEM 1.0

3.2.3 Open Source Code

3.2.4 Stylized Example of Proposed Algorithm

3.3 Numerical Evaluation

3.4 Case Study 1: Feasibility of Energy Arbitrage

3.4.1 Net Average Available Battery Capacity

3.4.2 Evaluation

3.5 Case Study 2: Quantifying length of a sub-horizon

3.5.1 Case Study: CAISO 2017 for equal buying and selling price of electricity

3.6 Case study 3: Effect of Uncertainty on Arbitrage

3.6.1 Threshold based structure for negative prices

3.6.2 Point Forecast with MPC

3.6.3 Scenario-Based MPC

3.6.4 Simulation Results

3.6.5 Key Observation

3.7 Conclusion and Perspectives

**4 Energy Arbitrage – Net Metering 2.0 **

4.1 Introduction

4.1.1 General applicability of proposed algorithm

4.1.2 Contributions of the chapter

4.2 Optimal Arbitrage Problem

4.2.1 Threshold Based Structure of the Optimal Solution

4.2.2 Proposed Algorithm

4.2.3 Open Source Codes

4.3 Online Implementation of Proposed Algorithm

4.4 Numerical Results

4.4.1 MPC with incrementally improving forecast

4.5 Comparing Run-Time of Algorithms

4.6 Case Study 1: Intermediate ramp rate

4.7 Case study 2: Sensitivity analysis for varying

4.7.1 Deterministic Simulations

4.7.2 Results with Uncertainty

4.8 Conclusion and Perspectives

**5 Battery Degradation and Valuation **

5.1 Introduction

5.2 Battery degradation and mathematical model

5.2.1 Battery Degradation

5.2.2 Battery Model

5.2.3 Tuning Cycles of Operation

5.3 Eliminating Low Returning Arbitrage Gains

5.3.1 Cycle Life

5.3.2 Calendar Life

5.3.3 Optimal Storage Control

5.3.4 Limiting Cycles of Operation

5.3.5 Numerical Results

5.3.6 Observations

5.4 Controlling Arbitrage Cycles

5.4.1 Energy Storage Arbitrage Algorithm with Negative Prices

5.4.2 Controlling Cycles of Operation

5.4.3 Open Source Codes

5.5 Battery Participating in Ancillary Service

5.5.1 Compensation Mechanism

5.5.2 Controlling the Cycles

5.6 Numerical Results

5.6.1 Short Time-Scale: A typical Day

5.6.2 Long Term Simulation – One Year

5.7 Conclusion and Perspectives

**6 Arbitrage & Power Factor Correction **

6.1 Introduction

6.1.1 Literature Review

6.1.2 Contribution

6.2 System Description

6.2.1 Energy Arbitrage

6.2.2 Power Factor Correction

6.3 Arbitrage and PFC with Storage

6.3.1 McCormick Relaxation based approach

6.3.2 Receding horizon arbitrage with sequential PFC

6.3.3 Arbitrage with penalty based PFC

6.3.4 Minimizing converter usage with arbitrage and PFC

6.3.5 Open Source Codes

6.4 Modeling Uncertainty

6.4.1 Model Predictive Control

6.5 Numerical Results

6.5.1 Results with uncertainty

6.6 Case Study: Degradation of PF at a substation

6.7 Power Factor Correction with Solar Inverter

6.8 Conclusion and Perspectives

**7 Co-optimizing Storage for Prosumers **

7.1 Introduction

7.2 System Description

7.2.1 Billing Structure

7.3 Co-Optimization of Energy Storage

7.3.1 Energy Arbitrage

7.3.2 Arbitrage with PFC

7.3.3 Peak Demand Shaving with PFC and arbitrage

7.3.4 Co-optimization with control of cycles

7.3.5 Open Source Codes

7.4 Real-time implementation

7.4.1 AutoRegressive Forecasting

7.4.2 Model Predictive Control

7.5 Numerical Results

7.5.1 Controlling and Tuning Cycles of Operation

7.5.2 Real-time Implementation

7.6 Conclusion and Perspectives

**8 Co-optimizing Storage in Madeira **

8.1 Introduction

8.2 Power System Norms in Madeira

8.2.1 Overview of the Madeira Electric Grid

8.2.2 Peak Power Contracts, Tariffs and Billing Cycles

8.2.3 Self-Consumption and Renewables in Madeira

8.3 Co-optimizing Energy Storage

8.3.1 ToU pricing + zero feed-in-tariff + Peak-Shaving

8.3.2 Storage for BackUp with Arbitrage + Peak Shaving

8.3.3 Open Source Codes

8.4 Real-time Control under Uncertainty

8.4.1 Modeling Uncertainty: ARMA Forecasting

8.4.2 Model Predictive Control

8.5 Numerical Results

8.5.1 Deterministic Solution for Popt

8.5.2 Co-optimizing with Power Backup

8.5.3 Real-Time Implementation (Forecast plus MPC)

8.6 Conclusion and Perspectives

**9 Storage for low voltage consumers in Uruguay **

9.1 Introduction

9.2 Energy Landscape in Uruguay

9.3 Electricity Consumer Contracts

9.3.1 Fixed and Active Energy Cost

9.3.2 Peak Power Contract for LV Consumers

9.3.3 Billing of Reactive Energy

9.3.4 Cost of Consumption

9.3.5 Net-Metering in Uruguay

9.4 Storage for LV Prosumers in Uruguay

9.4.1 Active Power Management

9.4.2 Compensation Strategy for Reactive Power

9.5 Control Algorithm for Storage in Uruguay

9.5.1 Storage Operation Immune to Uncertainty

9.6 Numerical Experiments

9.6.1 Arbitrage Potential

9.6.2 Consumer gains with/without storage

9.6.3 Energy Storage Profitability

9.7 Conclusion and Perspectives

**10 Effect of Electricity Pricing on Ancillary Service **

10.1 Introduction

10.1.1 Related Work

10.1.2 Contributions

10.1.3 Key Observations

10.2 System Description

10.2.1 Consumer Model

10.2.2 Generation Scheduling

10.2.3 Price Model

10.2.4 Real time Operation

10.3 Indices Used for Measurement

10.3.1 Volatility Indices

10.3.2 Measuring Ancillary Service Required

10.4 Numerical Results

10.4.1 Results with only schedulable generations

10.4.2 With RES Generation

10.5 Conclusion and Perspectives

**11 Control of a fleet of batteries **

11.1 Introduction

11.2 Distributed control design

11.2.1 Nominal model design

11.2.2 Controlled Markov model for an individual battery

11.2.3 Mean Field Model

11.3 Numerical results

11.3.1 Tracking and SoC Performance

11.3.2 Impact of efficiency loss

11.4 Conclusions and Perspectives

**12 Drift Control for a Fleet of Batteries **

12.1 Introduction

12.1.1 Frequency Regulation in PJM

12.2 Drift compensation for a fleet of batteries

12.2.1 Lossless batteries with zero mean tracking signal

12.2.2 Lossy batteries with zero mean tracking signal

12.2.3 Why drift compensation?

12.3 Drift Compensation Controller design

12.3.1 Linearized System Model

12.3.2 Least Square Fitting

12.3.3 Discrete to Continuous Transformation

12.3.4 Augmented State Matrix

12.3.5 Linear Quadratic Regulator Gain

12.3.6 Gain Scheduling

12.3.7 Optimal Controller Gain

12.3.8 Test Simulation

12.4 PJM Performance Scores

12.5 Numerical Evaluation

12.6 Conclusion and Perspectives

**13 Phase Balancing using Storage **

13.1 Introduction to Phase Balancing

13.1.1 Cause of unbalance in three-phase power network

13.1.2 Effect of unbalance in three-phase power network

13.1.3 Indices for measuring of unbalance in three-phase power network

13.2 Understanding the effects of phase unbalance

13.2.1 Simulation Results

13.2.2 Honeymoon and Divorce Cases

13.3 Architectures of Storage Solutions

13.3.1 Solution with one battery and phase selector

13.3.2 Solution with three storage with each dedicated to each phase

13.3.3 Solution with three storage with phase selector for each battery

13.3.4 Phase Balancing with Storage: Stylized Example

13.4 Case Study : Madeira Substation

13.4.1 Overview of the Local Grid

13.4.2 Case of a Distribution Substation in Madeira

13.4.3 Q&A with the EEM Madeira

13.5 Conclusion and Perspectives

**14 Conclusions and Future Directions **

14.1 Conclusions

14.2 Future Directions

14.2.1 Selection of best-suited energy storage

14.2.2 Optimal lookahead horizon for hydro generation facilities

14.2.3 Storage/DG/Load placement based on voltage profile

14.2.4 Modeling flexible loads as batteries

14.2.5 Minimizing renewable energy curtailment

14.2.6 Extension of topics covered in thesis

**A Appendix 1 **

A.1 Proof of Theorem 3.2.1

A.2 Convex Optimization: Conditions of Optimality

A.2.1 Convex Function and Subdifferential

A.2.2 Optimality condition for unconstrained problem

A.2.3 Constrained Optimization Primal Problem (P)

A.3 Proof of Theorem 4.2.1

A.3.1 For zi > 0

A.3.2 For zi < 0

A.4 Proof of Theorem 4.2.2

A.5 Proof of Remark 6

A.6 Proof of Remark 7

A.7 Arbitrage with NEM 1.0

A.8 Arbitrage with Convex Optimization using CVX

A.8.1 Only storage with NEM and losses

A.8.2 Arbitrage with load, renewable generation with NEM and losses

A.9 Proof of Theorem 9.4.1

A.10 Control Design Using LQG in Matlab

A.10.1 System Type I: Open Loop System

A.10.2 System Type II: Closed Loop Full-feedback

A.10.3 System Type III: Limited Measurement Feedback System

A.10.4 System Type IV: Limited Measurement Noisy Feedback System

**B Arbitrage using Linear Programming **

B.1 Introduction

B.2 Optimal Arbitrage with Linear Programming

B.2.1 Epigraph formulation of Linear Programming

B.3 Formulating LP Matrices

B.3.1 Lossless Storage with equal buy and sell price

B.3.2 Only Storage Case with net-metering and efficiency losses

B.3.3 Storage performing arbitrage with inelastic load and renewable generation under net-metering and storage losses

B.4 Real-time implementation

B.5 Conclusion

**Bibliography **