Effect of Electricity Pricing on Ancillary Service 

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Future Power System Challenges

Electrical power system is often considered the most complex man-made system and comprises of gener-ation, transmission and distribution assets facilitating electricity consumers commercial and residential, to use electrical energy. In order to ensure the electrical stability and reliability of power network so as the power can be transported from generators to distribution networks and to loads, independent system operators or ISOs are created (in context of the US). ISOs being independent from ownership by generators or market participants bring fairness as they do not tend to favor one over other in setting norms. An ISO performs the following tasks (not complete list):
(T1) instantaneous balancing of cumulative generation and load,
(T2) power quality5 in the system,
Power quality involves magnitude, frequency, and waveform of voltage and current. Well known indices such as frequency, power factor, total harmonic distortion etc are frequently used as indicators of power quality.
(T3) power grid upgrade for future. Often an ISO divides the responsibility to several Distribution System Operators or DSOs. DSO handles reliable operation of power network at a regional level. In cases where DSOs are unable to ensure power reliability, ISOs take the role at regional level too. The power network is undergoing a transformation at generation and load sides simultaneously. Dis-tributed generation (DG) facilities which consist of primarily renewable energy sources like wind and solar are being integrated in the power network. The share of DG is expected to increase. This transformation of traditional centralized generation to distributed generation will require a re-design of the system to at-tain the same levels of reliability. Contemporary power networks have very high reliability. Furthermore, more and more fossil fuel based generators will reach their usable life and will not be replenished by the same level of fossil fuel based generation due to environmental concerns. Large scale renewables will cause the aggregate generation intermittent and more challenging to achieve a balance between generation and demand. The renewable generation at electric consumer end is often interfaced via a converter which operates at close to unity power factor6 [172] leading to deterioration of power factor seen by the grid which meets all the consumer reactive power and only a fraction of active power. At the load side, new loads like Electric Vehicles or EVs will evolve in large-scale in near future. Effect of such loads needs to be evaluated. Both of these directions of power system transformation are heavily researched.
We summarize the effects caused by the above mentioned transformation presented in the literature.
Generation shift from dispatchable units to intermittent renewables: paradigm shift from traditional power network where generation used to follow load [202]. Furthermore, inverter interfaced renewable energy sources (RES) replacing rotor based generation will reduce power system inertia which implies higher rate of change of frequency during system disturbances. Distributed generation is intermittent, interfaced via single phase converter and solar PV also have a high impedance and low short circuit current making it more prone to cause unbalance7 in the power network [229], [155].
Bulk centralized generation facilities to decentralized DGs: For instance, in the UK electricity network is dominated by a centralized power generation model, where power flows from less than sixty large power stations to millions of consumers [26]. However, this will change with growth of DGs and small renewable generation plants. Due to growth of DGs compared to traditional power system with centralized generation the risk of local voltage problems and congestion will increase [202]. Central system operators will no longer have a system overview to effectively dispatch reserves and therefore, requiring localized corrective actions. Authors in [159] present case studies of how distributed generation should be considered for finding the feeder hosting capacity8 to prevent over-voltages and transformer overload. The hosting capacity depends on the network topology, line parameters and transformer rating. In case of overproduction from the hosting capacity level, soft or hard curtailment of generation will be required in order to ensure stable operation.
Localized impact of DG outage: this is the advantage the new power system with large amounts of DGs. Failure of DGs will have a localized effect, unlike presently power generation failures which can lead to cascaded effect leading to complete blackout. However, detailed analysis should be considered in redesigning the power grid, which has been designed for one way power flow, i.e. from bulk generation facilities to LV and MV consumers. The distribution feeders are designed such that the voltage magnitude becomes lower when moving along the feeder. Integrating DGs at distribution level makes the design condition of feeders invalid and thus over-voltages could occur [104].
Synchronized operation: The connection of single phase electric vehicles (EVs) and DGs are random and often clustered in a certain area. Authors in [278] note that voltage imbalance caused by single phase EVs is unlikely to exceed the prescribed limits set provided EVs are reasonably distributed among three phases. However, such a distribution cannot be guaranteed. In addition both EVs and PVs (PhotoVoltaics) tend to be active in a synchronized manner, i.e., majority EVs tend to get charged in the evening when people reach their homes after work and all PVs generate electricity when it is sunny. Such a synchronized operation of these loads and generation aggravates the problems for distribution system operators who are obliged to ensure power quality at all times. Huge ramping reserves (both up and down) will be required to cope up with bulk DG and EV integration.
Power factor measures the phase difference between the ac voltage and ac current.
Voltage unbalance is used to measure unbalance in power networks. Voltage unbalance measure is referred as Voltage Unbalance Factor or VUF. In Chapter 8 we describe in detail the various definitions used to measure unbalance.
8Feeder hosting capacity refers to the amount of resources (generators or loads) that can be accommodated on a feeder without impacting system operation under existing control and infrastructure configuration [223].
Figure 2.2: BPA demand supply mismatch with renewable generation for two consecutive weeks [5].
generation and the right plot shows significant amount of wind generation. Due to greater intermittancy brought by higher wind generation the amount of regulation required for achieving balancing between aggregate load and generation increases noticeably. The new power system will require active participation of grid participants: consumers and producers. More ancillary services9 and greater responsiveness of participants will be required. Greater observability of power network with sensors, information system and communication protocols will be required for adaptive decision making in real time.
With increasing share of RES the problem of supply and load balancing will become more challenging, due to the additional intermittency in power generation by RES. The various solutions to this problem proposed in the literature are:
Solution S1 : Install new fast ramping generation infrastructure and upgrade in transmission and distri-bution grid infrastructure [168].
Solution S2 : Induce demand response participation by end-users in exchange of incentives [248, 265].
Solution S3 : Direct load control by the balancing authority or independent system operators [289, 256].
Solution S4 : Generation and/or demand curtailment.
Solution S5 : Perform ancillary service [114], demand response, arbitrage [182], load balancing, infras-tructure deferral, generation and/or demand curtailment using batteries or storage devices.
In this thesis we focus on Solution S5.
Roles of ISO: The broad categorization of ISO tasks T1-T3 described previously, are coupled in nature. If T1 is not achieved then one or more indices of T2 will deviate beyond their prescribed limits. For instance in high voltage network where active power is coupled by frequency, if the active load exceeds active power generated then frequency will dip below 50/60 Hz [188]. The dip will be governed by the magnitude of unbalance between generated and consumed active power. The tasks T1 and T3 are coupled in a way that if power network does not have enough reserves than achieving T1 is not possible without load or generation shedding, a scenario which reduces power system reliability. ISO plans the growth of transmission, distribution and generation facilities taking into account the emergence of new loads, degradation of existing infrastructure, uncertainty in generation scheduling and intermittency of renewable generation. In this thesis we do not discuss T3.
For ensuring that tasks T1 and T2 are achieved, ISOs introduced new billing mechanisms for energy participants, created new energy markets, encouraged participation in ancillary service market and set power quality norms for different participating entities in the network. Below we describe the need and effect of these initiatives by ISOs. Fig. 2.3 shows the various ISOs in the US and Canada [34].

Need for innovative billing

In order to encourage electricity consumers to participate actively in facilitating goals T1 and T2 of the ISO, ISOs provides incentives (or penalties) to energy participants, i.e. consumers and/or generators, in exchange of their services. The new electricity bills have few or all of the following revenue sources for active participants. ISO also sets Locational Marginal Prices for participants of energy markets which consists of large loads, generation facilities and utilities/retailers that buy energy for their consumers.
Wholesale Energy Markets: Wholesale energy markets exist in many power networks. The PJM energy markets consists of two markets: a day-ahead market and a real-time balancing market [230]. The day-ahead market is a forward market in which hourly clearing prices called as day-ahead LMPs10 which are calculated for each hour of the next day based on offers and bids submitted into the day-ahead market. The real-time energy market based on real-time operation uses real-time LMPs calculated based on sys-tem operating conditions. All spot purchases and sales in balancing market are settled at real-time LMPs. Large loads and bulk generators participate in wholesale energy markets.
Electricity Price for Consumers: Traditionally utilities and ISOs used fixed electricity prices as most generators were developed to follow the load. However, with uncertainty in generation side, consumer responsiveness could help ISOs in avoiding developing new infrastructure to mitigate such intermittency. The real time electricity prices are set for consumers to incentivize their power consumption deviation.
Time-of-Use (ToU) Price: ToU pricing is a variable rate structure that charges for energy depending on the time of day and the season when the energy is used. Responsive end-users shift their load to low rate times thus facilitating in load shifting from the historical peak consumption periods to off-peak periods. ToU can reduce the peak aggregate load [105]. However, ToU rate is inadequate to reflect the real time conditions of the grid, because the peak rate times are determined based on past aggregate consumption and may not correspond to the actual peak load. This will only exacerbate with more renewable sources in the grid. This is exemplified by the case study of Northern Italy by authors in [310] pointing the non-effectiveness of ToU pricing in shifting peak demand. Therefore, more dynamic price structure are proposed which reflects the real time condition of the grid.
Real Time Electricity Price: electricity price vary dynamically with sampling time ranging from 5 minutes in CAISO to 15 minutes in NYISO to hourly variations in PJM [16]. Real time electricity price aim to reduce the peak- to-average load ratio, i.e. flatten the load, leading to peak shaving for the grid. For ex-ante type real time price (RTP) design where the electricity price set at the beginning of the time interval is most prevelent. Information asymmetry is caused by the time delay between setting RTP, consumption decision and intermittent generation. Setting RTP requires the prediction of aggregate demand and RES generation by the utility if the price is set ex-ante and prediction of price by the consumers if the price is set ex-post [287, 185]. Due to information asymmetry the application of RTP is limited in real-time load balancing [185], thus ancillary services are called for supply and demand balancing, see Section 2.1.2 and Chapter 10.
Peak Demand Charge: The maximum demand dictates the size of power grid infrastructure, i.e. generators, transmission lines, transformers, circuit breakers etc. Due to this many power utilities around the world have introduced peak demand charge that a consumer may seek to minimize over a longer pe-riod (weeks or months). For example in California, Pacific Gas and Electric company charge peak demand charges are applied based on the maximum demand over a month [295]. Peak Consumption Contract: In many places instead of peak demand charge, the utility offers peak demand contracts where the consumer should ensure their peak demand within the selected con-tract. In case the instantaneous power exceeds the contract level, the utility could either disconnect the consumer and/or penalize for contract violations. This contract level decides the fixed charge component of the end user electricity bill. For instance in Madeira in Portugal the utility Empresa de Eletricidade da Madeira (EEM) provides low voltage consumers with 8 peak power levels which consumers select as a contract [320]. In case the peak power of the consumer exceeds the consumer contract level, a localized disconnection happens. The consumer can manually reconnect. However, such disconnection could affect appliance life.
Demand Response Participation: There are several different mechanisms for implementation of demand response or DR11 programs. The demand response can be (dr1) price based, (dr2) consumers opting for contracts where they respond to balancing authority’s request and (dr3) consumers opting for contracts where the flexible resources are controlled directly using a centralized signal ensuring the local quality of service of consumer. There are many examples of demand response implementation world-wide. We list some literature on demand response type (dr1). Authors in [302] present how price-based demand-side management programs assist in the reduction of peak demand and present a case study of the impact of real-time pricing on a power network in the city of Gothenburg, Sweden. Note that demand-side management includes DR, energy-efficiency and conservation programs [319]. Authors in [224] present results for price structures from the Ameren Illinois Power Company, showing a reduction of up to 39% in overall domestic energy costs. Authors in [205] show that demand-side resources like space heating can be incentivized to alter their consumption pattern pertaining to variations in the price of electricity, leading to a reduction in the cost of consumption for the end user, while performing price-based DR for the grid. Authors in [337] proposes controller for residential HVAC12 systems for a significant reduction in peak loads and electricity bills with modest variations in thermal comfort. Authors in [279, 291] pro-pose real-time electricity pricing scheme that reduces the peak-to-average load ratio, i.e. flattens the load, leading to peak shaving for the grid. In many cases, DR participants are informed prior to an event to reduce consumption thus deferring investment in peak ramping power plants. For example, consumers can enroll in Florida Power and Light (FPL) Residential On Call savings program where FPL-approved contractor installs the On Call device to reduce energy demand during emergencies. This of the form demand response (dr2) consumers could save up to $137 a year even if FPL never turns off the appliances chosen by consumers to participate. Historically, this program has been implemented a few times per year in early to late afternoons on weekdays [30]. Extensive works of demand response of the form (dr3) are available. Some works of direct load control are [94, 246].
Penalties for violating power quality indices: Many ISOs also include power quality penalties, in order to encourage consumers to maintain power quality at their point of common coupling. Such penalties are often levied upon large consumers and commercial loads, however, we believe that as the power network evolves such tasks will also be mandatory for smaller loads. Actively participating consumers should aim to minimize the penalties by abiding by the power quality norms set. In this introduction we provide rules for power factor violation and penalties, similar norms are available for other power quality indices.
Power Factor Rules: Power factor (PF) which denotes the ratio of active power and the apparent power is denoted as cos(φ), where φ denotes the angle between active and reactive power. An alternate definition commonly used to denote the PF is tan(φ) represented as tg φ in national and ISO level power norm documents. tg φ denotes the ratio of reactive power over active power. Note | cos(φ)| denotes absolute value of PF and implies the rules for leading or lagging power factor are symmetrical. Maintaining PF of aggregate load seen by the transmission network is essential for reliable operation of distribution network. Power utilities worldwide have rules designed for consumers to comply with the minimum power factor that they should maintain. In case the consumer power factor goes below the pre-set limit defined by utility, the consumer has to pay a penalty under some utilities or the utility makes it compulsory for the consumer to install power factor correction equipment to improve the power factor within permissible limits. The cost of power factor correction devices are borne by the consumer and not the utility [12, 18].

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Table of contents :

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


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