power system operator decision support in the presence of...

A Holistic Assessment Method of Power System

Imbalances in the Presence of Variable

Energy Resources

by

Aramazd Muzhikyan

A Thesis Presented to the

Masdar Institute of Science and Technology

in Partial Fulfillment of the Requirements for the Degree of

Master of Science

in

Engineering Systems and Management

c�2013 Masdar Institute of Science and Technology

All rights reserved

Abstract

One of the main roles of power system operator is maintaining the balance between power generation

and consumption. In traditional power systems, mainly consisting of conventional (thermal) generation

units, the balance is maintained effectively by day-ahead scheduling and real-time control of necessary

resources (generation, reserves and regulation). The scheduled amount of reserves and regulation is as-

sessed partially following NERC requirements and partially from experience (specific to each power sys-

tem). However, penetration of variable energy resources (wind, solar, etc.) into power system changes

the established standards and requirements. Variable energy resources (VER) introduce a new level of

variability and uncertainty, which makes balancing of the system a challenging task. The assumptions

made for traditional power system are not true, making existing methods of resource assessment and

scheduling not effective. In this work power system imbalance mitigation is modeled as a consecutive

implementation of regulation, real-time markets and operator manual actions. This integrated represen-

tation allows better understanding of relations between power system operations different time scales.

This work establishes relations between scheduled resource adequacy and VER variability, forecasting

uncertainty and timescales of power system operations. The results show, that reserve and regulation

requirements depend on different characteristics of VER (day-ahead and real-time forecast, variability)

and the properties of the power system (available ramping capabilities). The validity of established

relations is demonstrated by simulations results.

ii

This research was supported by the Government of Abu Dhabi to help fulfill the vision of the late

President Sheikh Zayed Bin Sultan Al Nahyan for sustainable development and empowerment of the

UAE and humankind.

iii

Acknowledgments

I would like to thanks my research advisor, Dr. Amro M. Farid, without whom the current thesis would

be impossible. I wish to extend my gratitude to my RSC members, Dr. Kamal Youcef-Toumi and Dr.

Amer Al Hinai, for their valuable comments that helped to make this thesis better. I am also thankful to

the members of our research team for establishing creative and enjoyable working environment.

I am grateful to my family members who are constantly supporting me in any endeavour in my life.

I always feel their presence beside my from long distances away. I am thankful to the residents of

Villa 9 and all my friends for an excellent two-year life experience in Abu Dhabi.

Aramazd Muzhikyan,

Masdar City, May 15, 2013.

iv

Contents

1 Introduction 1

1.1 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Research Objective and Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Research Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Research Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.5 Novelty of Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.6 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Research Background 5

2.1 The Need for Holistic Assessment Methods for the Future Electricity Grid . . . . . . . . 6

2.1.1 Evolution of the Power Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Enhanced Grid Control Technologies and Strategies . . . . . . . . . . . . . . . 15

2.1.3 Adequacy of Existing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.4 Reconfigurable Framework for Holistic Power Grid Assessment . . . . . . . . . 22

2.2 Tools for Holistic Assessment of Power System Imbalances . . . . . . . . . . . . . . . . 24

2.2.1 The Physical Power Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.2 Operations Control of Power System Balance . . . . . . . . . . . . . . . . . . . 27

3 Methodology and Simulation Setup 32

3.1 Resources Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.1 Generation Commitment and Scheduling . . . . . . . . . . . . . . . . . . . . . 32

v

3.1.2 Adequacy of the Scheduled Generation . . . . . . . . . . . . . . . . . . . . . . 34

3.1.3 Reserve Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1.4 Reserve Requirements and Scheduled Reserves . . . . . . . . . . . . . . . . . . 36

3.2 Balancing Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.1 Measurement of the Power System State and Imbalances . . . . . . . . . . . . . 38

3.2.2 Regulation Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.3 Real-Time Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.4 Operator Manual Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 The Generation Model of Variable Energy Resources . . . . . . . . . . . . . . . . . . . 41

3.3.1 Penetration Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.2 Forecast Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.3 Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.4 The model of Variable Energy Resources . . . . . . . . . . . . . . . . . . . . . 44

4 Case Study and Results 45

4.1 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Test System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.2 Incorporation of Wind and Load Data . . . . . . . . . . . . . . . . . . . . . . . 46

4.1.3 Simulation Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.1 Wind Integration Impact on Power System Imbalances . . . . . . . . . . . . . . 48

4.2.2 Imbalance Mitigation by Increased System Flexibility, Reserves and Regulation . 52

5 Conclusion and Future Work 57

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6 Abbreviations 59

vi

List of Tables

2.1 The power grid outage statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

vii

List of Figures

1.1 The four-phase research approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Traditional Grid Generation and Demand Portfolio [46] . . . . . . . . . . . . . . . . . . 10

2.2 Normalized power spectrum of daily load (Data from Bonneville Power Administration) 11

2.3 Time scales of relevant power system dynamics [98] . . . . . . . . . . . . . . . . . . . 11

2.4 Future Grid Generation and Demand Portfolio [46] . . . . . . . . . . . . . . . . . . . . 12

2.5 Graphical Representation of the Evolving Power Grid Structure [46] . . . . . . . . . . . 13

2.6 Grid Enterprise Control to Enable Holistic Dynamic Properities . . . . . . . . . . . . . 16

2.7 Integrated Enterprise Control of the Power Grid . . . . . . . . . . . . . . . . . . . . . . 18

2.8 Conceptual model of a power grid enterprise control simulator . . . . . . . . . . . . . . 23

4.1 Traditional power system reserve requirement calculation . . . . . . . . . . . . . . . . . 49

4.2 Traditional power system regulation requirement calculation . . . . . . . . . . . . . . . 49

4.3 Power system imbalances for different levels of wind integration . . . . . . . . . . . . . 50

4.4 Power system imbalances for different levels of wind variability . . . . . . . . . . . . . 51

4.5 Power system imbalances for different values of wind day-ahead forecast error . . . . . 51

4.6 Power system imbalances for different values of wind short-term forecast error . . . . . 52

4.7 Traditional power system generation reserve requirement calculation . . . . . . . . . . . 53

4.8 Traditional power system ramping reserve requirement calculation . . . . . . . . . . . . 54

4.9 Traditional power system regulation reserve requirement calculation . . . . . . . . . . . 54

4.10 Power system imbalance mitigation in the presence of VER by increasing generation

reserves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

viii

4.11 Power system imbalance mitigation in the presence of VER by increasing generation

reserves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.12 Power system imbalance mitigation in the presence of VER by increasing regulation

reserves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

ix

CHAPTER 1

Introduction

1.1 Research Motivation

The impact of variable energy resource (VER) penetration on power system operations and planning has

been the subject of extensive research in recent years [42, 72]. Here, significant wind and solar penetra-

tion adds new levels of variability and uncertainty to power systems; thus impeding balanced operations

as defined by the North American Electric Reliability Corporation (NERC)’s control performance stan-

dards (CPS). The main conclusion of such studies is that renewable energy integration increases power

system reserves and regulation requirements. However, most of these results are based on specific case

studies that comment on the sufficiency of a power system’s flexibility in relation to VER penetration

[116, 8], thus limiting their generalizability [12]. Consequently, a recent review has motivated the need

for holistic assessment methods [45].

1.2 Research Objective and Questions

The motivation of the previous section defines the research objective of the current research as follows:

Research Objective: Develop a holistic assessment method of power system imbalances in the presence

of variable energy resources.

Achievement of this objective also assumes testing of the developed method on different VER inte-

gration scenarios. Thus, the following research questions are designed to achieve the research objective:

1

CHAPTER 1. INTRODUCTION 2

• Research Question 1. How may power system imbalances be holistically assessed as variable

energy resources are integrated?

• Research Question 2. What is the case independent impact of VER integration on power system

imbalances?

• Research Question 3. How power system imbalances can be mitigated by increasing generation

flexibility, reserves and regulation?

1.3 Research Approach

Based on the research questions identified in the previous section, the current research has taken four-

phase approach as presented in Fig. 1.1.

• The first phase includes review of the available literature and defining the research topic and

research scope.

• The second phase is the development of imbalance assessment holistic method, including the

architecture of the used power system model, assessment criteria, assumptions, etc.

• The third phase is the development of the actual simulator. This phase mainly includes coding and

testing of the simulator.

• The fourth phase is implementation of the case study. This phase includes choice of test system,

VER and load data, design of simulation scenarios, etc.

• The last phase is interpretation of results and conclusions.

Phase 2: Development of Imbalance

Assessment Method

Phase 3: Development of Power

System Simulator

Phase 1: Identification of Research

Phase 4: Case Study with

Different Scenarios Conclusions

Figure 1.1: The four-phase research approach

1.4 Research Scope

High complexity of the current research requires several assumptions and simplifications to make used

models tractable. The following assumptions are made in the scope of the current research:


• Steady-state power system models are used in this research. It is assumed that dynamics faster

than 1 minute is mitigated by the system inertia.

• Possible power system contingencies, such as generator or transmission line outage, is out of the

current research scope.

• Power system congestions are not considered in this research. Distribution of system load and

generation is organized in a way to avoid congestions.

• Perfect knowledge about the state of the system is assumed. This is done to avoid any impact of

state estimation imperfections on final results.

• System load is assumed to be perfectly forecastable. Since the goal is assess VER impact, uncer-

tainties in the load forecast are neglected.

1.5 Novelty of Research Contributions

This research makes a novel contribution regarding all three research questions:

• A holistic assessment method of power system imbalances is developed. The reconfigurable ar-

chitecture of this method extends its applicability to large scope of VER integration scenarios.

• Based on a selected set of scenarios, the impact of VER integration on power system imbalances

is assessed. Each scenario focuses on a single parameter of VER, which shows contribution of

each parameter in the imbalances.

• The application of the developed method is extended to assessment of reserve requirements for

power systems with VER penetration.

1.6 Thesis Organization

The thesis consists of 6 chapters and is organized as follows:

• Chapter 2 contains the background of this research. Particularly, the current trends of power

system evolution and its potential impact on power system operations and planning is discussed.

The importance of holistic approach to the assessment methods is highlighted. The second part of

the chapter presents the set of power system balancing tools available from the literature.


• Chapter 3 is devoted to the detailed presentation of the developed assessment methodology. The

three layer enterprise model of power system operations is presented and its different components

are described in detail. Also, the model of VER generation used in this research is developed.

• Chapter 4 presents the design of the case study and the simulation results. Two different sets of

simulation scenarios are performed seeking to address power system imbalance assessment and

mitigation issues. The obtained results are interpreted in connection to the characteristics of VER

and the power system.

• Chapter 5 draws the conclusions of the thesis and indicates possible directions of future work.

• Chapter 6 contains the list of abbreviations used in the text.

CHAPTER 2

Research Background

As driven by decarbonization, reliability, transportation electrification, consumer participation and dereg-

ulation, this future grid will undergo technical, economic and regulatory changes to bring about the in-

corporation of renewable energy and incentivized demand side management and control. As a result,

the power grid will experience fundamental changes in its system structure and behavior that will con-

sequently require enhanced and integrated control, automation, and IT-driven management functions in

what is called enterprise control.

While these requirements will open a plethora of opportunities for new control technologies, many

of which are largely overlapping in function. Their overall contribution to holistic dynamic properties

such as dispatchability, flexibility, forecast ability, and voltage stability is less than clear. Piece-meal

integration and a lack of coordinated assessment could bring about costly-overbuilt solutions or even

worse unintended reliability consequences. This work, thus has motivated the need for holistic meth-

ods of integrated assessment that manage the diversity of control solutions against their many compet-

ing objectives and contrasts these requirements to existing variable energy resource integration studies.

The presentation concludes with a reconfigurable framework for power grid analysis that is based upon

seven requirements distilled from the discussions. Initial demonstrations of this framework are already

reported and more holistic power system studies are envisioned.

5

CHAPTER 2. RESEARCH BACKGROUND 6

2.1 The Need for Holistic Assessment Methods for the Future Electricity

Grid

Traditional power systems have often been built on the basis of an electrical energy value chain which

consists of a relatively few, centralized and actively controlled thermal power generation facilities which

serve a relatively large number of distributed, passive electrical loads [136, 120]. Furthermore, the

dominant operating paradigm and goal for these operators and utilities was to always serve the consumer

demanded load with maximum reliability at whatever the production cost [53]. Over the years, system

operators and utilities have improved their methods to achieve this task [146, 55]. Generation dispatch,

reserve management and automatic control has matured. Load forecasting techniques have advanced

significantly to bring forecasts errors to as low as a couple of percent and system securities and their

associated standards have evolved equally. It does not appear however that this status quo is set to last.

Instead multiple drivers are set to dramatically change the basic assumptions upon which the electri-

cal power grid was built. The first of these is decarbonization [124]. The European Union, for example,

has committed to reduce greenhouse gas emissions in the power sector to 1990 levels by 2050 [5]. Such

targets create a strong pressure for renewable energy penetration in both the transmission as well as the

distribution system [44]. Next, electricity demand continues to grow sometimes as fast as 10% per year

in the quickly developing economies [65, 9]. Such demands motivate the need for “peak shaving” and

load shifting capabilities so as to avoid the installation of new power generation capacity and maximize

the capacity factor of already existing units [109, 23, 36, 53, 29, 127, 10]. Decarbonization drivers also

dramatically affect the transportation sector and the emerging consensus is that both public and private

transport should be increasingly electrified so as to improve well-to-wheel efficiencies [19]. This trans-

portation electrification driver requires the electrical grid to be fit for a new, significant and previously

un-envisioned purpose [51, 79, 78, 129]. Next, the trends towards electric power deregulation that began

at the turn of the century are likely to continue in the hope of achieving greater social welfare and im-

proved electricity price and service [70]. Finally, these deregulation trends have inspired and empowered

consumers who respond to both physical and economic grid conditions [36]. In short, these five drivers

require the steadily increasing penetration of solar and wind generation as well as evolving capabilities

to support demand side management for the tremendous diversity of loads that connect to the electrical

grid.

The integration of these three new grid technologies ultimately imposes fundamental changes to the

grid structure and behavior. As a result, the already existing suite of control technologies and strategies


are set to dramatically expand in both number and type. While existing regulatory codes and standards

will continue to apply [106], it is less than clear how the holistic behavior of the grid will change or

whether reliability will be assured. Furthermore, it is unclear what value for cost these control technolo-

gies can bring and what degree of control, automation, and information technology is truly necessary to

achieve the desired level of reliability. This work thus argues that a future electricity grid with a high

penetration of renewable energy and demand side management technologies requires holistic assessment

methods for the profile of newly adopted control technologies.

2.1.1 Evolution of the Power Grid

The emergence of new drivers in the power grid is likely to alter the traditional trajectory of incremental

improvements. Increasing concerns about power grid environmental impact and operations reliability

motivate fundamental changes in electrical power generation and consumption patterns, such as integra-

tion of variable energy resources (VER), electrification of transportation and introduction of demand-

side management (DSM) techniques. As a result, the overall structure and dynamics of the system is set

to evolve; potentially invalidating several traditional assumptions about power grid behavior.

2.1.1.1 Drivers for the Evolution of the Power Grid

Since the power grid’s inception more than a century ago, a number of fundamental assumptions have

driven its structure and operation. Since then, the power grid has received a number of incremental

upgrades in generation efficiency, operating procedures, and system security. However, this status quo

is set to change as new drivers come into effect. This section specifically addresses five new drivers:

grid decarbonization, reliability concerns, transportation electrification, implementation of demand side

management and changes in market design and regulatory paradigm [16].

Decarbonization has become the main driver of the power grid evolution as a result of increasing

concerns about greenhouse gas emissions and climate change. The Europe Union, for example, is tar-

geting to reduce greenhouse gas emissions to 80%� 95% of the 1990 level by 2050 [5]. In the future,

the choices of energy source are likely to be constrained by environmental considerations and not just

simply technological limitations and resource scarcity. The European Union Emissions Trading scheme

has imposed a price for carbon credits for power generation facilities [43, 44]. If this trend continues, the

cost of CO2 emissions can become one of the factors affecting generation capacity investment decisions.

This trend incentivizes renewable energy sources (RES) over oil and natural gas powered generation

units. RES have a number of advantages over traditional energy sources: environmental friendliness, no


Table 2.1: The power grid outage statisticsPeriod Occurrences of Occurrences of 50,000

100 MW or more or more consumersNERC 1991-1995 66 41

1996-2000 76 582001-2005 140 92

EIA 2000-2004 156 1492005-2009 264 349

danger of their depletion over time (sustainable energy sources), and no fuel expense requirements [7].

The first interest towards renewable sources of energy emerged after the oil crisis in 1970s, leading to

some investments in their technological development [4]. However, after the decline of oil and gas prices

during 1980s, renewable energy sources lost their competitive strength. Currently, the installation of re-

newable energy sources are mainly supported by governmental mandates and regulatory foundations

such as Renewable Portfolio Standards [1, 2, 3].

Power grid reliability enhancement is a second driver. Currently, most of the U.S. electrical power

infrastructure planning and operation aspects are supported by computer simulations to ensure system

reliability. However, many parts of the system are over 25-30 years old and have been built prior to the

emergence of extensive computer and communication networks, which raises questions about power grid

reliability [82]. A disparity between electricity demand and electric power infrastructure growths makes

the North American electricity infrastructure increasingly stressed, and further aggravates reliability

concerns. Table 2.1 contains power system outage data from US Energy Information Administration

(EIA) and the North American Electric Reliability Corporation (NERC). Both sources show that there

is a growing tendency of power system failure probability [16].

Decarbonization has led to a third driver: namely transportation electrification. The American trans-

portation sector accounts for approximately two-third of the U.S. fossil fuel demand [37]. Without viable

alternatives to the oil, increasing energy demand will continue to rely mostly on fossil fuel resources.

Alternatively, EV’s are nearly twice as energy efficient as vehicles with internal combustion engine and

have no emissions at the point of use. From a technological perspective, electrical vehicles (EV) have

reached maturity thanks to active investments by major automobile manufacturers [32], although its mar-

ket will take time to develop [149, 142]. Despite the decarbonization advantages, the electrification of

transport increases the dependence on the electricity grid [51, 79, 78, 129]. Advanced controls, together

with existing innovation in power electronics and energy storage, are enablers to simultaneously man-

age the operation of the grid and the electrical transportation system [51, 78]. Compared to independent


operations by the power grid and transportation sectors, collaborative control strategies can achieve a

series of benefits, solving some issues faced by both groups [50]. For example, the availability of decen-

tralized storage onboard transportation units can allow the use of the transportation system as a complex

demand-response system in what is commonly known as vehicle-to-grid applications [91, 111, 123]. In

such a scenario, the transportation system can generate revenue from energy stored during peak-periods.

Once, transportation elements are able to concurrently and dynamically plan their operations, these fu-

ture systems will enable reduced overall energy use by transportation system, as well as provide the

ability to accommodate the increased penetration of renewables in the power infrastructure.

Another major driver to the evolution of the power grid is highly enabled and participating electric-

ity consumers. Historically, the power system has operated in the paradigm, that the actively managed

power generation supply closely followed passive demand [136]. The power grid was designed and op-

erated on this unilateral basis. The size of the power peak determined the required generation capacity,

and sub-daily variability determined the required flexibility [55]. However, the emergence of advanced

technologies like smart meters [61, 150] and power line carriers (PLC) [76] into the grid has facilitated

communication with consumers and empowered them to make decisions based on the real-time grid

conditions [150, 61, 76, 81, 62]. These enabling technologies allow demand to migrate from a pas-

sive, non-dispatchable behavior to one that is response to dynamic prices and reliability signals [23].

The integration of demand-response technology introduces potentially millions of new consumer-driven

dynamical systems each with its own control loop. How the power grid will behave after the full in-

tegration of demand-side management is not yet clear, and will largely depend on the implementation

details. This can depend on the types of signals that customers receive and where the decisions are made.

Some recent work has demonstrated demand side management integration scenarios that cause grid in-

stability [118, 117]. Furthermore, those power system operators that have implemented price-responsive

demand-side management require complete visibility to energy resources [114]. This practice is unlikely

to continue given the shear scale and cost of telemetry and instrumentation.

Power system deregulation is the final driver for the evolution of the power grid. Throughout most

of its history, the power system has consisted of vertically integrated utilities, each having monopolies

over its own geographical area [125]. Since 1978, this vertically integrated value chain has become

increasingly unbundled to allow for diversified and competitive wholesale transactions [70, 71, 69, 75,

52, 34, 84, 121]. The overwhelming trend has been towards privatization, deregulation, restructuring,

and re-regulation. The new regulatory environment with its diversity of market players and associated

technologies has resulted in a new energy value chain consisting of five parts: 1) fuel/energy source,


2) power generation, 3) electricity delivery through transmission networks, 4) electricity stepping down

into distribution networks, and 5) delivery to end-consumers. Most of the existing focus has been on the

supply side but greater attention to the demand side is likely to occur.

These five drivers suggest major changes in the power system in the form of integration of variable

energy resources, demand side management and electrified transport.

2.1.1.2 Characteristics of Variable Energy Resources

The five drivers, discussed in the previous section, demonstrate the strong role of variable energy re-

sources, demand side management and electric vehicles in the future grid. This section addresses the

key characteristics of these resources and contrasts them to the conventional generation and demand

portfolio.

Past: Generation/Supply Load/Demand

WellͲControlled�&�Dispatchable

Thermal�Units:��Few,�WellͲControlled,�

Dispatchable

Stochastic/�Forecasted

Conventional�Loads:�Slow�Moving,�Highly�

Predictable

Figure 2.1: Traditional Grid Generation and Demand Portfolio [46]

As shown in Fig. 2.1, the power network has traditionally consisted of relatively few, centralized

and dispatchable generation units and highly predictable loads [136]. On the demand side, a spectral

characterization of a typical load profile is shown in Fig. 2.2. Variations span a wide range of frequencies

with slow variations having larger magnitude that correspond to the daily periodicity of the demand.

A similar spectrum has been previously reported [22]. These multiple time scales excite and affect

the different behavioral phenomena in the power grid shown in Fig. 2.3. The traditional method of

satisfying the demand consists primarily of dispatching the centralized generation to load forecasted at

the day ahead and hourly timescales and then allowing automatic feedback control techniques to address

the remaining difference [55]. Over time, load became highly predictable with the state of the art being

approximately 3% error [33, 98]. On the supply side, the economic and regulatory structure drove

power generation facilities towards economies of scale [35]. Consequently, different types of generation

fulfilled different parts of the load: large coal/nuclear power plants supply the base load, CCGT units


10−5 10−4 10−3

10−2

10−1

100

101

102

Load Power Spectrum

Frequency (Hz)

Nor

mal

ized

Pow

er (H

z−1/

2 )

Figure 2.2: Normalized power spectrum of daily load (Data from Bonneville Power Administration)

Tie-line regulation

Daily load following

Long-term dynamics

Transient stability

Sub-synchronous resonance

Line switching voltages

Lightning-over voltages

10-7 10-6 10-5 10-4 105 104 103 102 101 10-0 10-1 10-2 10-3 Time scale (s)

Figure 2.3: Time scales of relevant power system dynamics [98]

follow the changing load, and IC/GT come online during the peak load [146]. In summary, Fig. 2.1

demonstrates the clear distinction between generation and demand behaviors in the traditional power


system. Generation consists of only dispatchable units and has no stochastic component, while demand

is not dispatchable and its forecasted value is used in operations planning. However, the new drivers

change the picture of generation and demand portfolio.

Future: Generation/Supply Load/Demand

WellͲControlled�&�Dispatchable

Thermal�Units:��(Unsustainable�cost�&�

emissions)

Demand�Side�Management:�(Requires�new�control�and�

market�design)

Stochastic/�Forecasted

Renewable�Energy�Sources:�(Can�cause�unmanaged�grid�

imbalances)

Conventional�Loads:��(Growing�&�needs�curtailment)

Figure 2.4: Future Grid Generation and Demand Portfolio [46]

The drivers described in the previous section change the picture of the generation and demand port-

folio to the more balanced one shown in Fig. 2.4. From the perspective of dispatchability, VERs are

non-dispatchable in the traditional sense: the output depends on external conditions and are not con-

trollable by the grid operator [82]; except in a downward direction for curtailment. As VERs displace

thermal generation units in the overall generation mix, the overall dispatchability of the generation fleet

decreases. On the other hand, the introduction of demand-side resources and electrical vehicles al-

lows the flexible scheduling of consumption, which raises dispatchability of demand. In spite of this,

consumer-level dispatchability may not equate to the same from the grid operator’s perspective. In

regards to forecastability, variable energy resources increase the uncertainty level in the system [82].

Relative to traditional load, VER forecast accuracy is low, even in the short term [54]. There are two

major groups of wind forecasting techniques: numerical weather prediction (NWP) and statistical meth-

ods [100]. The former use more complicated models based on the current weather conditions.This kind

of model is mainly used for long term wind forecasts; 24 hours ahead and more. The latter is based

upon historical data input and is applied to shorter terms. Moreover and similar to wind generation,

the consumption pattern of demand side resources and electric vehicles have a stochastic nature from

the perspective of power grid operator. In short, Fig. 2.4 demonstrates a grid in which generation and

supply are on a much more equal footing. They both have stochastic and dispatchable components and

hence should assume similar roles in the power system operation. Naturally, power system assessment

techniques should correspondingly evolve to allow for both control as well as disturbance to originate

from either generation or demand.


Figure 2.5: Graphical Representation of the Evolving Power Grid Structure [46]

2.1.1.3 Changes in Power Grid Structure

In addition to their dispatchability and stochasticity, VER’s nature require subsequent changes in the

power grid structure; primarily in the distribution system. Traditionally, power network consists of

meshed transmission network, connecting centralized generation units on a wide area, and radial distri-

bution networks, delivering power to the final consumer. This clear separation between transmission and

distribution networks allows the study of these two types of networks separately and develop different

standards and requirements for each type of network [136]. However, because VERs do not typically

have the same technical and economic scale, they break the assumption of centralized generation and

allow generation in the distribution system. Fig. 2.5 shows the corresponding evolution of power grid

structure as a change in the spatial distribution of generation.

The change in power grid structure has implications on its operation. Distributed generation creates

the potential for upstream flow in the distribution system, where it was not generally permitted before

[57]. The protection system has to be redesigned accordingly [25, 141]. Another challenge is the

potential for over-voltages. The mitigation of these challenges may require new stabilizing connection

lines within the distribution system; thus turning it into a mesh network and potentially effacing the clear

separation between transmission and distribution. Such structural changes create the need for joint study

of transmission and distribution networks and suggests that assessment methods develop accordingly.


2.1.1.4 Changes in Power Grid Dynamics

The various power grid phenomena shown in Fig. 2.3 have induced a traditional hierarchical control

structure strictly separated by time scale. Ilic and Zaborsky classify this hierarchy as primary, secondary

and tertiary [74]. Primary control addresses transient stability phenomena in the range of approximately

10-0.1Hz [86]. Generator output adjustments on this time scale are performed by the implementation of

local automatic control techniques such as automatic generation control, (AGC) and automatic voltage

regulator (AVR) [55]. The former responds to fast imbalances between generation and consumption,

while the latter responds to changes in generator output voltage [97]. Secondary control, at the minutes

timescale, resides within the operations control center and fixes the set points for these automatic con-

trol techniques [146]. It also includes the manual actions of power system operators which assist the

automated and semi-automated techniques to secure operations in fastest possible way [146]. Finally,

tertiary control occurs at the time scale of tens of minutes or hours. Often called economic control, it

is implemented as the continuous re-dispatch based upon an optimization program that minimized the

total operational cost of the system subject the appropriate constraints such as generator capacity and

line limits [55]. The clear distinction in the time scale of these control has allowed the practical and

long-standing assumption that each control technique can be studied independently.

The integration of variable energy resources challenges this assumption and blurs the distinction

between control technique time scale. Recent reviews summarize the impact of VER integration [11]

and [80], and a spectral characterization of both wind[22] and solar generation [38] has been conducted

to show that VER integration affects all time scales of power system balancing operations. In response,

the Federal Energy Regulatory Commission (FERC), has recently changed its requirements on minimal

re-dispatch frequency from 1 hour to 15 minutes [47]. Individual power system operators have gone

even further; with the Pennsylvania-New Jersey-Maryland Independent System Operator (PJM-ISO)

dispatching every 5 minutes. Manual operator actions also are facing downward pressure. One recent

study in the German-based 50-Hertz Transmission System Operator shows that the increasing penetra-

tion of VERs has lead to more frequent manual operator actions – especially in regards to curtailment

[145]. In the meantime, the introduction of grid-scale storage [88, 50], smart buildings [139, 115], and

fast ramping generation facilities [128, 148] expands the scope of transient stability studies into slower

time scales dominated by dynamic poles in the hydraulic and thermal energy domains. In short, the

traditional dichotomy of primary, secondary, and tertiary control is increasingly blurred with the pene-

tration of VERs. Mathematically, the overlapping control techniques can be viewed as a convolution of


actions which would necessitate holistic assessment methods.

The introduction of mesh networks in the distribution system shown in Fig. 2.5 can also bring about

new power grid dynamics. This occurs when the power grid is operated in such a way as to have variable

rather than static network topology. In such a situation, the continuous-time transient stability dynamics

are superimposed on the discrete-event network switching [97]. Such hybrid dynamic systems have an

interesting property that while each network topology configuration may be dynamically stable in its

own right, the meta-system which allows switching between the configurations may not be so [28]. Fur-

thermore, many of the control theory concepts such as controllability and observability are inadequate

for hybrid systems [90]. Therefore, dynamically reconfigured power grids do not just motivate the need

for holistic assessment approaches but also represent a rich application area for hybrid control theory

contributions. The promise of such work is resilient, self-healing power grids that respond to distur-

bances and contingencies [15, 14, 13, 101, 17, 96]. In contrast, the San Diego Blackout of September 8

2011 is a reminder of the importance of even routine switching decisions [20, 140].

In conclusion, the need for holistic assessment methods is a consequence of the evolution of the

power grid. As generation and demand continue to evolve to take on balanced and similar roles, each

will contribute to the power system operation both from the perspective of control as well as stochastic

“disturbance”. Neglecting any of the quadrants in Fig. 2.4 risks either overstating the need for control

at extra expense or understating it at the risk of degraded reliability. Additionally, the blurring of the

distinction between transmission and distribution suggests distribution can no longer be viewed as a

passive participant fulfilled by an active and centralized transmission system operator. Instead, the

responsibility of grid operations management must increasingly be distributed across the power value

chain. Thirdly, a temporal blurring is occurring as the time scales of primary, secondary, and tertiary

power grid control continue to overlap and convolve the power grid response. Finally, hybrid control

theory necessitates holistic assessment in cases where the system structure is dynamically switched; in

this case to achieve the desirable properties of reconfigurability, self-healing and resilience.

2.1.2 Enhanced Grid Control Technologies and Strategies

The previous sections demonstrated a number of evolving trends which suggest a necessary rethink of

holistic power system assessment and control. First, generation and demand are set to take much more

equal responsibility over power grid operation. This appears in the degree of stochasticity but also in

the degree of dispatchability. Furthermore, the combination of these two properties suggest a grid that is

generally more dynamic in nature, and so requires greater attention to ramping capabilities and voltage


stability. This section raises the concept of integrated enterprise control[95] as a holistic strategy and

then briefly mentions the emerging technologies set to bring about such a strategy.

2.1.2.1 Grid Enterprise Control Strategy: Enabling Holistic Dynamic Properties

The ongoing evolution of the power grid can already be viewed through the lens of enterprise con-

trol. Originally, the concept of enterprise control [95] developed in the manufacturing sector out of

the need for greater agility [119, 60] and flexibility [24, 39, 112] in response to increased competition,

mass-customization and short product life cycles. Automation became viewed as a technology to not

just manage the fast dynamics of manufacturing processes but also to integrate [87] that control with

business objectives. Over time, a number of integrated enterprise system architectures [144, 85] were

developed coalescing in the current ISA-S95 standard [131]. Analogously, recent work on power grids

has been proposed to update operation control center architectures [147] and integrate the associated

communication architectures [150]. The recent NIST interoperability initiatives further demonstrate the

trend towards integrated and holistic approaches to power grid operation [21]. These initiatives form the

foundation for further more advanced holistic control of the grid [15, 18].What Types of Change in Control are Required?

16©Amro M. Farid 2012

Introduction Motivation Requirements Opportunity Challenge

All Hands On Deck! Generation & Demand will mirror each other andhave equal responsibility over the overall health of the electric grid

Generation DemandDispatchability • Low�– Wind,�Solar,�Run�of�River�Hydro

• Medium�– Hydro,�Solar CSP• High�– Thermal�Units

• Low�ͲͲ Lighting• Medium�– HVAC,�Commercial�buildings• High ͲͲ Industrial production

Flexibility/Ramping(Thermal Energy�to�Work�ratio)

• Low – Nuclear�&�Coal• Medium�– CCGT• High�– Hydro,�GT,�IC

• Low – Chemical,�petrochemical,�metals• Medium�– HVAC,�Commercial�Buildings,�

Refrigerators• High�– Heaters,�kettles,�EV�battery

Forecastability • Low – Solar�PV• Medium�– Wind�generation• High�– All�dispatchable generation

• Low – N/A• Medium�– lighting,�cooking,�hair�drying• High�– Scheduled�Industrial�Production

Voltage�Stability • Synchronous�Generators�w/�AVR• Wind�Induction��Generators�w/�low�

voltage�ride�through• Solar�PV�w/�power�electronics

• Synchronous motors�in�HVAC�applications• Induction�Motor�appliances�with�active�

harmonic�control• EV’s�w/�power�electronic�based�control

Source Adapted from: IEEE CSS Smart Grid Control Systems Vision

Figure 2.6: Grid Enterprise Control to Enable Holistic Dynamic Properities

These integrative initiatives are the first step towards power grid operation that is founded upon the

fusion of reliability and economic objectives. To that effect, the future electricity grid, with all of its new

supply and demand side resources, must holistically enable its dynamic properties. Fig. 2.6 shows the

balanced role of generation and demand in regards to four dynamic control properties: dispatchability,

flexibility, forecastability and voltage control.

Addressed holistically, different components of the power generation and demand have differing


levels of dispatchability. While thermal generation has traditionally fulfilled this role, it is not unlikely

that electricity-intensive industrial production can serve the counterpart role. A medium level of dis-

patchability can be achieved with hydro, concentrated solar power and commercial buildings. Finally,

wind, solar PV, run-of-river hydro, and lighting have the least dispatchability. This taxonomy of genera-

tion and demand resources effectively introduces a pareto analysis in regards to system dispatchability,

which of course is required to cover the stochastic elements in the future grid. More concretely, existing

power grids can generally accommodate modest levels of VERs because a certain level of existing dis-

patchability but if this penetration were to grow the system dispatchability may not be sufficient to meet

reliability standards.

While dispatchability is a necessary control property, on its own, it is insufficient due to the process

limitations of the various generation and demand resources. System flexibility, or resource ramping,

needs to be carefully addressed. Using another pareto analysis, one sees that ramping capabilities are

often very much tied to the ratio of stored thermal energy to mechanical work. Facilities with a very

large ratio such as nuclear, coal, chemicals and metals have relatively low ramping capabilities. In

contrast, facilities with a high ratio such as hydroelectric, gas turbines, internal combustion engines,

heaters and kettles can easily ramp. The integration of VERs is a challenge not just because of their

lack of dispatchability but because the stochastic nature can cause ramps of various speeds and not just

magnitude.

The aggregate dispatchability and flexibility must also able to meet the lack of forecast ability of the

stochastic elements on the power grid. The presence of uncertainties decreases the effectiveness of the

scheduling process significantly; raising the potential for system imbalances. Such imbalances create a

volatile situation which requires ever-more frequent and costly manual actions in concert with automatic

generation control.

This more dynamic mode of operation must also not neglect voltage stability [104, 135]. To maintain

this control objective, many types of generation and demand resources can potentially contribute to

voltage support. Recent literature advocates a highly decentralized approach to the responsibility of

voltage stability [130, 48].

2.1.2.2 Grid Enterprise Control Technology Integration

The four holistic dynamic properties of dispatchability, flexibility, forecast ability, and voltage stability

taken greater importance in the context of the vast number of emerging “smart-grid” technologies enter-

ing the market [105]. Individually, these technologies bring their own local function. However, in reality,


Generation Transmission & Distribution Demand

Measurement Actuation

Decision-Making

Figure 2.7: Integrated Enterprise Control of the Power Grid

their value emerges in the context of the full enterprise control loop of measurement, decision-making

and actuation shown in Fig. 2.7. While an in- depth review[105] of these emerging technology offerings

is beyond the scope of this work, a cursory mention the leading options serves to further motivate the

need for holistic assessment.

Although the transmissions system continues to introduce new control technology, perhaps the most

evident upgrades appear in the distribution system; further blurring the distinction between the two

systems. For example, in the measurement and communication infrastructure SCADA[6], as a well-

established transmission technology is quickly entering distribution. In complement, smart meters [61,

150], phasor measurement units [113], and dynamic line ratings [108] have received a great deal of

attention in both academia and industry. In decision-making, transmission energy management systems

functionality is being repackaged in distribution management systems [132]. An extension of these

is facility energy management systems which can integrate to the power grid [138]. Finally, a bloom

of actuation devices are set to appear all along the power value chain. Virtual and real generation

aggregators are being developed for economics oriented control in both generation and demand [77]. To

that effect, model predict control techniques [30] have advanced significantly to support both individual

as well as groups of facilities, be they for power generation or industrial production. FACTS devices

[66] such as static var compensators, once deemed cost prohibitive by many, have an active role in the

integration of VERs and in the real-time control of power flows across the power grid. At the residential

scale, market forces are driving towards smart energy appliance of nearly every type [61, 150].

In conclusion, the concept of enterprise control provides a working framework upon which to build


holistic approaches to assessment and control. Such an approach can facilitate methods that directly

address the four holistic dynamic properties discussed: dispatchability, flexibility, forecastability, and

voltage stability. These properties then become the guiding principles upon which the implementation

of control technologies can be based. Otherwise, it is possible to introduce solutions that are overlapping

in function, over-built and costly. Holistic assessment can help a transition from the existing technology-

push scheme to one which is much more requirements driven.

2.1.3 Adequacy of Existing Methods

Over the many decades the fields of electric power engineering and economics have developed a rich

and diverse set of assessment techniques to assure reliability and maximize overall economics[57][55].

Unit commitment, optimal power flow, contingency analysis, state estimation, as well as angular, fre-

quency and voltage stability are but a prominent few. Furthermore, they have been implemented in

countless technical standards, codes and regulations[106]. A full review of these is certainly intractable

and well beyond the scope of this work. Furthermore, the rationale presented in this paper advocates

the enhancement and combination of these many techniques in holistic frameworks rather than their

replacement.

Consequently, in assessing the adequacy of existing methods, the focus is placed on those approaches

that facilitate the evolution of the power grid. To that effect, numerous renewable energy integration

studies have emerged in the academic and industrial literature[41]. Amongst these, wind power has

attracted relatively more attention given its greater environmental potential in the geographies committed

to renewable energy integration. Although references [40, 122] summarize the key points of the most

prominent integration studies, the interested reader is referred to [41] for a more comprehensive list.

This section summarizes the key conclusions of these works and presents some of their limitations that

would motivate the need for more holistic assessment methods.

The main conclusion of these renewable integration studies is that intermittency and uncertainty will

increase reserve requirements in the power system; and consequently increase the marginal cost power

system operations[40, 122]. The exact degree of additional operational costs ultimately depends greatly

on system properties such as generation mix and fuel cost. In contrast, one reference states that wind

power variability will not have much impact on the operations because power grid operators already

have experience in dealing with variability in the load. The inconsistency of the results can be attributed

to the use of different methodologies, data, and assessment metrics.

Prior to discussing the limitations of these works, and given that much of the discussion centers


around reserves management, it is important to recognize that each integration study uses its own termi-

nology and classification of power system reserves depending on the region of interest. This work uses

the classification of reserves found in [72, 42]. Two major types of reserves are discussed: event-based

and non-event-based reserves. Event-based reserves respond to contingencies in the system and are also

named contingency reserves. Non-event based reserves are normal operational reserves that operate

continuously to balance the system in the presence of net load variability and forecast error. Since the

outage of any individual wind generation unit has a much smaller impact on the system than the largest

thermal plant, wind integration will not increase contingency reserves requirements [72]. Non-event-

based reserves are further classified by their response times: load following reserves handle intra-hour

variations, and regulation reserves handle minute-to-minute variations of the net load. Both types can

respond upwards and downwards. The conclusions concerning these non-event reserves is the focus of

this review.

Generally speaking, integration studies use variations of the statistical methods found in [73] to es-

timate the the load following and regulation reserve requirement. The standard deviation of potential

imbalances, s , is calculated using the probability distribution of net load or forecast error. Load follow-

ing and regulation reserve requirements are then defined to cover appropriate confidence intervals of the

distribution based on the experience of power system operators and existing standards. Normally, load

following is taken equal to 2s [73, 116] to comply with the North American Electric Reliability Cor-

poration (NERC) balancing requirements: NERC defines the minimum score for Control Performance

Requirements 2 (CPS2) equal to 90% [107]. This corresponds to 2s for a normal distribution. Other

integration studies have used a 3s confidence interval [8, 133] to correspond to the industry standard

of 95% [63]. Based on the experience of power system operators, regulation is normally taken to be

between 4s and 6s [116, 64, 73].

The first limitation of this approach is the lack of consensus of whether to use the probability distri-

bution of the net load or that of the forecast error. Intuitively speaking a perfectly forecasted but highly

variable net load still requires more non-event reserves than a modestly variable net load. Similarly,

a high forecast error will require greater reserves than a low error. Therefore, a true determination of

non-event reserves is likely to depend on both variables and not just one.

Another concern is the usage and treatment of different power system timescales in the integration

studies. Load following and regulation reserves operate at different but overlapping timescales. Net

load variability, as a property exists in all timescales, although with changing magnitudes. Forecast

error appears in exactly two timescales: 1 hour (day-ahead forecast error) and 5-15 minutes (short


term forecast error). Thus, VER intra-hour variability and day-ahead forecast error are relevant to load

following reserve requirements. Meanwhile, 5-15 minute variations and short-term forecast error are

relevant to regulation reserve requirements. This division of impacts is rarely considered in the literature.

In [73], the standard deviation s is measured based upon the total variability of the net load. The loading

following and regulation reserve requirements are then calculated on the basis of the total variability.

Such an approach contradicts that these two control techniques act in different timescales.

Similar timescale concerns apply to studies that use forecast errors. For example, one study[8] cal-

culates both load following and regulation requirements from the standard deviation of the day-ahead

forecast error, and does not consider short-term forecast error. In contrast, another study [63] distin-

guishes between three different timescales of power system imbalances. The first timescale is regulation

which is the difference between the 10 minute average net load and the minute-by-minute net load.

The second is load following which is the difference between the hourly average net load and the 10

minute average net load. The final timescale is imbalance, defined as the difference between the hourly

forecasted net load and the hourly average net load. In other words, the following three factors are con-

sidered: intra-hour variability, minute-by-minute variability and day-ahead forecast error. The timescale

distinctions in this study correspond well to the power system operating reserve definitions.

Another concern over operating reserve quantities and their timescales arises when considering the

power system’s operating procedures and control techniques. For example, the heuristic of 2s for load

following and 4s for regulation is based upon fixed dynamic characteristics of the power system en-

terprise control and practical experience of the system operators. For example, the recent FERC re-

quirement to change the minimum frequency of the balancing market from 1 hour to 15 minutes would

certainly change reserve requirements. Similarly, the time step of the resource scheduling (day-ahead)

market can change. Generally speaking, from a control theory perspective, it is insufficient to character-

ize the reliability of a system purely on the basis of the magnitude of a disturbance without equally con-

sidering the control functions that attenuate this disturbance. More plainly, the reliability of the power

grid depends not just on the quantity and timescale of the reserves but also the manual, semi-automatic

and automatic control procedures that utilize them.

Another point of focus is the definition of load following and regulation requirements based on

NERC requirements and operator experience. The statement that 2s approximately corresponds to

90% of probability is true when variability/forecast error has a normal probability distribution, which is

normally not true [68, 67, 54]. This assumption can be justified using the central limit theorem [59] in

the case of deep wind penetration with significantly wide geographical dispersion. This condition limits


the utility of the methodology for the cases of little penetration. Also, the definition of regulation as 5s

or 6s is based on the experience of operators, which is not necessarily applicable to the new conditions,

when the whole dynamics of the power system changes.

Of these limitations, one of the most evident is the lack of a holistic assessment approach. Many

integration studies are only limited to statistical calculations and their results are not validated by simula-

tion [12, 42]. Of these, some are limited to considering either only variability of the net load [73, 89, 64]

or only its forecast error [133, 93, 94, 92]. Furthemore, not all studies consider the different timescales

of operation. Reference [63] does not consider regulation because the available data has 10 minute res-

olution. Those wind power integration studies that do use simulation usually do so for a particular study

area[26]. References [89, 12] implement only unit commitment models, according to the assumption

that wind integration has the biggest impact on unit commitment.

In summary, a review of the existing literature on imbalance assessment methodologies shows a lack

of holistic methods. Most of the studies consider the impact of only a few factors on the imbalances of

the system, which can give only a partial picture of imbalances. Also, not all the control components are

considered, sometimes limited to only unit commitment. The system balancing should be studied with

the implementation of all relevant enterprise control functions in the coupled timescales so as to lead to

reasonable results. Moreover, most of the studies are limited to statistical calculations, which are yet to

be validated by simulations. Finally, many of the calculations are based upon the experience of system

operators which may not necessarily remain valid as the power system continues to evolve.

2.1.4 Reconfigurable Framework for Holistic Power Grid Assessment

To address the literature gap identified in the previous section, the authors proposed a reconfigurable

framework for the holistic assessment of the power grid. Gathering the discussions from the previous

sections, such a framework has the following requirements:

• allows for an evolving mixture of generation and demand as dispatchable energy resources

• allows for an evolving mixture of generation and demand as variable energy resources

• allows for the simultaneous study of transmission and distribution systems

• allows for the time domain simulation of the convolution of relevant grid enterprise control func-

tions


ConventionalGeneration

Transmission System

Physical Grid

Dispatch DecisionsM

easu

rem

ents

Balancing ActionsManual ActionsRT MarketRegulation

VERGeneration

Spinning Reserves

Residential Loads

Commercial Loads

Industrial Loads

Resource Scheduling Comm

itment Decisions

Reserve scheduling

Unit scheduling

Unit Commitment

Figure 2.8: Conceptual model of a power grid enterprise control simulator

• allows for the time domain simulation of power grid topology reconfiguration in the operations

time scale.

• specifically address the holistic dynamic properties of dispatchability, flexibility, forecastability

and voltage stability

• represents potential changes in enterprise grid control functions and technologies as impacts on

these dynamic properties.

The first five of these requirements are basically associated with the nature of the power grid itself

as it evolves. In the meantime, the last two are associated with the behavior of the power grid in the

operations time scale. To that effect, Fig. 2.8 represents a conceptual design of a reconfigurable power

system simulator that implements enterprise control. The simulator includes the physical electrical grid

layer and incorporates primary, secondary and tertiary control layers. These layers may be modified as

necessary to assess the impact of control function and technology on the time domain simulation.


One main advantage of this approach is that net load may be viewed as a system disturbance which

is systematically rejected by forecasting and relevant enterprise control functions to give a highly at-

tenuated system imbalance time domain signal. An implementation of this conceptual design has been

implemented to systematically study the evolution of power system imbalances in relation enterprise

control functions typically found in American transmission systems[102, 103].

2.2 Tools for Holistic Assessment of Power System Imbalances

2.2.1 The Physical Power Grid

2.2.1.1 Power Flow Analysis

The dynamics of the power system is generally represented by a set of differential algebraic equations.

For steady-state description of the system these equations simplify to a set of algebraic equations, known

as power flow equations [98]:

PGi �PL

i =Vi

NB

Âj=1

Vj (Gi j cosqi j +Bi j sinqi j) (2.1)

QGi �QL

i =Vi

NB

Âj=1

Vj (Gi j sinqi j �Bi j cosqi j) (2.2)

where the following notations are used:

PGi Active power injection on bus i.

QGi Reactive power injection on bus i.

PLi Active power consumption on bus i.

QLi Reactive power consumption on bus i.

Vi Voltage magnitude on bus i.

qi j qi �q j. Voltage angle difference between buses i and j.

Gi j Real part of i, j element of admittance matrix.

Bi j Imaginary part of i, j element of admittance matrix.

NB Number of buses.

Each bus is described by a set of four parameters {PGi ,QG

i ,Vi,qi}. Normally, only two of these param-

eters are known, the other two are obtained from power flow equations’ solution. Three types of buses


are distinguished:

• PV bus. For PV buses active power injection and bus voltage are known in advance. This types

of buses are normally generator connected buses.

• PQ bus. For PQ bus active and reactive power injections are known, and bus voltages and angles

are obtained from power flow equation.

• V q bus. V q bus is also known as slack or reference bus. Its voltage and angle is always known,

and power injections are obtained from power flow equations.

Thus, solution of power flow equations provide bus voltages and angles for all buses. Therefore, the

flows of the power through transmission lines can be calculated as follows: [55]:

Pi j =ViVj (Gi j cosqi j +Bi j sinq i j)�Gi jV 2i (2.3)

Qi j =ViVj (Gi j sinqi j �Bi j cosq i j)+Bi jV 2i (2.4)

where Pi j and Qi j are active and reactive power flows from bus i to bus j.

Power flow equations implicitly contain power balance requirement of the system. This fact can be

shown by the following manipulations. Summing (2.1) for all buses leads to the following equation:

NB

Âi=1

�PG

i �PLi�=

NB

Âi=1

NB

Âj=1

ViVj (Gi j cosqi j +Bi j sinqi j) (2.5)

Comparison with the Equation (2.3) shows that the right-hand-side of this equation is the sum of all line

flows of the system in both directions. Since sum of the power flow in opposite directions is the losses

on that specific bus, the right-hand-side of equation 2.5 is the total loss of the system [143]:

PLOSS =NB

Âi=1

NB

Âj=1

ViVj (Gi j cosqi j +Bi j sinqi j) (2.6)

which results in the following equation:

PG = PL +PLOSS (2.7)

where PG and PL are total generation and consumption of the system correspondingly. Equation (2.1)

indicates active power balance between total generation, total consumption and system losses. The same

calculations for reactive power balance can be derived from (2.2).


As discussed above, power flow equations guarantee power balance in the system. However, de-

pending on the generator levels and the loading level of the system, this balance may not be maintained,

making power flow equations non-solvable. This situation is overcome in steady-state power system

models by introducing slack a bus. Slack bus, also referred as reference or Vq bus, consumes all the ex-

cess power necessary to maintain power balance. Voltage and angle are known, and active and reactive

power injections change accordingly to maintain power balance. Slack bus is a theoretical abstraction

that makes power flow steady state solution possible. The angle of slack bus is considered as 0 and

serves as reference for angles on other buses.

2.2.1.2 Power System Response

Power generation and consumption balance is one of the main requirements for power system reliable

operations. Mismatch between generation and consumption also creates mismatch between mechanical

and electrical torques applied on generators. If generation exceeds consumption, generators accelerate,

and the system frequency increases. Likewise, if consumption exceeds generation, generators decelerate,

and the system frequency decreases. Deviations of the system frequency from the rated value may have

damaging effect on power system equipment, that is designed for working at a specific frequency.

The instantaneous power balance in the system with DF frequency deviation is given by the follow-

ing equation [55]:

DPm �DPD = DFDF +dWk

dt(2.8)

where DPm and DPD are changes in mechanical power and electrical power demand correspondingly, DF

is the aggregated damping parameter of generators, and dWk/dt is the rate of change in kinetic energy.

For a specific control area, power generation and consumption imbalance is called area control error

(ACE). ACE is a crucial parameter of power system imbalance monitoring and performance assessment.

For steady-state simulations, dWk/dt is zero, and Equation (2.8) takes the following form:

ACE = DFDF (2.9)

Equation (2.9) is used to measure ACE in real power systems. First, the deviation of the system fre-

quency from rated value is measured, then ACE is calculated from (2.9).

Power systems always experience imbalances due to forecasting uncertainties, generator outages,

equipment failures and other contingencies. Any imbalance triggers a counter action from the power

system to mitigate it. Traditionally, the power system dynamics are classified as a hierarchy of dy-


namics: primary, secondary and tertiary [74]. Primary dynamics and control address transient stability

phenomena in the range of 10-0.1Hz [86]. These represents the inertial response of generators and loads

and may be controlled by generator output adjustments implemented by automatic generation control

and automatic voltage control [55]. Secondary and tertiary control are managed by independent system

operators and balancing authorities and are the main focus of this work. Detailed descriptions of these

techniques are presented in the next section.

2.2.2 Operations Control of Power System Balance

Maintaining power balance is one of the most important factors for ensuring power system security and

reliability and is the main task of Balancing Authority (BA). In the balanced system, where total power

generation and total consumption (including line losses) are equal, the system frequency is fixed on a

rated value. Over-generation (generation is higher than consumption) and under-generation (generation

is lower than consumption) speed up and slow down generating units correspondingly, shifting system

frequency from the rated value. Some devices and controllers in power system are designed to work

on a given frequency. Shift of the frequency may damage those devices and threaten security of power

system [55].

2.2.2.1 Optimal Power Flow

One of the traditional tools for power system balancing is optimal power flow (OPF) problem. In its

original formulation power system optimization model had a non-linear form, called AC optimal power

flow (AC OPF) [31]:

minNG

Âi=1

⇣ai +biPG

i + ci�PG

i�2⌘

(2.10)

s.t. PGi �PL

i =Vi

NB

Âj=1

Vj (Gi j cosqi j +Bi j sinqi j) (2.11)

QGi �QL

i =Vi

NB

Âj=1

Vj (Gi j sinqi j �Bi j cosqi j) (2.12)

|Gi jV 2i �ViVj (Gi j cosqi j +Bi j sinq i j) | Fmax

i j (2.13)

PG,mini PG

i PG,maxi (2.14)

V mini Vi V max

i (2.15)

where ai, bi, ci are the cost curve coefficients of generator i.


Constraints (2.15) and (2.13) are bus voltage and line flow limits added to the traditional AC-OPF

formulation. This formulation is called Security-Constrained Optimal Power Flow (SC-OPF) [58].

2.2.2.2 Sensitivity Factors

Optimal power flow problem is a nonlinear optimization program, which limits its applicability. The

problems with convergence and required computational complexity convinced most of the power system

operators to move to linear optimization models. There are different types of linear models, but all of

them are using sensitivity factors [146]. Two sensitivity factors are used in the current study, namely

incremental transmission loss factor (ITLF) and generation shift distribution factor (GSDF).

ITLF indicates the sensitivity of the total system losses on changes of power injections on each bus:

gi =∂PLOSS

∂PXi

(2.16)

where PXi is the net power injection on bus i.

PXi = PG

i �PLi (2.17)

From Equation (2.16) it follows that for small incremental changes of power injections the total loss

changes can be calculated as:

DPLOSS =NB

Âi=1

gi�DPG

i �PLi�

(2.18)

For ITLF calculations, Equation 2.16 can be re-written in the following form [134]:

gi =NB

Âj=1

∂PLOSS

∂q j

∂q j

∂Pi+

∂PLOSS

∂Vj

∂Vj

∂Pi(2.19)

This equation can be represented in a matrix form:

2

66666664

g1

g2...

gNB

3

77777775

=

2

66666664

∂q1∂P1

· · · ∂qNB∂P1

∂V1∂P1

· · · ∂VNB∂P1

∂q1∂P2

· · · ∂qNB∂P2

∂V1∂P2

· · · ∂VNB∂P2

...

∂q1∂PNB

· · · ∂qNB∂PNB

∂V1∂PNB

· · · ∂VNB∂PNB

3

77777775

2

666666666666664

∂L∂q1...

∂L∂qNB

∂L∂V1...

∂L∂VNB

3

777777777777775

(2.20)


The matrix on the right-hand side of Equation (2.20) is the active part of the power system Jacobian

matrix [98], which can be calculated from power flow equations, while the column-vector on the right-

hand-side can be calculated from Equation (2.6) [143]:

∂PLOSS

∂qi=�2Vi

NB

Âj=1

VjGi j sin(qi �q j) (2.21)

∂PLOSS

∂Vi= 2

NB

Âj=1

VjGi j cos(qi �q j) (2.22)

It should be mentioned that ITLF factors depend on the state of the system and should be re-calculated

during each iteration.

The second sensitivity factor is generation shift distribution factor (GSDF), which is the sensitivity

of a specific line flow on a power power injection change on a specific bus [146]:

al,i =∂Pl

∂PXi

(2.23)

where Pl is the active power flow through line l. For small incremental changes of of bus power injec-

tions, line flow changes can be expressed linearly as:

DPl =NB

Âj=1

al,iD�PG

i �PLi�

(2.24)

GSDF factors are calculated from DC power flow equations:

al,i =∂Pl

∂Pi=

∂∂Pi

1xl(qn �qm)

�=

1xl

✓∂qn

∂Pi� ∂qm

∂Pi

◆=

1xl(Xni �Xmi)

where xl is the reactance of line l, and Xni, Xmi are elements of the line impedance matrix.

2.2.2.3 Unit Commitment

Generally, there are two approaches of handling uncertainties: reserve requirements and scenario-based

stochastic programming. The disadvantage of scenario-based approach is that huge number of scenarios

are required to represent stochastic nature of the wind [12].

Security-Constrained Unit Commitment is the traditional tool for day-ahead resource scheduling. In


the most general for it can be formulated as follows [49]:

min24

Ât=1

NG

Âi=1

(wi,tCi�PG

i,t�+CSU

i wi,t(1�wi,t�1)+CSDi ⇤wi,t�1(1�wi,t)) (2.25)

s.t. Pi,t(Vt ,qt) = PGi,t �PL

i,t (2.26)

Qi,t(Vt ,qt) = QGi,t �QL

i,t (2.27)

wi,tPG,mini PG

i,t wi,tPG,maxi (2.28)

wi,tQG,mini QG

i,t wi,tQG,maxi (2.29)

V mini Vi,t V max

i (2.30)

q mini qi,t q max

i (2.31)

|Fl,t(Vt ,qt)| Fmaxl (2.32)

RG,downi Dt PG

i,t �PGi,t�1 RG,up

i Dt (2.33)

Âwi,tPG,maxi �Âwi,tPG

i,t � Pres (2.34)

2.2.2.4 Balancing Requirements

Due to existing uncertainties in the power system resource scheduling and balancing, ideal balance

between power generation and consumption can never be achieved. According to NERC Standard BAL-

001-0.1a [107], to maintain interconnection steady-state frequency within defined limits, the following

requirements should be satisfied:

R1. Each Balancing Authority shall operate such that, on a rolling 12-month basis, the average of the

clock-minute averages of the Balancing Authoritys Area Control Error (ACE) divided by 10B (B

is the clock-minute average of the Balancing Authority Areas Frequency Bias) times the corre-

sponding clock-minute averages of the Interconnections Frequency Error is less than a specific

limit. This limit e21 is a constant derived from a targeted frequency bound (separately calculated

for each Interconnection) that is reviewed and set as necessary by the NERC Operating Commit-

tee.

average✓

ACEi

�10Bi

◆⇤DF1

� e2

1 (2.35)

R2. Each Balancing Authority shall operate such that its average ACE for at least 90% of clock-ten-

minute periods (6 non-overlapping periods per hour) during a calendar month is within a specific

limit, referred to as L10.

average10�minute (ACEi) L10 (2.36)


where

L10 = 1.65e10p(�10Bi)(�10Bs) (2.37)

e10 is a constant derived from the targeted frequency bound, and Bs is the sum of the Frequency

Bias Settings of the Balancing Authority Areas in the respective Interconnection.

R3. Each Balancing Authority providing Overlap Regulation Service shall evaluate Requirement R1

(i.e., Control Performance Standard 1 or CPS1) and Requirement R2 (i.e., Control Performance

Standard 2 or CPS2) using the characteristics of the combined ACE and combined Frequency Bias

Settings.

R4. Any Balancing Authority receiving Overlap Regulation Service shall not have its control perfor-

mance evaluated (i.e. from a control performance perspective, the Balancing Authority has shifted

all control requirements to the Balancing Authority providing Overlap Regulation Service).

CHAPTER 3

Methodology and Simulation Setup

The power system enterprise model, used in this study, is comprised of three interconnected layers: the

physical grid, resource scheduling and balancing actions. Fig. 2.8 shows the conceptual diagram of the

model.

Resource scheduling occurs prior to the operating day. At this point, the optimal set of generation

units for the operating day is defined, along with their schedules. Also, the required reserve amount

is scheduled. The scheduled resources are then managed in the real-time to maintain power system

balance. Three balancing actions, namely regulation, real-time market and operator manual actions, are

implemented. The implementations of balancing actions are described in the following subsections.

3.1 Resources Scheduling

Reliable operations of the power system start one day prior the operating day with the scheduling of

necessary resources. According to Fig. 2.8, it accomplishes three parallel actions, namely: unit commit-

ment, unit scheduling and reserve scheduling.

3.1.1 Generation Commitment and Scheduling

The ultimate goal of the scheduling layer is to choose the right set of generation units, that are able to

meet real-time demand requirements with minimum cost, and define their schedules. This procedure

is implemented via a software-based optimization tool, called Security-Constrained Unit commitment

32

CHAPTER 3. METHODOLOGY AND SIMULATION SETUP 33

(SCUC), which has a mathematical formulation in the form of a linear mixed-integer program [49]:

min24

Ât=1

NG

Âi=1

(wi,tCFi +CG

i PGi,t +wu

i,tCUi +wd

i,tCDi ) (3.1)

s.t.NG

Âi=1

PGi,t = PD

t (3.2)

�RG,maxi DT PG

i,t �PGi,t�1 RG,max

i DT (3.3)

wi,tPG,mini PG


wi,t = wi,t�1 +wui,t �wd

i,t (3.5)NG

Âi=1

wi,t

⇣PG,max

i �PGi,t

⌘� Pres (3.6)


CFi ,C

Gi ,C

Ui ,C

Di fixed, generation (fuel), startup and

shutdown costs of generator i

PGi,t power output of generator i at time t

PDt total demand at time t

PG,maxi ,PG,min

i max/min power limits of generator i

RG,maxi maximum ramping rate of generator i

DT scheduling time step, normally, 1 hour

NG number of generators

wi,t ON/OFF state of the generator i

wui,t ,w

di,t startup/shutdown indicators of generator i

Pres system reserve requirements

The objective of this model is to find the optimal set of generators and their schedules, that will meet

the demand with minimal total operating cost of the system. Constraint (3.2) is the power balance

equation, required to keep the system balanced. The other two constraints, (3.3) and (3.4), are the

physical limitations on generators’ ramping rates and power outputs respectively. The solution to this

mathematical program yields optimal wi,t commitment and PGi,t generation schedules for each generator.


3.1.2 Adequacy of the Scheduled Generation

The unit commitment model takes power system characteristics, such as generation levels, ramping

limits, and demand forecasts as inputs. Later, the scheduling of resources is performed to satisfy those

requirements. However, the scheduled resources rarely match the real-time requirements due to a series

of objective limitations. Three main factors can be distinguished as potentially causing this mismatch.

First, the information about real-time power demand is limited to the day-ahead demand forecast.

Even the best possible forecasting techniques are able to provide the demand forecast with limited ac-

curacy.. The resulting forecast error is the power mismatch that emerges during real-time operations.

The second factor is the difference between resource scheduling and real-time balancing time steps.

Normally, the unit commitment model schedules resources with a 1 hour time resolution. During these 1

hour intervals, the generation schedules does not change, which makes it practically impossible to match

the scheduled generation to the variations of the load. Ideally, the presence of a perfect forecast may

only guarantee matching the scheduled generation and the average demand for 1 hour intervals. The

deviations of the actual demand from its average value on 1 hour intervals are referred to as intra-hour

variations.

The third factor is lossless transmission assumption reflected in constraint (3.2). Generally, as a

direct consequence of the power flow equations, the power balance consists of three components, namely

generation, demand and transmission line losses[98]:

NG

Âi=1

PGi,t = PD

t +PLOSSt (3.7)

where PLOSSt is the total transmission loss in the system. Exclusion of the loss component is necessary

to maintain a linear SCUC model. As a result, some portion of the scheduled generation is ‘consumed’

by transmission lines and does not fill the demand.

3.1.3 Reserve Scheduling

The discussion of the previous section establishes the objective limitations that make matching the

scheduled generation and the actual demand impossible. Normally, this issue is easily solved by the

procurement of reserve generation in addition to the scheduled generation. The reserve requirements are

settled based on the existing standards and the experience of power system operators. Constraint (3.6)

in the unit commitment model reflects the reserve procurement, where Pres is the reserve requirement.

One important fact is neglected in the formulation of the unit commitment problem, however. Gen-


erally, the scheduling process has two components. The scheduling of generation and the scheduling

of the necessary ramping capabilities are reflected in the constraints (3.2) and (3.3) respectively. The

symmetry of these two components becomes more obvious if constraint (3.3) is split into two separate

constraints as follows:

RGi,t =

�PG

i,t �PGi,t�1

�/DT (3.8)

RG,mini RG

i,t RG,maxi (3.9)

where RGi,t is the difference between consecutive values of scheduled generation and can be referred to

as scheduled ramping. As a result, the differences between day-ahead generation scheduling and real-

time requirements are also reflected in the ramping domain. Real-time ramping requirements tend to be

always different from the day-ahead scheduled value. However, the provision of ramping reserves is not

included in the unit commitment model.

In the case of ramping scheduling, it is assumed that the committed generation units have enough

ramping capabilities to follow variations of the load. This assumption is valid for traditional power

systems with slowly changing load. However, the integration of VER is likely to increase the variability

of the net load. As a result, the system may chronically suffer from not enough ramping capabilities.

To overcome this problem, the provision of ramping reserves is incorporated into an enhanced unit

commitment model for use in this study. After the proposed modifications, the unit commitment model


transforms into the following form:

min24

Ât=1

NG

Âi=1

⇣wi,tCF

i +CGi PG

i,t +wui,tC

Ui +wd

i,tCDi

⌘(3.10)

s.t.NG

Âi=1

PGi,t = PD

t (3.11)

RGi,t =

�PG

i,t �PGi,t�1

�/DT (3.12)

wi,tPG,mini PG


�RG,maxi RG

i,t RG,maxi (3.14)

wi,t = wi,t�1 +wui,t �wd

i,t (3.15)NG

Âi=1

wi,t

⇣PG,max

i �PGi,t

⌘� Pres (3.16)

NG

Âi=1

wi,t

⇣PG

i,t �PG,mini

⌘� Pres (3.17)

NG

Âi=1

wi,t

⇣RG,max

i �RGi,t

⌘� Rres (3.18)

NG

Âi=1

wi,t

⇣RG,max

i +RGi,t

⌘� Rres (3.19)

where constraints (3.18) and (3.19) are for ramping up and ramping down reserves respectively. Also,

the introduction of ramping reserve requirements gives a lever by which to vary the flexibility of the

system. This is important for testing the impact of system flexibility on imbalance mitigation.

3.1.4 Reserve Requirements and Scheduled Reserves

The reserve procurement via constraint (3.6) in the unit commitment guarantees that the actual amount of

reserves is greater or equal to the reserve requirement Pres. The left-hand-side is the difference between

the maximum available generation capacity and the total scheduled generation, which is, by definition,

the actual amount of available reserves.

Since the left-hand-side of constraint (3.6) can only change discretely with the commitment of new

generation units, the actual reserves usually exceed the minimum required amount. The difference

between the available reserves and the minimum requirement depends on different factors, such as the

generation portfolio of the system, the demand level, etc. Generally, this difference may have any value

in a range from 0 to the largest generation unit capacity.

This kind of situation may significantly affect the results of VER integration studies. For example, in

power systems with mostly large generation units, available reserve capacity is likely to exceed minimum


reserve requirement significantly. This creates the possibility of VER integration into the power system

without any additional requirements. As a result, one may conclude, that the integration of VERs into

the system brings no additional requirements on reserves, which is not generally true.

To increase generalization capabilities of the results in the current study, it is assumed that the actu-

ally available reserves and the minimum requirements always match. In other words, there is no extra

reserve capacity in addition to the requirement. Obviously, this is the worst case scenario, that shows

how big the imbalances can be and how low CPS can drop. This approach reduces the case-dependency

of results.

The quantity of actual reserves is limited by manipulating the maximum generation levels of sched-

uled generators after the SCUC program has completed. First, the scaling factor is defined as a ratio of

the required reserve to the actually scheduled reserves:

aPt =

PresNG

Âi=1

wi,t

⇣PG,max

i �PGi,t

⌘ (3.20)

Equation (3.20) shows that the scaling factor depends on time. This is because the unit commitment

schedules a different amount of reserves for different time intervals. The scaling factor is then used to

change the maximum output of generators, so that the available reserves equal the reserve requirements:

PG,maxi,t = PG

i,t +aPt ·

⇣PG,max

i �PGi,t

⌘(3.21)

Note, that the maximum outputs of generators PG,maxi,t used in the real-time market change over time.

While this is a non-physical situation, it is required to demonstrate the impact of increased reserves on

the system imbalances. Failing to do so would cause the quantity of actual reserves depending on the

inequality in the SCUC program.

The same reasoning applies to the scheduling of ramping reserves. The scaling factor for ramping

reserves is defined similar to generation reserves:

aRt =

RresNG

Âi=1

wi,t

⇣RG,max

i �RGi,t

⌘ (3.22)

Accordingly, the adjusted maximum ramping rates of the generators are given by the following equation:

RG,maxi,t = RG

i,t +aRt ·

⇣RG,max

i �RGi,t

⌘(3.23)


Unlike generation and ramping reserves, the provision of regulation reserves is market based. The

requirements are announced in the market, and the generators with the cheapest offers are chosen. As a

result, the actually available regulation reserves always match the requirement.

3.2 Balancing Actions

Day-ahead resource scheduling defines the set of generators available for the operating day. During

the operating day, scheduled resources are managed in real-time to ensure balancing of the system at

any moment. Fig. 2.8 shows that balancing actions consist of three components operating at different

timescales: regulation, real-time market and operator manual actions. Each component is described in

detail in further subsections.

3.2.1 Measurement of the Power System State and Imbalances

Effective balancing of the power system requires up-to-date information about system state. In real

power systems, this function is carried by the state estimator, which provides information about bus

voltages and angles, generation and consumption levels at every bus and the ACE.

Rather than introducing the complexity and errors associated with state estimation implementation,

a simpler model of estimating state of the system is used. The values of bus voltages and angles are

obtained at every simulation step by running power flow analysis for the given levels of generation and

consumption. This gives the exact values of bus voltages and angles, which is similar to perfect state

estimation.

Referring to Equation 2.9, ACE estimation requires measurement of the system frequency deviation.

However, for steady-state simulation the concept of frequency is not applicable. Instead, a designated

slack generator consumes the mismatch of generation and consumption to make steady-state power flow

equations solvable. Therefore, for steady state simulations the power system imbalances are measured

as the output slack generator [55].

3.2.2 Regulation Service

Generally, regulation service is represented by a dynamic model [98]. However, for steady state simu-

lations a simplified model is implemented. At a time scale slower than 1 minute the effective transfer

function simplifies to a gain with saturation limits. Thus, in the current study the regulation is im-

plemented as follows. At each simulation step the regulation service responds to the imbalances by


moving its output to the opposite direction. The regulation output changes until imbalance mitigation or

regulation service saturation.

3.2.3 Real-Time Market

Real-time market operates in parallel to regulation service to suppress imbalances, but in a slower time-

scale. It moves available generator outputs to new setpoints in the most cost-efficient way. In its original

formulation, generation re-dispatch is implemented as a non-linear optimization model, called AC opti-

mal power flow (ACOPF) [31]. Due to problems with convergence and computational complexity [49],

most of the US independent system operators (ISO) moved from ACOPF to linear optimization models.

The most commonly used models is Security-Constrained Economic Dispatch (SCED), formulated as

incremental linear optimization program [126]:

minNG

Âi=1

(biDPGi,t +2ciPG

i,tDPGi,t) (3.24)

s.t.NB

Âi=1

(1� gi,t)(DPGi,t �DPL

i,t) = 0 (3.25)

NB

Âi=1

al,i,t(DPGi,t �DPL

i,t) Fmaxl �Fl,t (3.26)

�RGi Dt DPG

i,t RGi Dt (3.27)

PGi,t �PG,min

i DPGi,t PG,max

i �PGi,t (3.28)


bi,ci generator i offer curve linear and quadratic

coefficients

DPGi,t ,DPL

i,t bus i incremental generation and load

Fl,t ,Fmaxl line l power flow level and flow limit

NB number of buses

gi,t bus i incremental transmission loss factor

al,i,t bus i generation shift distribution factor to line l

Dt real-time market time step, normally, 5 minutes.

Use of incremental values for generation and load allows the incorporation of sensitivity factors and


the linearization of the program. Sensitivity factors establish linear connections between changes of

power injections on buses and state-related parameters of the system [146].

Two sensitivity factors are used in the current model, namely the incremental transmission loss

factor (ITLF) and the generation shift distribution factor (GSDF). ITLF for bus i shows how much the

total system losses will change, if the injection on bus i increases by a unit [83]:

gi,t =∂PLOSS

t∂Pi,t

(3.29)

where PLOSSt is total system loss at moment t, Pi,t is bus i power injection, both generation and consump-

tion. Incorporation of ITLF into the model results in a linearized power balance constraint (3.25).

GSDF shows how much line l power flow will change, if injection on bus i increases by a unit

[83, 134]:

al,i,t =∂Fl,t

∂Pi,t(3.30)

Incorporation of GDSF into the model results in linearized line flow limit constraint (3.26).

The other two constraints (3.27) and (3.28) are the physical limits of the generator ramping rates

and outputs. The objective function in Equation (3.24) is the minimization of total generation cost. The

values for bi and ci are linear and quadratic coefficients of generator offer curves submitted for day-ahead

scheduling.

Observation of the model shows that some input parameters, such as PGi,t , Fl,t , gi,t , al,i,t , depend on

the current state of the system. These parameters are calculated before each SCED iteration based on

full AC power flow analysis of the system. In the literature, this kind of models are referred to as hot

start models [126].

3.2.4 Operator Manual Actions

In the normal operations mode of the power system, the regulation service and the real-time market

are able to maintain the generation and consumption balance effectively. Available generation reserves

and generator ramping rates are enough to follow the slowly changing load. However, in the case of

contingencies, the situation changes. Sudden outage of a major generation unit creates big imbalances

that cannot be mitigated by real-time markets and regulation services. Online generation units do not

have enough reserve capacity and enough ramping rates to fill the gap quickly. These kinds of situations

require system operator manual actions, in the form of deployment of contingency reserves, decisions

on the location of activated reserves, etc. Manual actions, unlike other two components of balancing,


have no dedicated operations timescale and are used as necessary.

In the absence of operator models in the literature, their actions are implemented in the following

way. The system imbalances are monitored during the interval of simulations. The trigger of operator

manual intervention into the balancing procedure works, when the actual imbalances exceed 80% of

the largest generation unit. The actions of the operators include balancing of the system manually and

bringing new generation units online to suppress imbalances.

3.3 The Generation Model of Variable Energy Resources

SCUC and SCED optimization programs, presented in previous sections, are traditional scheduling and

balancing tools, without a specific accent on VER integration. However, due to its non-dispatchability,

variability and uncertainty, it has similar properties with the system load. Therefore, VER generation is

usually considered as negative load on a specific bus, and load component in SCUC and SCED models

is replaced with net load:

Pneti,t = PL

i,t �PV ERi,t (3.31)

Similar to the load, two types of VER data are used for simulations: VER output forecast data, which

is used in optimization models, and actual VER output data, which is used to assess actual state of the

system. For this study it is assumed that load has no forecast error, so that all imbalances are results of

VER generation. The connection between actual and forecasted VER generation can be expressed as

follows:

PV ER(t) = PFV ER(t)+ e(t) (3.32)

where PV ER(t) and PFV ER(t) are the actual and forecasted VER generation accordingly, and e(t) is the

error term.

Four main parameters of VER are indicated, that can potentially affect the imbalances of the system:

penetration level, day-ahead forecast error, short-term forecast error and variability. Changes of these

parameters create different VER profiles and, as a result, different integration scenarios. In accordance

to these four parameters, four integration scenarios are designed. Definitions of these parameters and

incorporation into the wind power model are represented in the following subsections.


3.3.1 Penetration Level

In the current study, the penetration level is defined as the ratio of total installed VER capacity to the

annual peak load, similar to reference [137]:

PEN = PmaxV ER/Ppeak

L . (3.33)

Using this definition, VER generation can be expressed in the following way:

PV ER(t) =PV ER(t)

PmaxV ER

· PmaxV ER

PpeakL

·PpeakL =

= PV ER(t) ·PEN ·PpeakL (3.34)

where PV ER(t) is VER power, normalized to unit installed capacity. Equation (3.34) shows, that VER

generation profiles for different penetration levels can be obtained from a single normalized profile. This

approach is very useful for running simulations with different penetration levels.

3.3.2 Forecast Error

Two types of forecasts are used in the power system simulations, day-ahead and short-term. The day-

ahead forecast is used in the SCUC model for day-ahead resource scheduling. It normally has a 1 hour

resolution and up to 48 hours forecast horizon. The short-term forecast is used in the SCED model for

real-time balancing operations. It has a 10 minute time resolution and up to 6 hour time horizon [54].

Forecast error can be defined in different ways, such as mean absolute error (MAE), mean square

error (MSE), etc [100]. It is often convenient to use normalized values of forecast error, by dividing it

by installed VER capacity. For simplicity of calculations, in this research, the forecast error is defined

as the normalized standard deviation of errors (NSDE) (3.32):

ERR =s (e(t))

PmaxV ER

(3.35)

where s (e(t)) is the standard deviation of the error term in (3.32). This definition of forecast error

allows representation of error term in the following way:

e(t) =e(t)

s (e(t))· s (e(t))

PmaxV ER

· PmaxV ER

PpeakL

·PpeakL =

= e(t) ·ERR ·PEN ·PpeakL (3.36)


where e(t) is the forecast error term, normalized to unit standard deviation. An interesting fact follows

from Equation (3.36), that the error term increases with both the increase of forecast error and penetra-

tion level. This allows generation of different simulation scenarios by independently varying these two

parameters.

Equation (3.36) is used for both day-ahead and short-term forecast errors. However, the normalized

error term e(t) is different for these two cases. This separation is absolutely necessary, since they may

differ by their probability distribution and power spectra. Also, for these two forecasts, forecast error

ranges are different. Normally, short-term forecast error has higher accuracy compared to day-ahead

forecast.

3.3.3 Variability

Variability is the fourth parameter of VER studied in this work. To the knowledge of the authors, there

is no mathematical formulation of variability in the existing literature. In this section a mathematical

definition of variability is introduced and its impact VER generation model is presented.

Intuitively, variability should describe how quickly VER changes its output. To establish that con-

nection, the derivative of the power output is used:

RV ER(t) =dPV ER(t)

dt(3.37)

Based on its definition, RV ER(t) should be zero-mean random process, otherwise VER output would

tend to infinity, which is not possible. Thus, the probability density function (PDF) of RV ER(t) actually

shows how quick the output of VER can change.

Based on the definition in equation (3.37), the variability of VER is defined as follows:

VAR =s (RV ER(t))

PmaxV ER

(3.38)

where s (RV ER(t)) is the standard deviation of RV ER(t). The definition includes normalization to in-

stalled capacity, since RV ER(t) proportionally increases with penetration level. Unlike the two other

parameters, variability has a measurement unit, which is the inverse of time. Simple derivations using

Parseval’s theorem leads to the following representation of variability:

VAR =s (RV ER(t))

PmaxV ER

=

rZ +•

�•w2G(w)dw

PmaxV ER

(3.39)


where G(w) is the power spectral density (PSD) of VER output. This definition of variability can be

applied to not only VER, such as wind, solar, but also the system of the load.

The numerator of Equation (3.39) shows, that variability is proportional to the width of the power

spectrum: the wider the spectra, the higher variability. Since VER power spectra mostly have fixed

shapes [22, 38], the spectra for different variability levels represent stretched or squeezed copies of each

other. This transformation corresponds to a change of the time scaling. It applies on both VER output

and the error term:

PV ER(t) = PV ER(at) ·PEN ·PpeakL (3.40)

e(t) = e(at) ·ERR ·PEN ·PpeakL (3.41)

where a is the scaling factor. The higher scaling factor, the higher resulting VER variability. The

dependence is linear:

a =VARVAR0

(3.42)

where VAR0 is the variability of PV ER(t).

3.3.4 The model of Variable Energy Resources

As already stated above, the simulations of VER integration require two sets of data: actual and fore-

casted VER output. The derivations from the previous subsections can be summarised in the following

models for actual and forecasted VER:

PV ER(t) = PV ER(at) ·PEN ·PpeakL (3.43)

PFV ER(t) =

�PV ER(at)�ERR · e(at)

�·PEN ·Ppeak

L (3.44)

a =VAR/VAR0 (3.45)

This set of equations defines the continuous-time VER model used in the current study. As an input,

it requires the actual VER profile PV ER(t) normalized to installed capacity, and the error term profile

e(t), normalized to unit standard deviation. The model explicitly includes four major parameters of VER

identified for this study. For computer simulations, discrete-time version of the model is implemented,

which is described in the next subsection.

CHAPTER 4

Case Study and Results

4.1 Case Study

The proposed assessment method is tested for different scenarios of wind power integration. Four differ-

ent integration scenarios are simulated. During each scenario, one of four VER parameters is changed

within a reasonable range holding all others constant. This approach allows the study of the impact of a

particular parameter on the imbalances of the system. The performance of balancing actions is evaluated

by compliance to CPS’s.

Prior to assessing these four scenarios, a traditional power grid without wind integration is simulated

to determine the amount of reserves and regulation the traditional system needs to maintain system

balance. This approach ensures that imbalances are result of wind integration.

The scenarios are implemented as steady-state simulations in the Matlab environment. The simula-

tions run for one week period with a time step of 1 minute that corresponds to the regulation timescale.

It is assumed that faster dynamics are mitigated by inertia response of generation and demand resources.

4.1.1 Test System

The IEEE RTS-96 reliability test system is used as the physical grid model [56]. It is composed of

three nearly identical control areas, with a total of 73 buses and 99 generators. The yearly peak load is

8550MW.

45

CHAPTER 4. CASE STUDY AND RESULTS 46

4.1.2 Incorporation of Wind and Load Data

Wind and load data from Bonneville Power Administration repositories [27] are used for the current

case study. The best available data has a 5-minute resolution which does not satisfy the requirement of

simulations with 1-minute time step. This difficulty is overcome by up-sampling the available data to

1-minute resolution. The up-sampling process is performed with use of sinc functions to not introduce

distortions into the power spectrum and not change the spectral width [110].

Besides the four parameters discussed above, the VER integration into the actual physical system

requires an allocation to system buses. This choice defines potential congestion occurrences which may

significantly alter the results of imbalances for the same scenario. Since congestions are outside the

scope of this research, the VER capacity distribution is implemented in a way that minimizes congestion

probabilities: wind generation on each bus is proportional to the system load on that bus. As a first

analysis, the temporal power generation profile of each wind turbine across the topology is assumed to be

entirely correlated spatially. Future work can generalize this model to investigate systematic approaches

to partial geographic correlation to confirm recent empirical evidence in this regard [99]. Because all the

VER profiles are temporally correlated, they have the same variability, and forecast error. This facilitates

addressing these parameters as single values across the power system.

4.1.3 Simulation Scenarios

Two different sets of scenarios are simulated. The first scenario assess the imbalances of the system

induced by integration of wind power, while the second one tests imbalance mitigation capabilities of

the system reserves.

4.1.3.1 Imbalance Assessment Scenarios

Four scenarios are simulated to study the impact of wind power integration on the power system imbal-

ances. During each scenario, the impact of changing one parameter on imbalances is studied, holding

the others constant. Brief descriptions of each scenario are presented in the following paragraphs.

Scenario 0: Balancing of the traditional power system. The traditional power system is simulated

without wind integration. This is the base case and defines reserve and regulation requirements for

balancing the traditional system.

Scenario 1: The impact of wind penetration level ceteris paribus. The penetration level ranges from

0% to 20% of annual peak load. This scenario shows how much wind power the traditional system can


accommodate, while maintaining CPS requirements.

Scenario 2: The impact of wind variability ceteris paribus. The wind variability increases from its

default value by a factor of two and three. This scenario shows how the wind pattern may impact the

integration experience.

Scenario 3: The impact of wind day-ahead forecast error ceteris paribus. The day-ahead forecast

error ranges from 0% to 10% of installed wind capacity. This scenario shows the actual benefits that

improved wind forecast may bring into the system.

Scenario 4: The impact of wind short-time forecast error ceteris paribus. The day-ahead forecast

error ranges from 0% to 5% of installed wind capacity. The range here is smaller because short-term

forecast error typically has better prediction accuracy.

4.1.3.2 Imbalance Mitigation Scenarios

Three simulation scenarios are designed to study the mitigation of imbalances by enhancing the three

attributes of the power system: generation, ramping and regulation reserves. Each simulation scenario is

conducted by varying a single parameter while holding all other parameters constant. Brief descriptions

of simulation scenarios are presented below.

It is important to mention, that since generation and ramping reserves share the same timescale,

low availability of one reserve may be not allow detection of mitigation capabilities of its counterpart.

The performance assessment system is likely to miss incremental improvements in the presence of huge

imbalances. To avoid this issue, during mitigation assessment of one reserve, the second one is kept very

high, to exclude possibility of its impact on the assessment process.

Scenario 0: Balancing of the traditional power system. The traditional power system without wind

integration is simulated. This is the base case scenario, and determines reserve requirements for the

traditional power system effective balancing. This is necessary, to make sure that all imbalances in the

system are results of wind integration.

Scenario 1: Imbalance mitigation by increasing generation reserves ceteris paribus. Imbalance mit-

igation capabilities of generation reserves are tested. For the fixed values of ramping and regulation

reserves, the value of generation reserve varies. The process continues until the performance improve-

ment goes to saturation.

Scenario 2: Imbalance mitigation by increasing ramping reserves ceteris paribus. Mitigation capa-

bilities of ramping reserves are tested. The generation reserves are set to the saturation value from the

first scenario, since more reserves will not contribute to the performance improvement.


Scenario 3: Imbalance mitigation by increasing regulation reserves ceteris paribus. Imbalance

Mitigation capabilities of regulation reserves are tested. Since regulation service acts at a faster timescale

and, therefore, has better balancing abilities, it is used to mitigate imbalances not addressed in the first

two scenarios.

4.2 Simulation Results and Discussion

The simulation results of two sets os scenarios are presented below.

4.2.1 Wind Integration Impact on Power System Imbalances

In the base case scenario, the traditional power system is considered. The goal is to find the reserve and

regulation amount necessary to keep the system balance at the required level. Thus, the optimizations

are carried in two stages.

The first stage tests the system imbalances for incremental values of reserves. The results are pre-

sented in Fig. 4.1, where the horizontal axis is the reserve requirements, normalized to the system peak

load. The performance of the system without any reserve and regulation is close to zero. Later, increase

of reserve requirements also increases CPS index. However, the improvements go to saturation when

amount of reserves reaches 0.027. Since further increase of reserves does not contribute to effective bal-

ancing, the amount of reserves is fixed at that level. Interestingly, the 81% saturation level is below the

required 90% level. This is explained by the fact that load variability exists on all timescales. Reserve

capacity can only mitigate imbalances slower than the real-time market step. Further improvements

should be done by the regulation service.

The second stage of the bas case scenario adds regulation to the traditional system. Further im-

provement of balancing performance is recorded as regulation amount increases. The horizontal axis is

the regulation amount normalized by the system peak load. Fig. 4.2 shows that CPS index crosses the

required 90% level at regulation value of 0.0008. This value is also fixed for the rest of the scenarios.

The first scenario tests the impact of wind penetration level on the imbalances. For this scenario,

the wind is assumed to have a perfect forecast. In this case, only the introduced additional variability

may affect the performance of the balancing actions. Fig. 4.3 shows the decay of the CPS index as

wind integration increases. The horizontal axis represents the normalized penetration level as defined in

Equation (3.33). Note that at the beginning of the simulation the performance of the the system improves

a little, which seems to be inconsistent with the rest of the graph. At a low level of penetration, the wind


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variability may be comparable to the load variability. From that perspective, it is possible that the net

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Figure 4.3: Power system imbalances for different levels of wind integration

The second scenario further emphasises the impact of wind variability. While keeping the pene-

tration level fixed at 20% level, the variability increases from its default value 2 and 3 times. Unlike

other scenarios, the wind variability is only tested for a few values. This is because the discrete domain

implementation of Equation 3.40 only allows for integer scale changes. The results found in Fig. 4.4

show a doubling of variability drops the CPS value to around 30%. This is an indication that the system

experiences severe lack of ramping capabilities. Interestingly, further increases in variability result in

limited further degradation of the CPS index. This is because, in both cases, these system is not able to

cope with the variability and is constantly out of balance.

The previous two scenarios demonstrated that even in the case of perfect forecast, the system perfor-

mance suffers due to wind high variability. In the third scenario, the day-ahead forecast error is added

to the wind generation. Building off the 20% wind penetration level, Fig. 4.5 shows a steep drop of the

CPS index as the forecast error approaches 10%. The horizontal axis represents the day-ahead forecast

error as defined in (3.35).

The fourth and final scenario tests the impact of short term forecast error on the imbalances. Building

off the 20% wind penetration level and 10% day ahead forecast error, Fig. 4.6 shows that that after the


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introduction of the short-term forecast error, the performance of the system balancing drops drastically

to a level below 25%.

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Figure 4.6: Power system imbalances for different values of wind short-term forecast error

Thus, wind integrations into the power system brings new levels of variability and uncertainty. As

the case study shows, both variability and uncertainty create significant imbalances in the system. This

problem occurs because reserves and regulation requirements were calculated based on a traditional

power system. To be able to maintain the system balance in the presence of, additional reserves, reg-

ulation and system flexibility should be procured. Estimation of these parameters in the case of VER

integration is the subject of the sequel paper [103].

4.2.2 Imbalance Mitigation by Increased System Flexibility, Reserves and Regulation

In the base case scenario, the traditional power system is considered. The goal is to find the generation,

ramping and regulations reserves required to keep the system balanced. Thus, three simulations are

performed to determine requirement of each reserve.

The first simulation of the base case scenario calculates generation reserve requirements for the

traditional power system. The results are presented in Fig. 4.7, where the horizontal axis is the reserve

requirement, normalized to the system peak load. The graph shows that without generation reserves CPS

index around 30%. Later, as reserve amount increase, the performance of the system start to improve.


As reserve amount reaches 0.03, the improvements saturate at around 80%, below the required 90%

level.

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The second simulation of the base case scenario adds ramping reserves to the traditional system. The

results are presented in Fig. 4.8. The horizontal axis indicates the ramping reserves. The graph shows,

that additional ramping capabilities also affect the performance of the system positively. It should be

mentioned, that for all points of this simulation generation reserves are set to the saturation value from

the first simulation. This demonstrates, that absence of one reserve makes efforts of the other one not

valuable, as was discussed earlier. In this simulation as well, the CPS index saturates at 80% level,

that corresponds to the right scheduling of both reserves. Further improvements are only possible with

scheduling of regulation reserves.

The third simulation of the base case scenario adds regulation to the traditional system. Further

improvement of balancing performance is recorded as regulation amount increases. The horizontal axis

is the regulation amount normalized by the system peak load. Fig. 4.9 shows that CPS index crosses the

required 90% level at regulation value of 0.0012. This value is also fixed for the rest of the scenarios.

The first scenario tests imbalance mitigation capabilities of generation reserves. Fig. 4.10 shows

that wind integration drops CPS index below 60%. However, additional generation reserves are able to

improve the situation greatly. CPS index crosses 80% as total system reserves reach 0.12. At this level


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CPS improvements saturate. Other types of reserves are required to bring the balancing performance to

the satisfactory level.

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Figure 4.10: Power system imbalance mitigation in the presence of VER by increasing generation re-serves.

The second scenario tests imbalance mitigation capabilities of ramping reserves. Fig. 4.11 shows that

additional ramping capabilities brings only a small performance improvements. This can be explained

by the fact, that in the current case study, the variability introduced by wind power is proportional to the

variability of the load, and no additional ramping capabilities are required.

The third scenario tests imbalance mitigation capabilities of regulation reserves. Fig. 4.12 shows,

that scheduling of additional ramping capabilities brings the system to the desired level of CPS index.


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CHAPTER 5

Conclusion and Future Work

This chapter presents conclusions of this thesis and indicates possible directions for the future work.

5.1 Conclusions

This thesis has proposed a generalized approach to the power system imbalance assessment. The power

system is modelled as an integrated enterprise consisting of three layers, namely resource scheduling,

balancing actions and the physical grid. The balancing layer consists of the real-time market, the reg-

ulation service and operator manual actions. These three components work in parallel on different

timescales to maintain the balance of the system.

The proposed method is tested on a wind integration case study. The results show that wind integra-

tion generally tends to increase the system imbalances. For the first two scenarios, the penetration level

and variability impacts are tested. The simulations show that the system experiences a lack of ramping

capabilities, which is reflected in the reduction of balancing performance. The other two scenarios test

the impacts of day-ahead and short-term forecast errors. These two scenarios indicate a high sensitivity

of balancing performance to uncertainties of wind. Thus, the impact of VER on the imbalances may

arise from either the variability or uncertainty of the VER.

57

CHAPTER 5. CONCLUSION AND FUTURE WORK 58

5.2 Future Work

The current research creates a solid background for further enhancement of holistic assessment methods.

Particularly, the following possible modifications can be made:

• Incorporation of higher fidelity models of the physical grid such as dynamic models of the gen-

eration and demand. In real power systems, imbalances affect the rotation speed of synchronous

generators, changing system frequency. The differential equations of the system are required to

study the changing dynamics of generators and the system as a whole at faster time scales.

• More active participation of operator manual actions. Integration of RES variability into the sys-

tem increases probability of different contingencies. Contingencies, in the form of generator or

transmission line outages, cannot be resolved by automatic tools and require manual actions of

the system operator.

• Enhanced tools for power system scheduling and operations. Currently used tools are designed

for traditional systems. To better incorporate RES variability and uncertainty, enhancements of

the tools are necessary.

• New methodology of reserve and regulation requirements assessment. Signal processing methods

can establish analytical relations between statistical parameters of RES and power system reserve

and regulation requirements.

• Incorporation of demand side management at different levels of aggregation. Incorporation of

demand side resources is likely to bring a new complicated set of dynamics to the system, poten-

tially created by millions of customers. It will make load dispatchable, but not necessarily from

the power system operator perspective.

CHAPTER 6

Abbreviations

ACE Area Control Error

AGC Automatic Generation Control

BA Balancing Authority

CPS Control Performance Standard

DA Day-Ahead

ED Economic Dispatch

EMS Energy Management System

GSDF Generation Shift Distribution Factor

ISO Independent System Operator

ITLF Incremental Transmission Losses Factors

LMP Locational Marginal Prices

MCP Market Clearing Price

NERC North American Electric Reliability Corporation

NOAA National Oceanic and Atmospheric Administration

59

CHAPTER 6. ABBREVIATIONS 60

NYISO New York Independent System Operator

OPF Optimal Power Flow

RE Renewable Energy

RT Real-Time

SCED Security-Constrained Economic Dispatch

SCOPF Security-Constrained Optimal Power Flow

VER Variable Energy Resources

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