Economic Dispatch of the Combined Cycle Power Plant Using Machine Learning

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IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2019,

Economic Dispatch of the Combined Cycle Power Plant Using Machine Learning

DHRUV BHATT

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

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Abstract

Combined Cycle Power Plant (CCPP)s play a key role in modern power system due to their lesser investment cost, lower project execution time, and higher operational flexibility compared to other conventional generating assets. The nature of generation system is changing with ever increasing penetration of the renewable energy resources. What was once a clearly defined generation, transmission, and distribution flow is shifting towards fluctuating distribution generation. Because of variation in energy production from the renewable energy resources, CCPP are increasingly required to vary their load levels to keep balance between supply and demand within the system. CCPP are facing more number of start cycles. This induces more stress on the gas turbine and as a result, maintenance intervals are affected.

The aim of this master thesis project is to develop a dispatch algorithm for the short-term operation planning for a combined cycle power plant which also includes the long-term constraints. The long- term constraints govern the maintenance interval of the gas turbines.

These long-term constraints are defined over number of Equivalent Operating Hours (EOH) and Equivalent Operating Cycles (EOC) for the Gas Turbine (GT) under consideration. CCPP is operating in the open electricity market. It consists of two SGT-800 GT and one SST- 600 Steam Turbine (ST). The primary goal of this thesis is to maximize the overall profit of CCPP under consideration. The secondary goal of this thesis it to develop the meta models to estimate consumed EOH and EOC during the planning period.

Siemens Industrial Turbo-machinery AB (SIT AB) has installed sensors that collects the data from the GT. Machine learning techniques have been applied to sensor data from the plant to construct Input- Output (I/O) curves to estimate heat input and exhaust heat. Results show potential saving in the fuel consumption for the limit on Cumu- lative Equivalent Operating Hours (CEOH) and Cumulative Equiva- lent Operating Cycles (CEOC) for the planning period. However, it also highlighted some crucial areas of improvement before this economic dispatch algorithm can be commercialized.

Keywords: Combine Cycle Power Plant, Equivalent Operating Hours, Equivalent Operating Cycles, Gas Turbine, Turbine Inlet Temperature, Turbine Exhaust Temperature

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Sammanfattning

Kombicykelkraftverk spelar en nyckelroll i det moderna elsystemet på grund av den låga investeringskostnaden, den korta tiden för att byg- ga ett nytta kraftverk och hög flexibilitet jämfört med andra kraftverk.

Elproduktionssystemen förändras i takt med en allt större andel för- nybar elproduktion. Det som en gång var ett tydligt definierat flöde från produktion via transmission till distribution ändrar nu karaktär till fluktuerande, distribuerad generering. På grund av variationer- na i elproduktion från förnybara energikällor finns ett ökat behov av att kombicykelkraftverk varierar sin elproduktion för att upprätthålla balansen mellan produktion och konsumtion i systemet. Kombicykel- kraftverk behöver startas och stoppas oftare. Detta medför mer stress på gasturbinen och som ett resultat påverkas underhållsintervallerna.

Syftet med detta examensarbete är att utveckla en algoritm för kort- tidsplanering av ett kombicykelkraftverk där även driften på lång sikt beaktas. Begränsningarna på lång sikt utgår från underhållsintervallen för gasturbinerna. Dessa långsiktiga begränsningar definieras som an- talet ekvivalenta drifttimmar och ekvivalenta driftcykler för det aktu- ella kraftverket. Kombikraftverket drivs på den öppna elmarknaden.

Det består av två SGT-800 GT och en SST-600 ångturbin. Det främs- ta målet med examensarbetet är att maximera den totala vinsten för kraftverket. Ett sekundärt mål är att utveckla metamodeller för att skatta använda ekvivalenta drifttimmar och ekvivalenta driftcykler under planeringsperioden.

Siemens Industrial Turbo-machinery AB (SIT AB) har installerat sensorer som samlar in data från gasturbinerna. Maskininlärningstek- niker har tillämpats på sensordata för att konstruera kurvor för att uppskatta värmetillförseln och avgasvärme. Resultaten visar en po- tentiell besparing i bränsleförbrukningen om de sammanlagda ekvivalenta drifttimmarna och de sammanlagda ekvivalenta driftcyklerna begränsas under planeringsperioden. Det framhålls dock också att det finns viktiga förbättringar som behövs innan korttidsplaneringsalgo- ritmen kan kommersialiseras.

Nyckelord:Kombicykelkraftverk, Ekvivalenta drifttimmar, Ekvivalen- ta driftcykler, Gasturbiner, Turbine Inlet Temperature, Turbine Exhaust Temperature

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Acknowledgement

Coming to Sweden and pursue my higher education at KTH Royal In- stitute of Technologywas one of the best decisions I have made. This short journey is about to finish. It was my first-time experience away from my home country. It is true that life begins out of the comfort zone. It was not easy to sail through this journey without the whole- hearted support of my family and friends. They have always sup- ported my choices. Their silent contribution is priceless.

I would like to thank Priyanka Shinde, who is my friend and supervi- sor at KTH for her continuous support and motivation. It was amazing to know you.

I would like to thank my examiner Mikael Amelin for his guidance throughout my time at KTH. I still remember my first meeting with him when I joined KTH. We had a very open discussion about course selection. It had put my foundations for my studies at KTH.

I would like to thank Patrik Hilber, program director for Electric Power Engineering for his continuous support and guidance right from the time when I got admit from KTH. He has always addressed my con- cerns with an open mind and assisted me with innovative inputs.

I would like to thank my supervisors Edgar Bahilo Rodríguez and Davood Naderifor providing such an uncountable amount of knowl- edge, field expertise and rewarding guidance during this entire project.

They have always given me the freedom to innovate. I will always cherish the wonderful discussions we used to have.

I would like to give a special thanks to Erik Ärlebäck, the manager at SIT AB who granted me this opportunity and treat me always like one member more of the team.

Last but not least, I would like to thank Stefano Rosso and Mohamed Elhafiz Hassan, who were also pursuing their master thesis at SIT AB.

It was always fun to have discussions with you folks.

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List of Figures

2.1 Functioning of CCPP [3] . . . 6

2.2 Various configurations of CCPP . . . 7

2.3 Operation of the gas turbine [5] . . . 8

2.4 Optimization logic [5] . . . 9

2.5 Integrated methodology for optimizing CCPP operation [9] . . . 12

2.6 State space transition diagram [12] . . . 14

3.1 Correlation Matrix . . . 17

3.2 Histogram of α . . . 19

4.1 Box model for maintenance plans . . . 25

4.2 Historical data . . . 26

4.3 Method to develop the meta models . . . 27

4.4 Approach - 1 . . . 27

4.5 Estimated Turbine Inlet Temperature (TIT) from % load . 28 4.6 Estimated Turbine Exhaust Temperature (TET) from measured TIT . . . 28

4.7 Approach - 2 . . . 29

4.8 Estimated TET from % load . . . 30

4.9 Estimated TIT from measured TET . . . 30

4.10 Histogram of TIT . . . 31

4.11 Variation in residuals . . . 32

4.12 Meta model used in the optimization process . . . 33

4.13 Approach to estimate E[Cd] . . . 34

5.1 Approach to estimate EOC and EOH . . . 36

5.2 Estimated and Measured EOC and EOH for GT01 . . . . 37

5.3 Estimated and Measured EOC and EOH for GT02 . . . . 38

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x LIST OF FIGURES

6.1 Active load for power plant under consideration . . . 41

6.2 Inclusion of meta models with approach 1 . . . 41

6.3 Inclusion of meta models with approach 1 and 2 . . . 42

6.4 I/O curves for GTs . . . 44

6.5 Case studies . . . 45

7.1 Results: S1, week - 1, month - 1 . . . 58

7.4 Results: S8, month - 1 . . . 61

7.6 Results: S9, month - 2 . . . 63

7.7 Results: S13 (cost/EOH = 1.0 pu), week - 1, month - 1 . . 64

7.8 Results: S14 (cost/EOH = 0.1 pu), week - 1, month - 1 . . 65

A.1 Best fitted line [20] . . . 75

A.2 K-fold cross validation . . . 76

A.3 Re-sampling techniques [23] . . . 77

B.1 Model construction process [24] . . . 80

B.2 Multi-period planning problem [24] . . . 81

B.3 Formulation of warehouse problem in Pyomo . . . 85

B.4 Constraint formulation using disjuncts in Pyomo . . . 87

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List of Tables

2.1 Operating Modes of CCPP . . . 13

4.1 Relationship between TIT and Ca . . . 22

4.2 Relationship between TET and Cc . . . 23

4.3 Type of unloading event and Cd . . . 24

5.1 Consumed EOH and EOC for the planning period (from historical data) . . . 38

7.1 Summary of results (minimize total fuel consumption) . 54 7.2 Summary of results (minimize total operating cost) . . . 55

B.1 Cost of delivery from warehouse m to customer n . . . . 83

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List of Abbreviations

S⁺ Start. 36 S⁻ Stop. 36

CCC Combined Cycle Component. 13, 14 CCM Combined Cycle Mode. 13, 14

CCPP Combined Cycle Power Plant. iii, vi, vii, ix, xi, 2, 3, 5–8, 12–14, 17, 40, 43–46, 52, 53, 55, 56, 66–68, 82

CEOC Cumulative Equivalent Operating Cycles. iii, 24, 43, 45, 52–55 CEOH Cumulative Equivalent Operating Hours. iii, 24, 43, 45, 52–55 CIT Compressor Inlet Temperature. 53, 54, 67

ENS Energy Not Served. 46, 55, 57

EOC Equivalent Operating Cycles. iii, vii, ix, xi, 2–4, 21, 23–25, 31, 33, 34, 36–43, 45–49, 52–56, 66–68, 77

EOH Equivalent Operating Hours. iii, vii, ix, xi, 2–4, 8, 21, 22, 24, 25, 29–31, 33, 35–43, 45–49, 52–56, 66, 68, 77

FFH Factored Firing Hours. 9 FL Full Load. 18, 19

FS Fast Start. vi, 23, 33

GT Gas Turbine. iii, vi, vii, x, 6, 7, 9, 10, 15–20, 23, 25, 40, 43–47, 49, 53–56, 66–68

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List of Abbreviations xiii

HRSGT Heat Recovery Steam Generator. 6, 7, 45, 67 I/O Input-Output. iii, vii, x, 44, 45

MILP Mixed Integer Linear Programming. 3, 51, 52 PPO Power Plant Operator. 3, 22, 23, 31, 43, 55

SIT AB Siemens Industrial Turbo-machinery AB. iii, 1–3, 40, 43, 45, 46

ST Steam Turbine. iii, vii, 2, 6, 7, 13, 44–46, 49, 50, 53, 55, 67

TET Turbine Exhaust Temperature. ix, xi, 23, 25–31, 33, 37, 41, 42, 66, 77

TIT Turbine Inlet Temperature. ix, xi, 15, 16, 19, 21, 22, 25–33, 37, 41, 42, 66, 77

UC Unit-commitment. 36 UL Unloading. 24

VER Variable Energy Resources. 2

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Chapter 1 Introduction

Siemens Industrial Turbo-machinery AB (SIT AB) in Sweden is part of the Siemens Energy Sector. The Energy Sector is the world’s leading supplier of products, services and solutions for the generation, transmission and distribution of power and for the extraction, conversion and transport of oil and gas. Combined cycle power plants play a key role in modern power system due to their lesser investment cost, lower project execution time, and higher operational flexibility compared to other conventional generating assets. The nature of generation system is changing with ever increasing penetration of the renewable energy resources. What was once a clearly defined generation, transmission, and distribution flow is shifting towards fluctuating distribution generation. Because of variation in energy production from the renewable energy resources, CCPP are increasingly required to vary their load levels to keep balance between supply and demand within the system. This induces more stress on the gas turbine and as a result, main- tanance interval is affected. The aim of this master thesis project is to develop a dispatch algorithm for the short-term operation planning for a combined cycle power plant which also includes the long-term constraints. The long-term constraints govern the maintenance interval of the gas turbines. delivers gas turbines, steam turbines, turn-key power plants, service and components for heat and power production.

In an attempt to maintain its prominent role as one of the leading turbo machinery manufacturers, increase its business intelligence;

expand the offered range of services, and to create the value for its customers, SIT AB has taken a step forward to utilize the vast amount of precious data resource, collected from sensors that are installed in

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2 CHAPTER 1. INTRODUCTION

the operating machines all over the world. This master thesis is per- formed in the data analytics department in SIT AB. The data analytics department has been working extensively using this data to automate decision making process for the power plants operators, as well as to provide useful information to other departments within SIT AB.

1.1 Overview

This Master thesis is part of SIT AB efforts done to develop decision support algorithms to help the power plant operators in their daily life with the decisions they need to take. The final goal of the project is to develop a mathematical model that maximizes the profit of the power plant if they are selling all their electricity in the day ahead electricity market. The inclusion of any bilateral contracts, spinning reserves, and up and down regulation capacity of the power plant under consideration is not in the present scope of this master thesis.

The idea of this master thesis is to develop a constrained optimization model for the combined cycle power plant (CCPP) that optimizes the dispatch of the power plant under consideration. The modeling of CCPP is quite challenging due to the tight interaction between the gas turbine and the steam turbine (ST). Furthermore, constraints regarding the maximum available capacity, minimum operating time, start-up time, start-up cost, ramp rate, power balance, and maintenance shall be considered.

One of the reasons to incorporate maintenance cost in the optimization model is increasing penetration of variable energy resources (Variable Energy Resources (VER)). VER are fluctuating in nature and hence, it also affects the production cost of dispatchable machines.

Variation in VER is likely to change the operating point of machines which may not be the operating point that offers the best efficiency.

Furthermore, number of operating cycles for any machine is also increased due to the variation in VER. This puts stress on the mechanical component of the machine which ultimately results into more frequent maintenance and hence, an effort shall be made in this master thesis to capture the cost associated with the maintenance.

In addition to this, there are two more ongoing master thesis projects at SIT AB. First project emphasizes on developing economic dispatch algorithm for a CCPP without any constraints on EOH and EOC to

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CHAPTER 1. INTRODUCTION 3

minimize the total fuel consumption during the planning period. Sec- ond project emphasizes on forecasting of electricity price and fuel cost using various machine learning methods. The idea is to integrate these projects with the previous work done at SIT AB in an attempt to develop an end to end decision support tool for the Power Plant Operator (PPO).

1.2 Objectives

The present master thesis project aims to:

• The need of inclusion of the long-term operational constraints in the short-term operation planning of the CCPP.

• Study the in-house models to estimate the equivalent operating hour (EOH) and equivalent operating cycle (EOC) for the gas turbine under consideration.

• Identify the power plant to perform the studies

• Estimate the maximum available capacity of the gas turbines for the power plant under consideration.

• Develop meta-models to link the output of the dispatch optimization algorithm to the the parameters that influence EOH and EOC consumption using machine learning techniques.

• Develop mathematical mixed integer linear programming (Mixed Integer Linear Programming (MILP)) using Pyomo.

• Describe the need of future studies and areas of further improve- ments at SIT AB.

1.3 Thesis structure

• Chapter 2 gives an overview about the previous studies done in the area of unit-commitment problem formulation for the combined cycle power plants. Reader is envisaged to refer this to get brief idea about the topic. This section also gives brief idea about functioning of a CCPP along with typical configurations of a CCPP.

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4 CHAPTER 1. INTRODUCTION

• Chapter 3 explains about the estimation of the maximum avail- able capacity for the gas turbine. The maximum amount of power that a gas turbine can produce is a function of ambient conditions and hence, it is envisaged to use the maximum available capacity as an upper bound of the generation constraint instead of using the fixed rated value of the gas turbine.

• Chapter 4 gives the idea about the life of the gas turbine under consideration. It introduces the concept of equivalent operating hours (EOH) and equivalent operating cycle (EOC). Further- more, meta-models to estimate the parameters influencing the EOH and EOC are explained.

• Chapter 5 validates the models developed to estimate EOH and EOC. Furthermore, analysis of actual measurements and estimated values is represented.

• Chapter 6 highlights about selection of the power plant followed by the optimization model developed for this project. It also explains about some features of the optimization solver.

• Chapter 7 discusses about the results obtained from the opti- mization algorithm along-with some sensitivity analysis to observe the change in the dispatch results with respect to any change in the input parameters.

• Chapter 8 draws the conclusion of the study along with the area of further studies.

• Appendix A provides an idea about the linear regression tech- nique used in the machine learning. It also explains about the K-fold validation and imbalance in the data set.

• Appendix B introduces the programming in Pyomo to formu- late the dispatch optimization problem with relevant examples.

Basic syntax about coding is also explained here for the better understanding of the reader.

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Chapter 2 Literature Review

This section highlights of the background concepts of the thesis topic.

It is envisaged to go through to make yourself familiar about important concepts about the topic. Gas-fired power plants have been an important part of power systems for several decades. The success of gas-fired power plants has been motivated by, among other things, their shorter construction times, lower investment cost and higher efficiency and flexibility compared to other power generation technolo- gies [1], [2]. Furthermore, the gas will become more prevalent due to the increased production in shale gas. Literature review is divided in three sections. Section 2.1 gives brief idea about operation of a CCPP.

Section 2.2 explains about need of inclusion of long-term constraints in the dispatch optimization problem along with some useful approaches for modeling. Section 2.3 explains about different models to formulate the unit commitment problem for the combined cycle power plant (CCPP).

2.1 Overview of CCPP

This section provides brief overview about functioning of a CCPP.

A CCPP uses both a gas turbine and a steam turbine to produce the power.

A CCPP relies on the simple fact that a gas turbine produces both power and hot exhaust gases. The compressor sucks the air from the atmosphere at ambient conditions. CCPP can also have provision of pre-cooling systems like a chiller to reduce the temperature of the air.

It increases the air density and increases the air mass flow to the com-

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6 CHAPTER 2. LITERATURE REVIEW

pressor. Air is compressed in the compressor. The compressor is often connected to the shaft of the GT. This means that a part of power generated by the GT is consumed by the compressor. Hot compressed air is mixed with the fuel. The hot air-fuel mixture moves through the gas turbine blades, making them spin. The generator connected with GT produces the electric power. In a CCPP, the exhaust gas from the GT is directed to the heat recovery steam generator Heat Recovery Steam Generator (HRSGT). HRSGT produces the super-heated steam.

HRSGT can also have the auxiliary firing system with supplementary fuel to supply more heat to the water. The high pressure super-heated steam is delivered to the ST where it will expand and produce the mechanical power. The ST is connected to the generator to produce the electric power. The functioning of a CCPP is represented in figure 2.1.

Figure 2.1:Functioning of CCPP [3]

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CHAPTER 2. LITERATURE REVIEW 7

The configuration of CCPP can vary from plant to plant. Let us assume that a CCPP has two GTs. It is possible to have single or separate HRSGT for both of the GTs. If there are separate HRSGTs for the GTs, it is possible to have single or separate ST connected to HRSGT system. This is visualized in figure 2.2. Combination of GT along with its ST is described as a block. The CCPP under consideration has configuration - 2 in reality. However, it is modeled as configuration - 3 for this project. It is due to lack of availability of data regarding HRSGT.

Figure 2.2:Various configurations of CCPP

2.2 Long-term constraints in dispatch opti- mization

Presently in electric power systems, an emphasis is being put on providing low-carbon energy while ensuring security and supply. The rising share of the renewable generation has reduced the load factor of the CCPP. However, these renewable generation sources are inter- mittent and not dispatchable. CCPP technology is more flexible owing to the lower star-up time and faster ramping rates. Therefore, CCPP power plants are having an increased number of start-ups during a year. Traditionally, CCPP plants are designed for the base-load operation with the limited number of start-ups in a year. Start-ups and shut- downs cause the variation in the boundary conditions. This causes variation in the stress throughout the material of each component. Due to the increased number of start-ups in the current scenario, the CCPP

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plant owners are facing higher maintenance costs. Therefore, it is essential to include the long-term constraints to optimize the short-term operation of the power plant in order to maximize the overall profit.

Long term maintenance optimization of CCPP plants in Spain is analyzed in [4]. During 2006 to 2010, the installed capacity of CCPP is increased. However, the relative energy supplied is decreased. Fur- thermore, the number of starts is increased. [4] presents a formulation of a mixed-integer mathematical optimization problem that in- corporates the long-term maintenance constraint and daily operation to minimize the total operation cost of a power plant under consideration. The operating hours are classified into valley and peak hours as it might be beneficial to run the power plant when the electricity price is less during the valley hours to avoid the maintenance cost due to the cyclic operation. This paper uses the concept of the equivalent operating hours (EOH) to formulate the maintenance constraint however, the estimation of EOH is not analyzed in detail.

Figure 2.3:Operation of the gas turbine [5]

One of the patent applications by GE [5], leverages ambient and market forecast data as well as asset performance and part-life to generate the operating schedule that maximizes the profit subjected to the operating constraints and the part-life constraint. It is developed on

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the concept of a hot load path and cold load path operation. As represented in figure 2.3, the gas turbine can produce the same amount of output power at various temperatures. This flexibility is exploited here. When the turbine produces power at a higher temperature it results in higher efficiency, but it also consumes more part life because of higher working temperature. On the other hand, the cold load operation results in lower efficiency but consumes lower part life. There- fore, the choice of operation is a trade-off between the efficiency and the part life consumption.

Sometimes, the plant operator can peak-fire the gas turbine to produce more output to above the base capacity during the peak hours to make more profit at the expense of faster part-life consumption. This may also result in shorter maintenance intervals. In this patent, the operational impact on the part life is considered by defining the factored fired hours (Factored Firing Hours (FFH)) and the maintenance intervals are defined over FFH. Every hour when the GT is operated up to its base capacity, 1 FFH is consumed from the part life. However, when the GT is operated in a peak-fire mode to produce more power, 1 hour of operation is more than 1 FFH. Such operation will result in reduced maintenance interval. The plant operator can compensate this by operating the GT in cold part-loading in some hours. 1 hour of such operation will result in less than 1 FFH. Such operation will increase the maintenance interval but will offer lower efficiency.

Figure 2.4:Optimization logic [5]

The cold path operation results in the generation of the FFH while the hot path operation results in increased consumption of the FFH.

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Cold path operation has lower efficiency and hence, increased fuel consumption whereas peak fire operation increases the maintenance cost due to shortened maintenance interval. It is also important to consume the part life before the maintenance else it will result in the loss of part life. The idea of dispatch optimization represented in [5]

utilizes the balance between the creation and consumption of part-life credits across the scheduled maintenance interval by determining the optimal hours for cold path and hot path operation. Figure 2.4 represents the optimization logic. Readers are envisaged to refer [5] for more technicalities.

Doctoral thesis in [6] emphasizes the reliability-based maintenance scheduling for the gas turbines. Though it is not directly related to dispatch optimization, it gives valuable insights about the importance of the part-life estimation. There are several damage mechanisms for the GT parts, and this makes the GT unreliable. The wear out can lead to failure of parts and hence, unplanned outages. Therefore, it is essential to keep track of the part’s life consumption to plan the outages.

The maintenance concepts for the GT are based on one life counter i.e.

number of firing hours or factored firing hours or equivalent operating hours. This is relatively convenient to plant the outages, but it has some disadvantages. If the planned outage falls when the electricity prices are high, the plant operator has two options. Either the operator can proceed with the outage and lose the opportunity to make more profit or prepone the outage and lose the remaining part life. Fur- thermore, multiple life counters for that includes the various turbine parts are envisaged to maximize the life consumption of various parts.

However, having multiple life counters makes the outage coordination challenging as it is beneficial to combine the outages of different parts due to dependencies in the dismantling process.

One of the patent applications by Siemens [7], emphasizes the integrated optimal outage coordination in the energy delivery system.

The electricity markets generally include two types of commodity i.e.

power and energy. Markets for energy trade net generation output for the number of intervals by the supplier and the consumer. Markets for power are managed by the market operators to ensure reliability.

It includes ancillary services. Repair and maintenance of the system components result in scheduled outages in the system. It is important to coordinate these outages without compromising the system’s security and stability. Outages also result in a change in the marginal

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cost which will also affect the electricity price. Therefore, coordinating the outages is more of an iterative process in which the system operator solves the complex optimization process to approve the outage requests by the asset owners.

Various methods to model the major overhaul cost of gas-fired plant in the unit commitment problem are represented in [8]. Traditionally, the operation and maintenance O&M costs were introduced in the unit commitment problem by adding an additional cost adder component.

O&M costs are reflected in the long-term service agreements. It can be modeled as a function of the number of firing hours and the number of starts. The traditional approach of modeling the O&M costs assumes a lower number of starts. However, when the gas turbine has a greater number of starts, cyclic stress is more on the components. The inad- equacy of modeling of O&M cost in the unit commitment problem is highlighted by PJM, ERCOT, and CAISO. Three modeling approaches to formulate the maintenance interval function are discussed in this paper.

Modeling of the fatigue cost due to the cyclic operation of the gas turbines is studied in [9]. Models for the estimation of the fatigue costs is developed along with feasible transition modes. These models are later introduced in the unit commitment problem. Figure 2.5 represents the overall idea behind this process.

Research paper presented in [10] gives highlights about formulat- ing dynamic costs related to the related to start-up and ramping. Lin- ear, piece-wise linear, and step-shaped cycling costs functions are created to capture the costs related to the cycling operation in the dispatch optimization. It gave ideas about the importance of having different states in the optimization algorithm. In this thesis, this is achieved by implementing generalized disjunctive programming in Pyomo. More details about Pyomo is explained in the following chapters.

Master thesis presented in [11] highlights about inclusion of long- term constraints in short-term operation planning by including the use value to reflect the opportunity cost. It investigates the dispatch results obtained from DiMOI and MaStock. The used value is a way to value an asset scarcity by assessing the would-be future profits. Asset in scarcity is referred as a stock. It can be number of operating hours or cycles for the gas turbine. In a first phase, the optimization phase, the Bellman values for the opportunity cost is calculated. In the second phase, the simulation phase, the optimal functioning to operate the

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Figure 2.5:Integrated methodology for optimizing CCPP operation [9]

power plant is generated.

2.3 Modeling of combined cycle power plants

This section gives brief information about the research work done in the area of modeling of combined cycle power plants. Inclusion of combined cycle plants into the unit commitment is challenging due to close interdependence between the operation of the gas turbine and the steam turbine. In the combined cycle power plant, the exhaust heat from the steam turbine is utilized to heat the water. However, it takes time to achieve the steam parameters before it can be used to generate power. For example, if the power plant is in a cold state i.e.

all the machines were out of operation for a considerable amount of time then the steam turbine generator cannot produce the power at

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very first-time stamp when the demand arises. This physical depen- dence must be modeled in the unit commitment problem. There are mainly two types of models, combined-cycle component (Combined Cycle Component (CCC)) and combined-cycle mode (Combined Cy- cle Mode (CCM)) to formulate the unit commitment problem for the combined cycle power plants.

[12] and [13] represents the CCM modeling approach to formulate the mixed integer linear problem for the combined cycle units. Let us assume that there are two identical gas turbines (GT1 and GT2) and one steam turbine (ST) in a power plant. Table 2.1 lists possible operating modes. At any time, the CCPP can only be in one mode.

Mode Configuration

0 OFF

1 GT1 or GT2

2 GT1 + GT2

3 GT1 + ST or GT2 + ST 4 GT1 + GT2 + ST Table 2.1:Operating Modes of CCPP

When CCM modeling approach is used, the constraints for the transition between modes and minimum up and downtime must be formulated. Furthermore, not all the modes are feasible at any given period. For example, the CCPP cannot go to mode 4 from mode 0 directly. This is represented in figure 2.6. Each mode of operation can be treated as a pseudo unit with its own constraints. To implement CCM, it is important to have the information and data about the plant configuration. For example, if the plant has separate heat recovery boiler for each turbine and if the boilers have supplementary firing. It is often challenging to find such detailed information about the plant.

CCC modeling approaching for CCPP is investigated in [14] and its results are compared with the results obtained using the CCM model.

In the CCC model gas turbines and steam turbines are considered as an individual component rather than considering them as operating modes. Input-output (IO) curves of components are included in the model. The results obtained from CCM models gives the power output of each mode at each time stamps. However, the plant operator must divide it among the generators based on the experience which

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Figure 2.6:State space transition diagram [12]

may not be optimal. On the other hand, CCC models will give the output from each component individually. Most of the time, it is possible that the CCPP is operating in a certain mode. Under such a scenario, there will not be enough data points for other modes of operation to model them accurately. One of the disadvantages of the CCM models is the number of components. As the number of components increases, the number of operating modes will also increase. This increases the complexities in mapping the state transitions. In CCM model, degradation of any component will affect multiple operating modes and hence, it asks for re-calibration of all modes to include the effects of degradation. While in CCC models, the only component of interest can be re-calibrated. It is also highlighted that CCM models have a greater number of integer variables and constraints compared to CCC models. This also increases the computational cost.

In this thesis CCC modeling approach is used as the data of heat recovery boiler is not available. Furthermore, the main objective of this thesis is to include machine life in the unit commitment problem.

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Chapter 3 Maximum Available Capacity of the GT

It is important to estimate the maximum available capacity of the gas turbine as it sets the generation constraints. If it is under-estimated, then the machine may not produce the power that it can produce, and this results in the monetary loss for the power plant owner. In a similar way, if it is overestimated then it will seriously affect the life of the machine and personal safety. In this thesis, two methods to estimate the maximum available capacity are investigated.

3.1 Method-1

There is a signal for % load in the system. Method to calculate this signal is developed internally by using three parameters. These parameters are available only in the internal report. However, these parameters are related to the following phenomenon.

• Parameter A is related to the density of the air hence, with the number of air molecules per kg that go through the compressor.

• Parameter B is related to the effective area of the compressor, therefore, the mass flow of the air that goes through the compressor.

• Parameter C is related to the turbine inlet temperature (TIT) during combustion process and with the turbine efficiency.

15

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16 CHAPTER 3. MAXIMUM AVAILABLE CAPACITY OF THE GT

While checking these values, it was found that there were so many missing values (Not a Number). This is because the algorithm used to calculate % load considers the value of TIT in degree Celsius however, the measurement is reported in degree Fahrenheit. Therefore, instead of using the % load values directly, it is calculated using the same algorithm with the TIT measurement converted to degree Celsius.

While investigating the calculated values of % load, it was found that some of these values were not realistic. For example, the calculated value of % load is 100 but the value of parameter B at that time- stamp is not maximum. When the gas turbine is operating at 100 % load, the value of parameter B must be at its highest value to offer the maximum effective area to get highest air mass flow. Furthermore, the active power load was also lower than its maximum rated capacity and hence, such values of % load must be corrected. However, the value of TIT is near its maximum rated value. This leads to one hypothesis that the way % load is calculated here represent the thermal loading of the machine than the power loading. However, further investigation into this is not in the scope of this thesis work and is subjected to future research. Maximum available capacity can be calculated by dividing the active power load by the % load as represented in equation 3.1.

M axCap^method1 = ActiveLoad

%Load [M W ] (3.1)

3.2 Method-2

The performance of the gas turbine is dependent on the operating conditions. This issue of having varying thermal efficiency has been considered by gas turbine manufacturers by means of ISO-rating stan- dards (ISO 19859:2016). The ISO rating algorithm allows calculating the performance in real-time considering the operating ambient conditions.

Some of these parameters are directly related to the density of the air and hence, any change in ambient condition from the ISO conditions will affect the performance of the gas turbine. This is mainly because of the change in the air density and therefore the mass flow of the air. Therefore, the maximum power that can be produced by the gas turbine is a function of the ambient conditions.

Increases in the ambient temperature can highly affect the gas tur-

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CHAPTER 3. MAXIMUM AVAILABLE CAPACITY OF THE GT 17

bine performance. When the inlet air is hot the net power of the gas turbine reduces. For every 1^◦C increment in the ambient temperature, the amount of the reduction in power output is nearly 0.9% (Petch- ers, 2002). Air density reduces with increase in the temperature. This reduces the air mass flow which will result in reduced output power.

With decrease in the barometric pressure, the air density reduced.

As a result, the air mass flow rate reduces which in turn reduce the output power.

The atomic mass of the H2O is less than N2 and O2. Due to that reason mass of the humid air is less than the mass of the dry air (same volume). Therefore, the humid air has less density than the dry air. As a result of low-density air, the amount of dry air mass entering the gas turbine reduces. Thus, the performance of the gas turbine reduces.

Figure 3.1 represents the correlation matrix for the GTs for the CCPP under consideration. This is also used to estimate the heat input and exhaust heat using multiple linear regression in chapter 6.

Figure 3.1:Correlation Matrix

Few important parameters that affect the performance of the gas turbine are as below.

• Ambient temperature (T0)

• Relative humidity (RH)

• Barometric pressure (P0)

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• Inlet pressure losses (Pi)

• Outlet pressure losses (Po)

• Power factor correction (P F )

• Fuel quality (Fq)

Each variable is represented by a coefficient Ci. An overall parameter is a multiplication of individual parameters as represented in equation 3.2. Furthermore, the value of each parameter is calculated using polynomials over their range. These polynomials are part of an internal report and are strictly confidential.

CP ower = CT0 ∗ CRH ∗ CP0 ∗ CPi∗ CP_O ∗ CP F ∗ Cfq (3.2)

M axCap^method2 = C_power∗ P_N[M W ] (3.3)

Where,

P_N = Nominal power [MW]

In this thesis, CT0, CRH, C(P0 are used to estimate the Cpower as the quality of these signal is good. These signals are for ambient conditions that can be forecasted. Therefore, the maximum available capacity can be estimated for the planning period using the forecasted ambient conditions.

3.3 Correction

As highlighted in the previous sections, method 1 lacks accuracy for some values of % load near 100%. While method 2 does not consider all parameters, which affects the maximum available capacity of the machine. This section describes the method used to correct the maximum available capacity to use it further to develop the meta models in the next chapter.

There is one signal “full load operation (Full Load (FL))”. It is a binary signal. When it is ‘1’, the machine is operating at its full load capacity and hence, when the FL signal is ‘1’, the active power load can be considered as the maximum available capacity. At this time instance % load = 100%

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CHAPTER 3. MAXIMUM AVAILABLE CAPACITY OF THE GT 19

Let, α = ActiveP ower^{F L=1}

M axCap^method2 (3.4)

αis defined to quantify the error in the maximum available capacity and the active power output when FL = 1. These two must be the same when FL = 1. Figure 3.2 represents the distribution of α.

Figure 3.2:Histogram of α

Mean value of α is used to estimate the maximum available capacity at each time-stamp as represented equation 3.5.

M axCap_t= M axCap^method2_t

α_mean (3.5)

When a single mean value of α is used to estimate the maximum available capacity, there were some instants when the maximum available capacity was less than the active power load of the generator. This is mathematically logical. Furthermore, the machines were not doing the peaking operation. This was evident as the value of TIT was not above its nominal values. Therefore, for such instances, the maximum available capacity is considered to be the active power load at that time-stamp. Such time-stamps only represent a small fraction of the historical data.

Finally, method 2 shall be used to estimate the maximum available capacity using the forecasted ambient conditions and the α correction.

However, further, development is envisaged in order to develop more

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general algorithms to estimate the maximum available capacity with the highest accuracy.

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Chapter 4 Meta-models

In this section formulation of EOH and EOC is explained. Value of EOH and EOC at time-stamp depends on the physical operating parameters and the design limits. These limits are strictly confidential and hence, numerical values are not mentioned in this section.

4.1 Equivalent operating hours

According to the engine control specification of SGT-800, the equation to calculate the EOH is given by equation 4.1.

EOH = f (Ca, Cb, H, EOC) (4.1)

Where,

Ca= Factor that depends on TIT

C_b = Factor that depends on the type of fuel H = Number of operating hours

EOC = Equivalent operating cycles

4.1.1 Factor C

a

Factor Ca, is dependent on the turbine inlet temperature, TIT. Based on the type of the turbine, the limits on the TIT are set. Type of machine is the main attribute corresponding to the nominal capacity of the gas turbine. It consists of three main sections. These are the compressor,

21

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22 CHAPTER 4. META-MODELS

combustor, and turbine. Each machine type has some specific charac- teristics. The power output of the gas turbine depends on the climatic conditions. Change in the ambient conditions will change the air density and subsequently the pressure ratio. To compensate for this, more fuel would be required to produce the same output power. However, this will increase the turbine inlet temperature that might go above the melting point of the material used and hence, there must be an upper limit for the turbine inlet temperature. Machine type also depends on the type of material used in the turbine. Depending on this material the temperature limits for the operation is determined. For this machine type, the Cafactor is given in table 4.1. The measurement unit of TIT is^◦C. The value of Caincreases with increase in TIT.

Turbine Inlet Temperature C_a TIT ≤ T IT1 C_a₁ TIT1 < T IT ≤ T IT₂ C_a₂ TIT2 < T IT ≤ T IT₃ C_a₃ TIT> TIT3 C_a₄ Table 4.1:Relationship between TIT and Ca

It is interesting to observe that the value of Cafactor is always more than Ca1 and hence, it will always increase the EOH. This is a more conservative approach. When the machine is operated at lower temperatures, Cacan be less than Ca1. For such operation, the efficiency is likely to be less, and the fuel consumption will be more to generate the same amount of power. However, such operation is likely to be beneficial when the fuel price and electricity demand faced by the power plant is less. Under such operation, 1 hour of operation will be lesser than 1 EOH. That means, by compromising the efficiency, the power plant operator (PPO) can consume lesser life of the machine. This will allow PPO to consume more machine life when the electricity price is higher. PPO can operate machines at higher temperatures to generate more power at better efficiency to maximize the profit. This idea is documented well in one of the patent applications filed by the GE [5]. However, in this application, the idea is developed considering the firing hours only. Presently, there are no documents that highlight such provision for the SGT-800 and hence, in this thesis, the idea of developing the model with Ca<Ca1 is not included. However, it is sub-

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CHAPTER 4. META-MODELS 23

jected to future research and development. Its inclusion will give more flexibility to PPO to utilize the life of the gas turbines.

4.1.2 Factor C

_b

Parameter Cb is dependent on the type of fuel used during the operation. For the gas fuel, Cb= Cb1 while for the liquid fuel, Cb= Cb2

4.2 Equivalent operating cycles

According to the engine control specification of SGT-800, the equation to calculate the EOC is given by equation 4.2.

EOC = f (C_c, C_d, S^up, S^down) (4.2)

Where,

C_c= Factor that depends on the type of start-up of the GT Cd= Factor that depends on the type of shut-down of the GT S^up= Start-up variable

S^down= Shut-down variable

4.2.1 Factor C

c

Factor Cc depends on the turbine exhaust temperature. It is given in table 4.3. The measurement unit of TET is^◦C.

Turbine Exhaust Temperature Cc

TET ≤ T ET1 C_c₁ TET > TET1 C_c₂ TET > TET1(F S₁) C_c₃ TET > TET1(F S₂) C_c₄ Table 4.2:Relationship between TET and Cc

The fast start - 1 and fast start - 2 are the optional features for the customer. While investigating the customer data, it was found that the machines at plant under consideration do not have these optional features.

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4.2.2 Factor C

d

Factor Cd depends on the type of unloading (Unloading (UL)) event during the shutdown. It is given as below. It is given in table 4.3.

Unloading Event Type C_d Normal unloading C_d₁ Unloading - 1 C_d₂ Unloading - 2 C_d₃ Unloading - 3 C_d₄ Table 4.3:Type of unloading event and C_d

Ramp-down rate during the shut down events are different. The stress induced in the machine is proportional to the ramp-down rate during the shutdown. Numerical relationship among different values of Cdrepresented in equation 4.3.

Cd1 < Cd2 < Cd3 < Cd4 (4.3)

4.3 Meta-models

The maintenance interval of the turbines is specified in terms of the EOH and EOC. This is referred to as a box model. There are two types of maintenance plans for the SGT-800, basic maintenance plan, and extended maintenance plan. These plans consist of remote minor inspection, hot gas path inspection, and major overhaul.

The basic maintenance plan offers the greatest flexibility in terms of combining the high number of starts and operating hours. It allows 20,000 EOH or 1,000 EOC, whichever is earlier between hot gas path inspection and major overhaul. This plan is adopted for normal power plants.

The extended maintenance plan allows 30,000 EOH or 500 EOC, whichever is earlier between hot gas path inspection and major overhaul. This plan is adopted for base-load power plants. The maintenance plans are represented in in figure 4.1. This is used to set limit on maximum allowable CEOC for maximum allowable CEOH during the planning period.

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Figure 4.1:Box model for maintenance plans

The maintenance intervals for the other parts of the turbines like compressor and burner are different. However, in this thesis, the major focus is on the hot gas path inspection and the major overhaul. The dispatch algorithm can easily modify to include other part life constraints and to optimize the overall plant operation in the long-term.

It is evident that it is necessary to include EOH and EOC in the optimization algorithm to include the part life and maintenance interval constraints. The result of the dispatch algorithm consists of power output, unit commitment, start-up, and shut down. However, the parameters used to calculate EOH and EOC uses TIT, TET, fuel type, and unloading events and hence, it is necessary to estimate these parameters from the results of the dispatch algorithm and historical data of the plant. It was found that the the power plant under consideration was always operated with the gas fuel and hence, Cb is set to be Cb1. In the future, the type of operating fuel can be entered as a parameter.

This will make the model realistic in nature.

The aim of the meta-models is to estimate the physical operating parameters, used in EOH and EOC calculation from the result of the optimization algorithm. % load is used as a starting point to formulate the meta-models as % load, TIT, and TET are somehow correlated with each other (WGT=m*Cp*(TET-TIT )). % load is calculated as shown in equation 4.4.

%Load = ActiveLoad

M aximumAvailableCapacity ∗ 100[%] (4.4)

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The meta-models are developed using the historical data and hence, they do not include the effect of degradation. Further research and development are envisaged to include the degradation in the meta- models. As % load is a base of the meta models, it is essential to estimate maximum available capacity as accurately as possible. As highlighted in chapter 3, there are some errors in estimation of maximum available capacity.

Figure 4.2:Historical data

Figure 4.2 represents the historical data used to formulate the meta- models. Simple linear regression is used to establish the relationship between the desired parameters. Furthermore, the curves are divided in the number of regions to achieve better accuracy out of the linear regression.

Figure 4.3 represents an overall idea to develop the meta models. In this thesis, two approaches are checked to develop the meta-models.

4.3.1 Approach-1

As represented in figure 4.4, in this approach, TIT is estimated from % Load. TET is then estimated using TIT. TET is also estimated using the measured value of TIT to compare the residuals in estimated TET, estimated from the true values of TIT as well as from estimated values of TIT. Residual is the difference between the true value of the parameter and the estimated value of the parameter.

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Figure 4.3:Method to develop the meta models

Figure 4.4:Approach - 1

Estimate TIT from % load

Figure 4.5 represents the scatter plot of measured TIT and estimated TIT with respect to the % load along with the residuals in the estimated values of TIT. The value of residual is higher at lower values of

% load. This is because there are not enough data points for the linear regression as the machines are rarely operated at lower % load. This is also rational because the turbine offers higher efficiency when operated near its full load capacity. Furthermore, at lower % load, TIT values are not so high that error in magnitude of 0.1 pu will give the wrong estimation of the Ca factor. However, this error in estimated TIT may give more error in the estimation of TET.

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Figure 4.5:Estimated TIT from % load

Estimate TET from TIT

Figure 4.6 represents the scatter plot of measured TET and estimated TET with respect to TIT residuals in the estimated values of TET.

Figure 4.6:Estimated TET from measured TIT

4.3.2 Approach-2

In reality, TIT is back-calculated from TET and hence, there are chances of error in the value of TIT due to calculation delay as well. As represented in figure 4.7, in this approach, TET is estimated from % Load.

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TIT is then estimated using TET. TIT is also estimated using the measured value of TET to compare the residuals in estimated TIT estimated from the true values of TET as well as from estimated values of TET. Residual is the difference between the true value of the parameter and the estimated value of the parameter.

Figure 4.7:Approach - 2

Estimate TET from % load

Figure 4.8 represents the scatter plot of measured TET and estimated TET with respect to the % load along with the residuals in the estimated values of TET. The value of residual is higher at lower values of % load. This is because there are not enough data points for the linear regression as the machines are rarely operated at lower % load.

This is also rational because the turbine offers higher efficiency when operated near its full load capacity. This problem is referred to as the imbalanced data in data science. In the case of the imbalanced data, majority classes dominate the minority classes. This creates biased results. This challenge can be addressed during the pre-processing stage by doing re-sampling. However, the same is not implemented as the found results are satisfactory as far as the modeling of EOH is con- cerned.

Estimate TIT from TET

Figure 4.9 represents the scatter plot of measured TIT and estimated TIT with respect to TET residuals in the estimated values of TIT.

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Figure 4.8:Estimated TET from % load

Figure 4.9:Estimated TIT from measured TET

4.3.3 Required level of accuracy

It is always good to have the highest level of accuracy when it comes to estimating any parameter associated with the turbine operation. In this case, Caand Ccdepend on the TIT and TET respectively. However, their values are defined over the interval therefore, if the estimated values of TIT and TET in the correct interval, it is enough to estimate C_a and Cc. Furthermore, the accuracy of estimated TIT must be good as the Ca factor contributes to EOH at each time-stamp. Residuals in the values of TIT can be observed from figure 4.5 and figure 4.9. The accuracy requirement for estimated TET is relatively less stringent as there is only one break-point at TET=T ET1 for the machines under

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consideration. Furthermore, Cc will contribute EOH and EOC only when there is a start-up. To further quantify this, it is important to estimate the probability of a start-up when the residual of TET is highest.

However, it is not included in the scope of this thesis. Therefore, after investigation, approach 1 is finalized to use to develop meta-models to estimate TIT and TET.

Figure 4.10 represents the histogram of TIT of the gas turbines at plant under consideration. It is interesting to note that the machines are never operated above T IT1. This also indicates that the PPO is never doing peaking operation. It would be interesting to develop the meta models for the power plant that performs the peaking operation as well. It is also envisaged to test the historical data with a 1-minute resolution to see if the value of TIT ever goes above T IT1.

Figure 4.10:Histogram of TIT

Furthermore, while performing the linear regression, the available data set is divided into training and test data randomly. 80% of data points are used to train the model while 20% of data points are used to test the model. Since this selection of the data-points is random, it is likely to give the different value of slope and intercept. One such example is shown in figure 4.11.

The maximum value of the residual is way more than what is obtained in figure 4.5. This is because there are only a few numbers of data points when the value of % load is less. Under such circum- stances, the random selection of training data set is likely to give in- accurate estimation. In this thesis, values of slope and intercept that

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Figure 4.11:Variation in residuals

gives best values of residuals is used as input parameters in the optimization algorithm. It is represented in figure 4.12. It is interesting to observe that TIT is almost flat at higher load % even after 100%. This is not realistic. During the peaking operation, the TIT is expected to increase. However, the plant under consideration does not have any history of peaking operation and hence, there are no data points that can be used to model the machine’s behavior under peak operation.

The machine will not generate 1.5 times its rated capacity. From figure 4.12, with the current meta model, TIT will never go beyond T IT1and hence, the value of Ca will always be Ca1. Therefore, for this specific case, it can be omitted from the optimization algorithm in order to reduce the number of integer variables. However, it is kept in order to estimate the computation cost.

One approach would be to run the process of finding slope and intercept of the best-fitted line using the linear regression multiple time and select the weighted average of the result. Another approach to handle this would be to use the K-fold cross-validation. More information about this is highlighted in A. However, with the imbalance in the data set, it is not feasible to implement the K-fold cross-validation technique and hence, the first approach is more suitable. In addition to this, the random split misses the effects of degradation over the period and hence, it is also envisaged to re-celebrate the meta-models over a period or develop more sophisticated methods to incorporate the degradation effects inherently. Later seems more challenging as the

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Figure 4.12:Meta model used in the optimization process

aim is to utilize the output of the optimization algorithm to calculate the EOH.

One of the limitations of this approach of estimating the value of TIT and TET is that there will be a fixed value of TIT and TET when % load = 0. However, when the machine is not producing any power, the value of TIT and TET varies a lot. This is evident from figure 4.2. This does not have any implication on the estimation of EOH and EOC.

4.3.4 Inclusion of the fast start (FS)

When there is a fast start, it will stress the machine more due to more thermal stress. However, it is challenging to make meta-model for it.

One simple solution to this is to include the probability of having a fast start and calculate the expected value of Cc. However, such results will be biased as the probability of fast start is calculated from the historical data sample. The more accurate method would be to capture the fast start is to run the optimization with a 1-minute time stamp. The developed optimization algorithm uses 15-minute data.

Gas turbines can reach to its full load capacity in less than 15-minutes and hence, the optimization algorithm is less likely to capture the need of fast start to maximize the profit. If 1-minute data is used, then it is likely to increase the computation time and cost. The main aim after developing this optimization algorithm is to include the part life and the maintenance constraints and hence, the planning duration is rela-

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tively longer.

4.3.5 Model of C

d

As highlighted in table 4.3, the value of Cd depends on the type of unloading event which is related to the shut-down ramp rate. Type of unloading event is selected by the plant operator. As the model developed in this thesis is using the 15-minute data, it misses the pref- erence for the unloading event furthermore, it is also not possible to assign any shutdown to the emergency shut down from the optimization model. One simple approach is to calculate the expected value of Cd based on the probability of occurrence of the unloading events.

This approach is represented in figure 4.13.

Figure 4.13:Approach to estimate E[Cd]

E[Cd] =

4

X

i=1

Pi∗ Cdi (4.5)

Where,

E[Cd] = Expected value of Cd

P_i = Probability of i^th type of unloading event i = 1 for normal unloading

i = 2 for U L1 event i = 3 for U L2 event i = 4 for U L3 event

E[Cd] is used as a fixed parameter to calculate EOC when there is a shutdown. As this value is fixed, it is envisaged to use updated E[Cd] after the actual shut down event in real-time.

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U L₁, U L2, and U L3 are available as a digital signal in the system.

However, there is no such digital signal for the normal stop. A digital signal for the normal stop is created using the value of active load and U L₁, U L2, and U L3 signals. When the active load is changed to zero after the shutdown and none of the U L1, U L2, and U L3 signals have been set to ‘1’ then this stop is considered as a normal stop.

The data quality of U L1, U L2, and U L3is not so good. It is observed that sometimes this signal attains its value with some time delay. Un- der such a scenario, the type of shut down will be marked as a normal shut down as explained above. However, to investigate deeper into the data measurement system is not in the scope of this thesis. How- ever, it is recommended to improve the data quality of these signals.

Furthermore, there were time-stamps when the value of U L1, U L2, and U L3 signals is ‘1’ even though the active power load is zero in previous periods. Such values must be discarded. This could be due to the aborted starts as well.

For this thesis, the accuracy requirement for the E[Cd] is not so crit- ical as it contributes to EOH only when there is a shutdown.

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Chapter 5 Meta-model validation

In this section, the models developed chapter 4 to estimate EOH and EOC are validated. EOH and EOC are estimated for the time period under consideration using meta-models to estimate Ca, Cc, and Cd. These estimated values are then compared with the measured values of EOH and EOC for the validation purpose.

To compute EOH and EOC, Unit-commitment (UC), Start (S⁺), and Stop (S⁻) variables are used. These variables are estimated from the % load. This is represented in figure 5.1.

Figure 5.1:Approach to estimate EOC and EOH

Figure 5.2 and figure 5.3 represent the comparison between estimated EOH and EOC for GT01 and GT02 for the time period under consideration. The values of EOH are quite close to each other for GT01 however, it is not the case of GT02. This is due to the sudden spike in measured EOC for GT02. Therefore, there is an offset between the measured and estimated values of EOH. Furthermore, the mea-

36

Economic Dispatch of the Combined Cycle Power Plant Using Machine Learning

Economic Dispatch of the Combined Cycle Power Plant Using Machine Learning

DHRUV BHATT

Abstract

Sammanfattning

Acknowledgement

Contents

I Appendix 72

List of Figures

List of Tables

List of Abbreviations

Chapter 1 Introduction

1.1 Overview

1.2 Objectives

1.3 Thesis structure

Chapter 2

Literature Review

2.1 Overview of CCPP

2.2 Long-term constraints in dispatch opti- mization

2.3 Modeling of combined cycle power plants

Chapter 3

Maximum Available Capacity of the GT

3.1 Method-1

3.2 Method-2

3.3 Correction

Chapter 4

Meta-models

4.1 Equivalent operating hours

4.1.1 Factor C

4.1.2 Factor C

4.2 Equivalent operating cycles

4.2.1 Factor C

4.2.2 Factor C

4.3 Meta-models

4.3.1 Approach-1

4.3.2 Approach-2

4.3.3 Required level of accuracy

4.3.4 Inclusion of the fast start (FS)

4.3.5 Model of C

Chapter 5

Meta-model validation