GIS-Based Simulation Studies for Power Systems Education

Transcription

1 Electric Power Networs Efficiency and Security, Edited by Laine Mili and Jaes Mooh. ISBN XXXXX-X Copyright 2000 Wiley[Iprint], Inc. Chapter 4.2 GIS-Based Siulation Studies for Power Systes Education Ralph D. Badinelli 1, Virgilio Centeno 2, Boonyarit Intiyot 3 1. Professor, Departent of Business Inforation Technology, Paplin College of Business, Virginia Tech 2. Associate Professor, Bradley Departent of Electrical Engineering, Virginia Tech 3. Graduate Research Assistant, Departent of Industrial and Systes Engineering, Virginia Tech Editor s Suary: This chapter advocates the application of two educational ethods, naely case studies and decision odeling, as the best way to teach design and anageent ethods in power systes. A saple of case studies is presented, which includes public policy studies aied at transission and generation expansion subject to a cap on electricity prices and generation eissions. The second educational approach aes use of the structured decision odeling under ultiple, conflicting perforance easures; the objective is to see a set of desirable and feasible solutions aong nuerous alternatives. As illustrative exaples, the authors discuss several interesting case studies that deal with the selection of the right site and size of DG or of FACTS to itigate instabilities in power systes. Furtherore, exaples of siulation results are presented to illustrate the cost, spatial, and teporal relationship of the interconnection of the DG to the distribution feeders. A very coprehensive forulation of unit coitent is exained too. The chapter also includes the description of the woring software pacage that the authors developed. Tered the Virginia Tech Electricity Grid and Maret Siulator (VTEGMS), the ain coponent of this pacage aes use of

2 object-oriented prograing as a eans to axiize the robustness and flexibility of the software. A good reference of available optiization ethods and siulation pacages are suarized in the quoted references and in a table of coparison of software. $.1 Overview In this chapter we prescribe coputer siulation as a robust tool that should be integrated into any coprehensive educational curriculu in the field of power systes design, engineering and anageent. Our advocacy of coputer siulation is based on the essential role that this ethodology plays in two foundational eleents of power systes education case studies and decision odeling. These eleents, in turn, are necessary in the education of future power-syste designers, engineers and anagers who need to understand the ever-expanding coplexities of these systes fro the points of view of their any staeholders. Coputer siulation is unique aong odeling techniques to support case analysis and decision odeling for such coplex systes. In conjunction with case studies, text and lecture aterials coputer siulation fors a flexible educational support syste (ESS). In this chapter we will provide an overview of the role of case analysis and decision odeling in power-systes education and the basic eleents of siulation odels along with an explanation of the essential role they play in this education. We are otivated by two concoitant features of the educational landscape. First, the iportant role played by power systes in the econoic health, environental quality and national security of the United States and other countries has becoe evident. As a consequence, operation, design and anageent of power systes have becoe disciplines that are gaining in popularity and iportance. Second, the operation, design and anageent of power systes involve large nubers of inter-related systes that are utually dependent in atheatically coplex ways. New developents in generation technologies, aret deregulation, environental regulations, reliability standards and security concerns are aggravating the coplexity and interdisciplinary nature of this topic. New and existing personnel in the fields of power-syste engineering, grid operation, power plant control, energy portfolio anageent, public- 2

3 policy and consulting deand up-to-date and holistic education in the rapidly changing power-systes discipline. Decision aing is the coon foundation of all of the challenges in the fields entioned above and we view all learners as future decision aers. Hence, our design of educational tools will revolve around decision analysis. Exaples of the decision doains that our educational tool ust support include, Public policy decision probles - environental policy planning, aret regulation planning, infrastructure planning Engineering decision probles protection syste design, generation and transission technology selection Business decision probles generation capacity planning, unit coitent, optial dispatch, deand side response, trading strategy, financial ris anageent For each of these decision probles the cause-effect relationship between decision alternatives and ey perforance indicators (KPI) such as cost, reliability, pollution, aret equity, etc. ust be understood and analyzed by the decision aer. For the learner, odeling the decision of a case study is the ost effective ethod for identifying the tradeoffs inherent in the KPIs. The learning process can be brought to fruition only by quantifying these tradeoffs and experienting with the cause-effect relationship inherent in each decision a tas that deands coputer siulation. Electric generation units, power grids and energy arets for a coplex syste that evolves over tie through the decisions of syste anagers, engineers, unit operators and aret participants as well as through the influence of weather, load variation, aret prices, forced outages and the physical behavior of networ coponents. Soe of these influences have a rando coponent to their variations over tie aing the trajectory of the power syste stochastic. Coputer siulation is unique aong odeling techniques in its ability to capture the effects of nuerous interacting influences as well as of randoness on the perforance of a syste. Furtherore, the raw output of a siulation in the for of the trajectory of perforance easures over tie can be suarized in statistically valid ways to evaluate the long-run behavior of a syste over tie and over a representative saple of rando scenarios. 3

4 $.1.1 Case studies A case study is a presentation of a proble in the context of realistic conditions, people and events. Unlie traditional textboo probles, a case study does not present a well-forulated proble but rather a situation of conflicting needs and desires instigated by the disparate points of view of various staeholders. Each case presents the learner with a situation in which a decision is needed. The learning process is pursued through the learner s attepts to create a odel of the decision proble and to use the odel to deterine the best choice of alternatives. See Bodily, 2004 [7]. Case studies are the ost effective for of learning assignent for the education of professionals for several reasons (see Barnes, Christensen, and Hansen, 1994 and Wasseran, 1994): Students becoe active instead of passive learners. Students learn by doing. Students are forced to define questions, not just answers. Students ust identify, respect and consider several points of view on a proble. Students are forced to apply theory in order to create structure for the case as opposed to applying a structured ethod to a well-defined, contrived proble. Students are forced to coproise and loo for worable, feasible solutions when there are conflicting needs and constraints. Students acquire general proble-solving sills within a field of study instead of ere forulaic solution ethods that, in real situations, ust be applied with odifications and adjustents in consideration of assuptions that are not et and factors that were ignored in the developent of the ethods. Students gain aturity and confidence by facing the abiguity of realistic cases. In every industry the decision probles that coprise the public policy, engineering and anageent naturally fall into a hierarchical order. The solutions to decision probles that have long-ter consequences and that are updated infrequently becoe paraeters that influence decisions that have shorter-ter consequences and that can be updated ore frequently. For exaple, the choice of technology for a new 4

5 generation unit will influence the way that this unit is coitted and dispatched. Hence, a hierarchy of decisions eerges in which longer-range, less-frequent decisions are placed above shorter-range, ore frequent decisions. We assert that a holistic understanding of a subject such as the design, engineering and anageent of power systes requires the learner to attept to solve all of the essential decision probles associated within this subject as well as to see these decision probles in their hierarchical order. A collection of case studies in hierarchical order integrated with text and lecture aterial coprises a well-designed educational experience for future professionals in the field of powers systes. The list below fors such a collection. These cases include probles of operating a conventional power syste as well as probles of designing and operating power systes of the future. Level 1: Public Policy Cases How to set the eissions liits on generation units in a given power grid How to liit the prices that can be cleared in a given power aret How to liit the prices that can be charged to different consuer groups in a given power aret Where to install new transission lines, gas pipelines or publicly-owned generation in a given power grid Level 2: Power Systes Design Cases How to select non-traditional generation technologies for distributed generation (DG) How to select the best location for DG. How to select the type of generation plant to add to a given power grid How to plan the installation of new capacity in a given power grid How to coordinate protective devices for a given power grid. How and where to change protection coordination for DG. How to select fast, alternating-current transission (FACT) devices to strengthen transission systes. 5

6 How to coordinate protections and placeent of FACT devices for voluntary islanding during catastrophic events. How to deterine locations that are exposed to catastrophic hidden failures. Level 3: Power Systes Manageent Cases How to set circuit breaer liits in a given power grid How to configure FACT controllers. See Acha, et. al., How to coit the generation units to a given power grid How to dispatch the generation units in a given power grid How to bid or offer energy in a wholesale energy aret for a given power grid How to configure a portfolio of financial derivatives to support the ris anageent of an energy trading position within a given power aret How to coit and dispatch generation units to a power grid that is practicing various fors of o DSR o environental restrictions o aret regulations o deand growth rates o fuel cost volatility How to encourage consuers to shape load in order to balance cost and convenience. The educational cases have several unique characteristics that carry the learner through these decisions in a realistic anner: Interactive students are able to change different aspects of a power syste s eleents, arets or regulatory environent in order to experient with different scenarios for the configurations of physical assets, tie series of loads and failures, location and type of generation, contractual arrangeents between custoers and suppliers and regulatory constraints. For each scenario entered by a student, the KPIs of the syste ust be coputed by a coputerized odel. 6

7 Realistic the educational cases are based on prototypes of real and proposed power systes, arets and regulatory environents. Configurable the developent of a case-based ESS will yield not only a saple of case studies for use in courses, but also structures for the database, student interface and cases that can be odified with new data for the developent of new case studies. Clearly, a qualitative overview of the decision probles listed above does not prepare a prospective power systes engineer, anager or regulator for the real world. An understanding of the tradeoffs presented by these decision probles requires a quantitative analysis of the. Decision support systes that are ore sophisticated than a collection of siple forulas are necessary. Specifically, our case analyses require decision support systes that ebody atheatical decision odels. Many powerful ethodologies for building and optiizing decision odels have been developed over the last fifty years. The lexicon of odeling tools includes coputer siulation, linear prograing, integer prograing, nonlinear prograing, dynaic prograing and any others. Mooh (2004) provides a coprehensive overview of decision odels for power-syste cases and their associated optiization ethods. Although these ethodologies have been available for several decades, they have not enjoyed rapid adoption by businesses and institutions. One reason for their slow adoption is that ost people find odel forulation very difficult. The coputerized tools for describing and prescribing solutions can be applied only after a descriptive decision odel has been created -- a tas that generally is accoplished through the art and science of an operations researcher who understands the proble doain and the structure of decision odels. For the practicing anager or analyst, odel application is the process that delivers business perforance. Therefore, our educational goal is to teach the application of odels to the decision probles described earlier. A general understanding of the structure of decision odels and their application is necessary for both the learner and the teacher. We provide such an overview below. 7

8 $.1.2 Generic decision odel structure A decision odel quantifies the cause-effect relationships between actions and outcoes. The outcoes of an action are expressed in ters of perforance easures, which, for any decision alternative, are used by the decision aer to deterine the alternative s feasibility and desirability. For exaple, the perforance easures for the unit dispatch decision in a given tie period include the total cost of generation across all dispatched units, the total grid power loss, the line load on each transission line, the load coverage for each load bus, the reliability of the syste, etc. To the challenge of quantifying these perforance easures we propose the application of decision odels. Models are the brains within a decision support syste that transfor asses of data into nowledge. In order to specify the scope of the decision the odeler categorizes the causative factors into two sets: a set of controllable factors that are used to define the alternatives available to the decision aer and a set of uncontrollable influences on the perforance easures. The alternatives of a decision represent the choices, options or actions that a decision aer is epowered to execute within the scope of a given decision. Matheatically, we ust represent these alternatives in ters of a well-defined set of data eleents that we call decision variables. For exaple, the alternatives for the unit dispatch decision in a given tie period can be represented by the set of power output values for each generation unit that is available. This vector of power output values would constitute the decision variables for this decision. Aong all of the possible sets of values for the decision variables, the decision aer sees the one that yields the ost desirable, feasible perforance. This solution is called the optial solution to the decision proble for which the odel is built. The uncontrollable factors of a decision are the influences on the perforance easures that cannot be chosen by the decision aer. We call these uncontrollable factors paraeters. For exaple, the paraeters of the unit dispatch decision for a given tie period include the capacities of each available generation unit, the theral capacity of each transission line, the real and reactive load at each load bus, the coefficients of the operating cost function of each available generation unit, etc. A paraeter could 8

9 reain constant throughout the analysis or could be a rando variable. If soe paraeters are rando variables, then the perforance easures that depend on these paraeters also are rando variables a characteristic of the odel that earns it the label stochastic. Paraeters, or their probability distributions, ust be easured, estiated or forecasted in order to build the database for a decision odel. Contrary to coon belief, the presence of rando paraeters does not preclude the application of decision odels. In fact, the ability to odel decision-aing under conditions of uncertainty can be considered the highest for of the odeler s science. In order to construct a stochastic odel we ust ae use of the probability distributions of the rando paraeters. Doing so requires specification of these probability distributions as, for exaple, the estiates of the ean and the standard deviation define the probability distribution of a norally distributed paraeter and the coefficients and volatility of a ean-reversion forecasting forula define the probability distribution of a future coodity price. Perforance easures that cannot be predicted with certainty introduce the eleent of ris into the decision. In these cases, the distributions of rando perforance easures ust be suarized over all scenarios into easures that capture both ris and reward. For exaple, for the unit dispatch decision in a given tie period the total cost of generation is a rando variable because the total load is not nown with certainty in advance. Variations in the load fro its forecasted value are handled by autoatic dispatch of reserve power. Consequently, the actual total cost of power generated during the given tie period can be predicted by a decision odel only up to the probability distribution of this cost. Suarizing this probability distribution over all possible load scenarios in ters several suary easures such as the distribution s ean and its upper and lower quartile points gives the decision aer a representation of expected financial cost as well as the ris associated with this cost. Most decision alternatives associated with the design and anageent of a power syste have raifications that extend over long tie horizons. The trajectory of a perforance easure over a tie horizon can exhibit various inds of cyclic, trended or eory-influenced behavior. In order to provide useful indicators of the perforance of an alternative, a decision odel ust suarize these trajectories over a tie horizon 9

10 that is long enough to capture all of the tie-varying behavior of the perforance easures. For exaple, for the unit dispatch decision over ultiple tie periods the total cost of generation will exhibit fluctuations and eory due to load variation over tie, load oentu, generator startup costs and raping constraints. Suarizing the tie series of generation cost in ters of its tie average provides the decision aer with a useful indicator of overall cost perforance. When a odel suarizes perforance easures over rando scenarios and over tie, as necessary, the resulting easures are called ey perforance indicators (KPI) as they are used directly to evaluate the feasibility and desirability of each alternative. In order to specify the feasibility and desirability of perforance, the decision aer iposes a decision criterion on each KPI. There are two possible fors for each criterion: a KPI can be constrained fro above or below in order to ipose bounds on perforance or a KPI can be axiized or iniized in order to pursue perforance to its greatest possible extent. The cause-effect relationships fro decision variables and paraeters to KPI s for a descriptive decision odel. The qualifier descriptive indicates that the odel s value is to predict or describe the perforance of a syste for a hypothetical set of inputs to that syste. Hence, a coputerized descriptive odel provides the decision aer with an efficient eans to test any proposed alternative and a trial-and-error capability for searching for the best alternative. Given enough tie, the decision aer can arrive at an alternative that yields optial or near-optial, feasible perforance. Soe decision odels can also help select the best course of action fro aong an overwhelingly large set of alternatives. An extension of a descriptive odel engages a coputerized search algorith that, in effect, autoatically perfors an, intelligent trial-and-error procedure for the decision aer. Such an extended odel is called a prescriptive odel. Prescriptive odels provide draatically enhanced decision support when a decision involves so any feasible alternatives that anual trial-and-error is ipractical. The first step in building a decision odel is to define data eleents and to derive the atheatical relationships that constitute the descriptive odel. The categories of data eleents are: 10

11 Decision variables Paraeters Perforance easures KPI s Criteria $-1 shows the general structure of a decision odel. The ost iportant perspective to draw fro Figure $-1 is the fact that a descriptive odel fors the core of a prescriptive odel. Furtherore, the search routine of the prescriptive odel is usually perfored by a coercially available code of a search algorith (e.g., linear prograing, integer prograing, etc.). However, the rest of the construction in Figure $-1, without which the search routine is useless, is the responsibility of the odeler. 11

12 OPT Optial Solution Prescriptive Model Search Routine An optial solution is found by intelligent trial-anderror evalution of the criteria for different choices of the DV's CRIT Criteria evaluation feasibility and desirability Decision Criteria Each KPI is placed in a constraint or the objective function Descriptive Functions Scenario & Tie Suary DV Decision Variables Cause-effect relationships fro decision variables and paraeters to perforance easures PM Perforance easures Perforance easures that are rando variables or tie-varying are suarized into one or a few easures KPI Key perforance indicators PARMS Model Paraeter Database Descriptive Model DB MS Power Syste Database Figure $-1: The data flow of descriptive and prescriptive odels $.1.3 Siulation odeling Decisions related to power systes have outcoes (perforance easures) that play out over a long tie and that can tae on any scenarios due to randoness in syste paraeters such as loads and aret prices. Furtherore, the relationship between decision variables and perforance easures for power-systes decision probles is typically very coplex and nonlinear. Of all of the fors of decision odeling, siulation is uniquely capable of capturing coplex cause-effect relationships, tie varying perforance easures and stochastic effects. In fact, for any of the 12

13 decision probles that the learner needs to odel, siulation is the only odeling technique that can produce a reasonably accurate descriptive odel. For exaple, siulation can be used to identify the vulnerabilities of the protection syste propted by the interconnection of DG to a distribution feeder. By coparing the total DG shortcircuit contribution passing through protection devices with the pic up settings of the devices the required protection coordination changes for a specific DG location can be deterined, Depablos (2004). Figure $-2 shows a siulation of a fault at bus 2 that results in a DG short-circuit contribution greater than the pic up setting of the protective device B. This will clearly result in iss-operation of unit B and unnecessary loss of load. Figure $-2: Effect of DG insertion in the coordination of protective devices. Every siulation odel is a coputerized description of a syste. A syste can often be visualized as a collection of interacting operations with flows of aterial, power, cash or other coodities aong the. The siulation odel tracs the state of the syste as it evolves over tie through the occurrence of events such as changes in load, outages, unit dispatching, short circuits and the passage of tie. In order to do this a siulation odel is created in the for of a coputer progra that consists of the following fundaental eleents. Rando Nuber Generator Event Scheduler 13

14 State Transition Procedures Syste State Data Manageent Perforance Measure Output Through the creation of an artificial cloc that ars siulated syste tie the siulation progra schedules the events that cause the syste to evolve. Transitions in the state of the syste tae place at points in tie deterined by the Event Scheduler. In the case of a typical siulation of a power grid, the Event Scheduler would be prograed to update the tie on an hourly basis. At each of these transition ties, the State Transition Procedures update the state of the siulated power syste to reflect changes caused by the events that occur at the transition tie. The current state of the syste is represented by the Syste State Data. The Syste State Data is used by the Perforance Measure Output routines to store values of perforance easures over the tie period that has just ended. Once the updated perforance easures are filed, the siulation progra returns to the Event Scheduler to process the next syste-changing event. Soe of the state-changing events, such as load variations and outages ay be the result of rando effects. Coputer siulation odels are able to introduce rando events into the event schedule through the use of rando nuber generators. Through this echanis, coputer siulation odels can represent realistically the perforance that results fro planned syste interventions as well as unplanned syste influences. Events are defined by the odeler in ters of the siplest changes that can tae place in the syste that is odeled. By odeling the detailed interactions of syste coponents over sall intervals of tie and aggregating the results of these interactions coplex behavior can be described through the use of nuerous, relatively siple transition procedures. In fact, coputer siulation is the only odeling technique that can capture the coplexity and randoness of a typical power syste. In a siulation odel of a power syste, the power flows through each networ eleent and the cash flows associated with the power flows can be odeled for each hour of each day. Fro hour to hour, the siulation progra updates the 14

15 status of each generation unit, load and networ eleent and stores this status in coputer eory. The perforance easures of the power syste are coputed and the results filed. Another siple exaple of siulation odeling is found in the case of the unit dispatch decision. The siulation odel for this decision would copute, for any given dispatching plan and for any given scenario of loads, the total generation cost as well as other perforance easures. $-3 portrays a tie series of generation costs over a 24-hour period for one scenario of loads. This tie series would be suarized ost appropriately in ters of its average. A siulation odel could generate this tie series if the scenario of loads was provided as input paraeters. We call the coputation of perforance easures over a tie horizon for one scenario of paraeters a replication of the siulation odel. Generation Cost Tie Series $ thousands Hour Figure $-3: Generation cost tie series exaple In order to assess the KPI s of ris and expected cost of a dispatching plan, we would lie to copute the generation cost over any 24-hour tie horizons, each one 15

16 of which represents one possible scenario. In this way we obtain a representative saple of syste perforance fro the population of all possible scenarios. Figure $-4 shows a saple of scenarios of the tie series of generation cost. By coputing the tie average of each of these tie series we obtain an overall easure of perforance for that scenario. Table $-1 shows these tie averages and Figure $-4 shows the distribution of the saple of costs given in Table $-1. Finally, we suarize the data in Table $-1 by coputing their average and the value at ris evidenced by these data. Value at ris is a easure of financial ris that is coonly used in the energy industry. In this case, we copute VAR as follows: VAR = C 90 μ c where μc = the ean cost, estiated fro the saple to be 1,774 and C90 = the cost at the 90 th percentile point of the distribution of costs, estiated fro the saple to be 1,850. The two easures of expected cost and VAR are KPI s for the dispatching decision odel that capture the expected financial value of the dispatching plan and a easure of financial ris associated with the dispatching plan. Gen Cost Scenarios $ thousands Hour Figure $-4: Generation cost scenarios 16

17 Table $-1: Scenario Averages Scenario Average Cost Average= 1774 VAR= 76 Distribution of Cost < 1,691 1,691-1,744 1,744-1,797 1,797-1,850 > 1,875 Figure $-5: Distribution of Saple of Costs 17

18 $.1.4 Interfacing As a practical atter, a coputerized educational support syste is effective only if its interfaces for learners and teachers are transparent and easy to learn. To these users of a siulation progra, the siulation is a tool for analyzing tradeoffs associated with decisions related to the design and anageent of a power syste. Clearly, the underlying details of the siulation odel, such as rando nuber generators, statistical evaluation of perforance easures, event scheduling should be hidden fro these users. The learner s interface to the siulation pacage should be designed for entry of decision variables and viewing of KPI s that result fro these settings of the decision variables. The teacher s interface should include the ability to odify the paraeter database in order to create different configurations of a power syste for different sets of learners. One of the ost natural representations of the assets of a power syste is that of a geographic inforation syste (GIS). A GIS is fundaentally a database of objects, each of which can be indexed by a location in ters of an x-coordinate, a y-coordinate and elevation coupled with a graphical interface that displays these objects on a ap. Generation units, power lines, transforers, substations, and buildings or other sites where loads occur can be represented in a GIS database and displayed on a coputer screen so that a learner or a teacher can see clearly the coponents that ae up the power syste under study. In addition, GIS provides a connection that perits lining the physical and econoic databases of the electric grid to available sociopolitical databases, opening the possibility to study the effect public policy, public perception and other sociopolitical factors that influence decision aers in real systes. Coupling the GIS syste to the siulation progra provides a sealess interface for the user between data entry and KPI s. Figure $-6 shows a flow chart of the ind of ESS that we advocate in this paper. 18

19 User Case Study Siulation Experiental Design 1 GIS User Interface GIS Database & Case Configurator Reliability, Security, Volue Grid Perforance Profit, Ris Business Sector Perforance Cost, Reliability, Ris Consuer Sector Perforance 2 GIS/EGMS Interface GIS Database & Case Configurator 3 EGMS Electricity Grid and Maret Siulator Generators, Loads, Lines, Protections Grid Configuration Energy Maret Configuration Contracts, Marets, Dealers,Policies Derivatives Maret Configuration Contracts, Marets, Dealers, Policies Figure $-6: Data Flow Diagra of ESS The Electricity Grid and Maret Siulator (EGMS) is a crucial part of the siulation progra. Because of the odular nature of the coponents in an energy grid, object oriented prograing (OOP) is a good choice of coding paradig for EGMS. In OOP, the coputer progra consists of objects. An object pacages data (or properties) and data processing functions (or ethods) into one unit. For exaple, a Tie object ay contain hour, inute, and second as its properties. The ethods of Tie object ay include assigning values to these properties and printing the in different tie forats. The way an object-oriented progra wors is that the objects counicate with one another by sending and receiving essages aong the. A essage that an object receives can be an inquiry for a property of the object or a request for the object to perfor one of its ethods. After receiving essages fro other objects, an object will process the data, and send the result to other objects. OOP has been widely-used in large- 19

20 scale software developent for years because of the odularity, expandability, and reusability of the code. Unlie the traditional prograing, eeping the OOP code up-todate is relatively easy and cost-effective. These advantages are so copelling that we cannot iagine coding an EGMS without OOP. In order to progra EGMS using OOP, we define the following ain objects: 1. Grid Operations Model (GOM) is an object that siulates planning, scheduling, dispatching and controlling an electrical grid. 2. Ris Manageent Model (RMM) is an object that assesses the financial ris and develops strategies to anage it. 3. Energy Maret Model (EMM) is an object that evaluates aret perforance. 4. Syste Configuration Model (SCM), Siulation Controller (SC), Output Strea Suarizer (OSS), Output Statistical Analyzer (OSA) are objects for the anageent of the siulation progra, data entry and output reporting. Figure $-7 depicts the relationships aong these objects. When the siulator runs, GOM reads the grid configuration, siulates the electricity flows, and updates the grid perforance. RMM reads the grid perforance and derivatives aret configuration, perfors ris analysis, and updates the ris portfolio perforance. EMM reads the ris portfolio perforance as well as the aret configuration and grid perforance and outputs the consuer sector perforance and business-sector perforance. All of these events are executed for each tie interval of the siulation. 20

21 User Horizon, Reps, Factors 3.1 SCM Syste Configuration Model Updates the database that defines electrical grid and energy arets Siulation Experient Design 3.5 SC Siulation Controller Generates Rando Nubers Schedules Iterations Records Output Scenarios Contracts, Marets, Dealers, Policies Energy Maret Configuration Generators, Loads, Lines, Protections Contracts, Marets, Dealers, Policies Price Variations Price Variations Cost, Reliability, Ris 3.2 EMM Energy Maret Model Profit, Ris Consuer Perforance Business Perforance Ris Portfolio Perforance Cash Flows 3.3 RMM Ris Manageent Model 3.6 OSS Output Strea Suarizer Suarizes the output streas fro each replication Replication Suary Grid Configuration Derivatives Maret Configuration Reliability, Security, Volue, Spot Prices Grid Perforance 3.7 OSA Output Statistical Analyzer Load Variations 3.4 GOM Grid Operations Model Response Surface Load Variations Load Variations DFD level 2 Figure $-7: Data flow diagra of EGMS To siulate the power flows with GOM, we need to solve a set of power-flow optiization probles (see Mooh 2001). Solving such optiization probles is the 21

22 ost coputationally intensive part of the siulator. Since the flows ust be updated for every siulated tie interval, the speed of the siulator could becoe a proble if the code for solving the optiization probles is not efficient. Writing an efficient optiization routine fro scratch could be very tie-consuing. Fortunately, soe proprietary software pacages, such as CPLEX and IMSL, provide routines for these purposes. With years of research and developent invested in these software pacages, their routines are proven to be efficient and reliable. Consequently, the construction of EGMS should be integrated with these routines. 22

23 $.2 Concepts for odeling power syste anageent and control The deterination of optial power flow in a grid over a sequence of tie periods can be odeled as a set of decisions and actions that execute the worings of the energy arets and the technical control of the electricity grid. In the operation of real energy arets and grids as well as in a siulation of these systes, the operational decisions are supported by coputerized odels. These odels anifest several challenging features of atheatical odeling and optiization, which we describe below in a constructive sequence. $.2.1 Large-scale optiization and hierarchical planning The control of arets and electricity grids requires coordinated decision-aing across five decision doains. 1. Configuring: installed generation capacity, grid configuration, aret regulations 2. Planning: bi-lateral contracts, wholesale bids & offers, unit availability 3. Scheduling: unit coitent, ancillary service contracts, reserve requireents 4. Dispatching: unit dispatch, deand anageent, regulation 5. Controlling: voltage control, frequency control, circuit protection The large nuber of variables that these decisions encopass classifies this collection of decisions as a large-scale optiization proble. There is no practical decision-support syste that can siultaneously optiize all of these decisions. Consequently, power grid and aret anageent is carried out through the application of soe conventional heuristic approaches. A heuristic approach that is often used is one that is based on a hierarchical sequence of decisions that lead, through successive levels of detail, to a final solution. The basic idea behind hierarchical planning is that the solution to a rough-cut representation of a decision in ters of aggregated decision variables can serve as a set of guidelines and constraints for a refined decision in ters of detailed decision variables. In other words, the final solution to a proble can be achieved by first coarse-tuning the solution and then fine-tuning the solution. In the case of energy grid anageent, the conventional hierarchy of decision aing confors to the ordered list shown earlier. For exaple, the probles of 23

24 deterining the unit availability, unit coitent and unit dispatch are all related through perforance easures such as profit and service level, which depend on all of these three decisions. Rather than attept to find solutions to all three decisions siultaneously so that a globally optial solution is obtained, a hierarchical planning approach would specify three separate decisions to be solved in stages. The deterination of unit availability, based on approxiate representations of total deand over the upcoing wee, provides capacity constraints on the coitent and dispatching decisions. The coitent decision, based on a forecast of load variations over the next 36 hours for which real-tie dispatching will be needed, consues the bul of the generation capacity and leaves a judicious aount of capacity for support of the ibalance dispatching decisions. The intuitive appeal of this approach is found in the selection of decision variables for each level of the hierarchical planning process. The first level generally, involves strategic decisions that have long-ter effects such as unit availability. The second level involves decision variables that describe how the available assets are to be coitted. The third level involves decision variables that describe how coitted assets are to be dispatched. The fourth level and fifth levels involve decision variables that describe how dispatched assets are to be controlled. Under the hierarchical schee, long-range, strategic decisions are ade first. These decisions then ipose constraints on the shorter-range, ore detailed decisions that follow. At each level the plan for the entire syste is developed in ore detail. The approxiation inherent in hierarchical planning is introduced in the odeling of the perforance of lower-level solutions at any stage in the hierarchy. In order to siplify each stage s proble, the effects of the lower-level decision variables on the current stage s constraints and the objective function are approxiated. In turn, the solution to a higher-level proble specifies constraints on the next lower-level proble, and so on. Using the hat notation to indicate approxiations, the hierarchical planning approach is described as follows: Suppose we have four sets of decision variables x 1,x2,x3, x4 for the following decision odel, 24

25 ax f ( x1,x2,x3,x4 ) subject to: g ( x g... g 1 2 n ( x ( x 1 1 1,x,x,x 2 2 2,x,x,x 3 3 3,x,x,x ) 0 ) 0 ) 0 By approxiating the effects of variables x 2,x3, x4 we construct the following aggregate planning proble. fˆ 1( x1 ) f ( x 1,x 2,x 3,x 4 1 j ( x1 ) g j ( x1,x2,x3,x ) for j = 1,..., n ĝ 4 The first optiization in the hierarchy is, ax fˆ( x1 ) x 1 subject to: ĝ ĝ... ĝ n ( x ) 0 1 ( x ) 0 1 ( x ) 0 1 ) Resulting in a solution, x 1, which becoes a paraeter in for all of the succeeding probles. The second approxiate decision odel is, 2 2 ) f ( x 1 fˆ ( x,x 2,x 3,x ĝ2 j ( x2 ) g j ( x1,x2,x3,x4 ) 4 ) ax fˆ( x1,x2 ) x 2 subject to: ĝ ĝ... ĝ n ( x ( x ( x 1 1 1,x,x,x ) 0 ) 0 ) 0 The reaining optiization probles are forulated in a siilar anner. 25

26 $.2.2 Sequential decision processes and adaptation The control of arets and electricity grids ust be done on a continuous basis, which necessitates ongoing decision-aing regarding the supply availability, deand anageent, unit coitent, dispatching, ancillary services and regulation. For practical reasons, the planning horizon is divided into discrete tie periods and the planning decisions are expressed and solved in ters of actions for each period. Of course this discrete representation of the tie scale for a process that changes continuously introduces an approxiation. However, the notion of developing a plan in finer and finer detail as each level of hierarchical planning is executed applies to the tie scale as well. Higher-level, ore strategic decisions are given a longer planning horizon and longer planning periods. By their nature these decisions can be ade ore crudely than tactical or operational decisions. As one oves down the hierarchy of decisions, the planning horizons and the planning periods are ade shorter. Table $-2 shows the basic scope and definition of the five levels of hierarchical planning that ae up our odel of power grid anageent. Table $-2: Planning horizons and periods Decision Doain Planning Horizon (typical) Planning Period (typical) Configuring > 1 year > 1 onth Planning 1 day - 1 year 1 day Scheduling 36 hours 1 hour Dispatching 1 hour 5 inutes Controlling 0.5 hour < 5 seconds A sequential decision process (SDP) is sequence of decisions ade over tie in a way that each decision can adapt to the effects of all previous decisions and adapt to the outcoes of uncontrollable influences on the perforance easures. A general ethodology for optiizing SDP s is nown as decoposition or dynaic prograing. Dynaic prograing decoposes an optiization by segregating the decision variables into subsets and creates a group of nested optiization probles. For exaple, suppose we have four sets of decision variables x 1,x2,x3, x4 representing the actions that can be taen at each of four tie periods that ae up the planning horizon and p are the probability distributions of the rando variables that influence the 1,p2,p3, p4 26

27 perforance easures of the syste that is to be controlled. Each perforance easure ay be expressed in ters of soe easure of ris with respect to these rando influences. The decision odel for optiizing the plan can be stated, ax f ( x1,x2,x3,x4 ; p1,p2,p3,p4 ) subject to: g ( x,x,x,x ; p,p,p,p ) 0 1 g ( x,x,x,x ; p,p,p,p ) g ( x,x,x,x ; p,p,p,p ) 0 n The dynaic prograing ethodology transfors this optiization into a nested sequence of optiization probles with the decisions of later tie periods nested with the decisions of earlier tie periods. The optiization procedure starts with the innerost nested proble (last tie period) and wors in stages to the outerost proble (first tie period). A dynaic prograing forulation of the proble described above is built fro the following nested set of optiizations, ax ax ax ax f ( x1,x2,x3,x4 ; p1,p2,p3,p4 ) x 1 x 2 x3 x4 At each stage, the optiization procedure derives optial decision rules as opposed to optial decisions. A decision rule is a set of contingency-based decisions. In this case, the contingencies at any stage are the cobined effects of all outer decisions (not yet deterined by the optiization procedure) as well as the range of uncontrollable influences on the perforance easures over the tie periods prior to the stage s decision. Through this ethodology we can explicitly express the decision rule for each tie period in ters of the outcoes of the rando variables of all previous periods. Such a representation of the decision rule accurately portrays the real situation that is faced by the decision aer in each tie period. The correct solution to a stochastic, sequential decision process consists of the state-contingent decision rules generated by the dynaic prograing solution. However, the derivation of the large nuber of such decision rules that would be necessary for a proble as coplex as that of unit coitent and dispatch precludes 27

28 the use of dynaic prograing. Instead, planning for stochastic load and generation levels is achieved through the use of a control heuristic nown as rolling horizon and adaptation. This procedure is used coonly in the coitent and dispatching of generation units. Rolling horizon and adaptive control is executed through the cobination of three planning techniques: Rolling the plan: Plans are updated at regular intervals. The tie between updates is called the planning interval. Planning over a horizon: Each plan extends over a nuber of future tie periods. The tie over which a plan is derived called the planning horizon. Adapting the plan: At each update of the plan, the plan is adjusted within liits that are deterined by the syste s constraints on the rates at which resource flows can change. The planning horizon for each plan consists of a horizon over which the plan ust be frozen followed by a horizon over which adjustents are allowed. The boundary between the fixed portion of a plan and the adjustable portion of a plan is called the planning fence. In the case of electricity scheduling and dispatch there are four adaptation options. Table $-3 defines these options. Each option is constrained to be exercised within the capacities that are set by the capacity reservation decisions ade at a higher level of the decision-aing hierarchy (see previous section). The update intervals, planning horizons and tie fences given in Table $-3 are typical values in the operation of a large power grid. 28

29 Table $-3a: Capacity and deand constraints on scheduling options Scheduling option Capacity constraint Deand constraint Day-ahead unit coitent Day ahead offers Day-ahead bids Ibalance coitent Ibalance offers Ibalance bids Regulation reserve Regulation reserves Regulation forecast coitent Spinning reserve coitent offers Spinning reserves offers Control error forecast Table $-3b: Scheduling option paraeters Scheduling option Update interval Planning Tie fence horizon Day-ahead unit coitent 24 hours 36 hours 12 hours Ibalance coitent 24 hours 30 hour 6 hours Regulation reserves 8, 16 hours 9, 17 hours 1 hour Spinning reserves 8, 16 hours 9, 17 hours 1 hour Table $-3c: Capacity and deand constraints on dispatching options Dispatch/Control Capacity constraint Deand constraint option Day-ahead dispatch Day-ahead coitents Day-ahead coitents Real-tie dispatch Ibalance coitents Deand forecast Ancillary service Regulation reserve Regulation error regulation coitents Voltage/frequency control Spinning reserve coitents Control error feedbac Table $-3d: Dispatching option paraeters Dispatch/control option Update interval Planning Tie fence horizon Day-ahead unit coitent 8, 16 hours 9, 17 hours 1 hour Real-tie dispatch 1 hour 1.5 hours 30 inutes Ancillary service regulation 5 inutes 30 inutes 5 inutes Voltage/frequency control 4 seconds 30 seconds 4 seconds The approxiation that is inherent in a rolling horizon and adaptation procedure stes fro the use of a deterinistic forecast for each plan update. The accuracy of this forecast increases as the forecast horizon decreases. Consequently, the adaptation options with the shortest tie fences enjoy the ost accurate forecasts and can be viewed 29

30 as fine tuning actions with respect to the coarse tuning of the plans produced by the longer-fence options. $.2.3 Stochastic decisions and ris odeling Deand for electricity and, to a lesser degree, supply, are not nown with coplete certainty, a priori. For this reason, decisions regarding supply availability, deand anageent, unit coitent, dispatching, ancillary services and regulation involve soe ris. Such decisions are labeled stochastic. There are several approaches to coping with ris, all of which incorporate soe cobination of buffering and adaptation. In our odel we use a easure of financial ris nown as value-at-ris (VAR). For every business decision, the decision aer has soe desired level of financial perforance that is considered satisfactory. However, due to the uncertainties of the real world, the financial perforance of any decision is a rando variable that can tae on a range of values with probabilities given by a distribution that is nown through the odeling of the decision. Raning all of the scenarios for this rando variable according to their associated financial perforances, the decision aer can apply his/her own perspective on ris by specifying a probability that identifies the portion of these scenarios that constitute the downside ris of the decision. For exaple, a decision aer could consider the lowest-perforing 10% of scenarios as the downside potential of a decision. Once this probability is set, the iniu financial loss that the downside scenarios can generate, easured relative to the pre-defined satisfactory level of return, is called the value-at-ris. VAR is typically coputed over a ris horizon of one day and suffices to represent the exposure of a portfolio of contracts to downside ris fro falling prices or falling deand. Figure $-8 illustrates the concept of VAR. 30