Eee Vii Power System Planning [10ee761] Notes

Power System Planning

10EE761

POWER SYSTEM PLANNING

Subject Code: 10EE761 No. of Lecture Hrs. / Week: 04 Total No. of Lecture Hrs. 52

IA Marks: 25 Exam Hours: 03 Exam Marks: 100 PART – A

UNIT - 1 Introduction of power planning, National and regional planning, structure of power system, planning tools, electricity regulation, Load forecasting, forecasting techniques, modeling. 8 Hours UNIT - 2 & 3 Generation planning, Integrated power generation, co-generation / captive power, power pooling and power trading, transmission & distribution planning, power system economics, power sector finance,financial planning, private participation, rural electrification investment, concept of rational tariffs. 10 Hours UNIT - 4 Computer aided planning: Wheeling, environmental effects, technological impacts, insulation co-ordination, reactive compensation.

green

house effect, 8 Hours

PART – B UNIT - 5 & 6 Power supply reliability, reliability planning, system operation planning, load management, load prediction, reactive power balance, online power flow studies, state estimation, computerized management. Power system simulator. 10 Hours UNIT - 7 & 8 Optimal Power system expansion planning, formulation of least cost optimization problem incorporating the capital, operating and maintenance cost of candidate plants of different types (thermal hydro nuclear non conventional etc), Optimization techniques for solution by programming. 16 Hours TEXT BOOK: 1. Electrical Power System Planning, A.S.Pabla, Macmillan India Ltd, 1998

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Table of Contents Sl.No 1

Chapters

Page no

Unit 1:Introduction of power planning, National and regional planning structure of power system, planning tools planning tools,

4-12

electricity regulation Load forecasting forecasting techniques, modeling. 2

Unit 2&3:Generation planning Integrated power generation co-generation / captive power power pooling and power trading transmission & distribution planning 13-23 power system economics power sector finance,financial planning private participation rural electrification investment concept of rational tariffs

3

Unit 4: Computer aided planning Wheeling 24-27 environmental effects green house effect

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technological impacts insulation co-ordination reactive compensation 4

Unit 5&6: Power supply reliability reliability planning system operation planning load management load prediction 28-32 reactive power balance online power flow studies state estimation computerized management Power system simulator.

5

Unit 7&8:Optimal Power system expansion planning. formulation of least incorporating the capital

cost

optimization

problem

operating and maintenance cost of candidate plants of 33-36 different types (thermal, hydro, nuclear, nonconventional etc), Optimization techniques for solution by programming

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UNIT-1

Introduction to Power System Planning: 

Recent cost reductions and the increases in production of solar photovoltaics (PV) are driving dramatic growth in domestic PV system installations.

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Programs such as Solar America Initiative are setting out to make solar energy costcompetitive with central generation by the year 2015.

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As the costs decline, distributed PV becomes an increasingly significant source of power generation and, at some point, its further growth might be limited by the challenges of its integration into the power grid.

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To prevent these integration challenges from limiting the growth of solar PV installations and to maximize the overall system benefit, it is necessary to consider solar PV in all areas of power system planning, and to evolve the planning practices to better accommodate increased energy supply from solar PV.

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This report reviews the entire power system planning process, including generation, transmission, and distribution. It discusses how the planning practices are changing to accommodate variable renewable generation, with a focus on future changes required to accommodate high penetration levels of solar PV and how to maximize the positive impact of other technologies such as load control and energy storage. The report also proposes several areas for future research that will help evolve planning methodologies and enable easier and more-effective integration of solar PV.

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Electricity produced by solar PV currently is not cost-competitive with electricity generated by central stations, consequently solar PV has limited penetration in grid-connected applications. As the technology develops and solar PV becomes more competitive, it is expected that it will start supplying residential and commercial loads at the customer‘s side of the meter. This area of the power system has the highest cost of electricity, therefore it is where cost-competitiveness will be achieved first.

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Understandably, a sharp increase in the use of any one source of generation is likely to present integration challenges, but this especially is the case with the distributed solar PV for the following reasons.

 Solar PV is a variable source of generation—its power output depends on insolation and it is subject to potentially abrupt changes due to cloud coverage.  Solar PV will evolve as a distributed source of generation first used to offset the connected load. As the penetration levels increase even further, two options are possible. Energy storage could be used to ensure that no power is returned to the system, and the power could be sent to other loads in the system to avoid capital investment for dedicated storage. The second option necessitates shipping power ―backwards‖ through a part of the electricity delivery network—the distribution system—and backwards power flow is not a design feature of present-day distribution systems.

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 The codes and standards that guide the integration of solar PV are focused on simplifying installations and prescribe grid interconnection requirements that cause minimal interaction with the grid. When solar PV becomes a significant overall source of generation in the power system, some of the present interconnection requirements likely will be counterproductive.

National and Regional Planning: 1. All issues relating to planning and development of Transmission System in the country are dealt in the Power System Wing of CEA. 2. This includes evolving long term and short term transmission plans. The network expansion plans are optimized base on network simulation studies and techno economic analysis. 3. This also involves formulation of specific schemes, evolving a phased implementation plan in consultation with the Central and State transmission utilities and assistance in the process of investment approval for the Central sector schemes, issues pertaining to development of National Power Grid in the country and issues relating to trans-country power transfer. 4. Transmission planning studies are being conducted to identify evacuation system from generation projects and to strengthen the transmission system in various regions. 5. The studies for long-term perspective plans are also being carried out on All India basis for establishing inter regional connectivity aimed towards formation of the National Power System. 6. The National Power System is being evolved to facilitate free flow of power across regional boundaries, to meet the short fall of deficit regions from a surplus region as well as for evacuation of power from project(s) located in one region to the beneficiaries located in other region(s).

Structure of Power System:

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1. An essential component of power systems is the three-phase ac generator known as synchronous generator or alternator. 2. The source of the mechanical power, commonly known as the prime mover, may be hydraulic turbines, steam turbines whose energy comes from the burning of coal, gas and nuclear fuel, gas turbines, or occasionally internal combustion engines burning oil. 3. The transformer transfers power with very high efficiency from one level of voltage to another level. The power transferred to the secondary is almost the same as the primary, except for losses in the transformer. 4. An overhead transmission network transfers electric power from generating units to the distribution system which ultimately supplies the load. 5. High voltage transmission lines are terminated in substations, which are called highvoltage substations, receiving substations, or primary substations. 6. The distribution system connects the distribution substations to the consumers‘ serviceentrance equipment. The primary distribution lines from 4 to 34.5 kV and supply the load in a well-defined geographical area. 7. Industrial loads are composite loads, and induction motors form a high proportion of these loads. These composite loads are functions of voltage and frequency and form a major part of the system load. Planning Tools: 1. Planning engineer‘s primary requirement is to give power supply to consumers in a reliable manner at a minimum cost with due flexibility for future expansion. 2. The criteria and constraints in planning an energy system are reliability, environmental economics, electricity pricing, financial constraints, society impacts. 3. reliability, environmental, economic and financial constraints can be quantified. Social effects are evaluated qualitatively. 4. The system must be optimal over a period of time from day of operation to the lifetime. 5. Various computer programs are available and are used for fast screening of alternative plans with respect to technical, environmental and economic constraints.

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The available tools for power system planning can be split into: Simulation tools: these simulate the behavior of the system under certain conditions and calculate relevant indices. Examples are load flow models, short circuit models, stability models, etc. Optimization tools: these minimize or maximize an objective function by choosing adequate values for decision variables. Examples are optimum power, least cost expansion planning, generation expansion planning, etc. Scenario tools: this is a method of viewing the future in a quantitative fashion. All possible outcomes are investigated. The sort of decision or assumptions which might be made by a utility developing such a scenario might be: should we computerize automate the management of power system after certain date.

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Least Cost Utility Planning: There are two fundamental problems inherent in traditional planning. The first is that demand forecasting and investment planning are treated as sequential steps in planning, rather than as interdependent aspects of the planning process. The second problem is that planning efforts are inadequately directed at the main constraints facing the sector, namely the serious shortage of resources. 1. Demand forecasts are little more than extrapolations of past trends of consumption, no attempt is made to understand neither the extent of unmet demand nor the extent to which the prices influence the demand growth. Greater attention should be paid to end use efficiency, plant rehabilitation, loss reduction program, etc. 2. Least cost planning (LCUP) is least cost utility planning strategy to provide reliable electrical services at lowest overall cost with a mix of supply side and demand side options. 3. The LCUP uses various options like end use efficiency, load management, transmission and distribution options, alternative tariff options, etc. 4. This planning process can yield enormous benefits to consumers and society because it affords acquisition of resources that meet consumer energy service needs that are low in cost, environmentally friendly. 5. LCUP as a planning and regulatory process can greatly reduce the uncertainty and risks faced by utilities. The logic for least cist planning is shown in the figure below:

6. For an investment to be least cost, the lifetime costs are considered. These include capital costs, interest on capital, fuel cost and operation and maintenance costs.

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Fig: flowchart for least cost planning Electricity Regulation: THE ELECTRICITY REGULATORY COMMISSIONS ACT, 1956 

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Act to provide for the establishment of a Central Electricity Regulatory Commission and state Electricity Regulatory Commissions, rationalization of electricity tariff, transparent policies regarding subsidies, promotion of efficient and environmentally benign policies and matters connected therewith or incidental there to. Be it enacted by Parliament in the Forty-ninth Year of the republic of India as follows:

STATEMENT OF OBJECTS AND REASONS 

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India's power sector is beset by problems that impede its capacity to respond to the rapidly growing demand for energy brought about by economic liberalisation. Despite the stated desire for reform and the initial measures that have been implemented, serious problems persist. As the problems of the Power Sector deepen, reform becomes increasingly difficult underscoring the need to act decisively and without delay. It is essential that the Government exit implement significant reforms by focussing on the fundamental issues

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facing the power sector, namely the lack of rational retail tariffs, the high level of crosssubsidies, poor planningand operation, inadequate capacity, the neglect of the consumer, the limited involvement of private sector skills and resources and the absence of an independent regulatory authority. 

Considering the paramount importance of restructure power sector, Government of India organised two Conferences of Chie Ministers to discuss the whole gamut of issues in the power sector and the outcome of these meetings was the adoption of the Common Minimum National Action Plan for Power (CMNPP).

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The CMNPP recognised that the gap between demand and supply of power is widening and acknowledged that the financial position of State Electricity Boards is fast deteriorating and the future development in the power sector cannot be sustained without viable State Electricity Boards and improvement of their operational performance.

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The CMNPP identified creation of regulatory Commission as a step in this direction and specifically provided for establishment of the Central Electricity Regulatory Commission (CERC) and State Electricity Regulatory commissions (SERCs). After the finalisation of the, national agenda contained in CMNPP, the Ministry of Power assigned the task of studying the restructuring needs of the regulatory system to Administrative Staff College of India (ASCI), Hyderabad. The ASCI report strongly recommended the creation of independent Electricity Regulatory Commissions both at the Centre and the States.

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To give effect to the aforesaid proposals, the Electricity Regulatory Commissions Bill. 1997 was introduced in the Lok Sabha on 14th August, 1997, However it could not be passed due to the dissolution of the Eleventh Lok Sabha.

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This has resulted in delay in establishing the Regulatory Commissions leading to confusion and misgivings in various sections about the commitment of the Government to the reforms and restructuring of the power sector. Needless to say, this has also slowed down the flow of public and private investment in power sector.

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Since it was considered necessary to ensure the speedy establishment of the Regulatory Commissions and as Parliament was not in session, the President promulgated the Electricity Regulatory Commissions Ordinance, 1998 on 25th day of April, 1998.

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The salient features of the -said Ordinance are as follows: (a) It provides for the establishment of a Central Electricity Regulatory Commission at the Central level and State Electricity Commissions at the State levels-, (b) The main functions of CERC are: -

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(i) To regulate the tariff of generating companies owned or controlled by the Central Government; (ii) To regulate inter-State transmission including tariff of the transmission utilities; (iii) To regulate inter-State sale of power; (iv) To aid and advise the Central Government in the formulation of tariff policy. (c) The main functions of the SERC, to start with, shall be: (i) To determine the tariff for electricity, wholesale, bulk, grid and retail; (ii) To determine the tariff payable for use of the transmission facilities; (iii) To regulate power purchase the procurement process of the transmission utilities; and (iv) Subsequently, as and when each State Government notifies, other regulatory functions could also be assigned to SERCS. (d) It also aims at improving the financial health of the State Electricity Boards (SEBS) which are loosing heavily on account of irrational tariffs and lack of budgetary support from the State Governments as a result of which, the SEBs have become incapable of even proper maintenance, leave alone purposive investment. Further, the lack of creditworthiness of SEBs has been a deterrent in attracting investment both from the public and private sectors.  Hence, it is made mandatory for State Commissions to fix tariff in a manner that none of the consumers or class of consumers shall be charged less than fifty per cent. of the average cost of supply, it enables the State Governments to exercise the option of providing subsidies to weaker sections on condition that the state Governments through a subsidy compensate the SEBS. 

As regards the agriculture sector, it provides that if the State Commission considers it necessary it may allow the consumers in the agricultural sector to be charged less than fifty per cent, for a maximum period of three years from the date of commencement of the Ordinance.

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It also empowers the State Government to reduce the tariff further but in that case it shall compensate the SEBs or its successor utility, the different between the tariff fixed by the State Commission and the tariff proposed by the State Government by providing budgetary allocations.Therefore, it enables the State Governments to fix any tariff for agriculture and other sectors provided it gives subsidy to State Electricity Boards to meet the loss.

Forecasting Techniques: Load forecasting is vitally important for the electric industry in the deregulated economy. It has many applications including energy purchasing and generation, load switching, contract evaluation, and infrastructure development. A large variety of mathematical methods have been developed for load forecasting. In this chapter we discuss various approaches to load forecasting.

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Forecasting Methods  Over the last few decades a number of forecasting methods have been developed. Two of the thods, so-called end-use and econometric approach are broadly used for medium- and long-term forecasting. Avariety of methods, which include the so-called similar day approach,various regression models, time series, neural networks, expert systems,fuzzy logic, and statistical learning algorithms, are used for short-term forecasting.  The development, improvements, and investigation of the appropriate mathematical tools will lead to the development of more accurate load forecasting techniques.Statistical approaches usually require a mathematical model that represents load as function of different factors such as time, weather, and customer class.  The two important categories of such mathematical models are: additive models and multiplicative models. They differ in whether the forecast load is the sum (additive) of a number of components or the product (multiplicative) of a number of factors. For example, Chen et al. [4] presented an additive model that takes the form of predicting load as the function of four components: L = Ln + Lw + Ls + Lr, where L is the total load, Ln represents the ―normal‖ part of the load,which is a set of standardized load shapes for each ―type‖ of day that has been identified as occurring throughout the year, Lw represents the weather sensitive part of the load, Ls is a special event component that create a substantial deviation from the usual load pattern, and Lr is a completely random term, the noise.  A multiplicative model may be of the form L = Ln · Fw · Fs · Fr, where Ln is the normal (base) load and the correction factors Fw, Fs, and Fr are positive numbers that can increase or decrease the overall load. These corrections are based on current weather (Fw), special events (Fs), and random fluctuation (Fr). Factors such as electricity pricing (Fp) and load growth (Fg) can also be included. Rahman [29] presented a rulebased forecast using a multiplicative model. Weather variables and the base load associated with the weather measures were included in the model. Forecasting Modeling

Depends on 1. Degree of Accuracy Required 2. 2 Cost of Producing Forecasts 3. 3 Forecast Horizon 4. 4 Degree of Complexity Required 5. 5 Available Data Classification of Estimation Methods 1. Time Series Methods 2. Causal Methods 3. Judgemental Methods Time Series Methods: Use historical data as a basis, Underlying patterns are fairly stable. 1. Autoregressive Moving Average (ARMA) Dept. of EEE, SJBIT

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Exponential Smoothing Extrapolation Linear Prediction Trend Estimation Growth Curve Box-Jenkins Approach

Causal Methods Belief that some other time series can be useful. Assumption that it is possible to identify the underlying factors 1. 2. 3. 4.

Regression Analysis Linear Regression Non-Linear Regression Econometrics

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Generation Planning The electric utility planning process begins with the electricity load-demand forecast. The demand for electricity initiates actions by utilities to add generation, transmission, or distribution capacity. Because of the long lead time required to construct new facilities, decisions are often to be made 2 to 10 years in advance. A load forecast was developed for the Kingdom and the results are presented in the following sections covering the study period 2008 to 2023. Load forecasts are developed for all SEC operating areas. The methodology and the basis of development of demand forecast are highlighted below: ● Multiple regression analysis is used to forecast the Energy for the KSA. ● Independent variables are chosen to be the population and the Gross Domestic Product (GDP). ● The dependent variable is the Energy forecast for KSA. ● The data for the historical and the forecasted GDP has been obtained from the Ministry of Planning. The forecast for the total sold energy for the Kingdom was obtained using the regression model. The total sold energy was then divided between the four operating areas using historical value of percentage energy sales for each operating areas. This gives the total sold energy forecast for each of the operating areas. Peak Demand is calculated using the equation Forecasted Peak Demand in Region= Forecasted Energy in Region/8760*Load Factor. Co-Generation/ Captive Power Captive power plants are associated with specific industrial complexes, and their output is almost entirely consumed by that industrial plant. Another term that may sometimes be synonymous is 'cogeneration' in which the power plant produces multiple forms of energy (e.g., electric power and steam), and where both are raw-materials for a related industrial process. Probably the most classic example is that of a paper mill. Boilers produce steam. The steam passes through a turbine that spins a generator to produce electricity. Exhaust steam from the turbine is then used as a source of heat to dry freshly-made paper before is is finally condensed into water and returned to the boiler. The boiler itself burns the bark that itself cannot be used to make paper and would otherwise be a waste material. In addition, the process of making pulp produces a chemical waste called "black liquor' that can also be burned as a fuel in a boiler. Captive power plants don't necessarily have to be islands that are disconnected from 'the grid'. In fact, it is often the case that the demand of the industrial process exceeds the capacity of the captive plant, and power must be taken from the grid to make up the difference. Also, there must be some provision to 'bootstrap' the integrated process into operation - often this means relying Dept. of EEE, SJBIT

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on grid power to start-up the plant following an outage. And it is possible that there are times when the captive plant will produce more power than can be consumed in the industrial process, and rather than throttle back the excess is sold to the grid. TYPES OF COGENERATION SYSTEMS 1. Steam Turbine Cogeneration System Steam turbines are one of the most versatile and oldest prime mover technologies still in general production. Power generation using steam turbines has been in use for about 100 years, when they replaced reciprocating steam engines due to their higher efficiencies and lower costs. The capacity of steam turbines can range from 50 kW to several hundred MWs for large utility power plants. Steam turbines are widely used for combined heat and power (CHP) applications. 2. Back Pressure Steam Turbine A back pressure steam turbine is the simplest configuration. Steam exits the turbine at a pressure higher or at least equal to the atmospheric pressure, which depends on the needs of the thermal load. This is why the term back- pressure is used. It is also possible to extract steam from intermediate stages of the steam turbine, at a pressure and temperature appropriate for the thermal load. After the exit from the turbine, the steam is fed to the load, where it releases heat and is condensed.

Fig. Back Pressure Steam Turbine 3. Extraction Condensing Steam Turbine In such a system, steam for the thermal load is obtained by extraction from one or more intermediate stages at the appropriate pressure and temperature. The remaining steam is exhausted to the pressure of the condenser, which can be as low as 0.05 bar with a corresponding condensing temperature of about 33°C. It is rather improbable that such low temperature heat finds useful applications. Consequently, it is rejected to the environment. In comparison to the back - pressure system, the condensing type turbine has a higher capital cost and, in general, a lower total efficiency. However, to a certain extent, it can control the electrical power independent of the thermal load by proper regulation of the steam flow rate through the turbine. 4. Gas Turbine Cogeneration System Dept. of EEE, SJBIT

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Gas turbine systems operate on the thermodynamic cycle known as the Brayton cycle. In a Brayton cycle, atmospheric air is compressed, heated, and then expanded, with the excess of power produced by the turbine or expander over that consumed by the compressor used for power generation. Gas turbine cogeneration systems can produce all or a part of the energy requirement of the site, and the energy released at high temperature in the exhaust stack can be recovered for various heating and cooling applications (see Fig 4 below). Though natural gas is most commonly used, other fuels such as light fuel oil or diesel can also be employed. The typical range of gas turbines varies from a fraction of a MW to around 100 MW.

5. Closed-cycle gas turbine cogeneration systems In the closed-cycle system, the working fluid (usually helium or air) circulates in a closed circuit. It is heated in a heat exchanger before entering the turbine, and it is cooled down after the exit of the turbine releasing useful heat. Thus, the working fluid remains clean and it does not cause corrosion or erosion. As shown in Fig.5 below.

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6. Reciprocating Engine Cogeneration System Reciprocating engines are well suited to a variety of distributed generation applications, industrial, commercial, and institutional facilities for power generation and CHP. Reciprocating engines start quickly, follow load well, have good part-load efficiencies, and generally have high reliabilities. In many cases, multiple reciprocating engine units further increase overall plant capacity and availability. Reciprocating engines have higher electrical efficiencies than gas turbines of comparable size, and thus lower fuel-related operating costs.

Power Pooling: Power pooling is used to balance electrical load over a larger network (electrical grid) than a single utility. It is a mechanism for interchange of power between two and more utilities which Dept. of EEE, SJBIT

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provide or generate electricity. For exchange of power between two utilities there is an interchange agreement which is signed by them, but signing up an interchange agreement between each pair of utilities within a system can be a difficult task where several large utilities are interconnected. Thus, it is more advantageous to form a power pool with a single agreement that all join. That agreement provides established terms and conditions for pool members and is generally more complex than a bilateral agreement. In one model, the power pool, formed by the utilities, has a control dispatch office from where the pool is administered. All the tasks regarding interchange of power and the settlement of disputes are assigned to the pool administrator. The formation of power pools provide the following potential advantages: 1. decrease in operating costs 2. saving in reverse capacity requirements 3. help from pool in unit commitment 4. minimization of costs of maintenance scheduling 5. more reliable operation The formation of a power pool is associated with a number of problems and constraints. These include: 1. pool agreement may be very complex 2. costs associated with establishing central dispatch office and the needed communication and computational facilities 3. the opposition of pool members to give up their rights to engage in independent transactions outside the pool. 4. the complexity towards dealing with regulatory authorities, if pool operates in more than one state. 5. the effort by each member of the pool to maximize its savings. Power pooling is very important for extending energy control over a large area served by multiple utilities Power Trading In economic terms, electricity (both power and energy) is a commodity capable of being bought, sold and traded. An electricity market is a system for effecting purchases, through bids to buy; sales, through offers to sell; and short-term trades, generally in the form of financial or obligation swaps. Bids and offers use supply and demand principles to set the price. Long-term trades are contracts similar to power purchase agreements and generally considered private bi-lateral transactions between counterparties. Wholesale transactions (bids and offers) in electricity are typically cleared and settled by the market operator or a special-purpose independent entity charged exclusively with that function. Market operators do not clear trades but often require knowledge of the trade in order to maintain Dept. of EEE, SJBIT

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generation and load balance. The commodities within an electric market generally consist of two types: power and energy. Power is the metered net electrical transfer rate at any given moment and is measured in megawatts (MW). Energy is electricity that flows through a metered point for a given period and is measured in megawatt hours (MWh). Markets for energy-related commodities trade net generation output for a number of intervals usually in increments of 5, 15 and 60 minutes. Markets for power-related commodities required and managed by (and paid for by) market operators to ensure reliability, are considered ancillary services and include such names as spinning reserve, non-spinning reserve, operating reserves, responsive reserve, regulation up, regulation down, and installed capacity. In addition, for most major operators, there are markets for transmission congestion and electricity derivatives such as electricity futures and options, which are actively traded. These markets developed as a result of the restructuring of electric power systems around the world. This process has often gone on in parallel with the restructuring of natural gas markets.

Transmission and Distribution Planning: Electricity distribution is the final stage in the delivery of electricity to end users. A distribution system's network carries electricity from the transmission system and delivers it to consumers. Typically, the network would include medium-voltage (2kV to 34.5kV) power lines, substations and pole-mounted transformers, low-voltage (less than 1 kV) distribution wiring such as a Service Drop and sometimes meters. 

The modern distribution system begins as the primary circuit leaves the sub-station and ends as the secondary service enters the customer's meter socket by way of a service drop. Distribution circuits serve many customers.

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The voltage used is appropriate for the shorter distance and varies from 2,300 to about 35,000 volts depending on utility standard practice, distance, and load to be served. Distribution circuits are fed from a transformer located in an electrical substation, where the voltage is reduced from the high values used for power transmission.

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Conductors for distribution may be carried on overhead pole lines, or in densely populated areas, buried underground

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. Urban and suburban distribution is done with three-phase systems to serve both residential, commercial, and industrial loads. Distribution in rural areas may be only single-phase if it is not economical to install three-phase power for relatively few and small customers.

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Only large consumers are fed directly from distribution voltages; most utility customers are connected to a transformer, which reduces the distribution voltage to the relatively low voltage used by lighting and interior wiring systems.

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The transformer may be pole-mounted or set on the ground in a protective enclosure. In rural areas a pole-mount transformer may serve only one customer, but in more built-up areas multiple customers may be connected.

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In very dense city areas, a secondary network may be formed with many transformers feeding into a common bus at the utilization voltage. Each customer has a service drop connection and a meter for billing.

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A ground connection to local earth is normally provided for the customer's system as well as for the equipment owned by the utility. The purpose of connecting the customer's system to ground is to limit the voltage that may develop if high voltage conductors fall down onto lower-voltage conductors which are usually mounted lower to the ground, or if a failure occurs within a distribution transformer.

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If all conductive objects are bonded to the same earth grounding system, the risk of electric shock is minimized. However, multiple connections between the utility ground and customer ground can lead to stray voltage problems; customer piping, swimming pools or other equipment may develop objectionable voltages. These problems may be difficult to resolve since they often originate from places other than the customer's premises.

Distribution network configurations 

Distribution networks are typically of two types, radial or interconnected.

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A radial network leaves the station and passes through the network area with no normal connection to any other supply. This is typical of long rural lines with isolated load areas. An interconnected network is generally found in more urban areas and will have multiple connections to other points of supply.

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These points of connection are normally open but allow various configurations by the operating utility by closing and opening switches. Operation of these switches may be by remote control from a control center or by a lineman. The benefit of the interconnected model is that in the event of a fault or required maintenance a small area of network can be isolated and the remainder kept on supply.

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Within these networks there may be a mix of overhead line construction utilizing traditional utility poles and wires and, increasingly, underground construction with cables

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and indoor or cabinet substations. However, underground distribution is significantly more expensive than overhead construction. 

In part to reduce this cost, underground power lines are sometimes co-located with other utility lines in what are called common utility ducts. Distribution feeders emanating from a substation are generally controlled by a circuit breaker which will open when a fault is detected. Automatic circuit reclosers may be installed to further segregate the feeder thus minimizing the impact of faults.

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Long feeders experience voltage drop requiring capacitors or voltage regulators to be installed.

Characteristics of the supply given to customers are generally mandated by contract between the supplier and customer. Variables of the supply include: 

AC or DC - Virtually all public electricity supplies are AC today. Users of large amounts of DC power such as some electric railways, telephone exchanges and industrial processes such as aluminium smelting usually either operate their own or have adjacent dedicated generating equipment, or use rectifiers to derive DC from the public AC supply

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Nominal voltage, and tolerance (for example, +/- 5 per cent)

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Frequency, commonly 50 or 60 Hz, 16.7 Hz and 25 Hz for some railways and, in a few older industrial and mining locations, 25 Hz.

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Phase configuration (single-phase, polyphase including two-phase and three-phase)

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Maximum demand (some energy providers measure as the largest mean power delivered within a 15 or 30 minute period during a billing period)

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Load factor, expressed as a ratio of average load to peak load over a period of time. Load factor indicates the degree of effective utilization of equipment (and capital investment) of distribution line or system.

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Power factor of connected load

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Earthing systems - TT, TN-S, TN-C-S or TN-C Prospective short circuit current

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Maximum level and frequency of occurrence of transients

Power System Economics:  Power is the rate of flow of energy. Similarly, generating capacity, the ability to produce power is itself a flow. A megawatt (MW) of capacity is worth little if it lasts only a minute just as a MW of power delivered for only a minute is worth little.

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But a MW of power or capacity that flows for a year is quite valuable. The price of both power and energy can be measured in $/MWh, and since capacity is a flow like power and measured in MW, like power, it is priced like power, in $/MWh. Many find this confusing, but an examination of screening curves shows that this is traditional (as well as necessary). Since fixed costs are mainly the cost of capacity they are measured in $/MWh and can be added to variable costs to find total cost in $/MWh. When generation cost data are presented, capacity cost is usually stated in $/kW. This is the cost of the flow of capacity produced by a generator over its lifetime, so the true (but unstated) units are $/kW-lifetime. This cost provides useful information but only for the purpose of finding fixed costs that can be expressed in $/MWh. No other useful economic computation can be performed with the ―overnight‖ cost of capacity given in $/kW because they cannot be compared with other costs until ―levelized.‖ While the U.S. Department of Energy sometimes computes these economically useful (levelized) fixed costs, it never publishes them. Instead it combines them with variable costs and reports total levelized energy costs.This is the result of a widespread lack of understanding of the nature of capacity costs. Confusion over units causes too many different units to be used, and this requires unnecessary and sometimes impossible conversions.

Private Paticpation:  Private participation in 1991 to hasten the increase in generating capacity and to improve the system efficiency as well. However, although several plants are under construction, till early 1999, eneration had commenced at private plants totalling less than 2,000 MW. 

In contrast, some state undertakings have completed their projects even earlier than scheduled.Independent power producers (IPPs) claim that their progress has been hindered by problems such as litigation, financial arrangements, and obtaining clearances and fuel supply agreements. On the other hand, the State Electricity Boards have been burdened by power purchase agreements (PPAs) that favour the IPPs with such clauses as availability payment irrespective of plant utilization, tariffs reflecting high capital costs and returns on equity, etc.



The process of inviting private participation in the power sector and the problems experienced seem to have spurred on the restructuring of the power sector, including the formation of Central and State Electricity Regulatory Commissions.



However, some important problems have not been addressed. Additions to the generation capacity without corresponding improvement of the transmission and distribution facilities are likely to further undermine the system efficiency.

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What is more, issues like the reduction of "commercial losses" appear to have been ignored.Most importantly, investment in infrastructure has been a state responsibility because the intrinsically long gestation coupled with the relatively low returns from serving all categories of consumers have rendered such projects commercially unprofitable. Whether or not private participation can take on such tasks is to be seen.

Rural Electrification Investment:



Rural Electrification Corporation Limited (REC) is a leading public Infrastructure Finance Company in India‘s power sector.



The company finances and promotes rural electrification projects across India, operating through a network of 13 Project Offices and 5 Zonal Offices, headquartered in New Delhi. The company provides loans to Central/ State Sector Power Utilities, State Electricity Boards, Rural Electric Cooperatives, NGOs and Private Power Developers.



REC is a Navratna Company functioning under the purview of the Ministry of Power – Government of India. The company is listed on both National Stock Exchange of India and Bombay Stock Exchange.

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The company is primarily engaged in providing finance for rural electrification projects across India and provides loans to Central/ State Sector Power Utilities, State Electricity Boards, Rural Electric Cooperatives, NGOs and Private Power Developers.



The company sanctions loan as a sole lender or co-lender or in consortium with or without the status of lead financer. It also provides consultancy, project monitoring and financial/ technical appraisal support for projects, also in the role of nodal agency for Government of India schemes or projects. REC finances all types of Power Generation projects including Thermal, Hydel, Renewable Energy, etc. without limit on size or location.



The company aims to increase presence in emerging areas like de-centralised distributed generation (DDG) projects, and new and renewable energy sources to reach remote and difficult terrains not connected by power grid network.

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In Transmission & Distribution (T&D), REC is primarily engaged in ascertaining financial requirements of power utilities in the country in the T&D sector along with appraising T&D schemes for financing.

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REC has financed T&D schemes for system improvement, intensive electrification, pump-set energisation and APDRP Programme. The company is also actively involved in physical as well as financial monitoring of T&D schemes.

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

REC also offers loan products for financing Renewable Energy projects. The company has tied up a line of credit for EUR 100 mn(approximately 6000 mn) with KfW under Indo-German Development Cooperation for financing renewable energy power projects at concessional rates of interest.



Eligible projects include Solar, Wind, Small Hydro, Biomass Power, and Cogeneration Power & Hybrid Projects.

Wheeling: 

In electric power transmission, wheeling is the transportation (megawatts or megavolt-amperes) over transmission lines.[1]



Electric power networks are divided into transmission and distribution networks. Transmission lines move electric power between generating facilities and substations, usually in or near population centers. From substations, power is sent to users over a distribution network. A transmission line might move power over a few miles or hundreds of miles.



An entity that generates power does not have to own power transmission lines: only a connection to the network or grid. The entity then pays the owner of the transmission line based on how much power is being moved and how congested the line is.

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Some power generating entities join a group which has shared ownership of transmission lines. These groups may include investor-owned utilities, government agencies, or a combination of these.



Since prices to move power are based on congestion in transmission line networks, utilities try to charge customers more to use power during peak usage (demand) periods. This is accomplished by installing time-of-use meters to recover wheeling costs.

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Computer aided Planning: With the increasing complexity of electrical power systems, the need for accurate tools for their design, planning and operation become a necessity. Investigations are made on the appropriate design tools for analyzing complicated energy system configurations under different contingencies in order to cope with the challenges. Education and training using these tools requires familiarization with software and hardware employed in this process. Studies shows that the new delivery modes using the full advantage of digital computers in a multi-media environment will improve the efficiency of instruction, and understanding of complex problems.

Environmental impact: 

The environmental impact of electricity generation is significant because modern society uses large amounts of electrical power. This power is normally generated at power plants that convert some other kind of energy into electrical power. Each system has advantages and disadvantages, but many of them pose environmental concerns.



The amount of water usage is often of great concern for electricity generating systems as populations increase and droughts become a concern. Still, according to the U.S. Geological Survey, thermoelectric power generation accounts for only 3.3 percent of net freshwater consumption with over 80 percent going to irrigation. Likely future trends in water consumption are covered here. General numbers for fresh water usage of different power sources are shown below.



Steam-cycle plants (nuclear, coal, NG, solar thermal) require a great deal of water for cooling, to remove the heat at the steam condensors. The amount of water needed relative to plant output will be reduced with increasing boiler temperatures. Coal- and gas-fired boilers can produce high steam temperatures and so are more efficient, and require less cooling water relative to output. Nuclear boilers are limited in steam temperature by material constraints, and solar is limited by concentration of the energy source.



Thermal cycle plants near the ocean have the option of using seawater. Such a site will not have cooling towers and will be much less limited by environmental concerns of the discharge temperature since dumping heat will have very little effect on water temperatures. This will also not deplete the water available for other uses. Nuclear power in Japan for instance, uses no cooling towers at all because all plants are located on the coast. If dry cooling systems are used, significant water from the water table will not be

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used. Other, more novel, cooling solutions exist, such as sewage cooling at the Palo Verde Nuclear Generating Station. 

Most electricity today is generated by burning fossil fuels and producing steam which is then used to drive a steam turbine that, in turn, drives an electrical generator.Such systems allow electricity to be generated where it is needed, since fossil fuels can readily be transported. They also take advantage of a large infrastructure designed to support consumer automobiles.



The world's supply of fossil fuels is large, but finite. Exhaustion of low-cost fossil fuels will have significant consequences for energy sources as well as for the manufacture of plastics and many other things. Various estimates have been calculated for exactly when it will be exhausted (see Peak oil). New sources of fossil fuels keep being discovered, although the rate of discovery is slowing while the difficulty of extraction simultaneously increases.



Nuclear power plants do not burn fossil fuels and so do not directly emit carbon dioxide; because of the high energy yield of nuclear fuels, the carbon dioxide emitted during mining, enrichment, fabrication and transport of fuel is small when compared with the carbon dioxide emitted by fossil fuels of similar energy yield.



A large nuclear power plant may reject waste heat to a natural body of water; this can result in undesirable increase of the water temperature with adverse effect on aquatic life.

Green House Effect: The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases. Solar radiation at the frequencies of visible light largely passes through the atmosphere to warm the planetary surface, which then emits this energy at the lower frequencies of infrared thermal radiation. Infrared radiation is absorbed by greenhouse gases, which in turn re-radiate much of the energy to the surface and lower atmosphere. The mechanism is named after the effect of solar radiation passing through glass and warming a greenhouse, but the way it retains heat is fundamentally different as a greenhouse works by reducing airflow, isolating the warm air inside the structure so that heat is not lost by convection.

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Insulation Co-ordination: 





The term Insulation Co-ordination was originally introduced to arrange the insulation levels of the several components in the transmission system in such a manner that an insulation failure, if it did occur, would be confined to the place on the system where it would result in the least damage, be the least expensive to repair, and cause the least disturbance to the continuity of the supply. The present usage of the term is broader. Insulation co-ordination now comprises the selection of the electric strength of equipment in relation to the voltages which can appear on the system for which the equipment is intended. The overall aim is to reduce to an economically and operationally acceptable level the cost and disturbance caused by insulation failure and resulting system outages. To keep interruptions to a minimum, the insulation of the various parts of the system must be so graded that flashovers only occur at intended points. With increasing system voltage, the need to reduce the amount of insulation in the system, by proper coordination of the insulating levels become more critical.

Reactive compensation: 









Except in a very few special situations, electrical energy is generated, transmitted, distributed, and utilized as alternating current (AC). However,alternating current has several distinct disadvantages. One of these is the necessity of reactive power that needs to be supplied along with active power. Reactive power can be leading or lagging.While it is the active power that contributes to the energy consumed, or transmitted, reactive power does not contribute to the energy. Reactive power is an inherent part of the ‗‗total power.‘‘ Reactive power is either generated or consumed in almost every component of the system, generation, transmission, and distribution and eventually by the loads. The impedance of a branch of a circuit in an AC system consists of two components, resistance and reactance. Reactance can be either inductive or capacitive, which contribute to reactive power in the circuit.Most of the loads are inductive, and must be supplied with lagging reactive power. It is economical to supply this reactive power closer to the load in the distribution system.Reactive power compensation in power systems can be either shunt or series.

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Shunt Capacitors: Shunt capacitors are employed at substation level for the following reasons:  Reducing power losses Compensating the load lagging power factor with the bus connected shunt capacitor bank improves the power factor and reduces current flow through the transmission lines, transformers, generators, etc. This will reduce power losses (I2R losses) in this equipment.  Increased utilization of equipment Shunt compensation with capacitor banks reduces kVA loading of lines, transformers, and generators, which means with compensation they can be used for delivering more power without overloading the equipment. Reactive power compensation in a power system is of two types—shunt and series. Shunt compensation can be installed near the load, in a distribution substation, along the distribution feeder, or in a transmission substation.  Voltage regulation The main reason that shunt capacitors are installed at substations is to control the voltage within required levels. Load varies over the day, with very low load from midnight toearly morning and peak values occurring in the evening between 4 PM and 7 PM. Shape of the load curve also varies from weekday to weekend, with weekend load typically low.  Shunt Reactive Power Compensation Since most loads are inductive and consume lagging reactive power, the compensation required is usually supplied by leading reactive power. Shunt compensation of reactive power can be employed either at load level, substation level, or at transmission level.  It can be capacitive (leading) or inductive (lagging) reactive power, although in most cases compensation is capacitive. The most common form of leading reactive power compensation is by connecting shunt capacitors to the line.  As the load varies, voltage at the substation bus and at the load bus varies. Since the load power factor is always lagging, a shunt connected capacitor bank at the substation can raise voltage when the load is high. The shunt capacitor banks can be permanently connected to the bus (fixed capacitor bank) or can be switched as needed. Switching can be based on time, if load variation is predictable, or can be based on voltage, power factor, or line current.

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Power Supply Reliability:  The term reliability is broad in meaning. In general, reliability designates the ability of a system to perform its assigned function, where past experience helps to form advance estimates of future performance.  Reliability can be measured through the mathematical concept of probability by identifying the probability of successful performance with the degree of reliability. Generally, a device or system is said to perform satisfactorily if it does not fail during the time of service. On the other hand, a broad range of devices are expected to undergo failures, be repaired and then returned to service during their entire useful life.  In this case a more appropriate measure of reliability is the availability of the device, which is defined as follows:  The indices used in reliability evaluation are probabilistic and, consequently, they do not provide exact predictions. They state averages of past events and chances of future ones by means of most frequent values and long-run averages. This information should be complemented with other economic and policy considerations for decision-making in planning, design and operation. The function of an electric power system is to provide electricity to its customers efficiently and with a reasonable assurance of continuity and quality.  The task of achieving economic efficiency is assigned to system operators or competitive markets, depending on the type of industry structure adopted. On the other hand, the quality of the service is evaluated by the extent to which the supply of electricity is available to customers at a usable voltage and frequency. The reliability of power supply is, therefore, related to the probability of providing customers with continuous service and with a voltage and frequency within prescribed ranges around the nominal values. Load management:  Load management, also known as demand side management (DSM), is the process of balancing the supply of electricity on the network with the electrical load by adjusting or controlling the load rather than the power station output.  This can be achieved by direct intervention of the utility in real time, by the use of frequency sensitive relays triggering circuit breakers (ripple control), by time clocks, or by using special tariffs to influence consumer behavior.  Load management allows utilities to reduce demand for electricity during peak usage times, which can, in turn, reduce costs by eliminating the need for peaking power plants. In addition, peaking power plants also often require hours to bring on-line, presenting challenges should a plant go off-line unexpectedly.

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Load management can also help reduce harmful emissions, since peaking plants or backup generators are often dirtier and less efficient than base load power plants. New load-management technologies are constantly under development — both by private industry and public entities.

Load Prediction: Electric load forecasting is the process used to forecast future electric load, given historical load and weather information and current and forecasted weather information. In the past few decades, several models have been developed to forecast electric load more accurately. Load forecasting can be divided into three major categories:  Long-term electric load forecasting, used to supply electric utility company management with prediction of future needs for expansion, equipment purchases, or staff hiring  Medium-term forecasting, used for the purpose of scheduling fuel supplies and unit maintenance  Short-term forecasting, used to supply necessary information for the system management of day-to-day operations and unit commitment. Reactive Power balance: The balance for the reactive power in a whole- or a part of a system is the next: ΣQE+QI=ΣQF+QH, where: ΣQE is the amount of the reactive power from the power plants QI is the balance of the imported reactive power flows (incoming is the positive) ΣQF is the amount of the substations reactive power consumptions QH is the amount of the system elements reactive power consumptions (wires, cables, transformers, reactors, static compensators, etc.). The reactive power flows from the capacitors and overexcited generators called reactive power production, the under excited generators and inductances reactive power called reactive power consumption. The reactive power is positive, if the current is delaying to the voltage, while the active power is positive compared to the power flows on an arbitrary system element S=P+jQ. These principles considers to the high/middle voltage level systems, but there is no reason to not to use in micro/smart grid systems as well. Online power flow studies: In power engineering, the power-flow study, also known as load-flow study, is an important tool involving numerical analysis applied to a power system. A power-flow study usually uses simplified notation such as a one-line diagram and per-unit system, and focuses on various forms of AC power (i.e.: voltages, voltage angles, real power and reactive power). It analyzes the power systems in normal steady-state operation. A number of software implementations of power-flow studies exist. Dept. of EEE, SJBIT

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

Many software implementations perform other types of analysis, such as shortcircuit fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch. In particular, some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per kilowatt hour delivered.



Power-flow or load-flow studies are important for planning future expansion of power systems as well as in determining the best operation of existing systems. The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive power flowing in each line.



Commercial power systems are usually too large to allow for hand solution of the power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory models of power systems; large-scale digital computers replaced the analog methods.



Newton-Raphson method is the most widely accepted load flow solution algorithm. However LU factorization remains a computationally challenging task to meet the realtime needs of the power system.



The application of very fast multifrontal direct linear solvers for solving the linear system sub-problem of power system real-time load flow analysis by utilizing the state-of-the-art algorithms for ordering and preprocessing.



Additionally the unsymmetric multifrontal method for LU factorization and highly optimized Intel Math Kernel Library BLAS has been used. Two state-of-the-art multifrontal algorithms for unsymmetric matrices namely UMFPACK V5.2.0 and sequential MUMPS 4.8.3 (―Multifrontal Massively Parallel Solver‖) are customized for the AC power system Newton-Raphson based load flow analysis.



The multifrontal solvers are compared against the state-of-the-art sparse Gaussian Elimination based HSL sparse solver MA48. This study evaluates the performance of above multifrontal solvers in terms of number of factors, computational time, number of floating-point operations and memory, in the context of load flow solution on nine systems including very large real power systems.



The results of the performance evaluation are reported. The proposed method achieves significant reduction in computational time.

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State Estimation: State estimators allow the calculation of these variables of interest with high confidence despite measurements that are corrupted by noise measurements that may be missing or grossly Inaccurate. Objectives:  To provide a view of real-time power system conditions  Real-time data primarily come from SCADA SE supplements SCADA data: filter, fill, smooth.  To provide a consistent representation for power system security analysis  On-line dispatcher power flow  Contingency Analysis  Load Frequency Control  To provide diagnostics for modeling & maintenance Computerized management: Research shows that personal computers (PC) are not being actively used during the vast majority of the time that they are kept on. It is estimated that an average PC is in use 4 hours each work day and idle for another 5.5 hours. It's also estimated that some 30-40 percent of the US's work PCs are left running at night and on weekends. Office equipment is the fastest growing electricity load in the commercial sector. Computer systems are believed to account for 10 percent or more of commercial electricity consumption already. Since computer systems generate waste heat, they also increase the amount of electricity necessary to cool office spaces. For the Medical Center, we estimate the savings from PC power management to be hundreds of thousands of dollars annually, even without factoring in increased office cooling costs. Considerable savings are also possible from easing wear-and-tear on the computers themselves. Power System Simulator: Power system simulation models are a class of computer simulation programs that focus on the operation of electrical power systems. These computer programs are used in a wide range of planning and operational situations including: 1. Long-term generation and transmission expansion planning 2. Short-term operational simulations 3. Market analysis (e.g. price forecasting)

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These programs typically make use of mathematical optimization techniques programming, quadratic programming, and mixed integer programming.

such linear

Key elements of power systems that are modeled include: 1. Load flow (power flow study) 2. Short circuit 3. Transient stability 4. Optimal dispatch of generating units (unit commitment) 5. Transmission (optimal power flow)

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Optimal Power System Expansion Planning: Optimization Techniques: In everyday life, all of us are confronted with some decision makings. Normally, we try to decide or the best. If someone is to buy a commodity, he or she tries to buy the best quality, yet with the east cost. These types of decision makings are categorized as optimization problems in which the aim is to find the optimum solutions; where the optimum may be either the least or the most. Most of the operational and planning problems consist of the following three major steps • Definition • Modeling • Solution algorithm Decision variables are the independent variables; the decision maker has to determine their optimum values and based on those, other variables (dependent) can be determined. For instance, in an optimum generation scheduling problem, the active power generations of power plants may be the decision variables. The dependent variables can be the total fuel consumption, system losses, etc. which can be calculated upon determining the decision variables. In a capacitor allocation problem, the locations and the sizing of the capacitor banks are the decision variables, whereas the dependent variables may be bus voltages, system losses, etc. Mathematical Algorithms. A mathematical optimization technique formulates the problem in a mathematical representation; as given by (2.2) through (2.4). Provided the objective function and/or the constraints are nonlinear, the resulting problem is designated as Non Linear optimization Problem (NLP). A special case of NLP is quadratic programming in which the objective function is a quadratic function of x. If both the objective functions and the constraints are linear functions of x, the problem is designated as a Linear Programming (LP) problem. Other categories may also be identified based on the nature of the variables. For instance, if x is of integer type, the problem is denoted by Integer Programming (IP). Mixed types such as MILP(Mixed Integer Linear Programming) may also exist in which while the variables may be both real and integer, the problem is also of LP type. For mathematical based formulations, some algorithms have, so far, been developed; based on them some commercial software have also been generated. In the following subsections, we briefly review these algorithms. We should, however, note that generally speaking, a mathematical algorithm may suffer from numerical problems and may be quite complex in implementation. However, its convergence may be guaranteed but finding the global optimum solution may only be guaranteed for some types such as LP. There is no definite and fixed classification of mathematical algorithms. Here, we are not going to discuss them in details. Instead, we are going to introduce some topics which are of more interest in this book and may be applicable to power system planning issues.1 Some topics, such as game theory, which are of more interest for other power system issues (such as market analysis of power ystems), are not addressed here.

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Calculus Method: These types of methods are the traditional way of seeking optimum points. These are applicable to continuous and differentiable functions of both objective and constraints terms. They make use of differential calculus in locating the optimum points. Based on the basic differential calculus developed for finding the optimum points of C(x) , the method of Lagrange Multipliers has been developed in finding the optimum points; where equality constraints may also apply. If inequality constraints (2.4) are also applicable, still the basic method may be used; however, the so called Kuhn-Tucker conditions should be observed. The solution is not so straightforward in that case. Linear Programming (LP) Method: As already noted, LP is an optimization method in which both the objective function and the constraints are linear functions of the decision variables. This type of problem was first recognized in the 1930s by the economists in developing methods for the optimal allocation of resources. Noting the fact that • Any LP problem can be stated as a minimization problem; due to the fact that, as already described, maximizing C(x) is equivalent to minimizing (-C(x)). The problem can be stated in a form known as canonical. Then, a solution known as the simplex method, first devised in 1940s, may be used to solve the problem. Using the simplex method normally requires a large amount of computer storage and time. The so called revised simplex method is a revised method in which less computational time and storage space are required. Still another topic of interest in LP problems is the duality theory. In fact, associated with every LP problem, a so called dual problem may be formulated. In many cases, the solution of an LP problem may be more easily obtained from the dual problem. If the LP problem has a special structure, a so called decomposition principle may be employed to solve the problem in which less computer storage is required. Non Linear Programming (NLP) Method: We noted earlier that if the objective function and/or the constraints are nonlinear functions of the decision variables, the resulting optimization problem is called NLP. Before proceeding further on NLP problems, we should note that most practical problems are of constrained type in which some constraint functions should be satisfied. As for constrained problems, however, some algorithms work on the principle of transforming the problem into a unconstrained case, we initially review some existing algorithms on solving unconstrained problems. The solution methods for unconstrained problems may be generally classified as direct search (or nongradient) methods and descent (or gradient) methods. The former methods do not use the partial derivatives of the objective function and are suitable for simple problems involving a relatively small number of variables. The latter methods require the evaluations of the first and possibly, the higher order derivatives of the objective function. As a result, these methods are generally more efficient than the direct methods. All the unconstrained optimization methods are iterative in nature and start from an initial trial solution; moving stepwise in a sequential manner towards the optimum solution. The gradient methods have received more attention in power system literature. For instance, in the so called steepest descent method; widely used in power system literature, the gradient vector is used to calculate the optimum step length along the search direction so that the algorithm efficiency is maximized.

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Let us come back to the constrained case. Two types of methods, namely, direct and indirect methods apply. In the former methods, the constraints are handled in an explicit manner, while in most of the latter methods; the constrained problem is converted into a sequence of unconstrained problems and solved through available algorithms. As an example of the direct methods, in the so called constraint approximation method, the objective function and the constraints are linearized about some point. The resulting approximated LP problem is solved using LP techniques. The resulting solution is then used to construct a new LP problem. The process is continued until a convergence criterion is satisfied. As an example of the indirect methods, the so called penalty function method, works on the principle of converting the problem into an unconstrained type. It is, in turn, classified as interior and exterior penalty function methods. In the former, the sequence of unconstrained minima lie in the feasible region while in the latter, they lie in the infeasible region. In both, they move towards the desired. Dynamic Programming (DP) Method: Dynamic Programming is a widely used technique in power system studies. It is, in fact, a mathematical technique used for multistage decision problems; originally developed in 1950s. A multistage decision problem is a problem in which optimal decisions have to be made over some stages. The stages may be different times, different spaces, different levels, etc. The important point is that the output of each stage is the input to the next serial stage. The overall objective function is to be optimized over all stages. It is normally a function of the decision variables (xi) of all stages. The important fact is that one cannot start from optimizing the first stage; moving forward toward the final stage; as there may be some correlations between the stages, too. To make the problem clear, let us express a power system example. Suppose we are going to minimize the generation cost of a power system over a 24-h period. Some information is as follows • There are four generation units available; each of which may be either off or on (so that various combinations are possible, such as, 1111, 1101, 1001, 0011,…). • The unit efficiencies are different; so that if the system load is low and say, two units can meet the load, we should use the higher efficient units to supply the load. • The load varies throughout the 24-h period; changing at each hour (stage). The multistage decision problem is, in fact, deciding on the units to be on at each stage so that the overall generation cost over the 24-h period is minimized. We note that if no other constraint was imposed, we should optimize our problem at each stage and sum it over all stages. In other words, 24 single stage optimization problems2 have to be solved to find the final solution. Suppose that the final solution looks like Fig. 2.5 in which the unit combinations are shown at each stage. As shown, unit 1 is on at hours 1 and 2, off at hour 3, and on again at hour 4. Now what happens if a constraint is imposed expressing the fact that if unit 1 is turned off, it cannot be turned on unless a 5-h period is elapsed. Integer Programming Method: In the algorithms discussed so far, each of the decision variables may take any real value. What happens if a decision variable is limited to take only an integer value? For instance, if the decision variable is the number of generation units, taking a real value is meaningless. The optimization algorithms developed for this class of problems are classified as IP methods. If all decision variables are of integer type, the problem is addressed as IP problem. If some decision variables are of integer type while some others are of non-integer type, the problem is known as Dept. of EEE, SJBIT

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mixed integer programming problem. Moreover, based on the nature of the original problem, both integer linear programming and integer nonlinear programming methods have been developed. As a result, in power system literature, some terms such as MILP have appeared. 2.3.2 Heuristic Algorithms Most mathematical based algorithms can guarantee reaching an optimal solution; while do not necessarily guarantee reaching a global optimum. Global optimality may be only reached, checked or guaranteed for simple cases. On the other hand, many practical optimization problems do not fall in strict forms and assumptions of mathematical based algorithms. Moreover, if the problem is highly complex, we may not readily be able to solve them, at all, through mathematical algorithms. Besides, finding global optimum is of interest, as finding a local one would be a major drawback. Heuristic algorithms are devised to tackle the above mentioned points. They, normally, can solve the combinatorial problems, sometimes very complex, yet in a reasonable time. However, they seek good solutions, without being able to guarantee the optimality, or even how close the solutions are to the optimal point.

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