The Indian power sector has a history of only about 125 years. It has come a long way from a single small hydro unit set up in Darjeeling in 1880, followed by commercial production and distribution in Kolkata in 1889. The Government of India has an ambitious mission of 'POWER FOR ALL BY 2012'. This mission would require that our installed generation capacity should be at least 2, 00,000 MW by 2012 from the present level of 1,14,000 MW. To be able to reach this power to the entire country an expansion of the regional transmission network and inter regional capacity to transmit power would be essential. The latter is required because resources are unevenly distributed in the country and power needs to be carried great distances to areas where load centers exist.

The transmission system planning in the country, in the past, had traditionally been linked to generation projects as part of the evacuation system. Ability of the power system to safely withstand a contingency without generation rescheduling or load-shedding was the main criteria for planning the transmission system. However, due to various reasons such as spatial development of load in the network, non-commissioning of load centre generating units originally planned and deficit in reactive compensation, certain pockets in the power system could not safely operate even under normal conditions. This had necessitated backing down of generation and operating at a lower load generation balance in the past. Transmission planning has therefore moved away from the earlier generation evacuation system planning to integrated system planning.

With the National Power Grid expected to be in place by the end of the Eleventh Plan (that is, 2012), the interregional capacity is likely to be augmented from 17,000 MW at present to 37,700 MW, enabling scheduled and unscheduled exchange of power, boosting open access and encouraging competition in the power market. Open access means enabling non - discriminatory sale/purchase of electricity between two parties, utilizing the transmission/distribution systems of a third party, and not blocking it on unreasonable grounds. According to Para 5.3.2 of the National Electricity Policy, 2005, “Network expansion should be planned and implemented keeping in view the anticipated transmission needs that would be incident on the system in the open access regime''.

In traditional power system planning, generation planning is the core while transmission planning is based on generation planning. In deregulated environment generation planning is mainly a decision-making issue of generating companies or investors, and transmission planning is done separately in response to expected changes in the generation/load patterns. Therefore as the electric loads grow, transmission expansion planning should be carried out in timely and proper way to facilitate and promote competition.

The following are some of the main objectives of transmission planning in the deregulated environment:

• Encouraging and facilitating competition among electric market participants
• Providing non discriminatory access to cheap generation for all consumers.
• Providing a robust transmission network against uncertainties.
• Providing fair supply-side reserve for all generators and fair demand-side reserve for all consumers.
• Being value based instead of cost or reliability based.

Restructuring and deregulation of the power sector has changed the objectives of Transmission Expansion Planning (TEP) and increased the uncertainties.

In deregulated environment there is random uncertainty in,

• Load
• Generation costs and consequently in bid of generators
• Power and bid of IPPs
• Wheeling transactions
• Availability of generators, lines and other system facilities And non-random uncertainty in,
• Generation expansion/closures
• Load expansion/closures
• Installation/closure of other transmission facilities
• Replacement of transmission facilities
• Transmission expansion costs
• Market rules

In transmission planning it is generally true that “everything depends on everything else”. A power system is a complex network of injections and withdrawals of power flowing according to physics on multiple system lines and elements. Adding a new transmission line affects the flows on the entire network and will change the incentives for location of generation and the costs to loads. The human mind simply cannot deal with such complexity and therefore transmission infrastructure decisions must be informed by use of transmission modeling. Building a transmission line changes the economics of generation investment and location decisions. It also changes the economics of consumption decisions and distributed generation investments. And of course, the reverse is true, that investments in central station and distributed generation and changes in consumption decisions change the economics of transmission. Again, models are essential in measuring and predicting these effects and developing consensus among governmental entities, such interested stakeholders as environmental groups, and generation, transmission and end-user investors. In this paper we are reviewing two models namely PLEXOS and SDDP that are currently employed worldwide for transmission expansion planning.

PLEXOS is an electricity market simulation model developed by Drayton Analytics (www.drayton analytics.com and www.PLEXOS.info). This discussion provides background and motivation for the architecture and design philosophy of PLEXOS, then reviews salient features with reference to transmission modeling and long-term planning.

3.1. Architecture

Drayton Analytics recognized the need for a simulation model that is easily and efficiently maintained, extended, and modified and can be applied with no customization to every electricity market and modeling project. Clearly this required a paradigm shift in concept and design. The simulation architecture lays a foundation in which to cast the transmission-modeling problem, not a hardwired solution.

The solution simulations are founded in mathematical programming (MP) techniques (LP, QP, MIP, and DP8), which ensure the simulation outcomes are robust, consistent across scenarios, justifiable, and auditable. MP also provides valuable dual as well as primal solution information, such as the marginal value of a transmission expansion. Optimization code speed is improving as fast as computer speed, thus simulation performance is increasing rapidly, in many cases now out performing traditional rule-based approaches while providing compelling advantages.

The traditional approach to simulation is to decide the solution method, then build the model to populate the required data. In contrast, Dynamic Formulation (DF) developed by Glenn Drayton in 1996 and implemented in this model, allows the software to decide the solution approach and formulation based on data at runtime. In this approach, the data model is a framework for describing the "problem" (electricity simulation / transmission planning), and the 'engine' dynamically builds the optimization problem(s) at runtime 'from scratch'. The advantages are,

• the software can scale to any problem size;
• the analyst controls simulation performance by 'switching' data on/off–thus allowing exploration of tradeoffs between simulation runtime and result accuracy;
• there is no hardwired functional specification – model capabilities can be expanded at will; and
• simulation performance is maximized (problem size minimized) because the optimization problems are built at runtime to suit the data.

Further, the analyst may define any 'generic' constraint, which can involve a combination of decision variables or input data used inside the simulation. For example, complex transmission constraints such as transient stability or voltage restrictions may be modeled in a linear or piecewise linear form. Thus the data structures implement a flexible, comprehensive, efficient, and easily extensible object model.

3.2. Modeling Capabilities

The planning horizon length and resolution is fully configurable and any sized dispatch period can be modeled. PLEXOS includes a thermal model with unit commitment and inter-temporal constraints. The transmission OPF is fully integrated with the production model. Medium-term (MT) and short-term (ST) modeling are fully integrated. PLEXOS MT Schedule models energy, fuel, emission and any other user-definable constraints that span days, weeks, months, or years and automatically "decomposes" them to shorter term constraints suitable for detailed modeling in ST Schedule. Hydro resources e.g. pumped storage, as well as longand short-term storages are optimized – even detailed cascading hydro networks can be modeled. Energy and ancillary services co-optimization is comprehensive and fully integrated[10].

PLEXOS includes a comprehensive Monte Carlo model for generator and transmission forced outage modeling. Maintenance timing is also dynamic and can be optimized to account for transmission availability, i.e. reserve sharing between areas. Any input can be stochastic – commonly used examples are demand, hydro, and fuel prices. Any combination of historical sequences as samples or synthesized sequences based on input expected values and error distributions can be modeled. Solution of multiple sample runs is seamless, and statistics are produced on all outputs, e.g. distributions of augmentation benefits can be derived rather than provided just as a point estimate.

Any number of data scenarios can be set up in one database. Execution can be batched and automated from other programs. Thus, scenario analyses can be automated, and transmission expansion benefits can be calculated with 'the push of one button'. Reporting is comprehensive and easily extensible (new outputs can be added easily).

The optimal operation of a hydrothermal system determines, among many things, an operational strategy that produces generation targets for each hydro plant at each stage of the planning period. This strategy should minimize the expected value of the operational cost along the period, composed of fuel cost and penalties for failure to supply load. This is a very complex problem. It corresponds to the following optimization problem with a non-separable objective function (the worth of energy generated in a hydro plant cannot be measured directly as a function of the plant state alone[3]) ,

• A multi-period hydro reservoir operation with decisions coupled between stages
• Stochastic modeling because there is uncertainty in the forecasts of future inflow load, fuel prices, etc.
• Large-scale reservoir systems in sometimes-complex topologies including extensive transmission and thermal systems.

Because of these complexities, the hydrothermal operation of large-scale systems has been traditionally carried out without taking into account transmission constraints, or considering them in a very simplified way. Another traditional approach has been to consider the transmission system, but with a ver y simplified representation of the hydro system by, for example, specifying a “single” water value for hydro plants, neglecting time-related constraints or water inflow uncertainties, and conducting snapshot operation optimization (classical OPF problems). These approaches are not suitable for systems with a significant hydropower component and complex regional power exchanges. These modeling approaches do not adequately address the information necessary for: cost-benefit studies for transmission reinforcement; evaluation of spatial distributions of spot market prices through the electric network; and locational marginal pricing impacts, and other type of evaluations.

In the 1970s and early 80s, simple simulation tools were widely used to carr y out planning studies and hydrothermal scheduling. Hydro resources and inflow uncertainty often had a poor representation, using an aggregate model for the hydro system, which did not allow the detailed evaluation of transmission reinforcements in terms of energy benefits. The development of the economies in countries with significant hydro resources motivated the financial system (World Bank, IDB, etc.) to foster the development of integrated simulation and optimization tools capable of representing adequately transmission constraints and hydrothermal scheduling. In this context, SDDP was developed by Power Systems Research (PSR at www.psrinc. com) in the early 1990's with the following features:

4.1. Model Overview

SDDP is a transmission-constrained probabilistic hydrothermal scheduling model, which determines the optimal stochastic operation policy of a multi-reservoir hydrothermal system without aggregating hydro plants or using other approximation techniques. Since its inception, SDDP has become the operations simulation module in a group of related programs that deal with: optimal interconnections and generation expansion, optimized use of contracts and derivatives, and Nash-type decisionmaking by players in a deregulated environment[5,6,7]. In particular SDDP has been used with planning models OPTGEN and MODPIN to perform system expansion studies[9].

The solution algorithm is based on a decomposition scheme known as stochastic dual dynamic programming—hence the acronym SDDP[4] which approximates the expected future cost function of stochastic dynamic programming by piecewise linear functions. No state discretization [10] is necessary and the combinatorial “explosion” with the number of states – the well known “curse of dimensionality” of dynamic programming - is avoided. In a transmission-constrained hydro schedule, each stage in the SDDP algorithm corresponds to a linearized OPF with additional variables and constraints.

Moreover, the structure of the decomposition solution scheme allows the introduction of parallel processing in the algorithm and a significant reduction in CPU time. Parallel processing facilitates modeling of very largescale generation and transmission systems. It is standard to perform mid-long term operations studies for systems with hundreds of generators (hydro-thermal) with the representation of the full transmission network (thousands of bus bars and circuits) on a stochastic basis with a reasonable computer effort.

The formulation is readily modified to add new constraints and can explicitly deal with different bidding strategies, which is to some extent handled through data changes.

Besides the least-cost operating policy, the solution includes a wide variety of marginal (shadow) prices such as: bus spot prices; wheeling rates and transmission congestion costs; water values for each hydro plant; marginal costs of fuel supply constraints; and others. These prices provide important economic signals to either planners or an expansion-planning model. For instance, the distribution of circuit flows and the marginal cost at each node (bus marginal cost) together can indicate the need and payoff for circuit reinforcements.

PLEXOS is built from the ground up to evolve as requirements change and new solution methods become available. Many challenges remain in the context of long-term transmission planning. An outstanding problem is dealing with dimensionality. The shear size of the simulation can be problematic when transmission is modeled in its entirety for entire regions, for example the modeling of NREB (network which is the largest among all five regional electricity boards in India, comprising of nine states should include modeling of 400 and 220 kV networks consisting of 60 machines, 246 buses, 376 branches (lines/transformers) and 40 shunt reactors (Figure 1).

Figure 1. 246-bus NREB system network

A fast-solving OPF is available in this model, but it ignores losses. Automatic temporal aggregation allows rapid analysis of many scenarios. But further work is needed on full integration of stochastic sampling, strategic bidding using hot-started models to speed execution. PLEXOS can also make use of parallel processing LP codes. Perhaps the biggest challenge lies in overcoming the deterministic nature of mathematical programming codes. Although data may be stochastic, each 'sample' is solved in a deterministic fashion. This model partly overcomes this problem in its method of decomposition – ensuring the 'look-ahead' is not perfect, but in the medium-term, especially with long-term hydro, PLEXOS will benefit from a greater emphasis on realistic decision-making under uncertainty.

SDDP model has inherent advantages for Indian transmission expansion planning .This can be attributed to the fact that 63% percent of power comes from thermal power plants and around 25% of India's power generation comes from hydro power plants (Figure 2). The suitability of the model for Indian transmission expansion planning can also be attributed to the following aspects.

Figure 2. Fuel Mix in India (%)

The model is suitable for medium and long term operation studies from 1 to 15 years.

The model represented in detail,

•  Operational details of hydro plants (water balance, limits on storage and turbine outflow, spillage, filtration, head changes effect, environmental constraints etc.) along complex cascades.
• Detailed thermal plant modeling (unit commitment, "take or pay" fuel contracts, non-linear efficiency curves, fuel consumption constraints, multiple fuels etc.)
•  Representation of spot markets and supply contracts. Of the total power generated in the country, short-term transactions account for only 6.83 per cent. Of this, about 3.2 per cent is traded bilaterally, unscheduled interchanges (UI) comprise 3.1 per cent and the remaining 0.6 per cent is traded through power exchanges[11]. With restructuring of power sector the policy and regulatory environment within the country has become conducive to the development of power markets. The Indian power system operates on a twomarket concept: a day-ahead spot market, where the market clearing price (MCP) represents the electricity energy price; and a real-time market, where the price represents the system capability to balance generation and consumption in real time.
• Hydrological uncertainty: use of historic time series or multivariate stochastic inflow models that develop synthetic hydrology representing the system hydrological characteristics. This is primarily suited for Indian systems as our storage capacity in primarily dependent on normal occurrence of monsoon.
• Detailed transmission network: Kirchhoff laws, limits on power flows in each circuit, losses, security constraints, export and import limits for electrical areas etc.
• Load variation per load level and per bus, with monthly or weekly stages (medium- or long-term studies) or hourly levels (short-term studies).

The two state-of-the-art models highlighted in this paper have capabilities that go beyond those of other models currently used for transmission planning. The challenges in the Indian context are unique and non discriminatory in nature. The study reveals that the SDDP model poses better opportunities for transmission expansion planning for Indian market. With India's thrust towards the conventional power, the modeling of transmission expansion planning provides challenges in its own context. Development of better transmission models is essential because of changing electrical powers system paradigm.