Managing the Energy Trilemma in the Philippines

The transition to an energy mix with lower carbon emissions is hampered by the existence of the so-called energy trilemma. The primary consequence is a trade-off between various objectives of energy policy, e.g. equity and sustainability. This paper proposes a framework and methodology to manage the trilemma by applying methods related to multi-criteria decision making to assign weights to the various components of the trilemma. However, an expanded concept of energy security is adopted which translates to a version of the trilemma different from that of the World Energy Council. This study takes into account autarky, price, supply and carbon emissions. The values are generated by a software called PLEXOS and are incorporated in a welfare function. Policy options can be ranked using the values generated by the welfare function. In this manner, the trilemma can be managed even if it is not resolved.


Introduction
Energy poverty continues to be a major concern in the Philippines especially when compared with its neighbors in Asia. One aspect of energy poverty is household access to electricity. Table 1 shows that as of 2016 the Philippines has the lowest electrification rate among Asian countries with a similar level of development. Meanwhile, Table 2 shows that as of 2014 the Philippines has the lowest per capita consumption of electricity. 1 It is not a coincidence that the Philippines also has one of the lowest levels of development as measured by per capita GDP.
To address the problem of energy poverty, the Philippine Department of Energy targeted 100% electrification of households with access to the grid by 2022. For off-grid areas, the 100 percent electrification rate is expected by 2040. The objective dovetails with one of the major components of Sustainable Development Goal (SDG) 7 which is to ensure universal access to affordable, reliable, sustainable and modern energy by 2030. SDG 7 also targets a substantial increase in the share of renewable energy in the global energy mix. Hence, the increase in access must be accompanied by a transition from fossil fuels (e.g. coal) to renewable energy (e.g. solar).
Achieving increased access and a higher share of renewable energy requires managing the so-called Energy Trilemma. This refers to "the conflicting goals that governments face in securing energy supplies, providing universal energy access and promoting environmental protection" (World Energy Council, 2011). The Energy Trilemma is defined across three dimensions ( Figure 1). Energy Security reflects a nation's capacity to meet current and future energy demand reliably, withstand and bounce back swiftly from system shocks with minimal disruption to supplies. Energy Equity assesses a country's ability to provide universal access to affordable, fairly priced and abundant energy for domestic and commercial use. Environmental Sustainability of Energy Systems represents the transition of a country's energy system towards mitigating and avoiding potential environmental harm and climate change impacts.
The term "trilemma" implies that trade-offs are involved when energy policies are designed and implemented. For example, ten years ago, significantly increasing the share of variable renewable energy (VRE) like solar would have been infeasible because of the prohibitive costs involved (Table 3). The trade-off between equity, particularly affordability, and sustainability was quite clear-cut. Nowadays, because of the sharp decline in cost of solar power generation, the trade-off emanates from the feasibility of integrating VRE in the grid system. In this context, the high cost of battery storage is the major factor that prevents the full utilization of wind and solar power in the grid system.
Thus, despite the sharp decline in generation costs involving VRE, the energy trilemma remains to be a problem that has to be managed. This paper proposes a methodology to achieve this goal. The essence of the framework is specifying a welfare function W that is dependent on the components of the trilemma. One such specification is as follows: ! = $%&'()*+ , -.')*+ / $'0*1)213)4)*+ 5 Different policies will yield different values for the three components of the trilemma, i.e. security, equity, and sustainability, thereby generating a set of values for W. This will enable policymakers to rank the policies. A conventional simulation package can generate the values of the main components. The obvious challenge is to arrive at reasonable values for the parameters α, β, and ϒ. They represent the preferences of the policymakers who in turn should ideally reflect the aspirations of society. Methods under multi-criteria decision making (MCDM) can be applied for this purpose.
This study applies selected methodologies to demonstrate how the framework can be utilized to manage the energy trilemma. Policymakers can then adapt the framework to their preferred methodologies. The choice of the term "manage" is as deliberate as "resolving" the trilemma is a difficult task.

II. Review of Literature
The energy trilemma is recognized as a global challenge. To track progress in coping with this challenge, the World Energy Trilemma Index has been prepared annually since 2010 by the World Energy Council. In its latest publication, WEC presents a comparative ranking of 128 countries' energy systems. An assessment of a country's energy system performance is also provided, reflecting balance and progress in the three Trilemma dimensions. The performance of the Philippines is shown in Figure 2. The country is ranked 94 th in terms of balance and progress in the different components of the trilemma.
The literature identifies a strong version of the trilemma and a weaker version. The former depicts the need for policymakers to choose two among the three policy goals. This implies that the trilemma can never be resolved but only managed. On the other hand, the weaker version recognizes that political, economic and institutional reforms can lead to progress in all three components. Hence, the trilemma can be resolved but by overcoming deep-seated obstacles.
Examples of studies that adopt the weaker version when discussing the trilemma are country cases for the Philippines and Indonesia, respectively (La Viña, et al. 2018 andGunningham, 2013). The discussion largely revolves around policies that govern the transition into more low-carbon sources in the energy mix. In the case of the Philippines, the authors argue that policymakers can and should pursue two categories of reform simultaneously: rationalization and diversification.
"The rationalization of government policies and procedures will not only reduce political and regulatory risk, but will also encourage, support, attract, and retain investments to achieve energy security, equity, and sustainability goals. This can be done by first, deciding on a firm and consistent government direction on energy policy through the creation of a long-term energy plan that can withstand changes in government administrations; second, adequately preparing the government to adapt to and accommodate advancements in energy technology by removing unnecessary subsidies tied to specific energy sources while keeping abreast of developments in the international energy platform; and third, increasing government-private Electronic copy available at: https://ssrn.com/abstract=3516435 sector coordination and processing by using energy mapping systems that show optimal areas for energy development vis-à-vis available energy sources and transmission lines. Moreover, red tape in permitting and licensing and delays in regulatory approval must be minimized.
Ultimately, rationalization implies a shift from liberalization (or a market-led approach) to a hybrid of government regulation and market-led approach, giving government a greater role in directing energy policy." Meanwhile, the thrust of diversification is "reducing the country's overdependence on one, imported resource, coal, [and this] entails two courses of action: first, optimizing coal's share in the energy mix, and second, reducing the use of imported coal. Currently, the role of coal power plants as baseload plants is crucial and cost effective because of insufficient renewable sources that can serve as baseload. The problem lies in having a supply of coal plants beyond baseload needs, forcing some coal plants to serve the mid-merit requirement. Efficiency dictates that mid-merit plants are better suited for sources other than coal. To address this, a cap on approved coal endorsements using a portfolio-based regional energy plan detailing the baseload, mid-merit, peaking requirements in each of Luzon, Visayas, and Mindanao is necessary. This prevents an oversupply of coal plants beyond baseload needs, and, for the longterm, contractual lock-in of coal supply beyond what is economically, socially, and environmentally acceptable." 2 Indonesia is a resource-rich country, and a significant player in the world energy economy. However, its per capita consumption of electricity is relatively low ( Table 2). One reason for this is a strategy that encourages exports of energy resources and heavy dependence on coal. Gunningham recommends effective energy governance to increase access, reduce fuel subsidies and at the same time facilitate the transformation of the energy sector from a high to a low carbon economy. There are four critical components of this governance structure.
First, there is the need to instill norms-or standards of appropriate behavior-related to the importance of climate change. International organizations like the International Energy Agency (IEA) have an important role to play in convincing Indonesian policymakers of the importance of measures related to climate change adaptation and mitigation. "Second, there is the distinctive contribution that both international NGOs and certain international organizations have made to address the specific issue of fuel subsidies. 3 Third, there is the potential contribution of global energy governance in addressing Indonesia's most pressing energy challenge: the absence of anything remotely like the amount of money that might be necessary to fund an energy revolution. The most important existing financing mechanisms include the Global Environment Fund (GEF) and the climate change funds of the World Bank, most notably the Clean Technology Fund, although neither of these initiatives contemplates the provision of sums of money remotely sufficient to address the magnitude of Indonesia's climate change challenges. If such carrots do not achieve the necessary changes (and they are small compared to the current cost of energy subsidies to the Indonesian budget of some $20 billion per annum), there remains the possibility of the use of sticks. Of the latter, the most plausible are carbon border taxes: taxing goods from countries that do not commit to climate change mitigation in order to ensure that those who do are not disadvantaged." 4 The preceding discussion highlights the difficulty of designing policy to resolve the energy trilemma. Moreover, the policies will still likely involve trade-offs. Managing the trilemma can be facilitated if the trade-offs can be quantified. A straightforward approach is the adoption of portfolio-based techniques widely used in financial markets. The general objective is to balance short-term cost with medium-to long-term price stability. The standard methodology is Markowitz's mean-variance analysis to determine the optimal energy mix for electricity generation.
A recent application is the case of the Philippines (Balanquit and Daway-Ducanes, 2018).
In their study they consider eight generating technologies, each associated with two important parameters: the expected rate of return r i and the risk measured by the variance in the return.
These parameters are both derived from the technology's daily power price (PP) ratio, defined as the amount of energy sold or discharged over its average price.
On the other hand, the expected portfolio risk is given by where ? 6K is the covariance of two distinct technologies ) and M. The methodology then adopts the approach of Markowitz (1952) by minimizing a given portfolio's risk for every targeted rate of return r. The problem can be depicted as: Electronic copy available at: https://ssrn.com/abstract=3516435 The procedure will yield optimal shares of each type of technology. A set of optimal portfolios can be depicted on the return-risk plane ( Figure 3). The curve is the optimal portfolio frontier.
Any point to the left is infeasible while any point to the right is considered sub-optimal.
The energy trilemma is partially addressed in the portfolio model because energy security is associated with "risk" and equity is associated with "return". The authors claim that in their framework consumer welfare is maximized in terms of price stability, energy security, and cleanenergy investment, implying that the third horn of the trilemma, sustainability, is also incorporated. However, clean energy only figures in the discussion because VRE sources are among the eight technologies considered. There is no explicit procedure by which lower carbon emissions can be targeted.
Unlike the application using Philippine data, the study of Stempien and Chan (2017) makes categorical reference to the trilemma. Targeting "sustainability" is operationalized by adding another variable in the model: the expected return on emissions in terms of energy per unit of CO 2 , i.e. kWh per ton of CO 2 . Instead of having a two-dimensional optimal portfolio frontier, the efficient plane is as depicted in Figure 4. The three dimensions represent the constraints imposed by the trilemma under which the portfolio is optimized.
Neither the studies of Balinquit and Daway-Ducanes and Stempien and Chan provide a mechanism to choose among the options along the optimal portfolio frontier. This can be done by specifying a set of indifference curves-or planes in the multi-dimensional case. These are analogous to the aforementioned welfare function. The indifference curves (planes) are specified by determining the risk-return profile of the policymakers involved, which can also be accomplished through methods associated with MCDM.
The indifference curves should slope upward ( Figure 5). This indicates that in order to leave the investor with the same utility, the investor must be compensated with higher expected rates of return for greater levels of risk. A higher indifference curve implies a higher level of utility. The choice of generation mix is where the indifference curve is tangent to the optimal portfolio frontier (point A in Figure 5).

III. Framework
The IEA's website defines energy security as "the uninterrupted availability of energy sources at an affordable price. Energy security has many aspects: long-term energy security mainly deals with timely investments to supply energy in line with economic developments and environmental needs. On the other hand, short-term energy security focuses on the ability of the energy system to react promptly to sudden changes in the supply-demand balance." 5 Given this rather broad definition, the concept of the trilemma is modified in this study.
Energy governance seeks to promote energy security and one of the primary tasks is to manage the trade-off among its various components. Based on the IEA's definition, these would be the major components to be considered: 1) adequate supply; 2) price; 3) environmental impact; and 4) ability to react promptly to sudden changes in the supply-demand balance. Hence, there is a "quadrilemma" among these components. Heretofore, however, the term "trilemma" is retained.
A simulation package is obtained to generate values of these four variables over a selected time period under reasonable assumptions. Some of these assumptions reflect policy choices. The authors have access to PLEXOS and therefore the study is limited to power generation. 6 What is emphasized is that the framework and methodology presented and applied in this study are invariant to the specific software and assumptions.
The following components of Energy Security are generated from PLEXOS: autarky (AT), affordability (P), Supply (S) and Sustainability (C). Autarky is defined as the share of energy from indigenous sources and is related to the ability to react promptly to sudden changes in the supply-demand balance. Affordability is equated to the price or cost of electricity.
Meanwhile, the variable supply is proxied by the Capacity Reserve Margin = (Total generation capacity -peak load) / peak load. Sustainability is measured by carbon emissions.
In order to manage the trilemma, the variables will be combined in a welfare function thus: The parameters α, β, ϒ, δ are the weight of each factor in the welfare function and the most important objective is to maximize welfare, W. Let W* be the maximum welfare and by definition ! * = UV , * 7 / * $ 5 * W X * where B * , Z * , [ * , \ * are the weights that maximize W in the forecast period 2020-2040. The optimal weights can be obtained through simulation-based optimization.
However, a more practical application is to obtain the weights of a hypothetical DoE can be obtained from the Analytical Hierarchy Process (or a similar procedure as described in the Box). ! ] can then be used to evaluate policy options. As stated in the introduction, different policies will yield different values for the components of the trilemma, in this case AT, P, S and C, thereby generating a set of values for W. The policy associated with the highest W can then be implemented. Similar to the argument made earlier, the framework is invariant to the specific methodology to obtain the weights.

Box: Multi-criteria Decision Making
Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a subdiscipline of operations research that explicitly evaluates multiple conflicting criteria in decision making.
The literature identifies many methods to implement MCDM, particularly in giving weights to the criteria Electronic copy available at: https://ssrn.com/abstract=3516435 The AHP is applied in this study, the basic reference being Saaty (1980). It is a tool for dealing with complex decision making by allowing the decision maker to set priorities and make the best decision. By reducing a multifaceted process to a series of pairwise comparisons, and then synthesizing the results, the AHP helps to combine both subjective and objective aspects of a decision.
The AHP considers a set of evaluation criteria, and a set of alternative options among which the best decision is to be made. It is important to note that, since some of the criteria could be contrasting, it does not necessarily follow that the best option is the one which optimizes each single criterion. Rather, the best option is the one that achieves the most suitable trade-off among the different criteria. A more complicated process, the Stochastic Multi-criteria Acceptability Analysis or SMAA (Lahdelma and Salminen, 2010). This is a family of methods for aiding multi-criteria group decision making in problems with uncertain, imprecise or partially missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. SMAA was applied to the energy trilemma by Song et al. (2017). The different alternatives were evaluated based on three criteria which are the components of the trilemma. As an exercise, the authors used as alternatives the top ten countries based on the 2015 Energy Trilemma Index. Exact weights of the three criteria were not derived but these can be inferred from the reported rank acceptability indices.
It should be noted that in the actual simulation the welfare function is defined as: For the portfolio model, instead of a welfare function, a utility function U that depends on r and σ 2 is defined, i.e. U(r, σ 2 ). The appropriate weights for risk and return can also be determined through one of the MCDM procedures. Such an application is left for future study.

IV. Simulating the Energy Mix
Using PLEXOS, the power sector was forecast for the period 2020-2040 under a marketbased scenario ( Figure 6). In this approach, the electricity market is assumed to unfold along a path where growing demand is automatically satisfied in the least cost manner. There is no mandated generation mix across the study period and no carbon tax is applied. Variable renewable energy costs are anticipated to continue along a significant downward trajectory.
Meanwhile, domestic gas as it depletes gets replaced by the use of imported liquid natural gas (LNG).
Under a market-based scenario, coal remains to be a significant part of the mix as it is a cheap option for running on baseload function. Share of coal in the mix is anticipated to reach a peak of more than 70% in the first half of the study horizon. Renewable energy generation on the other hand, is seen to rise to unprecedented levels starting at the second half of the period. In 2040, the share of solar generation is estimated to increase by more than 10 times its original share in 2020. Following this market-based scenario, autarky is expected to fall from a high level of 54% in 2020 down to 30% in 2030. The drop is influenced by the increased dependence on imported fuel energy sources, namely coal and the switch to imported LNG as local gas gets exhausted.
Annual market price averages are projected to experience a slight increase from its initial price level by approximately 0.7 P/kWh (real 2018 terms) towards the period 2031-2040. The uplift is presumed to provide signals to encourage additional investment to support growing demand and reserve requirements. Capacity reserve margins remain stable at 25% throughout the horizon. Carbon intensity is anticipated to climb in the near term, starting from 854 tCO2/GWh in 2020, reaching a peak of 1048 tCO2/GWh in 2030. This will slowly pull back to a level of 990 tCO2/GWh in 2040. The rise of carbon intensity in the medium term is attributed to the increase in share in the generation mix of thermal coal. On the other hand, the slow decline of carbon intensity in the second half is a result of proliferation of variable renewable resources. Secretary 3 represents the optimal weights obtained from a simulation-based optimization procedure. A corner solution is obtained but this is not surprising since a policymaker who favors a market-based solution will definitely emphasize the least-cost alternative.
Under the market based scenario, the value of W is calculated as follows: It should be noted that the value of W is higher under Secretary 3 for both policy regimes. Does this imply that Secretary 3 is the ideal head of the Department of Energy? Not at all. The parameters generally reflect the preferences of society. The welfare function is a mechanism to rank different polices given these parameters.

V. Extensions of the Framework
The reverse question can be investigated: given the parameters α, β, ϒ, δ, what would be the values of the components to maximize welfare? These can be designated as UV * , 7 * , $ * , W * . A

Table 3: Summary of Mean Levelized Cost of Energy (LCOE) for Different Energy Sources
Electronic copy available at: https://ssrn.com/abstract=3516435 • The three goals that should be achieved to reach energy sustainability. • A balanced "triangle" implies integrated policy solutions and coherent innovation approaches. Electronic copy available at: https://ssrn.com/abstract=3516435

Appendix: PLEXOS Platform 8
PLEXOS is a commercial grade optimization based software used to model electricity markets. The forecasting approach using PLEXOS is largely simulation-based, which is in contrast to other known practices where forecasts are done by regression. Its core simulation engine is centered on mixed integer programming and the structure of the platform is comprised of interleaved simulation phases namely: 1 The phases are solved in sequence and the output of one becomes the input to the succeeding simulation steps. The LT Plan solves for the set of optimal builds and retirements across the horizon. PASA step looks to find the optimal timing of annual maintenance events of generating units. Outputs of LT and PASA steps are passed on to the MT and ST Schedules to further solve the more detailed dispatch optimization problem -the final solution of which contains parameters of interest such as the projected hourly dispatch schedule of each individual generating unit and hourly system market prices.

LT Plan
The LT phase seeks to solve the long term generation capacity expansion problem by finding an optimal set of builds and simultaneously solving for the dispatch optimization problem from a central planner's perspective. In particular, the LT plan looks to identify what type of generator units to put in, where to put them in the system, and when to build it. This is further subject to reliability constraints such as respecting capacity reserve requirements.
The general objective is to minimize net present value of capital and production costs of future generator build decisions and retirements. Costs can be classified into two categories: -Capital costs C(x), consisting of costs of attributed to building new generator capacity and generator retirements. Generator build costs include the fixed amounts required to pay for capital and service debts.
-Production costs P(x), which include cost of operating the system using the existing plant line-up plus a basket of candidate builds. Also included in the formulation of production cost is the notional penalty of unserved energy.

Figure A.1 Illustration of the objective of the LT Plan: minimize net present value of capital and production costs
Expansion candidates like variable renewable sources such as Solar and Wind are examples requiring relatively high capital costs and virtually minimal production costs.
Liquid fuel resources such as Oil-based generating units are expected to have high production costs. Adding carbon tax augments production costs of carbon-intensive generating resources and hence will prompt the simulator to look for a solution that moves away from these fossil fuel-based options and favoring renewable sources more.

Integrality
GenBuild (g,y) integer Capacity Adequacy ∑ ( g ) PMAX g ( Units g + ∑ i≤y GenBuild i ) + CapShort y ≥ PeakLoad y + ReserveMargin y ∀ y The formulation is illustrative only and is usually extended to include in the formulation terms to handle candidate generators subject to inter-temporal constraints such as hydro energy limits, ramp-rate limitations, storage units like batteries, or with contracts with minimum and maximum off-take requirements.

PASA Phase
The PASA simulation phase automatically schedules distributed maintenance events with the objective of equalizing capacity reserves across peak periods (e.g. daily, weekly, monthly peak periods). Capacity reserves is the spare capacity over peak load in a region. Distributed maintenance events refer to outage periods typically required annually by generating plants to allow maintenance activities such as periodic maintenance, inspection of facilities etc. Maintenance events are considered to occur in discrete periods and explicitly expressed to cover an expected number of hours and performed at a defined frequency in a year. This is in contrast to forced outage events where the number of times unplanned outages are drawn are implemented in a random fashion.
The PASA phase is done after the LT phase when the annual future plant line-up is finalized. The distributed maintenance events are outputs of PASA and are passed down as input to the subsequent MT and ST simulation steps as optimal maintenance schedules. The optimal schedule of PASA step is mainly based on capacity reserves only and not on production costs. This means maintenance timings handed down by PASA does not necessarily result in minimizing opportunity loss of an individual generator (due to lost revenue from the market).

MT Schedule
MT schedule deals with the key problem in power system modelling which is to handle medium and long terms decisions in a computationally efficient way. In particular, this includes effectively addressing inter-temporal constraints present in energy-constrained generating units such as hydro power, storage units like battery, and contracts requiring fuel minimum/maximum off-takes by solving the economic dispatch optimization problem under a reduced chronology scenario.
To illustrate, for instance take for example a forecast horizon spanning 20-years: the simulator is expected to simultaneously optimize decisions in the higher resolution level (in this case hourly) while respecting medium term constraints that span weeks for energy constrained hydro generator or up to a year for a gas contract with minimum gas off-take. A simple approach would be to formulate 20 x 8760 hours = 175,200 dispatch intervals and solve it mathematically through one giant step. This simple approach however in reality, is computationally expensive and impossible to solve even with modern day computers. To work around this, the MT Schedule finds an alternative solution over a reduced number of simulated periods by grouping together "similar" dispatch intervals and assigning them into blocks. Then, MT schedule optimizes decisions over this reduced chronology. The original medium term constraints are then reduced into a set of equivalent short-term constraint targets and objectives that can be seamlessly integrated to the more detailed ST schedule that runs on full chronology. For example, given an energy-constrained hydro power plant with monthly limits -the MT schedule because of its reduced number of chronological steps, will solve for an approximate hydro dispatch schedule based on the medium term constraint. According to this approximate medium term decisions, there is a set of shorter period target equivalents of the medium term constraint that can be seamlessly passed on and enforced to the ST schedule -for instance, from monthly into daily energy targets. The ST schedule takes these daily targets as constraints added directly to the short term formulation for its short term dispatch policy.
Because MT schedule runs on a reduced chronology, it deals with constraints that span longer periods such as weeks, months or even several years.
Strategic bidding models: Included in the MT schedule step are methods for strategic bidding such as -Long Run Marginal Cost (LRMC) recovery and Residual Supply Index methodology. SRMC or short run marginal costs refer to the variable costs of a generating unit's operation. LRMC refer to variable costs combined with the fixed costs covering fixed operation and maintenance and capital recovery fees to cover debt servicing and return to shareholders.
The PLEXOS LRMC cost recovery method is an automated price modification heuristic in which the price of generation from each Generator that belongs to a Company is modified to reflect the fixed cost burden of the Company as a whole. This price modification is dynamic, done iteratively, and designed to be consistent with the goal of recovering fixed costs across an annual time period.
Residual Supply Index "RSI" method is an empirical approach to modelling strategic bidding. It adapts a historical relationship (regression) between Price-cost Mark-up and certain system conditions and uses it to predict Bid-cost Mark-up under future system conditions and applies the bid-cost mark-ups to the supply bids and runs the model to determine dispatch and market clearing prices.

ST Schedule
The ST schedule is a full chronological production cost simulation model used to emulate the dispatch and pricing of the real time market clearing engine of the Wholesale Electricity Spot Market (WESM). The ST schedule solves both economic dispatch and unit commitment problems simultaneously.
In its core is the following economic dispatch and unit commitment formulation described as follows: Gen. unit operating limit , $ ∈ 0,1 On or off Other unit constraints Min up/down time, ramp rate, etc. Where: -# $ is fuel cost of gen unit i -+ $ is start up or shut down cost of gen unit i -, $ is decision variable of start-up or shutdown of gen unit i -% &$ is generation output of gen unit i -% @ is total demand plus losses at time t -% &$ is generation output of gen unit i -% 2 13145 is total demand -% 5377 is total transmission losses Marginal prices and nodal prices: The linear programming formulation described above refers to the primal problem which deals with physical quantities such as generation and demand. The formulation can be converted to a dual problem which primarily deals with economic values. The solution to the dual problem tells about the marginal price for energy which refers to the optimal value of the dual variable associated with the power balance constraint ( % &$ (() = % 2 13145 + % 5377 ). The marginal price represents the cost to system cost changes (in $) for every one unit change in load (in MW).