Electricity Scarcity pricing presents important challenges for the Market design. Simple in concept, but more complicated in practice, inadequate scarcity pricing is implicated in several problems associated with Electricity Markets. It contributes to the ‘Missing Money’ needed to support new generation investments and creation of capacity markets.
Practice of socializing payments for capacity investments compromises incentives for Demand Response and Distributed Generation when they are most needed. Intermittent energy resources such as solar and wind present complications in providing a level playing field in pricing.
Better and Smarter Scarcity pricing would mitigate or substantially remove the problems in all these areas. In addition, better scarcity pricing would contribute towards making up the ‘missing money’ and supports resource adequacy. The market design also defines and prices the reliability through the demand for operating reserves.
Definitions
- VOLL (VALUE OF LOST LOAD): The average cost to customers (Rupees per MWh) of un-served load when they are disconnected during involuntary Load Shedding. Interruptions to inflexible demand refers to involuntary Load Shedding.
- OP-RES (OPERATING-RESERVES): Generation supply in excess of demand scheduled to be made available on short notice to ensure the reliable operation of a control area. Operating Reserves vary by response time. Reserves are categorized as Primary, Secondary and Tertiary Reserves. These reserves are deployed for the purpose of Frequency Control, reducing Area–Control Error and relieving congestion.
- PLANNING – RESERVE: The difference between a control area’s expected annual peak capability and its expected annual peak demand expressed as a percentage of the annual peak demand.
- ELASTICITY OF DEMAND: The responsiveness of the quantity demanded (q) of a good to its own price (p). Percentage change in demand that occurs to a percentage change in price: (dq/dp) (p/q).
If a 10% change in price causes a 5%, 10% or 15%change in demand, elasticity of demand is said to be 0.5,1.0, 1.5 respectively.
Flatter the demand curve, lower will be the elasticity of demand.
- DEMAND: The economic definition of Demand allows supply and demand to differ. Engineering definition does not. Under normal conditions these two – Supply and Demand coincide.
- MARKET POWER: The ability to alter profitably prices away from competitive levels. When suppliers exercise market power, they do not act competitively as price takers. Instead, they produce less than their competitive output causing an increase in market price.
Short Run Electricity Market
Early Market Designs presumed significant Demand Response. In the absence of demand participation, markets implemented inadequate pricing rules equating prices to variable costs (marginal costs) even when capacity is constrained. This produces ‘missing money’ problem.
The short run electricity energy market design (Fig1) makes two points clear.
First, even when there is insufficient capacity from engineering perspective, price-responsive demand and supply will equilibrate and the wholesale electricity market will not necessarily crash, because some customers forego some consumption than pay the higher price at this situation.
Secondly, at the time of high demand, spot prices will be higher if there is no required planning-reserve margin.
In other words, specifying a minimum value of installed generating capacity would suppress spot prices at certain times. Even if minimum reserve margin is specified, there is no guarantee that supply (energy plus reserve) and demand will equilibrate.
Missing Money
Referring to Fig 2, at 7-7.30 pm there is a price cap introduced by the system administrator as the System operator introduces involuntary load shedding considering the constrained capacity. This is the payment to the generators that is avoided as a result of curtailment of prices although explicit price caps are not the usual means of restraining prices. A more likely constraint on generator revenues would arise from an offer cap on generators to mitigate the market power. (called the mitigated price).
Price-Duration Curve
Spot prices could be summarised over the year by a price-duration curve (similar to the load duration curve) depicting the cumulative number of hours – when prices exceed a given level. As shown in Fig 3 under perfect despatch, generation would operate according to its variable cost of production.
The most expensive peak generation (e.g.,Rs 6800/= per MWh) would operate relatively for few hours. The payments in area A above the operating cost (Rs1200/= per MWh) would be the returns to cover the fixed costs of not only the peak plant but all generators.
The magnitudes could be substantial. The magnitude of area A would be of the order Rs 52 lakh/MW-Year, although estimates may vary. Hence, average peak price of Rs 80,000/MWh above operating cost would be needed for 65 hours a year in order to meet the payment requirement for the peaking generation.
The missing money amounts to as much as half or more of Rs 52 lakh /MW-Year payment required for new peak load generation capacity investments. It is this missing money that motivates interest in supplementary resource adequacy programs to provide a return to existing plants or support investments in new facilities. Assuming that administrative measures will always be invoked to cap energy prices that will always lead to insufficient payments in the energy market to maintain the required level of capacity, the missing money leads inexorably to alternative approaches such as optimal installed capacity requirements and related designs.
The lowest cost (Rs. 1200/MWh) -based-generators would operate virtually all hours but rarely the price (System Marginal Price) would fall to the lowest level.
Demand
In real system demand divides into two segments:
Inflexible Demand represents those customers who do not have individual real time meters or real time individual controls. It is not possible for these customers to receive or respond to the incentives provided by the real time prices. Typically, these customers pay a fixed price over the period here assumed to be Rs 2400/MWh. (Fig 5)
However, these customers have some implicit demand curve and the load that results at Rs 2400/= will be the load assumed to apply no matter what be the spot market conditions.
The average opportunity cost of the involuntary curtailment would be the average VOLL defined by the implicit demand curve which represents the correct estimate of the cost of curtailment given the limits on the control of inflexible load. This average VOLL is assumed to be Rs 8,00,000/MWh. Under these circumstances the marginal cost of curtailment for the inflexible group will be the average cost of the involuntary curtailment, Rs 8,00,000/MWh.
By contrast, the Flexible Demand represents customers having real time price meters and controls. The demand curve is arrived through the bids and choices of load.
Horizontal addition of these two demand curves will be the total demand of electricity to be delivered to the customers.
Value of Lost Load (Voll)
To curb the demand load shedding is not the solution. It is expensive. It makes no distinction between those who need the power most and those who need it least because most customers do not know the price in real time and contemporary markets do not have ability to control demand with price. When it is necessary to ration the demand, system operator resorts to load shedding. In this case the value (economic value/ market value) of another Megawatt of power equals the cost imposed by involuntary load curtailment. This value is called the Value of Lost Load (VOLL).
Basic economic theory says it is efficient to pay the suppliers the value of supplying another unit of output. Because VOLL is very high assuming above Rs 8 Lakh / MWh, load shedding implies very high price. Implementing this policy causes extreme price spikes, however for brief periods and leads to optimal investment in generating capacity and optimum reliability.
Lost Load Pricing
When load is to be shed, System Operator (SO) must choose how much to offer for additional supply. Regulator chooses to offer the cost of additional generation. Market approach will be to offer the value that customers place on not being cut off. This value might be Rs 8 Lakh/MWh although the cost of last unit of power produced might be only Rs 0.4 Lakh / MWh.
If the market is perfectly competitive the cheaper approach will be to offer Rs 8 Lakh /MWh and pay this much whenever load is actually shed. This is the equilibrium price determined by the intersection of Supply and Demand. Setting the price of energy in the spot market to this price (Rs 8Lakh/MWh) whenever load is shed involuntarily is the VOLL Pricing.
Voll Pricing Is Regulatory
To apply VOLL Pricing, the value of Lost Load must be determined. Because customers do not respond to real-time prices (First Demand side flaw) there is no market information on the VOLL. Therefore, VOLL sets regulated price, not market price.
Cost of load shedding is great because load is arbitrarily disconnected (involuntary shedding) rather than demand is voluntarily reduced by customers in response to the market price. Blackouts shed high value (economic) loads and low value loads in the same proportion. A load that values its power at Rs 80 lakh /MWh is shed as one that values at just Rs 0.16 lakh/ MWh.
Definition of Voll (Vll)
Conceptually, the total loss of economic value to consumers (loss of consumer surplus) divided by the accumulated MWh of lost load (shed load) is equal average VOLL. However, this average value is different from the marginal definition of VOLL, which is to be used in the pricing policy.
Marginal VOLL measures the decrease in lost value (economic) divided by the decrease in lost load when installed capacity is increased by a small amount.
Let H be the average MWh of load that is shed and VH be the average consumer surplus of power consumption (economic /social). Let –dH be the decrease in H, dvH be the increase in VH, caused by small increase in installed capacity. Then VLL = -dVH / dH technically this expression defines the marginal VOLL. The same is used for defining the VOLL.
Optimal Load Shedding and Optimal Voll Pricing Condition for Optimal Load Shedding Connecting Voll to the Demand Curve
Assuming the unobservable demand function as shown in Figure 6, (as consumers do not respond to any real time price fluctuations) is implicit, the area under this curve measures total value of power to consumers, the consumer surplus (social/economic power) in the sense that consumers would pay that value for that power.
Assuming the demand for power is zero at a price of Rs 24 lakhs per MWh and increases linearly to 20,000 MW at the retail price. When load is shed there is reduction in the surplus. Assuming a 10% of demand is scaled back (with 2000MW of demand shed) the net reduction in the social power will be Rs 12Lakh per MWh.
The reduction in consumer surplus caused by 1 MWh of shed load is VLL.
When load shedding is optimal a reduction in installed capacity would cost consumers as much in lost value as would be saved by the reduction in capacity. The condition for the optimal load shedding (neglecting the impact of variable cost of Peaker generating unit)
Loss in consumer surplus = savings from reduced installed capacity
V LL = FCPeaker / DLS Where FCPeaker is the capacity cost (Fixed cost) of the Peaker generating unit.) Rs per MWh and
DLS is the optimal duration of load shedding in HOURS.
DLS = = FCPeaker / VLL
Optimal Value of Installed Capacity and Optimal Duration of Load Shedding
Generation Adequacy (represented by the installed capacity) is the fundamental matric of Reliability. Increasing K reduces the cost of lost load but increases the cost of serving load. This cost trade off determines the optimal value of K.
As K the installed capacity increases, DLS the duration for load shedding decreases. For low values of K, VLL X DLS will be greater than FCPeaker. It will cost less to increase K than will be saved by reduction in Lost Load. For high values of K reverse is true. At the optimal K the cost of installing another MW of Peaker capacity will be equal to cost saved in the value of lost load. Therefore
The condition for optimal K: FCPeaker = VLL X DLS
Optimal value of Duration of Load Shedding is given by DLS = FCPeaker / VLL VLL X DLS also is the price spike revenue which is long run equilibrium condition for the investment in Peaker generating unit.
Short Run and Long Run Incentives
VOLL pricing is not needed to induce generators to provide spinning reserves. Spin must be provided in advance of a contingency and so before the price increases. When price jumps to VLL generators provide energy but not spin. VOLL pricing is most advantageous as a short-term incentive for demand reduction. Adequate investment in generating capacity is the goal of VOLL pricing.
Operating Reserves and Pricing
Reliability
Adequacy and Security are the two components of Reliability. A system with adequate capacity can maintain enough security to reduce periods of involuntary load shedding to 1 day in 10 years. A system with inappropriate policy on operating reserves will have insufficient security in spite of adequate capacity. Adequacy is the crucial economic problem while security is economically secondary yet complex.
Types of Reserves
There are two types of reserves. Operating reserves are required to maintain system security by handling short term disturbance to the system. Planning reserves are required to maintain system adequacy by meeting annual peak demands.
Simple Model of Reliability
With generation installed capacity of K MW; generation outage g MW; defining Load L MW, as the economic demand for power (the amount of power that would be consumed if the system were operating normally) and defining operating reserves to be available whenever required within the limits of installed capacity (kept as hot reserve) that is neither out of service nor serving load; thus, defining Operating Reserves = OR = K – g –L
L is the sum of lost load LL and served load. L can exceed supply (L defined as economic demand) LL is measured by the extent to which OR is negative and zero whenever OR is positive. Thus:
LOST LOAD = LL=Max of (–OR, ZERO)
There is no correlation between excess loss of load (excess interruptions due to distribution network) and OR. With this expression nominal lost load LL can easily be computed and is all that matters.
Operating Reserves Pricing
Operating Reserves are needed to solve very short–run reliability problems. But their pricing controls the long run as well. Surprisingly their price depends on VOLL and on Long-Run Reliability considerations. By setting prices to a relatively modest level when the system is short of operating reserves (rather than to the extremely high value of VOLL when the system is short of capacity), OP-RES pricing can substitute for VOLL pricing. Markets that do not use VOLL pricing use OP-RES pricings, which are often higher than needed to attract operating Reserves from the local Market.
Comparison between Voll Pricing and Op-Res Pricing
As VOLL pricing induces optimal level of installed capacity, evaluation of the installed capacity induced by Op-Res pricing depends on both the required level of operating reserve ORr and on the price paid when the system is short of operating reserves Pcap
As an example:
A system is having optimal installed capacity level of K= 50,000 MW. Assuming a value of (economic) VLL of Rs 12 Lakhs per MWh and assuming the fixed cost of thePeaker Unit FC Peaker of Rs. 480/MWh. The optimal duration for load shedding will be:
DLS = 480/1200000=0.0004 year =0.0004×8760=3.5h / yr
For this system, assuming the level of operating reserves required
ORr =5000MW, Pcap will be used to design the optimal pricing policy.
When the system is short of min. operating reserves, Pcap will be the price cap or the purchase price. Price will be at the cap whenever:
Lg > K – ORr where Lg is the Augmented load
When Lg >45000MW .
The table presents durations of load shedding for various useful load levels.
The Table shows that with ORr=5000MW and K of 50,000 MW installed capacity the Reserve price will be set to P cap for 108.5 Hours/ year, so the price spike revenue will be equal to 0.0124 x Pcap.
To obtain the required price spike revenue for a long run equilibrium of Rs 480/=per MWh (Fixed cost of the Peaker Unit) the price cap must be set to Pcap = FCPeaker /optimal Duration of load shedding = Rs 480/0.0124 =Rs 38710/MWh Which is more than 31times less than VLL. With this price cap, with operating reserve requirement of 5000MW, market’s long run equilibrium level of installed capacity will be optimal. With any higher level of Pcap too much generation will be built (with reducing Op-res levels).
To be continued…
Dr. K. S. Gandhi is B.E. (Electrical) from Andhra University College of Engineering, Waltair; and M. Tech. (Electrical Power Systems) from JNTU, Hyderabad. His Ph. D. thesis is titled ‘Market Based Tariff Reforms – A Framework for Indian Power Sector’. After offering his service to many reputed Indian power companies for 50 years, he is now engaged in the teaching activity on regular guest faculty basis for M. Tech. (EPS) batches of a reputed engineering college at Hyderabad. He has delivered more than 30 papers at various seminars in the country and in the training sessions at Engineering Staff College, Institution of Engineers, CPRI etc.
