Cost of Valued Energy for design of renewable energy systems

Journal Pre-proof Cost of Valued Energy for design of renewable energy systems Juliet Simpson, Eric Loth, Katherine Dykes PII:

S0960-1481(20)30153-1

DOI:

https://doi.org/10.1016/j.renene.2020.01.131

Reference:

RENE 12994

To appear in:

Renewable Energy

Received Date: 27 September 2019 Revised Date:

24 December 2019

Accepted Date: 26 January 2020

Please cite this article as: Simpson J, Loth E, Dykes K, Cost of Valued Energy for design of renewable energy systems, Renewable Energy (2020), doi: https://doi.org/10.1016/j.renene.2020.01.131. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Cost of Valued Energy for Design of Renewable Energy Systems Juliet Simpsona, Eric Lotha, Katherine Dykesb

Corresponding author: Juliet Simpson, [email protected] a

University of Virginia, Department of Mechanical and Aerospace Engineering, 122 Engineer’s Way,

Charlottesville, VA 22903 b

Technical University of Denmark, Wind Energy Department, Frederiksborgvej 399, 4000 Roskilde,

Denmark

1

Abstract

2

The design of renewable energy systems such as wind turbines or solar panels

3

conventionally employs Levelized Cost of Energy (LCOE), but this metric fails to

4

account for the time-varying value of energy. This is true both for a single turbine or an

5

entire wind farm. To remedy this, two novel, relatively simple metrics are developed

6

herein to value energy based on the time of generation and the grid demand: Levelized

7

Avoided Cost of Energy simplified (LACEs) and Cost of Valued Energy (COVE). These

8

two metrics can be obtained with: 1) a linear price-demand relationship, 2) an estimate

9

of hourly demand, and 3) an estimate of predicted hourly generation data. The results

10

show that value trends for both wind and solar energy were reasonably predicted with

11

these simplified models for the PJM region (a mid-Atlantic region in the USA) with less

12

than 6% error on average, despite significant stochastic variations in actual price and

13

demand throughout the year. A case study with wind turbine machine design showed

14

that increasing Capacity Factor can significantly reduce COVE and thus increase

15

Return on Investment. As such, COVE and LACEs can be valuable tools (compared to

16

LCOE) when designing and optimizing renewable energy systems.

17 18

Keywords

19

LCOE, wind, solar, LACE, Net Value, renewable energy

20 21

1

1

Nomenclature g

Hourly power generation (MW)

p

Hourly spot price / time-averaged spot price

D

Hourly demand / time-averaged demand

R

Hourly residual demand / time-averaged demand

W

Hourly wind generation / time-averaged demand

S

Hourly solar generation / time-averaged demand

Q

Hourly variable renewable generation / time-averaged demand

X

Extrinsic factors influencing price such as the economy or government regulations

CF

Capacity factor

m

Price-demand slope

const.

Arbitrary constant

VRE

Variable Renewable Energy (such as solar or wind)

LCOE

Levelized Cost of Energy

LACE

Levelized Avoided Cost of Energy

sLCOE

System Levelized Cost of Energy

rsLCOE

Revised System Levelized Cost of Energy

VF

Value Factor

COVE

Cost of Valued Energy

ROI

Return on Investment

LACEs

LACE simplified

( )m

Modeled value

( )avg

Time-averaged value over a year

( )’

Temporal variation from the average, such that ( ) = ( )avg + ( )’

2

2

1

1. Introduction

2

Renewable energy production is increasing significantly, e.g. it reached 17% of

3

the US production in 2017 [1]. Wind energy alone now contributes over 10% of

4

electricity production in 8 countries [2], while cumulative solar capacity is expected to

5

double between 2019 and 2022 [3]. A key driver for the growth in deployment of wind

6

and solar energy systems has been their rapidly declining costs in per unit energy

7

production [4–6].

8

The common and current objective used when designing variable renewable

9

energy (VRE) systems is the Levelized Cost of the Energy (LCOE) of the system [7–14].

10

The LCOE of a power generation system is the estimated cost per kilowatt-hour of

11

produced electricity over the lifetime of the system based on the ratio between the

12

annualized total costs of the system and the expected annual energy production.

13

Herein, VRE system design is defined as the design of entire wind and solar power

14

plants or design of individual units (wind turbines and photovoltaic panels). Designing by

15

LCOE provides a straightforward metric that allows engineers and stakeholders to

16

compare the cost of energy produced by different designs, while avoiding the complex

17

relationship between renewable energy system performance and larger market

18

dynamics. Historically, this LCOE-based design approach was reasonable as renewable

19

power plants often received a fixed price for each kilowatt-hour produced and thus each

20

kilowatt-hour of energy produced could be treated equally. In contrast, energy

21

economists and system planners employ more sophisticated financial metrics (relative

22

to LCOE) to accurately assess the value that different electricity generation assets will

23

have within a particular system and market context.

24

As the renewable share in the electric grids increases, they are increasingly

25

expected to participate in electricity markets for services, energy, and capacity, similar

26

to conventional energy generation assets [15,16], and VRE generation may be well

27

suited for some services [17]. Therefore, the industry is preparing for a paradigm shift

28

where the objective is not simply to produce the cheapest possible electrons, but

29

instead to create the highest possible value from a renewable power plant over the

30

course of its lifetime [15].

3

1

As previously mentioned, LCOE does not take into account time-varying revenue

2

streams for power plants. If power plants generate revenue from their ability to provide

3

services and energy in markets with time-varying prices, then the overall profitability of

4

the power plant depends on the correlation of the plant’s output with the value of those

5

revenue streams over time. Depending on the market, the price of electricity can rise to

6

ten times the average price when demand is high and, in the other extreme, can even

7

go negative when there is too much energy in the system. To quantify the effect of

8

these price variations, other metrics have been introduced. One metric introduced to

9

quantify the effect of price variations is the Value Factor (VF), defined by Hirth as the

10

ratio of a VRE spot market price to the total average spot market price [18]. However,

11

other scholars define Value Factor more generally as the levelized value of energy

12

divided by the levelized value of a continuous baseload generation technology [19]. As

13

the share of wind and solar energy increases, the relative Value Factor of the electricity

14

they produce falls [18–21], since the amount of energy produced by sources with near

15

zero marginal costs (such as wind and solar which have no fuel costs) drives down the

16

market clearing price of electricity [18,22].

17

Determining the revenue from VRE production is further complicated by the

18

nonlinear relationship between energy production and value. This dependence of

19

energy price with VRE production highlights one of many deficiencies inherent in the

20

LCOE metric [8,18,23–27]. Joskow [23] examined economic values of dispatchable (i.e.

21

conventional) and intermittent (i.e. variable) power generation technologies and noted

22

that a grid system that chooses technologies based on LCOE, without regard for the

23

time of energy production, will be sub-optimal or even fail. Instead, Joskow proposed

24

that energy be valued based on the expected market value when the energy is

25

produced. Fig. 1 illustrates the major components of LCOE as well as three of the most

26

applicable current metrics that attempt to move beyond LCOE: Levelized Avoided Cost

27

of Energy (LACE), System LCOE (sLCOE), and Revised System LCOE (rsLCOE).

4

1 2 3

Figure 1. Factors influencing energy prices and current metrics used to quantify energy value including LCOE, LACE, sLCOE, and rsLCOE

4 5

The Department of Energy’s Energy Information Administration (EIA) has

6

proposed the use of LACE and Net Value (NV) to better compare the benefits of

7

proposed power generation options [25,28,29], similar to Mills and Wiser’s “marginal

8

economic value” [30]. LACE adds up the revenue that can be gained from a new power

9

generation system and levelizes it based on the expected annual energy production.

10

For example, the EIA uses an extensive version of LACE in conjunction with the

11

National Energy Modeling System (NEMS) to model the electricity grid and potential

12

avoided costs when adding a new project to the grid [28].The Net Value of a project is

13

then simply the difference of LACE and LCOE. Using Net Value is a promising

14

alternative as it takes both costs and revenues into account. However, calculating LACE

15

usually requires complex, site-specific electricity price models, and thus Net Value is

16

overly complex for use by power plant and machine designers.

17

Ueckerdt et al. propose a more complete cost metric than either LACE or LCOE

18

defined as the System LCOE (sLCOE) [24]. As shown in Fig. 1, sLCOE increases

19

metric fidelity as it includes the many factors included in Integration Costs: additional

20

costs felt by the electrical system when variable renewable energy generation is added.

21

These integration costs are due to variability, uncertainty, and locational-constraints of

22

the technologies [27,31], and are further detailed in [27]. Notably, the calculation of the 5

1

sLCOE for a particular VRE system design would require extensive modeling and

2

analysis and, furthermore, does not itself denote the economic viability of a project.

3

The National Renewable Energy Laboratory recently reviewed the benefits and

4

drawbacks of a number of energy competitiveness metrics based on the perspective of

5

a centralized planner [19]. They concluded that none of the previous metrics were able

6

to take into account a comprehensive view of system-wide cost and value so as to

7

determine economic viability with high fidelity. To address this, system profitability

8

metrics were utilized to propose a Revised System LCOE (rsLCOE) based on the ratio

9

of cost to value of the system and a benchmark price [19]. Using rsLCOE allows for a

10

direct comparison to traditional LCOE values, while incorporating a system-level view of

11

economic viability, but requires the choice of an accurate benchmark price.

12

Due to the complexity of the above metrics, as well as their historical irrelevance

13

in energy markets with fixed prices, VRE designers have overwhelmingly employed

14

LCOE for design optimization, even though LCOE does not have a method for valuing

15

energy price at the time of generation of energy or potential capacity payments for the

16

plant.

17

While valuable metrics to evaluate energy systems from the point of view of a

18

centralized planner have been outlined above, there is a critical need for a practical

19

metric that can be implemented by energy system designers. This is important for both

20

individual machine design – i.e. solar panels and wind plants – as well as for the design

21

of full power plants – which may contain solar panels, wind turbines, storage, or

22

combinations thereof (i.e. hybrid power plants).

23

The purpose of this study is to develop a metric for VRE system design that

24

values energy based on the time of generation, in a simple and easy-to-use manner.

25

Two new metrics are proposed herein to accomplish this goal: LACE simplified (which is

26

applied to calculate Net Value) and Cost of Valued Energy (COVE). As a case study for

27

how this concept could be applied, the Return on Investment of a wind turbine is

28

calculated for varying turbine parameters.

29

The contents of this study will be as follows: Section 2 will explain the proposed

30

linear price-demand model, Section 3 will outline data sources and applying the linear

6

1

model to calculate Value Factor, and Section 4 will include a case study applying COVE

2

and Return on Investment.

3 4

2. Proposed Model for Price

5 6

LCOE is the standard metric used today by energy system designers to compare alternative technologies and optimize their systems. $

ℎ



=

(

!

+ & ) Σ" = " ∫

(1)

7

In this expression, Capital Costs are the costs of designing, building, and installing the

8

system while operating and maintenance costs (O&M) are the costs of operating and

9

maintaining the system [25]. As shown, by the right-hand side of Eq. 1, LCOE is the

10

sum of the costs over a period of time divided by the integral of hourly generation g over

11

the same period of time.

12

Alternatively, the calculation of LACE is defined by the EIA in [25] as: =

'()*

"

"

∑0,12&

/

'()*,,

∗ℎ

="



,.

"

+ ("

3

" ℎ

∗"



/

"

"

)

(2)

13

Where

is the marginal generation price of energy in time period i, hours are the

14

generation hours in time period i, capacity payment is the annual revenue an energy

15

system can earn based on its ability to offset dispatchable resources used to meet peak

16

demand, capacity value is the annualized cost of a dispatchable resource used to meet

17

a reserve requirement, and capacity credit is the percentage of installed capacity that

18

can offset reserve requirements [25]. Capacity credit takes into account the “peak

19

demand correlation” shown in Fig. 1, the likelihood that generation occurs at times of

20

critically high demand. The revenue in LACE takes into account revenue from time of

21

production and capacity credit; thus, LACE assumes that the power plant participates in

22

both energy and capacity markets over its lifetime. Once the LACE and LCOE for a

23

system have been calculated, the Net Value (NV) of the system can be calculated as

7

45 = 1

−

(3)

Note that a positive NV indicates a net profit and a negative NV indicates a net loss.

2

One of the main obstacles to renewable energy system designers moving

3

beyond LCOE when optimizing a system is the need to model energy price. To simplify

4

that process, a linear relationship between price and residual demand is proposed and

5

combined with a simple demand profile to model price.

6

method is that the revenue from direct electricity production for VRE sources is much

7

more significant than the revenue from capacity and other grid services. As described in

8

the Introduction, energy markets currently dominate and while VRE generators qualify

9

for varying capacity values by region, technology, and current regulations, their typical

10

capacity value is only a fraction of total installed VRE capacity [32]. While this neglects

11

a potentially important source of revenue for VREs, this assumption allows a simpler

12

and more direct model to calculate value.

A key assumption in this

13

Residual demand (or residual load) is the demand that must be met by

14

conventional energy sources once VRE production has been subtracted from the total

15

energy demand. 7

8 /

=8 /

− 57

"



(4)

16

The proposed linear relationship between spot market prices and residual demand has

17

already been demonstrated by von Roon [33].

18

correlation between spot market prices of electricity and residual demand in Germany

19

between 2007 and 2009 (e.g. Fig. 2), with coefficients of determination between 0.54

20

and 0.77 [33]. Using residual demand as a key variable in models that predict price has

21

become a recent topic of many papers as well [34–37].

The study found a strong linear

22

8

1 2 3

Figure 2. Spot Market Price from European Energy Exchange (normalized here by natural gas price) versus Residual Load [33]

4 5 6

Herein, we express this residual demand relationship in a normalized fashion that will be adapted to develop our models for LACEs and COVE. = /7 + "

. +X′

(5)

7

In this expression, m is the price-demand slope (a relationship which also depends on

8

region and renewable energy shares), p is the hourly spot price divided by the time-

9

averaged annual spot price, R is the hourly residual demand divided by the annual

10

average demand, and X’ reflects the variations due to extrinsic factors (such as those

11

found in Fig. 1) which average to zero. As such, X’ can be thought of as random

12

fluctuations (as in a Markov chain) relative to the residual demand information.

13

Continuing with the model of Eq. 5, R can be replaced with D (hourly demand

14

divided by the annual average demand) and Q (the hourly VRE generation divided by

15

the annual average demand). Additionally, fluctuations in X’ will be ignored herein as

16

stochastic noise in the data set, simplifying the analysis but also introducing potential

17

bias in the linear fit if X’ is not normally distributed with a mean of zero. = /(8 − <) + "

.

(6)

9

1

Note that an increase in demand or a decrease in VRE generation causes a price

2

increase, a well-known trend in energy economics [18,34,38]. The constant in Eq. 6 can

3 4

be determined by taking the annual time-average of Eq. 6 and noting 8(=* =

yielding

1 = /(1 − <(=* ) + "

5 6

.

(=*

= 1, (7)

If one separates VRE production into average and variable components as < = <(=* + <′, then Eqs. 6 and 7 can be combined and rearranged as = /8 + (1 − /) − /<′

(8)

7

When price, demand, and VRE data are all available for a location over a one-year

8

period, an m-value can be fit to the data to predict price given a model for future

9

demand and VRE generation data. However, when VRE generation data is not

10

available, a simpler but less accurate correlation can still be found by neglecting Q’,

11

whose average is zero (as was the case for X’) given how it was defined. Modeling the

12

price in this way yields = /8 + (1 − /)

(9)

13

Note that the additional uncertainty that comes from ignoring mQ’ in Eq. 9 is likely to

14

increase with increasing VRE shares.

15

As an alternative for LCOE (Eq. 1), we define an original metric, the Cost of

16

Valued Energy (COVE), by weighting the energy produced with the normalized market

17

value at the time of production. 5 =



(

∫ ∗

+ & )

=

Σcosts

∫ C/8 + (1 − /)D ∗

(10)

18 19

The last form of COVE in Eq. 10 employs the linear price relationship of Eq. 9 (which

20

5 indicating that energy has the same effective value no matter when it is produced.

21 22

assumes Q’ =0), but could instead employ Eq. 8 if Q’ is known. When / = 0,

=

However, when / > 0, hourly generation is scaled up or down based on the modeled

23

hourly spot price. As such, COVE can better incorporate the value of energy production,

24

as well as the cost of the investment and operation, all in one metric. Thus, COVE 10

1

improves upon LCOE to support a design process that better aligns with the expected

2

profitability of the VRE asset. COVE is similar to rsLCOE when the benchmark price of

3

rsLCOE is chosen to be the annual average spot price; however, COVE applies the

4

linear price-demand assumption while rsLCOE has a broader definition of value and is

5

thus more involved to calculate.

6 7

As an alternative for LACE (Eq. 2), we similarly define herein a simplified LACE (LACEs) which ignores capacity payments and estimates price with Eq. 9. =

∫ C/8 + (1 − /)D ∗ ∫

(11)

8

This metric only requires the annual average spot price, the price-demand slope m, the

9

time variation of energy demand, and the time variation of energy generation. It can be

10

used in place of LACE to evaluate the relative potential economic performance of

11

various engineering systems.

12

The two new metrics defined above are mapped out with relevant components in

13

Fig. 3. COVE starts with the components of LCOE then adds energy and demand data

14

to estimate value. Furthermore, LACEs takes into account revenue from the energy

15

market but excludes Capacity Credit, unlike standard LACE.

16

11

1 2 3

Figure 3. Energy components of newly proposed (COVE and LACEs) and conventional metrics

4 5

To aid in characterizing the economic performance for different VRE systems,

6

the Value Factor (VF) is a useful measure that removes the relative costs of different

7

technologies to focus on just energy value. To evaluate how well the linear relationship

8

to modeled demand can predict spot prices, VF is computed in three different ways (in

9

order of decreasing accuracy) as follows using: actual prices (conventional approach),

10

demand-estimated prices, and modeled demand- estimated prices: ∫ ∗ ∫

(12)

∫ C/8 + (1 − /)D ∗ ∫

(13)

∫ C/8' + (1 − /)D ∗ ∫

(14)

5G = 5G = 5G = 11

Note that VF is dimensionless since it takes out the effect of the average annual spot

12

price (given p is hourly spot price normalized by annual average spot price) and is

13

related to the herein proposed cost metrics via 12

5G =

(=*

=

5

(15)

1

As such, the fidelity of VF using direct demand (Eq. 13) or modeled demand (Eq. 14)

2

will represent the relative fidelity for COVE and LACEs.

3 4

3. Results

5

In the following, the linear relationship between price and demand will be

6

investigated, followed by a model for the seasonal variations in energy demand. Finally,

7

wind and solar data will be employed to estimate VF and determine the accuracy of the

8

linear price-demand relationship.

9 10

3.1. Demand-Based Price Estimation

11

To test the demand-based value relationship of Eq. 9 (used by Eqs. 10 and 11),

12

the price as a function of demand is shown for a one year period in Fig. 4 for three

13

different regions where data is publicly available to perform the analysis: PJM (a

14

regional transmission organization in the Mid-Atlantic region of the US) [a,b];

15

Queensland, Australia [c]; and Ontario, Canada [d]. A linear regression for each location

16

is shown as a straight line on all three plots, indicating the price-demand slope

17

(represented by the m-value). For the PJM region, m=1.5, while larger values are found

18

for the other two regions. Note that m>1 indicates that price will go negative as demand

19

goes to zero, consistent with other recent studies [39,40]. As expected, the variation in

20

actual price about this sloped line is large since it ignores factors associated with both

21

extrinsic factors (X’) and VRE variation (Q’).

13

1 2 3 4

Figure 4. Hourly energy price (normalized by the average annual price) as a function of hourly demand (normalized by average annual demand) along with linear fit models for: a) PJM with H = I. J, b) Queensland with H = K. JL, and c) Ontario with H = M. I

5 6

It is interesting to consider how the price-demand slope correlates with

7

generation mix, including the share of renewable energy, for each region. Queensland

8

generates most of its electricity from coal power with a growing share of solar energy

9

[e]; Ontario generates most of its power from nuclear and a large portion from 14

1

hydropower and wind [f]; PJM generates power from coal, nuclear, and natural gas, with

2

a small portion of renewables [g]. Note that hydropower and biofuels are not considered

3

in the renewable energy share due to their lower variability compared to the high intra-

4

diurnal variability of wind and solar.

5

As shown in Fig. 5, regions with higher VRE shares tend to have an increased

6

price-demand slope. This is even true for PJM when comparing 2016 data to 2017 data

7

– considering that the system generation mix is different from one year to the next.

8

While the set of data is too small to draw a statistically relevant conclusion, one may

9

infer from these cases that the share of VRE in the system is a key determinant of the

10

price-demand slope. One exception is the von Roon data [33], which does not seem to

11

follow this relationship. However, that data point was difficult to convert into the

12

appropriate units using only the data provided in the paper, and thus may or may not be

13

representative of the larger trend.

14 15

Based on Fig. 5, an approximate relationship between price-demand slope and VRE is given as /~1 + 0.34 <(=*

(16)

16

This relationship is consistent with the expectation that m=1 for a system with no VRE

17

and that m increases as VRE penetration increases.

18

reasonable for low VRE shares (under 10% in the cases studied), since the impact of

19

variable generation for higher shares may become significantly non-linear.

20

calculation of m also does not address the variation in generation mix nor the impact of

21

the interconnection and transmission connection on the relationship between energy

22

prices and renewable shares.

However, this may only be

The

23

15

1 2 3 4 5

Figure 5. Price-demand m-values compared to renewable energy shares of total generation (Qavg) for PJM (2016), PJM (2017), Queensland (2016), Ontario (2015), and estimated value from von Roon [33] for residual demand in Germany in 2008, as well as a linear fit given by QRST = K. UKH − K. UK

6 7

3.2. Proposed Model for Demand

8

In the following, the region of PJM (which has a large and publicly available set of

9

self-consistent data on demand, generation, and prices) is used to construct a demand

10

model and to assess COVE and other metrics. While real-time data is the most accurate

11

to use for demand (as was used in Fig. 4), a “standard demand” weekly profile is used

12

to simplify modeling. Herein, three weekly standard profiles are developed based on

13

seasons (summer, winter and spring/fall) by averaging weeks of Mid-Atlantic region

14

demand data from PJM for 2016-2018 [b]. These are compared in Fig. 6 to a randomly

15

selected week of real demand for each season.

16

These standardized demand curves were used to create a “standard year” of

17

modeled demand (Dm) by stringing together these seasonally-averaged weeks so that

18

total demand is comparable to a year of actual demand data (Fig. 7). For PJM, the

19

season durations of winter, spring, summer, and fall were set as 16, 11, 17, and 8 week

20

periods, to best match the real demand data for a year. While the length of each 16

1

season may vary regionally, the general shape of the demand curves is typical of most

2

regions in the USA [h]. This standard year of demand was created to smooth out single

3

year irregularities which may occur due to weather, power plant or transmission

4

downtime, regulation changes, etc. The differences between demand and modeled

5

demand seen in Fig. 7 are examples of these irregularities which will vary year to year.

6

7 8 9

Figure 6. Seasonal demand profiles normalized by the annual average demand for a sample PJM week and for season-averaged (modeled) PJM week

10

17

1 2 3

Figure 7. Normalized 2016 PJM demand data compared to standard year of demand created using season-averaged (modeled) PJM data

4 5

To assess the accuracy of the standard year of demand, the Root Mean Square

6

Error (RMSE, Eq. 17) was used to evaluate how well real hourly demand was predicted.

7

The modeled year of demand was compared to three years of real hourly demand; the

8

three years of demand were also compared to each other. The results in Table 1 show

9

that using the modeled year of demand results in differences on the same order as real

10

demand; in fact, the modeled demand predicted all three years of demand with lower

11

RMS Errors than using real years of demand. Thus, in this case, the standard year of

12

modeled demand is preferred over using a single year of demand data to predict other

13

years of demand.

14 &YZ)[\,]^[\,, − Y_`a[)=[\,, . 7 V = WX 4 ,12 c

b

(17)

15 16

18

1 2

Table 1. Annual RMS Error comparing the difference between years of demand Modeled Demand

2017 Demand

2018 Demand

2016 Demand

0.0256

0.0393

0.0340

2017 Demand

0.0319

-

0.0333

2018 Demand

0.026

-

-

3 4

3.3. VRE Generation Data

5

Hourly generation data is needed to evaluate COVE and LACEs (via Eqs. 10 and

6

11). While historical data is the most accurate to use (as was used in Fig. 4), generation

7

can also be estimated from wind resource data, solar radiation (insolation) data, and

8

other plant output. To simulate future scenarios of solar and wind deployment in the

9

region of Virginia (within the PJM region) hypothetical hourly generation distributions

10

were obtained to represent generation from future installations of utility-scale VRE

11

power plants. For solar energy generation, PV production data was gathered from a

12

University of Virginia solar installation with a maximum output capacity of 126 kW for

13

2017-2018 [i]. Note that the size of the installation does not matter (for the assumption

14

of small solar share) as it is non-dimensional in the analysis below. For wind generation,

15

offshore wind energy (expected to be a significant player in Virginia in the future) was

16

employed by using one year of wind data at 90m from the DOE BUOY project off the

17

Virginia coast [j] combined with the NREL 5 MW offshore wind turbine power curve [41]

18

to calculate expected hourly wind power data. As with solar, the size of the wind turbine

19

plant and the plant loss factor do not factor into this analysis. This simplification enables

20

easier analysis of scaling the VRE generation up and down but does not account for the

21

potential correlation (positive, neutral or negative) of VREs that are distributed

22

geographically, which can mitigate against some of the impact to the price-demand

23

relationship in a region [42–45].

24

The above example wind and solar data from locations within the Mid-Atlantic

25

PJM region was used to investigate the potential correlation between generation and

26

hourly demand before applying the linear price-demand model. Standard summer and

27

winter demand curves are shown in Fig. 8, along with a representative week of solar 19

1

energy production and wind energy production for each season with hypothetical shares

2

of 10%. In addition, the resulting residual demand for the summer only is shown in Fig.

3

9 for both solar and wind. As can be seen in Figs. 8a and 8b, there is a general

4

correlation of solar energy production with demand, but the evening rise in demand is

5

not well correlated to solar energy, leading to a rise in residual demand during that

6

portion of the day (seen in Fig. 9a), a phenomena known as the “duck curve” [42,46]. In

7

contrast, wind energy based on PJM offshore data as shown in Figs. 8c and 8d is more

8

stochastic with little correlation between production and demand and higher wind seen

9

in the winter than summer.

10

As such, the residual demand for wind is relatively

stochastic about the standardized demand curve.

11 12 13

Figure 8. Electricity demand and generation for a hypothetical solar Savg=0.1 (a,b) and a hypothetical wind Wavg=0.1 (c,d) for an example week in the summer and winter

20

1

2 3 4

Figure 9. Residual Demand over summer week with hypothetical Savg=0.1 solar generation (a) and Wavg=0.1 wind generation (b)

5 6

3.4. Value Factor Validation

7

Pulling together the price, demand, and generation data described above, VF

8

was calculated by Eqs. 12-14 for wind and solar. The results are shown in Table 2a,

9

where Eq. 12 is applied to three years of real price data for PJM. The average and

10

standard deviations of the error using the linear price model with demand and modeled

11

demand (both relative to real-time price data) are given in Table 2b. While wind and

12

solar VFs see similar errors when using the linear model with real-time demand, solar

13

VF has a larger error than wind VF when using modeled demand. However, the VF

14

errors are generally small, especially given the simplifications and assumptions

15

associated with the linear-price model and the standardized demand curves.

16

Table 2a also gives important information about the relative values of wind and

17

solar installations at low share of VRE penetration. Wind tends to have a VF close to 1

18

since its generation is largely stochastic and does not often correlate positively or

19

negatively with demand. However, solar tends to have a higher VF that is above 1 since

20

its generation often aligns with times of high demand, especially during the middle of the

21

day.

22

21

1 2 3 4

Table 2. Value Factor for wind and solar examples: a) calculated with real price data (p) for PJM for 3 consecutive years, a linear relationship with a real demand (D), and a linear relationship with the modeled demand (Dm); and b) Percent error of real price data for the demand and modeled demand VF models.

5

a) VF

Wind

Solar

using p (2016)

0.974

1.185

using p (2017)

1.012

1.133

using p (2018)

0.995

1.119

using D

0.972

1.114

using Dm

0.966

1.080

6 7

b) Wind

Solar

VF

Avg. % Error

Error St. Dev.

Avg. % Error

Error St. Dev.

using D

2.20%

1.88%

2.68%

2.94%

using Dm

2.77%

1.86%

5.65%

2.85%

8 9 10

Figure 10 indicates the sensitivity of VF to price-demand slopes (associated with

11

changes in VRE penetration per Fig. 5) using the example wind and solar PJM data.

12

The m-values for each of the three evaluated regions are denoted with vertical dashed

13

lines, while the VF calculated with real spot prices (from Table 2a) are denoted with

14

points. The spot price data (Eq. 12) falls close to the predicted trends for solar and wind

15

(Eq. 14), but the modeled-demand values tend to under-predict VF. This may be

16

attributed to over-smoothing of demand data, which reduces modeled price spikes and

17

dips. It is recommended that further data should be collected from other regions with

18

different VRE shares, generation mixes and demand profiles to better characterize the

19

fidelity of modeled-demand VF.

20

For a given region, Fig. 10 shows that solar and wind will have significantly

21

different VFs, even for a moderate price-demand slope of m=1.5. This illustrates the

22

relative benefit of solar’s higher correlation of generation with demand, which only

23

becomes more extreme with increasing m. For example, if PJM were to shift over time 22

1

to m=4.1, solar would earn nearly a 50% higher VF than wind, using the linear price-

2

demand relationship.

3 4 5

Figure 10. Value Factor as a function of changing m values based on actual price for 2016, 2017, and 2018 (symbols) and modeled price (lines)

6 7

4. Wind turbine design case study

8

To illustrate the trade-offs in design that can affect LCOE and COVE, a simplified

9

example of the preliminary design of an individual wind turbine is considered. While this

10

example focuses on wind turbine design, the approach could be similarly used for

11

photovoltaic panel design, or even the design of entire wind and solar power plants.

12

Conventionally, a designer optimizes the turbine design to produce as much energy as

13

possible (within design load specifications) at the lowest possible cost for a given wind

14

class and machine rating. Designing in this way to minimize LCOE may not be

15

economically optimal. As an example of the separate influence of COVE beyond LCOE,

16

we consider the influence of rotor size on the system design and value. From a pure

17

LCOE perspective, “growing the rotor” for a fixed rating may have limitations, since the

18

mass of the turbine can outpace the increase in power capture. However, increasing the

19

rotor size relative to machine rating shifts the wind turbine power curve to allow for more 23

1

energy capture at lower wind speeds and thus increases the Capacity Factor (CF) of the

2

machine for a given site. With advances in technology, it may be possible for LCOE to

3

not vary significantly with increasing rotor diameter [47,48].

4

The effect of CF variations is considered in an example case study using the

5

offshore Virginia wind dataset. In particular, a set of turbine designs are considered for

6

a fixed generator rating (5 MW) but with a range of rotor diameters (from 90 m to 180 m)

7

and corresponding power curves. The result of the variation in rotor diameter on COVE

8

(for a fixed LCOE) is shown in Fig. 11, using Eq. 10 with two different m-values: one

9 10

based on the current PJM region (/ = 1.5), and one based on Ontario (/ = 4.1),

representative of a region with higher VRE shares. Based on the results in Table 2, an

11

estimated error of +/-2% is included in this plot as a shaded region to illustrate the

12

potential uncertainty of the COVE trends. However, this uncertainty may be higher in

13

regions with greater share of VRE, and there may be additional error from assuming

14

that LCOE changes are negligible over the range of rotor sizes considered.

15

16 17 18 19

Figure 11. Influence of Capacity Factor (CF) on Cost of Valued Energy (COVE) where PJM eRST = Kf. M $/hij and klmn = Ko. J $/hij (for future plausible design) with two different m-values applied. The baseline CF of 0.43 is denoted with a vertical dotted line.

20

24

1

For this particular dataset, wind has a slight negative correlation with demand,

2

and increasing Capacity Factor is shown to mitigate this effect, resulting in a favorable

3

decrease in COVE (Fig. 11). While the reduction in COVE is almost negligible for m

4

=1.5, a significant range of $1.5/MWh in COVE is seen with m =4.1. This indicates that

5

a region with a higher share of VRE will generally have a greater benefit when

6

increasing the CF of a wind turbine.

7

The economic perspective that COVE provides for VRE system design can be

8

shown more explicitly by considering the Return on Investment (ROI) for a particular

9

wind turbine design. ROI is a common profitability metric used by investors to compare

10

business options and economic performance of a system. 7 p=

7 3

−

=

∗∫ Σ"

(=*



−1

(18)

11

Maximizing ROI is a useful overall objective from a system design and investment

12

perspective. ROI can be approximately related to the herein proposed cost metrics as 7 p=

45

=

(=*

5

−1=

(=*

∗ 5G

−1

(19)

13

However, the actual ROI depends on a variety of factors including the economic

14

components in Fig. 1. As such, the above is only a first-order approximation of ROI with

15

respect to the influence of COVE (or VF or LACE). For the sake of this analysis, the

16

potential change in ROI as a function of the cost metrics is used: ∆7 p = ∆ r

(=*

5

− 1s = ∆ t

(=*

∗ 5G

− 1u

(20)

17

While many other factors outside of energy spot price influence ROI, Eq. 20 can

18

be used to directly relate the influence of COVE on ROI. This relationship also shows

19

that minimizing COVE (or equivalently maximizing VF while minimizing LCOE), may

20

result in different design decisions than only minimizing LCOE, since LCOE does not

21

take into account design trade-offs between producing higher value energy and

22

producing energy for the least cost. In the present wind turbine case example, the result

23

of the variation in capacity factor (through rotor diameter) on the change in ROI (for a

24

fixed LCOE) is shown in Fig. 12 using Eqs. 10 and 20 with two different m-values. While 25

1

there are significant uncertainties that are not accounted for in this simple model, the

2

results show that increases in CF (assuming a fixed LCOE) can lead to significant

3

improvement in ROI.

4

5 6 7 8

Figure 12. Influence of Capacity Factor (CF) on change in Return on Investment (Δ ROI) with two different m-values applied. The baseline CF of 0.43 is denoted with a vertical dotted line.

9 10

Limitations of this method include that COVE and ROI values calculated with Eq.

11

9 neglect variations in Residual Demand that will arise if VRE penetration increases. If

12

Residual Demand data were available, Eq. 8 could be used to predict price, which does

13

not neglect the variations described by Q’. Including this additional information is likely

14

to increase the model accuracy, a hypothesis which is recommended for future

15

investigation. This information may also increase the sensitivity of COVE to CF when

16

designing a wind turbine for use in a region with high wind shares; an increased

17

capacity factor would reduce the negative impact of producing energy at times of low

18

price (i.e. at low residual demand due to high wind production), creating an enhanced

19

levelization advantage.

20

26

1

5. Conclusions and Future Outlook

2

To improve upon the conventional use of LCOE for design of wind turbines and

3

solar panels, as well as full wind and solar power plants, two relatively simple metrics,

4

COVE and LACEs, are developed herein to take into account the changes in energy

5

value and the time of generation. Using the proposed linear price-demand relationship

6

combined with the LCOE value, LACEs and COVE can be obtained using: 1) season-

7

based standardized weekly demand curves (Dm), 2) a price-demand slope (m) that is

8

related to VRE penetration, and 3) predicted hourly VRE generation data. Both metrics

9

are more straightforward to employ as compared to utility-based metrics, such as

10

sLCOE or rsLCOE, which are more suited to grid-level decisions. As such, these

11

simplified models can be helpful to VRE system designers during the initial stages of the

12

design process.

13

The wind turbine design example showed that the ROI for a particular wind

14

turbine design could be improved by increasing the CF through increasing the rotor

15

diameter for the given machine rating (assuming LCOE remains unchanged). It also

16

showed that for a region with low m (such as PJM), ROI is relatively insensitive to

17

changes in rotor diameter, but a higher m region sees more significant effect on ROI

18

with changes to rotor diameter. As a single, simple metric, COVE is able to directly

19

relate to ROI for design decisions such as this one.

20

Future recommendations include additional data surveys for this design metric

21

using a range of price and demand datasets in different regions, with varying levels of

22

VRE shares, profiles of the overall generation mix, levels of transmission build-out, and

23

demand profiles. The potential future work may also investigate extending COVE or

24

LACEs to include aspects related to the technology capacity value and capacity

25

payments and also for VRE power plants that include storage technologies. Finally, the

26

impact of using COVE or LACEs on the design of renewable energy systems should be

27

investigated to understand how the objectives influence the designs compared to

28

traditional LCOE objectives.

29

27

1

6. Acknowledgements

2

The information, data, or work presented herein was funded in part by the Advanced

3

Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under

4

Award Number DE-AR0000667. The views and opinions of authors expressed herein

5

do not necessarily state or reflect those of the United States Government or any agency

6

thereof.

7 8

28

1

7. References

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Highlights •

LCOE is inadequate for valuing energy produced by a renewable energy system

•

Two new market-based cost metrics are proposed to improve upon LCOE: COVE and LACEs

•

A linear price-demand relationship provides a first-order value of energy

•

Return on Investment increases with wind turbine capacity factor (for a fixed LCOE)

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: