# Insuring a Small Retail Electric Provider’s Procurement Cost Risk in Texas

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Risk Management Problem of a Small REP in Texas

## 3. Demand for the Proposed Insurance

#### 3.1. Electricity Products

#### 3.1.1. Wholesale Electricity Products

#### 3.1.2. Retail Electricity Products

#### 3.2. Possible Buyers

## 4. Insurance’s Design, Pricing, and Implementation

#### 4.1. Design and Pricing

^{2}= Var(Y) = variance of Y. We can use the forward contract pricing formula in Woo et al. (2001) to calculate S:

#### 4.2. Implementation

## 5. Indicative Calculation of the Insurance’s per MWh Premium

^{2}may come from ERCOT’s least-cost generation dispatch [3], they are difficult to forecast for determining a forward-looking value for S. As an illustrative alternative, we calculate μ and σ

^{2}based on the per MWh price adder set by ERCOT’s ORDC [6].

^{2}are available from non-ORDC sources, they should replace those presented below.

^{2}is applicable to any price cap in effect at the time of the per MWh premium’s calculation.

_{U}, where R

_{U}= R’s upper threshold at which the ORDC price adder is $0/MWh.

_{U}> R > R

_{L}, where R

_{L}= R’s lower threshold at which the ORDC price adder is strictly positive. The coefficient α > 0 is the VOLL that can be replaced by a lower price cap. The coefficient β = −(α/R

_{U}) < 0 is the marginal effect of R on Y.

_{L}≥ R.

_{1}= 0 and Var(Y|Case 1) = 0.

_{2}= α + β μ

_{R}, where μ

_{R}= E(R|Case 2). Let σ

_{R}

^{2}= Var(R|Case 2) for R

_{L}< R < R

_{U}so that Var(Y|Case 2) = β

^{2}σ

_{R}

^{2}.

_{3}= α and Var(Y|Case 3) = 0.

_{2}and β

^{2}σ

_{R}

^{2}requires μ

_{R}and σ

_{R}

^{2}in Case 2. Hence, we find μ

_{R}and σ

_{R}

^{2}as follows. Let R = normally distributed reserve with mean η and variance λ

^{2}, ρ

_{L}= (R

_{L}− μ)/μ and ρ

_{U}= (R

_{U}− η)/λ. As a result,

_{R}= η − λM,

_{U}) − ϕ(ρ

_{L})]/[ϕ(ρ

_{U}) − ϕ(ρ

_{L})], ϕ(z) = normal density function, ϕ(z) = normal probability distribution function, and z = standard normal variate [35]. Further,

_{R}

^{2}= λ

^{2}(1 − M

^{2}− N),

_{U}ϕ(ρ

_{U}) − ρ

_{L}ϕ(ρ

_{L})]/[ϕ(ρ

_{U}) − ϕ(ρ

_{L})].

_{1}= Prob(R ≥ R

_{U}), π

_{2}= Prob(R

_{U}> R > R

_{L}) and π

_{3}= Prob(R

_{L}≥ R) = 1 − π

_{1}− π

_{2}. As indicated in Section 6, these probabilities can be estimated by an electric grid’s generation reliability criterion and ERCOT’s history of emergency hours.

_{2}θ

_{2}+ π

_{3}θ

_{3}.

^{2}= π

_{2}(θ

_{2}

^{2}+ β

^{2}σ

_{R}

^{2}) + π

_{3}α

^{2}− (π

_{2}θ

_{2}+ π

_{3}θ

_{3})

^{2}.

## 6. Empirics

#### 6.1. Results

_{L}= 2000 MW, R

_{U}= 5000 MW, and β = −9000 ÷ 5000 = −1.8. Without invoking Equation (2), we use the midpoint between R

_{L}and R

_{U}as a simple estimate for μ

_{R}= 3500 in Case 2, which enables a REP’s quick determination of the value of a competitively priced insurance premium. While this estimate for μ

_{R}is less than the appropriately found estimate of 4475 MW based on Equation (2), our sensitivity check indicates that our calculated S is insensitive to the size of μ

_{R}.

_{R}= 444.60. This calculation of σ

_{R}enables an insurer’s determination of the per MWh insurance premium’s probability of profitability.

_{3}= 2.4 h/8760 h = 0.000274 based on the loss-of-load-expectation criterion of 1 day in 10 years, which is commonly used to determine an electric grid’s target of generation reserve margin. We further assume π

_{2}= 12 h/8760 h = 0.00137, which is five times π

_{3}and based on ERCOT’s history of emergency hours of 10 to 20 h per year, excluding Winter Storm Uri’s year of 2021.

_{L}≈ $6.16/MWh at z ≈ 0 when there is fierce competition in a REP’s procurement auction. Thanks to Equation (4) that shows μ = π

_{2}(α + β μ

_{R}) + π

_{3}a; a REP can quickly determine S

_{L}based on the simple estimate of μ

_{R}= 0.5 × (R

_{L}+ R

_{U}), the price cap value of a, b = − (a/R

_{U}), and the readily available data for π

_{2}and π

_{3}. The upper bound for S is S

_{U}= $305.98/MWh at z = 1.65, reflecting S

_{U}’s profitability for an insurance seller with almost certainty.

_{U}− S

_{L}= $299.82. However, making this large profit with almost certainty is unrealistic because a REP can use S

_{L}= $6.16/MWh as the benchmark for selecting the winner of its procurement auction.

_{L}and S

_{U}are not materially affected by doubling or halving the values for η and λ. However, reducing α from 9000 to 5000, which is in effect as of 1 January 2022, leads to S

_{L}= $3.42/MWh and S

_{U}= $170.0/MWh.

#### 6.2. Discussion

_{L}is ∆G

_{L}= [0.8 × 60 + 0.2 × (60 + 6.16)] − 60 = $1.23/MWh = 2.05% of the average G value. The price increase based on an insurer’s highly profitable per MWh premium of S

_{U}is ∆G

_{U}= [0.8 × 60 + 0.2 × (60 + 305.98)] − 60 = $61.20/MWh = 102.0% of the average G value. To complete Table 1, we alternatively assume γ = 10% (30%). The estimates for ∆G

_{L}and ∆G

_{U}are 1.03% and 51.00% (3.08% and 153.0%) of the average G value.

_{L}.

_{L}and ∆G

_{U}estimates in Table 1, the REP may consider buying the insurance when its procurement auction’s winning S quote is close to S

_{L}. However, it should reject S quotes that resemble S

_{U}. Hence, our ∆G

_{L}and ∆G

_{U}estimates guide the REP’s decision on insurance purchase, notwithstanding that such a decision is ultimately made by the REP’s risk-averse management.

## 7. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Scatter plot of hourly DAM energy price vs. hourly RTM energy price for the period of 01 January 2011 to 31 December 2017. The OLS regression based on the efficient market hypothesis is RTM price = a + b × DAM price + error, where a ≈ 0 and b ≈ 1 are the regression’s coefficient estimates. Updating the figure with more recent data does not change its key message: DAM and RTM prices move in tandem and are highly volatile with infrequent but large spikes.

**Figure 2.**A hypothetical REP’s load duration curve, procurement of electricity forward contracts, and residually unhedged peak loads.

**Figure 3.**ERCOT’s physical reserve capability vs. ORDC price adder [6].

Per MWh Insurance | γ = 10% | γ = 20% | γ = 30% |
---|---|---|---|

S_{L} that results in ΔG_{L} | 1.03% | 2.05% | 3.08% |

S_{U} that results ΔG_{U} | 51.0% | 102.0% | 153.0% |

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**MDPI and ACS Style**

Woo, C.-K.; Zarnikau, J.; Tishler, A.; Cao, K.H. Insuring a Small Retail Electric Provider’s Procurement Cost Risk in Texas. *Energies* **2023**, *16*, 393.
https://doi.org/10.3390/en16010393

**AMA Style**

Woo C-K, Zarnikau J, Tishler A, Cao KH. Insuring a Small Retail Electric Provider’s Procurement Cost Risk in Texas. *Energies*. 2023; 16(1):393.
https://doi.org/10.3390/en16010393

**Chicago/Turabian Style**

Woo, Chi-Keung, Jay Zarnikau, Asher Tishler, and Kang Hua Cao. 2023. "Insuring a Small Retail Electric Provider’s Procurement Cost Risk in Texas" *Energies* 16, no. 1: 393.
https://doi.org/10.3390/en16010393