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Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards

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Abstract

Renewable portfolio standards (RPSs) are popular market-based mechanisms for promoting development of renewable power generation. However, they are usually implemented without considering the capabilities and cost of transmission infrastructure. We use single- and multi-stage planning approaches to find cost-effective transmission and generation investments to meet single and multi-year RPS goals, respectively. Using a six-node network and assuming a linearized DC power flow, we examine how the lumpy nature of network reinforcements and Kirchhoff’s Voltage Law can affect the performance of RPSs. First, we show how simplified planning approaches that ignore transmission constraints, transmission lumpiness, or Kirchhoff’s voltage law yield distorted estimates of the type and location of infrastructure, as well as inaccurate compliance costs to meet the renewable goals. Second, we illustrate how lumpy transmission investments and Kirchhoff’s voltage law result in compliance costs that are nonconvex with respect to the RPS targets, in the sense that the marginal costs of meeting the RPS may decrease rather than increase as the target is raised. Thus, the value of renewable energy certificates (RECs) also depends on the network topology, as does the amount of noncompliance with the RPS, if noncompliance is penalized but not prohibited. Finally, we use a multi-stage planning model to determine the optimal generation and transmission infrastructure for RPS designs that set multiyear goals. We find that the optimal infrastructure to meet RPS policies that are enforced year-by-year differ from the optimal infrastructure if banking and borrowing is allowed in the REC market.

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Notes

  1. For example, California utilities are required at the end of 2016 to report an equivalent renewable generation of 21.7 % of 2014 energy retail sales, with these percentages increasing to 23.3 % in 2015, and 25 % in 2016.

  2. Tier 1 includes solar, PV, wind, geothermal, tidal, and biomass energy. The non-compliance penalty is 50 $/MWh.

  3. In an empirical study, Wiser and Bolinger (2011) found that wind projects do not present important economies of scale. The California Solar Statistics webpage also reports moderate economies of scale for solar projects smaller than 1 MW (CSS 2012). Scale economics for combined- and single-cycle power plants, investment costs are generally larger than those from renewable power plants, but their optimal sizes are still small compared to the capacity of, e.g., 500 kV transmission lines.

  4. Although here we only focus on the integration of renewable generation into the system, our framework can also be used for studying the interaction of transmission planning with other market-based policies to put electricity production on a more sustainable footing, such as emissions trading programs.

  5. The model is stated as if \(H \)includes 8760 hours per year. If the sampled hours are fewer in number, then each sample hour’s variables would be weighted by \(8760/{\vert }H{\vert }\) in the objective function.

  6. See Schweppe et al. (1988) for a derivation of the linearized DC load flow model based upon explicit variables for bus voltage angles; this and other equivalent linear load flow models are widely used in power systems dispatch, planning, and market simulation models (Ventosa et al., 2007; 2012). KVLs are written as disjunctive constraints for the candidate lines. That is, for \(x_{l,n} =1\), (8) becomes an equality constraint, equivalent to (7). For \(x_{l,n} =0\), (8) does not constrain the power flow variables in the left-hand side since \(M\) is a large positive number. This is a common way to represent the KVL constraints in transmission expansion models (Munoz et al. 2012).

  7. We use a simple deterministic model with a sufficiently high penalty for loss of load such that demand is always met. Modeling reliability requirements such as the “one day in ten years” loss of load expectation rule is beyond the scope of this article.

  8. An important issue in the design of RPS systems is the ability to bank and borrow credits, which will dampen credit price volatility resulting from demand and wind output variations. Here we ignore this effect, as we do not model the inter-annual variability of wind production.

  9. Note that since solar generation is available at all buses, it is an alternative to meet renewable goals instead of building new transmission capacity to access remote resources. The model will automatically recommend Investments in solar generation at the load, instead of new transmission capacity if this configuration is more cost-effective than importing renewables from a distant bus, considering congestion effects.

  10. Here we are not considering the retirement of power generation units since it is not apparent that this would materially affect our conclusions. However, a more refined model could explicitly include going-forward costs and decisions to retire.

  11. In this case, KVL cannot be written as linear disjunctive constraints (Eq. 8), since \(x_{l,n} \) are defined as continuous instead of binary variables. We assume that suceptances are proportional to line capacities and enforce KVLs as nonlinear constraints: \(f_{l,n,h} -\gamma _l x_{l,n} (\theta _{b,h} -\theta _{p,h} )=0\). We find a local optimum using the nonlinear solver SNOPT 7.2 with the solution from the Continuous-Transportation approach as a starting point.

  12. Note that we are not stating that nonmonotonicity cannot occur in the Copper-Plate or Continuous-Transportation approaches; we are only highlighting how nonmonotonicity is enhanced by the lumpiness of transmission investments and KVL.

  13. Some analyses have suggested that higher RPS targets would result in lower spot prices (Felder 2011), which is a logical outcome if thermal capacity and loads are held constant. Under that assumption, adding renewable capacity shifts the short run supply curve to the right, lowering prices. However, in our long run analysis in which thermal capacity is a variable, this does not occur—load weighted LMPs are unchanged through RPS from 0 to 20 and 35 to 47 %, and are appreciably lower only for ranges of targets between 31 and 34 %, and greater than 47 %. The reason is that thermal capacity is not added unless it is profitable, so in any solutions in which such capacity is built, prices must rise to levels sufficient to cover fixed and variables costs. As a result, expansion of renewable capacity is compensated for by shrinkage in thermal capacity.

  14. Although there are issues about defining the marginal costs of RECs in the discrete cases, here we approximated them by finite-differences. Note that the price of RECs would not cover all incremental costs of meeting the RPS in those cases relative to a zero RPS target. This is an example of the duality gap phenomenon, which has been discussed extensively in the context of the use 0-1 unit commitment models to operate power systems (Hobbs et al. 2001).

  15. A more sophisticated model with additional 5-year stages did not yield qualitatively different results.

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Acknowledgments

The work reported in this article was partially supported by USDOE through the CERTS Reliability and Markets program, NSF through an EFRI-RESIN Grant number 0835879, the Fulbright Foundation through the NEXUS program, and CONICYT, FONDECYT/Regular 1100434.

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Authors and Affiliations

  1. Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD, 21218, USA

    Francisco D. Munoz & Benjamin F. Hobbs

  2. Department of Industrial and Systems Engineering, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Raúl Deves Hall, Piso 3, Macul, Santiago, Chile

    Enzo E. Sauma

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  1. Francisco D. Munoz
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Correspondence to Francisco D. Munoz.

Appendix

Appendix

See Tables 3, 4, and 5.

Table 3 Garver network lines characteristics and investment costs
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Table 4 Load and renewable generator capacity factors for the 20 time blocks
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Table 5 Correlations, means and standard deviations of load and capacity factors
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Munoz, F.D., Sauma, E.E. & Hobbs, B.F. Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards. J Regul Econ 43, 305–338 (2013). https://doi.org/10.1007/s11149-013-9209-8

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