Uncertainty-averse TRANSCO planning for accommodating renewable energy in CO_{2} reduction environment
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Abstract
The concern of the environment and energy sustainability requests a crucial target of CO_{2} abatement and results in a relatively high penetration of renewable energy generation in the transmission system. For maintaining system reliability and security, the transmission company (TRANSCO) has to make strategic planning to handle the uncertainty challenges from the intermittent renewable energy resources. In this paper, a stochastic multi-period multi-objective transmission planning (MPMOTP) model is proposed to reduce correlated uncertainties from renewable energy generation, conventional generation, demand-side variations, market price volatility, and transmission configuration. Three objectives, i.e. social CO_{2} reduction benefit, energy purchase and network expansion cost and power delivery profit, are optimized simultaneously by a developed two-phase multi-objective particle swarm optimization (MOPSO) method. The feasibility and effectiveness of the proposed uncertainty-averse MPMOTP model have been verified by the IEEE 24-bus test system.
Keywords
CO_{2} reduction Renewable energy Uncertainty Multi-objective planning TRANSCO MOPSO1 Introduction
The theme of energy sustainable development and conservations is widely recognized around the world, while the electric power industry is regarded as the major CO_{2} emission sector with the traditional fossil-dependent production. In the deregulated environment, CO_{2} reduction has already become the most significant concern involved in the decision making process within the multi-layer architecture of electricity generation, trading, transmission and distribution, even in the retail aspect, respectively dominated by generation companies (GENCOs), market operator (MO), transmission companies (TRANSCOs), distribution companies (DISCOs) and retailers.
From the last decade, numerous literatures and projects have already been carried out to demonstrate the feasible solutions to reduce CO_{2} emission, which can be categorized into three schemes, i.e. technological CO_{2} abatement, market-oriented based CO_{2} trading and alternative energy production. As firstly discussed in [1] and further investigated in [2], on perspective of GENCOs and power system operation, CO_{2} capture and storage (CCS) is addressed as a most promising technology for CO_{2} reduction. On basis of the low-carbon economy analysis in [3], for the conscious of the economic factors in day-ahead energy market and cap-and-trade carbon emission market, a flexible operation model is proposed in [4] to trade off the maximum profit with adaptive carbon emission for a generating unit combining with proper coordination of generation schedule, CCS schedule and market bidding strategies. Alternative energy production could be highly efficient energy resources or more environmental energy conversions, in which renewable energy is leading this role for CO_{2} mitigation from the current to the future, a huge amount of wind and photovoltaic (PV) energy will widespread in the transmission system to replace the conventional generation, as reviewed in [5].
However, the intermittent characteristics of the diverse renewable energies will derive huge uncertainties to the transmission system operation. Therefore, a strategic uncertainty-averse TRANSCO planning is necessary to ensure the adequacy and reliability of the power system operation for accommodating renewable energy in CO_{2} reduction environment.
Various approaches for handling uncertainties in transmission planning process have been summarized in [6]. In [7], the market uncertainties are identified as possible future scenarios solved by the mixed integer linear programming (MILP) on a flexible transmission planning model, and assessed with reliability and security criterions referring to the indices of expected energy not supplied (EENS), expected cost of interruptions (ECOST), and interrupted energy assessment rate (IEAR) [8]. Subsequently, a stochastic MILP approach complemented with risk aversion was proposed in [9]. Furthermore, to assess the robustness of expansion plans, a Brazil test grid is presented [10] to illustrate the stochastic approach is more suitable than the traditional deterministic method. Additionally, a stochastic multi-objective optimization framework is proposed in [11] to take security constrains into concern for transmission planning. In the other perspectives, a congestion surplus [12] is identified in a multi-objective transmission planning (MOTP) model for dealing with the risk of the network congestions. Recently, for integrating the large-scale wind power, a probabilistic MOTP model equipped with risk-control strategies is developed by [13] to avoid transmission overloading. Extensive uncertainty studies are allocated in [14] and [15] to conduct the distributed energy resources (DERs) impacts on distribution systems.
Till now, the uncertainties faced by the TRANSCO are normally considered as independent factors, however, immersed in the future smart grid surroundings, as a profit chasing commercial player, an extra pressure for the TRANSCO is to fully understand the high correlations among these uncertainty diversities hidden in the transmission planning process to flexibly balance the intermittent recourses and stochastic consumptions.
In this paper, the wind power and PV energy are selected to represent the renewable energy caused uncertainties. The effort of demand response (DR) is concerned in the demand side to intensify the consumption behavior. To assess the circumvent uncertainties in terms of the output of wind and PV generating units, demand response related load fluctuation, conventional generation units, market price volatility, and transmission path deployment, the correlation coefficient matrix is introduced to handle the dependency of the uncertainties in the paper. A stochastic MPMOTP model is proposed for this uncertainty-averse TRANSCO planning, incorporated with the following objectives: 1) maximize the social benefit via CO_{2} reduction, 2) minimize the TRANSCO cost of energy purchase and network expansion, 3) maximize the profit of power delivery. A two-phase MOPSO schema is employed to be the solver. The application of the proposed MPMOTP model is demonstrated on the IEEE 24-bus testing system to show its feasibility.
2 Modeling of uncertainties
Aiming to fulfill the critical target of CO_{2} reduction, in energy purchase and transmission processes, the TRANSCO has the natural attribute to take reactions to hedge the uncertainties associated with the government policy and the huge amount of renewable energy integration. The proper planning strategy can help the TRANSCO to maintain the power systems operated in an economic efficient and secure condition, constrained by various new uncertainty boundaries. In this paper, various uncertainties are taken into concerns, i.e. renewable energy generation (wind and PV), demand-side variations, conventional units’ production, market factor, and transmission path configuration. Precisely, the correlation characteristics of these uncertainties are taken into account and formulated as follows.
2.1 Correlation of uncertainties
The indication of stochastic variables for wind, PV, facilities configuration and demand identification can be seen as uncertain factors according to the forecast deviations, the measurement errors, the unpredictable system contingencies or the electricity market price volatilities. Therefore, the probabilistic analysis is the proper approach to handle the variations of these uncertainties. However, the uncertainty variables could be dependent to each other, e.g. the weather conditions can impact wind/PV generation and household consumption, simultaneously. Hence, in this work, the correlation coefficient matrix is used to illustrate the considerable dependency of the uncertainty variables. To define the degree of the dependence among variables, each correlation coefficient should be assigned in [−1, 1], where −1 and 1 indicate the perfect positive and negative relationship between the related variables.
2.2 Wind energy uncertainty
2.3 PV energy uncertainty
2.4 Conventional energy uncertainty
2.5 Market price uncertainty
2.6 Demand-side uncertainty
The fast growth of smart grid and intelligent control technology will offer a good opportunity to apply DR and flexible consumption in the demand side. Therefore, the uncertainty can be decomposed to be two portions, i.e. DR and load variation.
In addition, according to the predicted demand \( \overline{{P_{li} }} \), the load variation \( \widetilde{{P_{li} }} \) at i^{th} bus is imposed to follow the normal distribution \( N\left( {\mu_{i} ,\sigma_{i}^{2} } \right) \) for exhibiting the uncertainty of the natural load growth. Here, \( \mu_{i} \) is the expectation of the forecast load and \( \sigma_{i} \) is the standard deviation.
2.7 Transmission line uncertainty
Typically, the availability of the existing and candidate transmission lines can utilize the (0–1) distribution to represent the line uncertainty, where 0 indicates the line is in failure (or maintenance) status, while 1 shows the line is in the normal operating state.
3 Uncertainty-averse TRANSCO planning
3.1 Uncertainty characterization
For properly addressing the uncertainties mentioned above in the TRANSCO planning progress, the scenario-based stochastic programming approach is employed here to handle the issued uncertain conditions. A scenario is a sequence of time-based transmission system state, consisted of renewable energy, conventional generation, active demand, electricity price and transmission network. In this paper, the Monte Carlo simulation (MCs) method is applied to generate the set of numerous transmission system scenarios.
The repetitive process of the MCs method is built on the random sampling and statistical analysis. Generally, identifying the PDF of each uncertainty variable (as explained in Section 2) is the initial part, then further step is to attain some random samples via the random number generator (RNG). Consequently, the output values of these variables can be calculated in a deterministic model. For shortening the time consuming computation, a well-known scenario reduction technique [20] is introduced to eliminate the non-essential scenarios.
3.2 TRANSCO MPMOTP model
In this MPMOTP model, the DC optimal power flow (OPF) is used for the specific intention on various sources of uncertainty in the transmission level, equations (16) guarantee the power balance at each bus. Equations (17) enforce the power flowing through the line i-j, and further impose the capacity limits in (18). Constraints (19), (20) and (21) limit the production of the wind power, PV power and conventional generation unit within the particular maximum and minimum values, respectively. Likewise, the constraints (22) ensure the demand of each bus is bounded in the individual upper limit. Constraints (23) imply the capacity of the possible load shedding at i^{th} bus is limited to the actual demand P_{ditω}. Constraints (24) set the voltage angle bounds for each bus.
4 Methodology
In this section, the well-developed two-phase MOPSO algorithm is introduced to properly handle the proposed MPMOTP model, since it is a non-convex nonlinear mixed integer problem associated with the uncertainties’ penetration.
4.1 PSO algorithm
In general, the particle swarm optimization (PSO) algorithm [21] is a population-based self-adaptive method sorted as one of the heuristic methods. Incorporating with the components of particle and swarm, PSO encourages the local and global exploration of the problem space to obtain better convergence, in which a particle denotes the potential optimal solution and a swarm contains a set of particles. Each particle moves towards a multiple dimensions space to seek a possible solution experienced by the decisions of itself and its neighbors. In the searching space, the searching route of a particle can be recognized as the velocity (m) and position (n). The updating rule of PSO will steer the particle swarm to gather in a more promising area with better objective value.
4.2 Two-phase MOPSO schema
The primary aim of MOPSO is to find an optimal trade-off between several competing objectives for which usually no single optimal solution exists that minimizes all objective function values simultaneously.
4.3 MPMOTP planning implementation
5 Case study
The parameters of the two-phase MOPSO
MOPSO | Parameters |
---|---|
Swarm size | Ϟ = 160 |
Coefficient | ϖ = 0.9, c_{1} = 2.2, c_{2} = 3.0, r_{1} = 0.6, r_{2} = 0.8 |
Iteration | ϒ = 100 |
The physical parameters of wind and PV unit
Type | Parameters |
---|---|
Wind unit | V_{ci} = 4 m/s, V_{r} = 15 m/s, V_{co} = 22 m/s |
k = 2, c = 5.5 | |
PV unit | R_{r} = 1 kW/m^{2} |
α = 1.8, β = 4.5 |
The economic parameters of energy and CO_{2} emission
Factors | Parameters |
---|---|
CO_{2} emission | \( \xi_g=0.85\,{\text{Ton/MW}} \), \( \xi_{se}^{Av}=0.38\,{\text{Ton/MW}} \), \( \rho^{{CO_{2} }} \) = 20 $/Ton |
Load shedding | \( \lambda_{it\omega}^{LS} \) = 900 $/MW |
Energy purchase | \( \lambda_{wt\omega}^{Wind} \) = 150 $/MW, \( \lambda_{st\omega}^{PV} \) = 200 $/MW, |
\( \lambda_{gt\omega}^{CG} \) = 350 $/MW, \( \lambda_{lt\omega}^{Line} \) = 450 $/MW |
The MPMOTP planning schemes for various cases
Planning | 1^{st} 5-year | 2^{nd} 5-year | 3^{rd} 5-year | |
---|---|---|---|---|
Case 1 | Schemes | 1–5(1), 14–16(1) | 6–10(1), 12–23(1), 15–21(1) | 6–7(1), 7–8(1), 6–10(1), 15–24(1) |
O_{cr}(k$) | 56.28 | 77.13 | 89.61 | |
O_{pp}(k$) | 1325.27 | 1864.53 | 2487.11 | |
O_{rd}(k$) | 1385.42 | 1977.45 | 2672.37 | |
C_{inv}(k$) | 208.52 | 595.47 | 1072.01 | |
Case 2 | Schemes | 1–5(1), 7–8(1), 14–16(1) | 3–11(1), 6–7(1), 10–12(1) | 3–8(1), 5–10(1), 6–10(1) |
O_{cr}(k$) | 51.58 | 71.34 | 83.51 | |
O_{pp}(k$) | 1372.98 | 1527.58 | 1895.42 | |
O_{rd}(k$) | 1391.56 | 1803.17 | 2366.72 | |
C_{inv}(k$) | 539.64 | 613.74 | 658.14 | |
Case 3 | Schemes | 1–5(1), 3–11(1), 7–8(1), 14–16(1) | 3–8(1), 6–7(1), 16–17(1) | 4–5(1), 6–10(1), 17–18(1) |
O_{cr}(k$) | 49.87 | 68.34 | 74.08 | |
O_{pp}(k$) | 1401.95 | 1378.56 | 1458.16 | |
O_{rd}(k$) | 1417.82 | 1751.38 | 2195.85 | |
C_{inv}(k$) | 945.73 | 635.27 | 647.52 |
The planning schemes of the Case 1 concentrate on covering the uncertainty of the conventional generation growth to meet the demand variety, the significant investment of network persists in every planning period. The high fossil reliance inspires a high CO_{2} charge versus the social expect of reducing the CO_{2} emission, also causes an incremented price burden to the consumer (e.g. 2672.37 k$ in the 3^{rd} period), while the net income of the TRANSCO is increasing slowly from 60.15 k$ (1^{st} period) to 185.26 k$ (3^{rd} period).
Regarding the same situation for Case 2 and 3, on preliminary planning stages, the striking point is that a higher expenditure on energy purchase and branch update is visible to enhance the network more tightly to mitigate the plenty uncertainties mentioned in Section 2. However, according to the remarkable amount of wind and PV energy integration, the goal of social CO_{2} elimination is achieved. Highlighted in the 3^{rd} period of Case 3, the embedding capacity of renewable energy has touched upon 2048.00 MW, approximately dominating half of the energy supply (4334.49 MW). Comparing with Case 1, the decrement of CO_{2} reduction relieves a notable social benefit (15.53 k$), it can be also observed that, starting from the 2^{nd} period, the TRANSCO cost of energy stocking and network reinforcement is fairly decreased in Case 2 and 3. Further observation is that, not only as an uncertainty bearer, but as a beneficiary, accommodating huge quantity of renewable energy can facilitate the TRANSCO to stabilize the investment expectations and hedge the business risks, e.g. in the 3^{rd} period of Case 3, the net profit is growing dramatically to 737.69 k$.
The IMTP planning schemes for each case
Planning | 1^{st} 5-year | 2^{nd} 5-year | 3^{rd} 5-year | |
---|---|---|---|---|
Case 1 | Schemes | 1–5(1), 14–16(1) | 7–8(1), 12–23(1), 15–21(1) | 6–7(1), 7–8(1), 16–17(1), 15–24(1) |
C_{inv}(k$) | 185.08 | 559.20 | 927.11 | |
Case 2 | Schemes | 1–5(1), 14–16(1) | 7–8(1), 10–12(1), 14–16(1) | 3–8(1), 6–2(1), 7–8(1), 6–10(1) |
O_{rd}(k$) | 279.56 | 611.23 | 971.14 | |
Case 3 | Schemes | 1–5(1), 14–16(1), 3–8(1) | 6–7(1), 6–10(1), 14–16(1) | 3–8(1), 6–10(1), 16–17(1), 17–18(1) |
O_{rd}(k$) | 452.91 | 655.33 | 1095.06 |
Particularly in Case 1, ignoring the wind and PV penetration, the periodical investment is much lesser than MPMOTP plan, respectively declined 23.44, 36.27, and 144.90 k$ for each 5-year. That means the extra amounts are requested as the uncertainty-averse expenses on conventional generation, LMP volatility, demand response, and line availability.
For Case 2 and 3, the TRANSCO investment could not exhibit a specific trend as for three periods. However, concluded from the results of both MPMOTP model and IMTP model, the further observation shows that, the total 15-year investment tends to be an equivalent amount. In Case 2, the MPMOTP 15-year investment is 1811.52 k$, while that is 1861.93 k$ in IMTP. Accordingly, the value is 228.52 and 2203.30 k$, respectively in Case 3. That means, for a long term perspective, if a precise total amount control of investment is allocated, the proposed MPMOTP model can not only handle the heterogeneous uncertainties, but also ensure the robustness of phased investment in the strategic TRANSCO planning process.
6 Conclusion
Incorporating the ambition of the CO_{2} reduction, an uncertainty-averse MPMOTP planning model is proposed to handle the multiple uncertainties from renewable energy, conventional generation, market price, load deviation and network deployment. In this paper, the virtue of uncertainty codependency is evaluated by the correlation coefficient matrix and contributed to optimize three TRANSCO concerned objectives. Associated with an introduced two-phase MOPSO solving algorithm, the proposed model is implemented and applied on the IEEE 24-bus test system. The results show that, considering a variety of uncertain conditions, the released planning schemes can be feasibly and effectively put forward to issue the transmission network with high stable and reliable intention of the TRANSCO.
Notes
Acknowledgments
The authors gratefully acknowledge the financial supports of Danish national project iPower and the great contributions of Danish Energy Association and DONG Energy involved in this task.
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