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In part I of this paper, we proposed a Mixed-Integer Linear Program (MILP) to analyze imperfect competition of oligopoly producers in two-stage zonal power markets. In part II of this paper, we propose a solution algorithm which decomposes the proposed MILP model into several subproblems and solve them in parallel and iteratively. Our solution algorithm reduces the solution time of the MILP model and it allows us to analyze largescale examples. To tackle the multiple Subgame Perfect Nash Equilibria (SPNE) situation, we propose a SPNE-band approach. The SPNE band is split into several subintervals and the proposed solution algorithm finds a representative SPNE in each subinterval. Each subinterval is independent from each other, so this structure enables us to use parallel computing. We also design a pre-feasibility test to identify the subintervals without SPNE. Our proposed solution algorithm and our SPNE-band approach are demonstrated on the 6-node and the modified IEEE 30-node example systems. The computational tractability of our solution algorithm is illustrated for the IEEE 118-node and 300-node systems.

Zonal pricing with countertrading (a market-based redispatch) gives arbitrage opportunities to the power producers located in the export-constrained nodes. They can increase their profit by increasing the output in the day-ahead market and decrease it in the real-time market (the inc-dec game). We show that this leads to large inefficiencies in a standard zonal market. We also show how the inefficiencies can be significantly mitigated by changing the design of the real-time market. We consider a two-stage game with oligopoly producers, wind-power shocks and real-time shocks. The game is formulated as a two-stage stochastic equilibrium problem with equilibrium constraints (EPEC), which we recast into a two-stage stochastic Mixed-Integer Bilinear Program (MIBLP). We present numerical results for a six-node and the IEEE 24-node system.

It is well known that transmission investment yields two major benets: (a) it allows cheaper remote generation to substitute for more expensive local generation, (the efficiency benefit) and (b) by increasing the diversication of uncorrelated generation sources, allows a reduction in the volume of balancing services required (the diversification benefit). Conventional transmission planning processes tend to focus exclusively on the efficiency benefit. It is well known that increasing wind penetration increases the need for balancing services. Even where the market is able to provide the signals to generators as to when and how much to produce, increasing wind penetration increases the need for higher- exibility plant (such as OCGT or very fast start hydro plant) which typically has a higher long-run cost. The purpose of this study is to develop a mathematical model for quantifying the diversification benefit for transmission investment. To do this two-step economic dispatch of the day-ahead energy market and the real-time balancing market are mathematically formulated in a single optimization problem which calculates the results of day-ahead market dispatch and real-time market dispatch in one optimization problem. The new formulation is a linear programming problem which calculates the dispatch cost and the economic deviation from the dispatch cost. Firstly, this single optimization problem is used for quantifying the diversification benefit of the additional transmission capacity. Then, a stochastic optimization model for modeling the diversification benefit of additional transmission capacity in the transmission planning process is formulated. Uncertainty of system parameters are modeled using scenarios. ARIMA models anda scenario reduction technique based on Kantorovich distance are used for generating the scenarios. To explain the diversification benefit, two example systems are studied. Firstly, to evaluate the impact of additional transmission capacity on the dispatch cost of the day-ahead energy market and the real-time balancing market, IEEE thirty-node example system is studied. The diversification benefit is calculated and the conclusions are extracted. Then, a transmission planning approach, which considers the diversification benefit along with the efficiency benefi, is proposed. The proposed and conventional transmission planning approaches are applied to modied IEEE 24-node example system. Conventional transmission planning approach (which models only efficiency benefit in its formulation) is used as a benchmark in this study. The numerical results show that the proposed approach can effectively quantify the diversification benefit of additional transmission capacity.

It is well known that transmission investment yields two major bene_ts: (a) it allows cheaper remote generation to substitute for more expensive local generation, (the e_ciency bene_t) and (b) by increasing the diversi_cation of uncorrelated generation sources, allows a reduction in the volume of balancing services required (the diversi_cation bene_t). Conventional transmission planning processes tend to focus exclusively on the e_ciency bene_t. It is well known that increasing wind penetration increases the need for balancing services. Even where the market is able to provide the signals to generators as to when and how much to produce, increasing wind penetration increases the need for higher-exibility plant (such as OCGT or very fast start hydro plant) which typically has a higher long-run cost. The purpose of this study is to develop a mathematical model for quantifying the diversi_cation bene_t for transmission investment. To do this two-step economic dispatch of the day-ahead energy market and the real-time balancing market are mathematically formulated in a single optimization problem which calculates the results of day-ahead market dispatch and real-time market dispatch in one optimization problem. The new formulation is a linear programming problem which calculates the dispatch cost and the economic deviation from the dispatch cost. Firstly, this single optimization problem is used for quantifying the diversi_cation bene_t of the additional transmission capacity. Then, a stochastic optimization model for modeling the diversi_cation bene_t of additional transmission capacity in the transmission planning process is formulated. Uncertainty of system parameters are modeled using scenarios. ARIMA models and a scenario reduction technique based on Kantorovich distance are used for generating the scenarios. To explain the diversi_cation bene_t, two example systems are studied. Firstly, to evaluate the impact of additional transmission capacity on the dispatch cost of the day-ahead energy market and the real-time balancing market, IEEE thirty-node example system is studied. The diversi_cation bene_t is calculated and the conclusions are extracted. Then, a transmission planning approach, which considers the diversi_cation bene_t along with the e_ciency bene_t, is proposed. The proposed and conventional transmission planning approaches are applied to modi_ed IEEE 24- node example system. Conventional transmission planning approach (which models only e_ciency bene_t in its formulation) is used as a benchmark in this study. The numerical results show that the proposed approach can e_ectively quantify the diversi_cation bene_t of additional transmission capacity.