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Joint Investment and Operation of Microgrid

Hao Wang, Jianwei Huang

arXiv:1511.01984v1eess.SY

TL;DR

The paper addresses microgrid planning by jointly considering renewable generation, energy storage, demand response, investment, and operation. It develops a two-period stochastic framework and finds economic benefits from demand response and integrated renewable-energy and storage configurations.

  • Problem

    Existing studies treated microgrid planning and operation separately and did not holistically consider renewable energy, storage, and flexible loads across time scales.

  • Method

    A two-period stochastic program jointly optimizes renewable-energy and storage investment with operating decisions, including demand-response pricing and power scheduling.

  • Results

    Benchmark 4 costs 7.6 Million HKD versus 8.4 Million HKD for benchmark 3, while the optimal investment expense at TC is 4.6 million HKD.

  • Takeaways & Limitations

    Demand response and energy storage provide economic benefits, while wind power can dominate the investment portfolio when its output and unit capacity cost are more favorable.

Abstract

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In this paper, we propose a theoretical framework for the joint optimization of investment and operation of a microgrid, taking the impact of energy storage, renewable energy integration, and demand response into consideration. We first study the renewable energy generations in Hong kong, and identify the potential benefit of mixed deployment of solar and wind energy generations. Then we model the joint investment and operation as a two-period stochastic programming program. In period-1, the microgrid operator makes the optimal investment decisions on the capacities of solar power generation, wind power generation, and energy storage. In period-2, the operator coordinates the power supply and demand in the microgrid to minimize the operating cost. We design a decentralized algorithm for computing the optimal pricing and power consumption in period-2, based on which we solve the optimal investment problem in period-1. We also study the impact of prediction error of renewable energy generation on the portfolio investment using robust optimization framework. Using realistic meteorological data obtained from the Hong Kong observatory, we numerically characterize the optimal portfolio investment decisions, optimal day-ahead pricing and power scheduling, and demonstrate the advantage of using mixed renewable energy and demand response in terms of reducing investment cost.

NOMENCLATURE

The nomenclature defines the paper’s investment, operation, user-load, renewable-supply, pricing, and storage variables and parameters.

  • Acronyms: The model distinguishes period-1 investment and period-2 operation, alongside user cost-minimization and robust-optimization problems.These abbreviations organize the paper’s multi-stage formulation.
  • Parameters: Investment parameters include solar, wind, and storage costs, the investment budget, and generation and storage capacity variables.The listed capacities are α_s, α_w, and α_e, while c_s, c_w, c_e, and B represent costs and budget.
  • Parameters: User demand is separated into aggregate inelastic load and bounded elastic-load quantities, including minimum, maximum, and preferred power loads.The parameter list includes b_t, D_i, d_i,t, and y_i,t for these demand components.
  • Parameters: Renewable and grid-operation variables represent solar and wind supply, renewable power, grid procurement, aggregate supply, and day-ahead pricing.These variables are indexed by time and scenario where specified.
  • Parameters: Storage parameters describe charging and discharging limits, conversion efficiencies, state-of-charge bounds, depth-of-discharge, and battery state.The nomenclature includes η_c, η_d, SOC_min, SOC_max, DOD_max, and SOC_ω,t.

I. INTRODUCTION

The introduction motivates jointly optimizing microgrid investment and operation across renewable generation, storage, and demand response. It presents a Hong Kong-based stochastic framework that derives portfolio investments and operational decisions while addressing renewable uncertainty.

  • I. INTRODUCTION: Existing studies treated microgrid planning without flexible load or operation, or operation under fixed facilities, rather than jointly considering renewable energy, storage, and demand response.The paper identifies this as the central gap because these features affect planning and operation across different time scales.
  • I. INTRODUCTION: The paper develops a theoretical framework for optimal mixed renewable-generation and storage investment together with demand-responsive microgrid operation.The framework addresses the coupling between investment and operation decisions at different time scales.
  • I. INTRODUCTION: Hong Kong Observatory data are used to analyze solar–wind correlations across locations and motivate mixed renewable-energy investment.The data include hourly solar radiation and wind speeds from multiple Hong Kong locations.
  • I. INTRODUCTION: The joint problem is formulated as a two-period stochastic program, with a distributed algorithm for period-2 power scheduling and a single-level formulation for period-1 portfolio investment.This solution structure connects operational scheduling with investment optimization.
  • I. INTRODUCTION: The study analyzes renewable-generation prediction error through worst-case scenario analysis.This contribution focuses on how uncertainty affects renewable-energy investment decisions.
  • I. INTRODUCTION: Hong Kong case studies characterize optimal portfolio investments and demonstrate savings from mixed renewable investment and demand response.The stated application scope is numerical evaluation using realistic meteorological data.
  • II. RELATED WORK: Unlike transmission-level work on wind investment and network expansion, this paper studies distribution-level microgrids with solar, wind, storage, and demand response in one portfolio framework.It also jointly determines portfolio investment and demand-response pricing.

III. SOLAR POWER AND WIND POWER IN HONG KONG

The section models Hong Kong solar and wind generation from meteorological data and examines location-dependent correlations to motivate mixed renewable investment.

  • A. Correlation between solar power and wind power: Hourly solar and wind productions are calculated over 365 days from one year of measured solar radiation and wind-speed data.The study uses data from Sep. 1, 2012 to Aug. 31, 2013 and applies solar and wind power models.
  • A. Correlation between solar power and wind power: Wind generation correlates positively with solar generation at KP, TPK, SHA, and SKG, negatively at TC and WGL, and nearly zero at TMT.The correlations are computed from one-year hourly production series.
  • A. Correlation between solar power and wind power: TC and SKG are selected as representative mixed-investment locations, with solar-wind correlation coefficients of −0.22 and 0.15, respectively.The locations represent negative and positive correlations under a portfolio-selection perspective.
  • B. Scenario generation of solar power and wind power: Ten renewable-generation scenarios are produced by reducing historical daily realizations for solar in KP and wind in TC and SKG.The reduced scenarios preserve a subset of scenarios and assign new probabilities; KP solar is assumed representative across Hong Kong.
  • B. Scenario generation of solar power and wind power: Solar production peaks at noontime, whereas wind production differs substantially by location, supporting geographically differentiated portfolio analysis.The study assumes uniform solar radiation across Hong Kong but location-dependent wind patterns.

V. PERIOD-2 PROBLEM FOR MICROGRID OPERATIONS

The period-2 model coordinates user demand, renewable and conventional supply, and storage to minimize operating cost under renewable scenarios.

  • A. User’s model: Users’ loads are divided into elastic and inelastic components, with demand response controlling only elastic consumption.Elastic loads include electric vehicles, washing machines, and HVAC; lighting and refrigerators are treated as inelastic.
  • A. User’s model: Elastic-load schedules obey per-slot minimum and maximum consumption limits and each user’s total-energy requirement.These constraints govern feasible shifting across the operational horizon.
  • A. User’s model: Time-varying prices shift elastic consumption from high-price slots to low-price slots while adding discomfort costs for deviations from preferred use.The discomfort coefficient β_i measures each user’s sensitivity to deviation from preferred consumption.
  • B. Operator’s model: For each renewable scenario, the operator schedules renewable supply, conventional procurement, and storage charging or discharging to meet elastic and inelastic demand.The renewable supply and procurement variables are scenario-dependent, while renewable availability depends on invested capacities.

1) Power supply:

The microgrid models renewable supply from invested solar and wind capacities alongside storage, whose charging, discharging, and state-of-charge constraints provide operational flexibility.

  • Solar and wind generation in each scenario depends on the period-1 capacities invested by the operator.
  • Energy storage complements variable renewable generation by coordinating supply and demand through charging and discharging.
  • The model assumes renewable intermittency can be managed and microgrid stability guaranteed, while prediction-error effects are examined separately.
  • Charging and discharging amounts are bounded by storage capacity and per-unit power limits, with conversion efficiencies modeling battery losses.
  • The battery state of charge remains between SOCmin and SOCmax, and its terminal level equals the initial level so each day can be operated independently.

3) Operator’s cost:

The period-2 model coordinates aggregate supply and user consumption to minimize operator and user costs under power-balance, storage, and operating constraints.

  • The power-balance formulation represents aggregate supply and requires supply and demand to match in each time slot.
  • Renewable power is used first when available, while conventional grid power covers any remaining deficit and incurs a quadratic production cost.
  • Period-2 operation minimizes the operator’s generation cost together with users’ consumption costs over aggregate supply and individual power schedules.
  • The optimization is subject to user constraints and storage-related constraints, including the battery’s state-of-charge and operating limits.
  • The period-2 problem is convex, but centralized optimization may be impractical because the operator cannot directly control users’ consumption.

VI. PERIOD-1 PROBLEM FOR PORTFOLIO INVESTMENT

The period-1 problem selects solar, wind, and storage capacities under a budget by combining capital investment costs with expected period-2 operating costs across renewable scenarios.

  • The operator jointly chooses solar, wind, and storage capacities for the investment horizon, subject to a budget and nonnegative-capacity constraints.
  • Investment costs cover solar, wind, and storage expenditures, including deployment, installation, and maintenance-related equipment.
  • Scenario operating costs depend on invested capacities, renewable supply, and users’ demand responses, with scenario probabilities obtained through scenario reduction.
  • The objective combines capital investment cost with expected operating cost over all scenarios and D operating days.
  • The solution procedure first solves the period-2 operating problem with a distributed algorithm and then solves the period-1 investment problem.

A. Period-2: Optimal power scheduling

The paper replaces centralized control with iterative day-ahead pricing: the operator broadcasts prices, users optimize consumption, and the resulting decentralized algorithm converges to socially optimal scheduling.

  • 2) Optimal pricing and decentralized algorithm: The operator and users iteratively exchange aggregate consumption and prices, allowing users to respond without direct centralized control.
  • 2) Optimal pricing and decentralized algorithm: Each user minimizes energy and discomfort costs subject to consumption constraints in response to the operator’s price signal.
  • 2) Optimal pricing and decentralized algorithm: The optimal pricing scheme induces individual consumptions that solve the socially optimal period-2 problem.
  • 2) Optimal pricing and decentralized algorithm: The algorithm requires limited information exchange: users report consumption, while the operator broadcasts prices based on aggregate load without revealing private user information.
  • 2) Optimal pricing and decentralized algorithm: The iterative procedure updates prices and consumptions until successive price vectors differ by no more than the error tolerance.
  • 2) Optimal pricing and decentralized algorithm: With diminishing stepsizes, Algorithm 1 converges to the socially optimal prices and power consumption for each renewable scenario.

B. Period-1: Optimal energy portfolio investment

The paper separates investment and operation into a two-period framework, solving operation first and then investment. It also extends the operating and investment problems to worst-case renewable-generation prediction errors.

  • B. Period-1: Optimal energy portfolio investment: The period-1 investment problem is reduced to an equivalent convex quadratic program after solving the period-2 operating problem.The operator estimates user consumption behavior and solves the equivalent problem centrally with a standard interior-point method.
  • B. Period-1: Optimal energy portfolio investment: The robust formulation models bounded solar and wind prediction errors and seeks investment capacities that minimize worst-case overall cost.Robust period-2 operation is embedded into a period-1 investment problem sharing the structure of the original investment problem.
  • B. Period-1: Optimal energy portfolio investment: The robust operating problem maximizes actual operator cost over prediction errors while user cost remains independent of those errors.The analysis therefore focuses the inner maximization on the operator-cost component.
  • B. Period-1: Optimal energy portfolio investment: For fixed power scheduling, worst-case prediction errors lie on the uncertainty-set boundary and specifically attain their lower bounds.Theorem 4 establishes that the optimal solutions of the inner maximization hit the lower error bounds.

IX. SIMULATION RESULTS

The simulation uses a ten-year investment horizon, a preferred load curve, specified cost coefficients, and renewable scenarios derived from Hong Kong data.

  • IX. SIMULATION RESULTS: The investment horizon is D = 3650 days, or 10 years, with renewable scenarios obtained from the study’s Hong Kong data analysis.The simulations use a preferred power-consumption load curve and set β_o = 0.005 and β_i = 0.5.

A. Optimal investment

Optimal portfolios differ by location and budget: TC favors wind, while SKG allocates more toward solar. Demand response lowers investment expenditure and changes the solar, wind, and storage mix.

  • A. Optimal investment: At TC, wind is prioritized under tight budgets and remains dominant because its output is higher and demand response and storage improve its utilization.The optimal TC investment expense is 4.6 million HKD and remains unchanged above 5 million HKD budgets.
  • A. Optimal investment: At SKG, more investment goes to solar because wind output is less adequate and solar better matches the daily demand pattern.This makes wind less competitive at SKG than at TC.
  • A. Optimal investment: 9.4% lower investment expenditure at TC reduces the optimal total from 5.1 million HKD to 4.6 million HKD with price incentives.Demand response enables more wind investment and less storage investment by shifting elastic demand proactively.
  • A. Optimal investment: 6.1% lower investment expenditure at SKG reduces the optimal total to 5.1 million HKD with price incentives.The incentivized portfolio contains more solar power and less storage because solar better fits demand at SKG.

C. Optimal power scheduling and pricing

Power scheduling coordinates renewable supply, grid purchases, storage, and flexible demand across locations. Day-ahead prices shift flexible loads, while prediction errors increase investment for hedging.

  • C. Optimal power scheduling and pricing: At TC, wind-driven renewable supply is high at night and falls during 9AM–5PM, requiring storage discharge and main-grid purchases.Users shift the original peak load in response to day-ahead prices.
  • C. Optimal power scheduling and pricing: At SKG, solar-driven renewable supply peaks during 10AM–4PM, storage charges during high supply and discharges afterward, and the grid serves other periods.The described schedule reflects SKG’s larger solar share and daytime supply peak.
  • C. Optimal power scheduling and pricing: Flexible loads shift from high-price to low-price slots at both TC and SKG under the operator’s day-ahead prices.Price patterns differ by location because TC relies more on nighttime wind, whereas SKG relies more on daytime solar.
  • D. Impact of prediction errors: A 10% renewable-generation prediction error increases TC’s investment expense by 4.1% through over-investment against generation shortages.Investment expense rises as prediction errors increase under the robust formulation.
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