Dispatch Decisions Research Articles

Stackelberg competition between merchant and regulated storage investment in wholesale electricity markets

We investigate the interaction between the regulated and merchant storage investment made by the social planner and a merchant, through a Stackelberg competition model. In the upper level, the merchant storage owner maximizes its profit through storage investment decisions. Given the merchant storage investment, the social planner makes its own regulated storage investment, overall storage operation, and economic dispatch decisions to minimize the overall system cost in the lower level problem. Both the merchant and regulated energy storage is remunerated based on the inter-temporal difference in locational marginal prices (solved by the lower level problem). We show that the regulated storage profit (of the social planner) is always nonnegative if the storage investment cost is convex in the installed storage capacity with no fixed cost. In particular, the regulated storage profit must be zero (non-positive) if the storage investment cost is linear (affine, respectively) in the installed storage capacity. Numerical results (on the IEEE 57-bus test system) with real-world load data from the California Independent System Operator (CAISO) show that Stackelberg competition between merchant and regulated storage investment can reduce 2–3% of social cost compared to a market without storage. We also show that the merchant (profit-maximizing) investment can significantly reduce the social planner’s expense in storage investment, at the cost of only 0.5% increase in social cost (compared to the socially optimal investment). These results suggest that the government shall encourage merchant companies to invest on energy storage and to participate in wholesale electricity markets.

Risk-Based Distributionally Robust Real-Time Dispatch Considering Voltage Security

A risk-based distributionally robust real-time dispatch approach is proposed to strike a balance between the operational costs and risk as well as considering the nodal voltage security even when the distribution of uncertainties cannot be precisely estimated. To model uncertainties, a data-drive ambiguity set is developed based on the imprecise probability theory without any presumption on the probability distribution of uncertainties. The obtained ambiguity set is based on the confidence interval, which can be constructed according to actual needs by choosing the point-wise or family-wise confidence interval. Two strategies for wind farms to provide voltage support are incorporated in the proposed approach so that the nodal voltage security can be ensured. By incorporating the risk tractable estimation method and sequential convex optimization method, an efficient algorithm is developed to release the computational burden. Numerical results show that compared with the regular robust optimization, the proposed approach reduces the total operational cost to achieve statistically optimal dispatch decisions. The proposed approach also outperformances the stochastic programming in term of the operational risk reliability. Meanwhile, the nodal voltage security issues can be mitigated with the voltage support from wind farms. In conclusion, under the uncertainty of probability distributions, the proposed approach can efficiently strike a balance between the operational cost and risk while ensuring the nodal voltage security.

Representing cross-border trade of electricity in long-term energy-system optimization models with a limited geographical scope

Long-term energy system optimization models can be designed to model systems with a broad geographical scope that comprises multiple countries. However, due to computational limitations, often the geographical scope is restricted to a single country. This raises the problem of correctly accounting for cross-border trade of electricity in models with a limited geographical scope. Therefore, this paper assesses the impact of not correctly representing cross-border trade flows in geographically restricted long-term planning models. To this end, we use a planning model for the interconnected Central-Western European power system to compare technology choices and welfare estimates for Belgium when (i) cross-border trade of electricity is ignored and (ii) cross-border trade flows are an endogenous part of the planning model. Furthermore, this paper presents two sets of methodologies to account for transmission flows in planning models. A first methodology is to extend the model’s geographical scope and fix the capacity variables in the neighboring countries in line with pre-designed scenarios for those countries. A second methodology further reduces the computational cost by using specially tailored import and export curves to represent each country’s trade opportunities. The results indicate that for highly interconnected systems, neglecting cross-border trade or having a highly stylized representation of cross-border flows can lead to inaccurate welfare estimates and technology biases. In addition, a key insight presented in this paper is that congestion rents can constitute a major share of the welfare gains attained by trading electricity. Finally, endogenizing the dispatch decisions in neighboring countries is the most accurate method to deal with cross-border trade, while by correctly designing cross-border trade curves computational time can be reduced, but planning model outcomes become less accurate.

Online Learning for Network Constrained Demand Response Pricing in Distribution Systems

Flexible demand response (DR) resources can be leveraged to accommodate the stochasticity of some distributed energy resources. This paper develops an online learning approach that continuously estimates price sensitivities of residential DR participants and produces such price signals to the DR participants that ensure a desired level of DR capacity. The proposed learning approach incorporates the dispatch decisions on DR resources into the distributionally robust chance-constrained optimal power flow (OPF) framework. This integration is shown to adequately remunerate DR resources and co-optimize the dispatch of DR and conventional generation resources. The distributionally robust chance-constrained formulation only relies on empirical data acquired over time and makes no restrictive assumptions on the underlying distribution of the demand uncertainty. The distributional robustness also allows for robustifying the optimal solution against systematically misestimating empirically learned parameters. The effectiveness of the proposed learning approach is shown via numerical experiments. The paper is accompanied by the code and data supplement released for public use, see [27].

Adaptive Robust Dispatch of Integrated Energy System Considering Uncertainties of Electricity and Outdoor Temperature

The integrated energy system (IES) has bright prospects in engineering applications for its excellent performance in energy efficiency and renewable energy consumption. In the IES, the thermal comfort is affected by the heating power, buildings parameters, and outdoor temperatures simultaneously. Therefore, the uncertainty of the outdoor temperature will bring some adverse effects on thermal comfort, which need to be considered in the dispatch decision of the IES. In this article, we propose a day-ahead adaptive robust dispatch model (ARDM) for the IES to make a dispatch plan under the uncertainties of the net electrical-load and outdoor temperature, with the aim of guaranteeing the safe operation of IES and the thermal comfort of end-users. The thermal dynamic characteristics of the district heating network and buildings are utilized to provide operational flexibility and improve economic performance. To decrease the conservatism of dispatch results, the multi-interval uncertainty set is introduced to model the uncertainties. The ARDM model is a two-stage robust optimization with a linear recourse problem, and the column-and-constraint generation method is used to solve it. Two cases of different scale are studied to verify the effectiveness and advantages of the proposed method.

Statistical estimation of operating reserve requirements using rolling horizon stochastic optimization

We develop a multi-period stochastic optimization framework for identifying operating reserve requirements in power systems with significant penetration of renewable energy resources. Our model captures different types of operating reserves, uncertainty in renewable energy generation and demand, and differences in generator operation time scales. Along with planning for reserve capacity, our model is designed to provide recommendations about base-load generation in a non-anticipative manner, while power network and reserve utilization decisions are made in an adaptive manner. We propose a rolling horizon framework with look-ahead approximation in which the optimization problem can be written as a two-stage stochastic linear program (2-SLP) in each time period. Our 2-SLPs are solved using a sequential sampling method, stochastic decomposition, which has been shown to be effective for power system optimization. Further, as market operations impose strict time requirements for providing dispatch decisions, we propose a warm-starting mechanism to speed up this algorithm. Our experimental results, based on IEEE test systems, establish the value of our stochastic approach when compared both to deterministic rules from the literature and to current practice. The resulting computational improvements demonstrate the applicability of our approach to real power systems.

Utility-Owned Combined Heat and Power: Improving Reliability and Lessening Environmental Impact

Problem Definition: Combined heat and power (CHP) plants generate electricity and useful heat at the same time, reaching high efficiencies. There are many benefits to utilities of having CHP plants in their portfolio, including increasing power reliability, reducing transmission losses, and meeting environmental regulations. Despite these benefits, only 3% of all CHP capacity in the U.S. is utility owned. We study the economics of utility ownership of CHP plants and examine the impact of regulatory policies on such investments. Academic/Practical Relevance: There is little research on the economics of utility ownership of CHP. Given the low CHP adoption rate in the U.S., particularly by utilities, it is of general interest to understand the economics of CHP and how policies affect CHP adoption. Methodology: We solve for the optimal form of investment and dispatch decisions using analytic economic modeling. Following this, we present a numerical study calibrated with real data from three different utilities in the U.S., including their existing generation portfolio, uncertainties in demand and fuel prices, granular renewable intermittency, and grid reliability. Results: A utility’s investment in different generating technologies follows an Invest/Stay Put/Disinvest (ISD) policy for a given siting decision of CHP plants. Numerically, we find investment in many CHP plants to be attractive to utilities, even without regulatory policy intervention. A low to moderate emissions tax makes CHP even more attractive for utilities. Managerial Implications: There is significant interest in energy sustainability in the industrial and academic communities. We shed light on a technology that is well known to practitioners but less explored in academia and demonstrate its benefits rigorously. We show that utilities should seriously consider adopting CHP in their generation portfolios, and our model framework can aid such decisions.

Internal dispatch for RES-storage hybrid power stations in isolated grids

This paper deals with the internal dispatch policy for Hybrid Power Stations (HPS) consisting of renewable energy source (RES) based generation and storage facilities, operating in isolated island power systems in a coordinated manner to provide dispatchable power. Objective of the proposed dispatch method is the maximization of HPS revenues during real time operation, while avoiding deviations from the dispatch orders (DOs) issued by the System Operator (SO). DOs can be met either by RES production directly injected to the grid or by the storage facilities of the station. A Model Predictive Control (MPC) method is implemented to regularly update the internal dispatch decisions for HPS components, relying on an optimization problem built upon the Mixed Integer Linear Programming (MILP). In the proposed formulation the technical and operating constraints of the examined HPS configuration are taken into consideration, while a variable time resolution technique is also adopted to reduce computational complexity and achieve feasible solutions within acceptable time limits.

An Improved Statistical Approach to Generation Shift Keys: Lessons Learned from an Analysis of the Austrian Control Zone

During market coupling, trading of electricity across borders is subject to capacity limits, provided by transmission system operators. Flow-based market coupling is the preferred method of the EU for cross-border capacity calculations. It is part of the EU’s design for a single electricity market to maintain security of supply and achieve competitive energy prices while integrating growing shares of renewable energy to reach the reduction targets for greenhouse gas emissions. The algorithm of flow-based market coupling incorporates the physical restrictions of critical network elements during market clearing. For this, Generation Shift Keys are required to translate nodal into zonal information by predicting, which generating units participate in import-export balance changes. This analysis presents an improvement of an existing approach to Generation Shift Keys, further developed within a study for the Austrian transmission system operators, Austrian Power Grid. The proposed method allows for Generation Shift Key estimations based on regression analysis and actual dispatch decisions, decoupled from fixed power plant characteristics and merit-order assumptions. The unit selection process based on economic significance leads to statistically significant and robust Generation Shift Keys in the majority of cases. The results highlight the importance of computing time-dependent, but not necessarily hourly Generation Shift Keys and indicate a limited positive correlation between participation in zonal changes and power plant capacities. Both aspects confirm the purpose of the developed model’s flexible and data-based properties.

Approximating Economic Dispatch by Linearizing Transmission Losses

We study a non-convex Transmission-Constrained Economic Dispatch (TCED) problem that uses the traditional linear DC model of the transmission system together with a non-linear representation of losses. This problem is typically approximated by the convex problem obtained by linearizing the constraints around some base-case state. Electricity prices and dispatch decisions are then chosen based on the resulting linearly-constrained economic dispatch (LCED) problem. Different LCED problems have been suggested in the literature and they are all derived using one of two linearization techniques, which we call direct and indirect linearization, respectively. An LCED problem often used in practice that uses Loss Distribution Factors (LDFs) is derived using indirect linearization and is termed the common LCED problem. This paper studies the assumptions required to recover the optimal dispatch of the non-convex TCED problem from the solution of the common LCED problem. We show that the common LCED problem may have multiple minimizers, in which case small perturbations of the base-case state may result in large dispatch approximation error. Furthermore, even if the base-case state matches a minimizer of the non-convex TCED problem, it is proven that there does not always exist a choice of LDFs such that the optimal dispatch of the TCED problem is also optimal for the common LCED problem. On the other hand, such LDFs do exist and are identified for the special case where no line limits are binding.

MPC for Optimized Energy Exchange between Two Renewable-Energy Prosumers

Renewable energy and information technologies are changing electrical energy distribution, favoring a move towards distributed production and trading between many buyers and sellers. There is new potential for trading between prosumers, entities which both consume and produce energy in small quantities. This work explores the optimization of energy trading between two prosumers, each of which consists of a load, renewable supply, and energy storage. The problem is described within a model predictive control (MPC) framework, which includes a single objective function to penalize undesirable behavior, such as the use of energy from a utility company. MPC integrates future predictions of supply and demand into current dispatch decisions. The control system determines energy flows between each renewable supply and load, battery usage, and transfers between the two prosumers. At each time step, future predictions are used to create an optimized power dispatch strategy between the system prosumers, maximizing renewable energy use. Modeling results indicate that this coordinated energy sharing between a pair of prosumers can improve their overall renewable energy penetration. For one specific choice of prosumers (mixed residential–commercial) penetration is shown to increase from 71% to 84%.

Dynamic dispatching and preventive maintenance for parallel machines with dispatching-dependent deterioration

A dynamic decision model that coordinates dispatching and preventive maintenance decisions for failure-prone parallel machines in make-to-order (MTO) production environments is developed in this research. The primary objective is to minimize the weighted long-run average waiting costs of MTO systems. Two common but seldom studied stochastic factors, namely, the dispatching-dependent deterioration of machines and machine-health-dependent production rates, are explicitly modeled in the proposed dynamic dispatching and preventive maintenance (DDPM) model. Although the DDPM model is developed using Markov decision processes, it is equally effective in non-Markovian production environments. The performance of the DDPM model is validated in Markovian and non-Markovian production environments. Compared with several methods from the literature, simulation results show an improvement of at least 45.2% in average job waiting times and a minimum reduction of 48.9% in average machine downtimes. The comparison results between the optimal dynamic dispatching policies with and without coordinated preventive maintenance show that performance improvement can be mostly attributed to the coordination between preventive maintenance and dispatching decisions.

High-Resolution Modeling and Decentralized Dispatch of Heat and Electricity Integrated Energy System

The heat and electricity integrated energy system (HE-IES) has high energy efficiency and bright application prospects. In the HE-IES, the heat transmission in the heating network and the indoor temperature variation in the buildings are governed by (partial) differential equations, which bring the heat dynamics problem in the system operation. In this paper, we propose a comprehensive approach for the operation of the HE-IES to coordinate the electricity and heat dynamics, including modeling, evaluation, and dispatch procedure. First, we formulate a high-resolution model for the heating network and buildings to describe the heat dynamics; two indices are proposed to measure the impact of heat dynamics, which are then used to select the time resolution. Second, an optimal dispatch model with high resolution for the heat dynamics is formulated for the HE-IES; a decentralized and parallel solution method is proposed based on the alternating direction method of multipliers. Third, a two-stage procedure for the time resolution selection is proposed, which consists of a dispatch decision stage and a time resolution evaluation stage. A small illustrative case is studied to verify the effectiveness of the proposed method. A big case based on a real heating network in Jilin Province, China, is also simulated.

Performance Evaluation of Production Systems Using Real-Time Machine Degradation Signals

A machine’s degradation status directly influences the operational performance of the production system, such as productivity and product quality. For example, machines associated with different health states may have different remaining life before failure, thus impacting the system throughput. Therefore, it is critical to analyze the coupling between the overall system performance and the machine degradation to better production decision-making, such as maintenance and product dispatch decisions. In this paper, we propose a novel model to evaluate the production performance of a two-machine-and-one-buffer line, given the real-time machine degradation signals. Specifically, a phase-type distribution-based continuous-time Markov chain model is formulated to estimate the system throughput by utilizing the remaining life prediction from the degradation signals. A case study is provided to demonstrate the applicability and effectiveness of the proposed method. Note to Practitioners—Machine degradation is commonly observed in many industries, such as automotive, semiconductor, and food production, which gradually deteriorates the machine conditions in different operating processes and affects the production system performance. In practice, sensors are largely deployed on the factory floor to monitor the machine’s operating condition. However, a gap still exists between machine operating conditions and system performance. In this paper, we develop an analytical model to predict the machine remaining lifetime and estimate the system performance of a small scale production system, using the machine degradation signals from sensors. Furthermore, a Bayesian updating scheme is provided, which enables online evaluation by utilizing the real-time signals. Such a method provides an effective tool for production engineers to analyze the real-time system performance, and further conduct system improvements and control.

Visualisation of Probabilistic Access Forecasts for Offshore Operations

Access forecasting aims to predict the quality of transfer of maintenance technicians to/from vessels and the constituent offshore structures at the wind farm. This is highly dependent on sea state conditions as well as other environmental factors such as visibility. Typically, scheduling or dispatch decisions are made on the basis of deterministic forecasts of significant wave height, often coupled with service contracts where transfers are expected to be attempted below a threshold significant wave height. However, there is always uncertainty in a weather prediction which can be accounted for by probabilistic forecasts. The aim of this work is to explore visualisation ideas for transforming vessel specific access forecasts into an interpretable and intuitive decision-support tool. Three simple methods are proposed based on a score out of 10, classification of transfer conditions, and a threshold score. Methods for summarising access conditions for 2–5 days ahead are also developed. This new forecasting and visualisation capability has significant implications for marine coordinators and skippers who will be able to make better informed safety-critical decisions, with the potential for reductions in the cost-of-energy offshore.

Short-Term Forecasts of DNI from an Integrated Forecasting System (ECMWF) for Optimized Operational Strategies of a Central Receiver System

Short-term forecasts of direct normal irradiance (DNI) from the Integrated Forecasting System (IFS) and the global numerical weather prediction model of the European Centre for Medium-Range Weather Forecasts (ECMWF) were used in the simulation of a solar power tower, through the System Advisor Model (SAM). Recent results demonstrated that DNI forecasts have been enhanced, having the potential to be a suitable tool for plant operators that allows achieving higher energy efficiency in the management of concentrating solar power (CSP) plants, particularly during periods of direct solar radiation intermittency. The main objective of this work was to assert the predictive value of the IFS forecasts, regarding operation outputs from a simulated central receiver system. Considering a 365-day period, the present results showed an hourly correlation of ≈0.78 between the electric energy injected into the grid based on forecasted and measured data, while a higher correlation was found for the daily values (≈0.89). Operational strategies based on the forecasted results were proposed for plant operators regarding the three different weather scenarios. Although there were still deviations due to the cloud and aerosol representation, the IFS forecasts showed a high potential to be used for supporting informed energy dispatch decisions in the operation of central receiver units.

Developing new ways of measuring the quality and impact of ambulance service care: the PhOEBE mixed-methods research programme

BackgroundAmbulance service quality measures have focused on response times and a small number of emergency conditions, such as cardiac arrest. These quality measures do not reflect the care for the wide range of problems that ambulance services respond to and the Prehospital Outcomes for Evidence Based Evaluation (PhOEBE) programme sought to address this.ObjectivesThe aim was to develop new ways of measuring the impact of ambulance service care by reviewing and synthesising literature on prehospital ambulance outcome measures and using consensus methods to identify measures for further development; creating a data set linking routinely collected ambulance service, hospital and mortality data; and using the linked data to explore the development of case-mix adjustment models to assess differences or changes in processes and outcomes resulting from ambulance service care.DesignA mixed-methods study using a systematic review and synthesis of performance and outcome measures reported in policy and research literature; qualitative interviews with ambulance service users; a three-stage consensus process to identify candidate indicators; the creation of a data set linking ambulance, hospital and mortality data; and statistical modelling of the linked data set to produce novel case-mix adjustment measures of ambulance service quality.SettingEast Midlands and Yorkshire, England.ParticipantsAmbulance services, patients, public, emergency care clinical academics, commissioners and policy-makers between 2011 and 2015.InterventionsNone.Main outcome measuresAmbulance performance and quality measures.Data sourcesAmbulance call-and-dispatch and electronic patient report forms, Hospital Episode Statistics, accident and emergency and inpatient data, and Office for National Statistics mortality data.ResultsSeventy-two candidate measures were generated from systematic reviews in four categories: (1) ambulance service operations (n = 14), (2) clinical management of patients (n = 20), (3) impact of care on patients (n = 9) and (4) time measures (n = 29). The most common operations measures were call triage accuracy; clinical management was adherence to care protocols, and for patient outcome it was survival measures. Excluding time measures, nine measures were highly prioritised by participants taking part in the consensus event, including measures relating to pain, patient experience, accuracy of dispatch decisions and patient safety. Twenty experts participated in two Delphi rounds to refine and prioritise measures and 20 measures scored ≥ 8/9 points, which indicated good consensus. Eighteen patient and public representatives attending a consensus workshop identified six measures as important: time to definitive care, response time, reduction in pain score, calls correctly prioritised to appropriate levels of response, proportion of patients with a specific condition who are treated in accordance with established guidelines, and survival to hospital discharge for treatable emergency conditions. From this we developed six new potential indicators using the linked data set, of which five were constructed using case-mix-adjusted predictive models: (1) mean change in pain score; (2) proportion of serious emergency conditions correctly identified at the time of the 999 call; (3) response time (unadjusted); (4) proportion of decisions to leave a patient at scene that were potentially inappropriate; (5) proportion of patients transported to the emergency department by 999 emergency ambulance who did not require treatment or investigation(s); and (6) proportion of ambulance patients with a serious emergency condition who survive to admission, and to 7 days post admission. Two indicators (pain score and response times) did not need case-mix adjustment. Among the four adjusted indicators, we found that accuracy of call triage was 61%, rate of potentially inappropriate decisions to leave at home was 5–10%, unnecessary transport to hospital was 1.7–19.2% and survival to hospital admission was 89.5–96.4% depending on Clinical Commissioning Group area. We were unable to complete a fourth objective to test the indicators in use because of delays in obtaining data. An economic analysis using indicators (4) and (5) showed that incorrect decisions resulted in higher costs.LimitationsCreation of a linked data set was complex and time-consuming and data quality was variable. Construction of the indicators was also complex and revealed the effects of other services on outcome, which limits comparisons between services.ConclusionsWe identified and prioritised, through consensus processes, a set of potential ambulance service quality measures that reflected preferences of services and users. Together, these encompass a broad range of domains relevant to the population using the emergency ambulance service. The quality measures can be used to compare ambulance services or regions or measure performance over time if there are improvements in mechanisms for linking data across services.Future workThe new measures can be used to assess different dimensions of ambulance service delivery but current data challenges prohibit routine use. There are opportunities to improve data linkage processes and to further develop, validate and simplify these measures.FundingThe National Institute for Health Research Programme Grants for Applied Research programme.

Multi-stage robust transmission constrained unit commitment: A decomposition framework with implicit decision rules

With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment problem. Among all methods, two-stage and multi-stage robust optimization-based methods are the most widely adopted ones. In the two-stage methods, non-anticipativity of economic dispatch (ED) decisions are not considered. While in multi-stage methods, explicit decision rules (like affine decision rules) are adopted to guarantee non-anticipativity of ED decisions, the computational burden can be heavy and the optimality of the solution is affected. In this paper, a multi-stage robust TCUC formulation with implicit decision rules is proposed, as well as a decomposition framework to solve it. The solutions are proved to be multi-stage robust and non-anticipativity of ED decisions is guaranteed. Meanwhile, a computationally efficient time-decoupled solution method for the feasibility check subproblems is also proposed, such that the method is suitable for large-scale TCUC problems with uncertain power injections. Numerical tests are conducted on IEEE 118-bus system and Polish 2383-bus system. The proposed method outperforms the multi-stage robust method with explicit decision rules in solution’s economic performances, and is more computationally efficient than the all-scenario-feasible method. The effectiveness of time-decoupled solution method is also verified.

Development of battery intervention power supply for solar roof top installations

In India, battery storage and time‐based tariff are yet to be introduced in solar microgrid tied inverters. Here, the authors propose an improved multistage converter topology intended for single phase solar roof top applications with battery storage. It works in six modes depending on solar‐load‐battery‐grid profiles. The whole strategy is implemented in a battery intervention power supply (BIPS) that uses energy storage integrated with the solar generator that helps in smoothing of power, load shifting, load dispatch, and load angle control. Notably, load dispatch decision is arrived based on several independent parameters that take different values at a time. A Boolean equation is derived relating the different parameters so as to arrive at a single decision. This is achieved by a variable entity k‐map. A voltage control is also implemented which is done by load angle control of the inverter current. © 2019 American Institute of Chemical Engineers Environ Prog, 38: 570–583, 2019

Renewable Support, Intermittency and Market Power: An Equilibrium Investment Approach

Renewable energy sources (RES) play an increasing role in many electricity systems thanks to climate and support policies and subsequent cost reductions in recent years. Compared to conventional generation technologies, RES has two main important distinctive features: First, their cost pattern is characterized by high investment and negligible variable costs and second, their operational decision is governed by weather conditions limiting their availability. In this paper, we aim to analyze the role of RES in electricity markets focusing on the interplay of investment and dispatch decisions under different levels of market competitiveness and different support schemes; namely, feed-in tariff, feed-in premium, and investment subsidies. To this end, we develop a two-stage model of endogenous investment and operation with both intermittent and conventional technologies to obtain analytical solutions for investment and operation decisions. We show that there are feedback effects between the investments of different firms, and between the different technologies of the same firm. Exercise of market power results in underinvestment in the conventional technology; but the effect on renewables is ambiguous due to the interplay of opposing investment incentives. The results furthermore highlight that for the optimal design of a support policy the underlying competiveness of the market needs to be considered.